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The Chaos second level trigger McFarland, Sheila Joy 1993

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T H E C H A O S S E C O N D LEVEL T R I G G E R By Sheila Joy McFarland B.Sc. (Hons), University of Regina, 1991 A THESIS S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in THE FACULTY OF GRADUATE STUDIES D E P A R T M E N T O F PHYSICS We accept tins thesis as conforming „ • t9-4he"Tet[l3ired stq.ndard THE UNIVERSITY OF BRITISH COLUMBIA December 1993 © Sheila Joy McFarland, 1993 in presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of /^hn'^j'cS The University of British Columbia Vancouver, Canada Date Doc^^.^^h^ ^ /9?3 DE-6 (2/88) A b s t r a c t In the summer of 1993, a group at TRIUMF commissioned the Canadian High Accep-tance Orbit Spectrometer (CHAOS). This is a 360° spectrometer that was built to study TT p^ elastic scattering and the (TT, 2ir) reaction in order to investigate the possible effects of chiral symmetry in QCD. An important part of the vast readout electronics is the second level trigger, which performs several fast calculations in hardware to determine the merit of an event before writing it to tape. The trigger performs various cuts on single outgoing tracks: momentum, polarity, distance of closest approach to the origin of CHAOS, and momentum versus scattering angle. In addition, the trigger can look for two such acceptable tracks and then perform cuts based on the sum of the momenta and the comparison of the polarities; this section in particular is crucial for the success of the (TT, 2ir) program. Finally, the second level trigger can survey the incoming beam and reject events in which an incident pion decayed to a muon before reaching the CHAOS target. This thesis will first provide an introduction to the theoretical motivation be-hind CHAOS and also outline the various components of the spectrometer in brief. The remainder of the thesis wiU discuss in detail the purpose and operation of the different sections of the second level trigger. u Table of Contents Abstract ii List of Tables vii List of Figures viii Acknowledgements xi 1 Theoretical Motivation Behind CHAOS 1 1.1 Introduction to Chiral Symmetry and ChPT 1 1.1.1 What is Symmetry? 2 1.1.2 Spontaneous Symmetry Breaking 2 1.1.3 What is Chiral Symmetry? 4 1.2 Experimental Significance of ChPT 7 1.3 The CHAOS Physics Program 8 1.3.1 The (TT, 2ir) Reaction 9 1.3.2 TTjJ Elastic Scattering and the Strange Content of the Proton . . . 11 2 Overview of the Design of CHAOS 14 2.1 Design Motivation 14 2.2 Various Components in Brief 16 2.2.1 Sagane Magnet 16 2.2.2 CHAOS Targets 18 2.2.3 Wire Chamber Design 19 iii 2.2.4 CFT Blocks 25 2.2.5 Electronics 27 3 Introduction to the Second Level Trigger 33 3.1 Purpose of Momentum Sum Cut and Polarity Comparison 34 3.2 Purpose of Momentum versus Scattering Angle Cut 37 3.3 Need for Muon Rejection 39 3.4 Basic Design Philosophy 42 3.4.1 Use of DO Loops 42 3.4.2 Rotation Algorithm 45 3.4.3 Other Considerations 48 4 First Section of the Second Level Trigger 51 4.1 Description 51 4.1.1 The General Flow of Data 51 4.1.2 Momentum, Distance of Closest Approach and Polarity Determi-nation 54 4.1.3 The Start of 2LT Processing 59 4.1.4 Looping Sequence 62 4.2 Resolution and Accuracy 68 4.2.1 Momentum Resolution 72 4.2.2 Simulated Accuracy in Determining Distance of Closest Approach 73 4.2.3 Simulated Accuracy in Polarity Determination 76 4.3 Success of Operation 77 5 Momentum Addition and Polarity Comparison 82 5.1 Description of Electronics 83 IV 5.2 Simulating Resolution of Momentum Sum 86 5.2.1 Residts of Simulation 87 5.2.2 Using Simulation to Choose Settings 91 5.3 Success of Operation 91 6 Momentum versus Scattering Angle Cut 95 6.1 Electronics 97 6.2 Loading Program Algorithm 101 6.2.1 Determining the Center of the Rotated Track 102 6.2.2 Determining the Point of Closest Approach 104 6.2.3 Determining the Rotated Scattering Angle 105 6.2.4 Determining the Scattering Angle 108 6.3 Current Progress 109 7 Muon Rejection 110 7.1 Electronics 112 7.2 Final Second Level Trigger Decision 115 8 Conclusion 118 A Basics of the Second Level Trigger Modules 124 A.l Data Stacks - LeCroy 2375 124 A.2 Data Registers - LeCroy 2371 128 A.3 Arithmetic Logic Units - LeCroy 2378 128 A.4 Logic Gates - LeCroy 4516 130 A.5 Latches 130 A.6 Logic Delay/Fan-Out Modules - LeCroy 4418 131 A.7 Memory Lookup Units 131 V A.7.1 LeCroy Memory Lookup Unit - 2372 131 A.7.2 21-Bit Memory Lookup Unit 134 B ECL Program and TRIG2 Program 137 B.l ECL Program 137 B.2 TRIG2 Program 140 Bibliography 141 VI List of Tables 3.1 Rates for selected reactions involving incident TT"*" 37 3.2 Rates for selected reactions involving incident ir~ 37 4.3 Percentage of simulated events for which 2LT improperly determines point of closest approach to be outside target 74 4.4 Accuracy of 2LT in determining polarity 76 5.5 Statistics for (TT, 27r) reconstructed momentum sum 89 5.6 Statistics for irp reconstructed momentum sum 89 A.7 Dimensionality of the LeCroy 2372 133 A.8 Dimensionality of the CHAOS 21-Bit MLU 135 vu List of Figures 1.1 Partial list of chiral reactions 9 2.2 CHAOS radial magnetic field profile 17 2.3 PCOS clusterized data output format 30 3.4 Momentum histogram for outgoing irp and (7r,27r) charged particles in P„ = 396 ~ Monte Carlo examples 36 3.5 Monte Carlo results for momentum sum of irp and (7r,27r) final state charged particles with a beam momentum of P^ = 396 ^^^ 36 3.6 Plot of P versus 6^ for TT"*" scattering 38 3.7 Example of a muon trajectory reconstructed as two outgoing tracks . . . 41 3.8 Block diagram of the first section of the 2LT 44 3.9 Plot of P„.„ for 2LT 47 3.10 Trajectory of minimum momentum track for 2LT 47 3.11 Time for 2LT to make a YES decision as a function of number of clusters 49 4.12 Simple schematic of first section of 2LT 52 4.13 Illustration of the rotation algorithm for determining polarity 55 4.14 Illustration that y^ can never equal 0 56 4.15 Illustration of how the ADI signal is created 59 4.16 Full schematic of first section of 2LT 61 4.17 How the MLU RDY pulses are created 63 4.18 Actual and simulated 2LT momentum histograms 71 vm 4.19 Second level trigger momentum resolution 72 4.20 Standard deviation of the error in the 2LT distance of closest approach determination 74 4.21 Plots of 2LT dr values for 0.5T, LOT and 1.5T at track momenta of both 100 and 260 ^ ^ 75 c 4.22 Example of experimental ajid reconstructed momentum cut 79 4.23 Example of experimental and reconstructed target cut 81 5.24 Schematic of momentum sum/polarity comparison section 84 5.25 Exact and reconstructed charged particle momentum sums for the (7r,27r) reaction and irp elastic scattering at 396 ^^^ 88 5.26 Convolution of Monte Carlo momentum sum 90 5.27 Example of experimental and reconstructed momentum sum/polarity com-parison cut 94 6.28 Illustration of pion momentum versus 0s cut for Trp elastic scattering . . . 96 6.29 Example of a scattering angle by 2LT definition 98 6.30 Electronics schematic for momentum versus scattering angle cut 99 6.31 Illustration of the rotation/translation algorithm used in the calculation of scattering angle in 2LT 103 6.32 Signs of point of closest approach coordinates for all possible cases with polarity = 0 and x'^^^ 0 106 6.33 Trigonometric diagrams for calctdating 6^ 107 6.34 Average angle of beam at center of CHAOS 108 7.35 Illustration of rotation algorithm performed on muon track I l l 7.36 Electronics schematic of muon rejection section 113 IX 7.37 Electronics for the final 2LT decision 116 8.38 Diagram illustrating the order of the 2LT sections, as well as a condensed NEXT OR gate network 120 8.39 Illustration of how the momentum versus Og cut is implemented 121 8.40 Illustration of how to implement both optional sections 122 A.41 Illustration of data stack timing 127 A.42 Illustration of how MLU A' works 132 B.43 Illustration of the ECL main menu and a "configuration" submenu . . . 139 A c k n o w l e d g e m e n t s All facets of a person's Ufe are touched by others, including those related to career. Whether it be by offering technical support or writing ideas, or simply by showing con-tinued interest in the work even when they are not physicists, many people have an influence on any long term project. There are several people who deserve acknowledgement in this thesis. First, I would like to thank my supervisor. Dr. Greg Smith, for his guidance and advice throughout this project. Thanks is also due to my thesis co-reader. Dr. Garth Jones, and my original supervisor. Dr. Martin Sevior, who continued to provide advice after his career took him to Melbourne. I also would like to thank Dr. Kelvin Raywood for his design of the first stage of the second level trigger, which provided a good foundation for the remaining sections. Mr. Pierre Amaudruz also deserves thanks for his technical advice and module design work. Moral support is a crucial ingredient in the quality of any project. For this I would like to thank my friends, my mother Edna, my father David, and my brother JefF. In particular my mother deserves much thanks, for without her encouragement and under-standing through the years, I certainly would not be where I am today. Lastly, I would like to thank Mohammad, who supported my efforts and always made me feel better whenever the project seemed to be going awry. XI Chapter 1 Theoret ical Mot ivat ion Beh ind C H A O S TRIUMF is the site of a major project termed CHAOS (Canadian High Acceptance Orbit Spectrometer) that was recently commissioned during the 1992-1993 beam-time year with successful results. Many people have put much time and effort into the de-sign and building of CHAOS, which is a 360° spectrometer capable of measuring ^w^ for charged particles to better than 1%. Two major experimental programs have been approved, which involve the study of 7rp elastic scattering and the (TT, 27r) reaction re-spectively. The apparatus wiU now be used in pion investigations to m^easure various fundamental parameters of Quantum Chromodynamics (QCD) as predicted by chiral symmetry and Chiral Perturbation Theory (ChPT) . 1.1 Introduct ion to Chiral S y m m e t r y and C h P T Chiral symmetry, or the symmetry of "handedness" among quarks, is a relatively new concept in particle physics. It is, however, an important ingredient of low energy QCD theory. In reality, nature does not exhibit perfect chiral symmetry, and as such ChPT must be introduced. Lagrangians from ChPT can be used to make a wide variety of predictions, which can then be tested experimentally. In general, it has been found that QCD theory that does not reflect chiral symmetry cannot properly predict what is observed in nature. This section provides a background in the theoretical concepts relevant to the CHAOS program. A definition of symmetry and spontaneous symmetry breaking will be provided, and then chiral symmetry and ChPT will be discussed. Chapter 1. Theoretical Motivation Behind CHAOS 2 1.1.1 W h a t is S y m m e t r y ? Without the concept of symmetry, the field of particle physics would not be as devel-oped as it is today. Numerous symmetries and near-symmetries appear to exist in nature and by applying the corresponding mathematical techniques, physicists have been able to solve many complicated problems and gain further understanding regarding the nature of mat ter and the interacting forces. A symmetry is said to exist if one can perform a mathematical transformation upon a system, and the physics describing the system remains the same. In other words, the Lagrangian for the system will remain invariant under the transformation. If the system starts out in a particular state and the symmetry operation is performed, the system wiU be transformed into another equivalent state. An important consequence of symmetry is that for every invariance there is always a corresponding conservation. Several simple examples are evident in classical mechanics. For instance, the space and time translational invariance of such systems results in the conservation of linear momentum and energy respectively. Similarly, classical rotational symmetry gives rise to the conservation of angular momentum. Various conserved quan-tities exist in non-classical systems as well. An example from Quantum Electrodynamics (QED) is the conservation of electric charge in all weak interactions. Quantum numbers such as isospin, parity and baryon number are examples of conserved quantities in aU strong interactions (which are described by Quantum Chromodynamics or QCD). 1.1.2 Spontaneous S y m m e t r y Breaking An important concept in the study of invariances in physics is that of spontaneous symmetry breaking (SSB). The general idea of SSB can be seen by considering the simple example of a magnetic domain. The Hamiltonian of the system of spins, labelled Si, in Chapter 1. Theoretical Motivation Behind CHAOS 3 a domain is given by H=-^j:si-sj (1.1) which is invariant under any spatial rotation and thus exhibits fuU rotational symmetry. The vacuum (or ground state) of the system is characterized by the alignment of aU the spins. There is a continuous family of ground states, corresponding to the infinitely many possibilities of overall spin direction. The groundstate, or equivalently the direction in which the spins are orientated, is arbitrary, and nature's choice of vacuum depends upon the history of the spin system: its initial conditions and subsequent interactions. All the possible vacua are eqtiivalent due to the rotational symmetry of the Hamiltonian, but they are not each rotationaUy invariant. Given a fixed coordinate system, a spatial rotation performed on the chosen ground state does not yield the identical vacuum. Rather, the system is placed in a different ground state that corresponds to the new direction of spin alignment. Hence, the Hamiltonian that describes the physics of the system is rotationaUy invariant, but the ground states are not, and one says the rotational symmetry is spontaneously broken. The Goldstone Theorem states that the spontaneous breaking of a symmetry wiU result in the creation of massless bosons. These particles are called Goldstone Bosons and they relate the different ground states. In order for a system to make a transition from one vacuum to another, it must interact with a massless boson field. Consider again the example of a system of spins in a magnetic domain. Theoretically speaking, one can explain a change in spin alignment by the interaction of the magnetic domain with a spin wave of wavelength A. If A —» oo, the effect is that all spins will change alignment at once to match the infinitely small portion of the wave that they interact with, and another ground state will result. By the wave-particle duality, the spin wave corresponds to a particle moving with wavelength A and momentum p = j ex. j . Also, since the ground Chapter 1. Theoretical Motivation Behind CHAOS 4 states are assumed to have E = 0, the spin wave caused a vacuum —• vacuum transition of zero energy; thus one says a spin wave of A —» oo carries no energy. As A —> oo, £? —> 0 and therefore the relation between E and A is evidently of the form E (X — (X — oc pc A A The energy is also given by E = [{pcf + {mcy]^ Thus in order for ^ oc pc it foUows that m must be zero for the particle corresponding to the spin wave (through the wave-particle duality). In summary, the relation between E and A dictates the existence of massless Goldstone bosons. It should be noted that symmetries can also be explicitly broken by introducing certain terms into the Hamiltonian that are not invariant under the transformation in question. It could be that the terms which explicitly break the symmetry have small coefficients (coupling constants) and so have little weight in the Hamiltonian. In such a case, there is a near-symmetry. Goldstone bosons wiU result if this near-symmetry is spontaneously broken, but the particles will have mass. 1.1.3 W h a t is Chlral S y m m e t r y ? Chiral symmetry is an important part of QCD theory. The concept of chiral symmetry can be most easily seen in a high energy QCD example: an imaginary system of quarks with zero masses. Each quark has a left-handed helicity state, •0x,, and a right-handed helicity state, ipR. It is known that QCD interactions are independent of helicity and conserve helicity. Furthermore, in the limit where the quark masses go to zero, the helicity of a quark can never flip, because an observer can never accelerate to a different frame of reference in which this appears to happen. In the case of massive particles, an observer can boost to a frame of reference moving much faster than the par) therefore Chapter 1. Theoretical Motivation Behind CHAOS 5 opposite helicity to that which it had originally. However, massless particles move at the speed of light, so the observer can never boost to such a fcame of reference. Thus in this imaginary system, there are two entirely separate subsystems, . ht-handed quark states and the other of left-handed states. The total quark wave function is V* = V'L + i^R' There is a separate SU{N) invariance for each system (where N is the number of quark degrees of freedom of the system or, identically, the number of quark flavors found in the system) ^. An SU{N)R transformation on the right-handed quark system wiU have no effect on the left-handed system, and vice versa. SU{N)R and SU{N)i, operate on entirely different vector spaces between which there is no overlap. Together, the transformations are said to act upon the direct product of the spaces and the overall invariance is referred to as SU{N)ii (g) SU{N)L- A system of massless quarks made up of both right-handed states and left-handed states, which is invariant under such a transformation, is said to be chiraUy symmetric. The ideal case in which the quark masses are zero is referred to as the chiral limit. In the case of quarks with mass, the left-handed and right-handed systems are not distinct. These ideas can be seen by considering the example of a Dirac particle. There exist projection operators, TL and TR, where V'fl = ^Ri' = 2(1 - 75 )V' For massless particles, the operators project out the helicity of the particles. Otherwise, this is not quite true, and the resulting projections are referred to as the left and right chirality of the particle. We can substitute the expression, V* = V'L + V'iij ^^^^ ^^^ Dirac ^Note that fields with > 3 flavors of quarks (beyond u, d and s) are not within the scope of this discussion, but the higher order examples follow in the same manner. Chapter 1. Tbeoretical Motivation Behind CHAOS 6 Lagrangian L = i[){ip — m)i}) and carry through the math using the properties of 7 matrices and the relations ri = r^ ; r | = r« ; TRTL = o to get Evidently, the mass terms have the effect of coupling the left-handed system to the right-handed system. The Lagrangian is no longer invariant under SU{N)ji (g) SU{N)L, and the chiral symmetry of the quark system is explicitly broken. If the quarks have zero mass, no relation exists between the two types of quarks, and the Lagrangian is once again invariant under this transformation. As with any symmetry based on an SU(N) transformation, chiral symmetry is also spontaneously broken, giving rise to the Goldstone bosons of the theory: TT'S, K^S and 7/'s. SSB is different from the symmetry breaking that occurs in the theory when the quark masses are considered. It happens only in the chiral limit, and recall that SSB is defined as the situation in which the equations of the system (ie: Lagrangian or Hamiltonian) are invariant under the SU{N)R (8) SU{N)i, transformation, while the vacuum or ground state is not invariant under the same operation. In the chiral limit, there is a continuous spectrum of ground states, corresponding to an arbitrary fraction of left-handed and right-handed quarks. The QCD interactions are identical for quarks of each helicity, and the ratio R = ^ can never change for massless quark systems; as such there are many different equivalent vacua, each identified by a particular R. One ground state is 'chosen' by nature. Chiral symmetry is spontaneously broken, however, because the QCD Lagrangian is invariant under SU{N)R ® SU(N)i, Chapter 1. Theoretical Motivation Behind CHAOS 7 transformations, while the individual vacua are not invariant. Theoretical studies of the vacuum expectation value < oiv-V-lo > where tp = tpi + IJ}R, have shown that if this matrix element is nonzero, the vacuum is noninvariant under the transformation and the symmetry is spontaneously broken. This is indeed the case in chiral QCD. It can be theoretically shown that this implies the existence of massless Goldstone bosons in the form of TT'S, ^ ' S and T/'S. An apparent problem with this discussion is that the TT'S, iiT's and T/'S are known to have mass. However, this can be explained by the fact that quarks are not massless. The Lagrangians that describe high energy particle systems include quark mass terms which couple the left-handed states with the right-handed states and break the chiral symmetry. This is thought to cause the Goldstone bosons to acquire mass. Because the quark masses are relatively small in terms of the energy scale of high energy QCD, chiral symmetry is still a useful concept. 1.2 Exper imenta l Significance of C h P T In the low energy region of particle physics {E < ^ GeV), the theoretical analysis methods of QCD break down. In the 1970's, Weinberg developed his theory of meson interactions that included a 0~ field expressed as a matrix of fields raised to an exponential power, which was acted upon by a Lagrangian with second order derivatives. However, this theory was oidy calculable to first order by using the approximation lim exp X = l-\- X a;-»0 to simplify the meson field expansion. Infinities occurred when the next order of the field was considered. For years further development did not take place, until it was hypoth-esized that the TT'S, Kh and T/'S were the Goldstone bosons resulting from spontaneous Chapter 1. Theoretical Motivation Behind CHAOS 8 chiral symmetry breaking in QCD. At this point theorists reconsidered Weinberg's the-ory, and development began on chiral perturbation theory (ChPT) to bet ter describe the interactions of the light mesons. Weinberg showed that his original Lagrangian could be improved upon by including higher order effects such as TTTT rescattering. Gasser and Leutweyler bmlt upon Weinberg's research and constructed an effective Lagrangian that included derivatives of up to fourth order and displayed all the symmetries of QCD, including unitarity, isospin invariance and chiral symmetry. With further mathemati-cal manipulation, they found that the TTTT scattering amplitudes could be expressed as a power series in terms of j ^ ^ and nine renormalization constants a,- ^. This is the framework of ChPT. ChPT is used to predict observables in a wide range of light meson reactions. Figure 1.1 contains a partial list of reactions for which chiral perturbation theory is a useful tool of analysis. The two areas of research of particular interest to the CHAOS group, namely the (TT, 27r) reaction and irp elastic scattering, wiU be described briefly to demonstrate the importance of the theory. 1.3 T h e C H A O S Phys ics Program The main goal of the CHAOS physics program at TRIUMF is to measure QCD observables whose values are predicted by chiral perturbation theory. For the most part , these observables are the TTTT a" and a" scattering lengths and TTN scattering ampHtudes as well as TTN a^^ and af^ scattering lengths. In order to determine these observables, the group plans to measure analyzing powers for irp elastic scattering at several energies and to measure (TT, 2W) differential cross sections at various energies above threshold. The information obtained is required to compute the pion-nucleon a term, which is theorized 'E is the total energy and F.^ is the pion decay constant. Chapter 1. Theoretical Motivation Behind CHAOS K K K K K K K K TT TT K K Ks Ki 7 ^ jl V •^ 1\ T\ ^ 371 -»TT e 1/ -^  TT 7 7 ^ TT TT 7 + --> e y e e -> e 1/ 7 p -> JT p P -* 7T TT p + --* 71 e e •* 37r 7 -»77 , ^ 7 7 K-^7K T T ^ e i / ^ / i y 7 7 - » 7 ) 0 + 7 r - > 7 i e v ^ 3 7 t j y ^ i] 7 r - > e i / e e - 7 r i / 7 )^37r n -^ J J - 7 r 7 7 7 / ^ 2 7 1 7 7 r ^ 7 e e ^ 7 r 7 r 7 7 | ^ 7 r 7 r 7 + -7 7 -^  TT TT 7 7 ^ 7 r 7 r K - > e i / 7 E ^ p T r 7-+7r7r7r H ^ A 7 r ' 0 7 7 ^ TT T -> 3711/, K -> 71 e 'e ' f ^ ^ + TT TT T - > 2 7 r i / , - ^ 3 7 r 7 T ^ T + 7r7r T -> 471 y, Ks -> 7 7 T' -> T + T T V 7r7r^7r7r K. ^ 7 7 B ^ T r e i / B ^ 7T 7r e 1/ Figure 1.1: Partial list of chiral reactions. to be a measure of both the strength of chiral symmetry breaking and also the strange content of the proton as predicted by chiral perturbation theory. 1.3.1 T h e (7r,27r) React ion The main goal of the (TT, 27r) experiments is to measure jy dn dT dii ^^^ ^^^ ^°^' lowing reactions: Tr~p —> ir'^ir~n - - 0 TT p —> TT IT p •K'^P -^ ir'^ir'^n TT'^P —> ir'^TT^p Chapter 1. Tbeoretical Motivation Behind CHAOS 10 To the lowest order consideration, these reactions involve an incoming pion undergoing a strong interaction with a nucleon, mediated by a virtual pion. As such, the reactions can shed light on the ir + ir —^ ir + TT interaction. These reactions will be studied at several energies from just above threshold to 300 MeV. The differential cross sections will be compared to the predictions of several models, in particular that developed by Oset and Vicente-Vacas and expanded by Sossi, Fazel and Johnson [5]. Phase shift analysis will be performed on the differential cross sections in order to extract the cross section for the production of only an S-wave final state in the underlying TTTT interaction. In comparing the data to the various models, the cross section for the TTTT interaction can be separated from higher order processes. The TTTT scattering amplitudes will then be obtained using the Chew-Low extrapolation method, which allows one to extract amplitudes at the unphysical point where the four-momentum-transfer to the nucleon = m^ [E568]. These data will be used to determine the S-wave isospin 0 and isospin 2 TTTT scattering lengths OQ and fflj* The TTTT amplitudes and scattering lengths will then be compared to the predictions of chiral perturbation theory. The expected values for the scattering lengths are a° = (0.20 ± 0.01)m;^ (1.2) a° = (-0.042 ± 0.002)m;^ (1.3) How close the experimentally determined values are to those predicted by chiral pertur-bation theory wiU give an indication of both the validity of the theory and the strength of chiral symmetry breaking. In addition, the scattering lengths wiU be used in the calculation of the irp a term, to be discussed in the next section. Cbaptei 1. Tbeoietical Motivation Behind CHAOS 11 1.3.2 irp Elastic Scatter ing and the Strange Content of the P r o t o n There is a great deal of interest in the study of the strange quark content of the proton using chiral perturbation theory. The process in question is irN —» TriV elastic scattering. In the following brief explanation, note that fi and m are the masses of the pion and proton, u = ^aE~> and a, t and u are the Mandelstam variables used in the description of scattering processes t = (pi — P3Y = q^ = (four—momentum—transfer)^ S = {Pl+ P2Y = (P3 + P4Y U = {Pl -Pif = {P2-P?if where the pion has ingoing and outgoing momenta pi and pa, and the nucleon has mo-menta P2 and P4. Chiral perturbation theory relates the TriV^  scattering amplitude, D , to the -KN S term at the unphysical Cheng-Dashen point (where i/=0, t = fi^) through the expression F.^ is the pion decay constant, the latest value of which has been experimentally deter-mined to be 92.4 MeV [6]. Using chiral symmetry arguments, it is predicted that S is related to the (X-term matrix element o-(i) = -— < p3\m(uu + dd)\pi > (1.4) where m = |(Tn„ + rrid). In the chiral limit one finds that S at the Cheng-Dashen point equals a, where a is simply a{t) for a soft scattering process, in which t = q^ = 0 and so Pi = Pa = p. In the case of quarks with mass, chiral perturbation theory predicts that a should be smaller than S and the latest calculations suggest that S = c + 15 MeV [6]. Chapter L TbeoTetical Motivation Behind CHAOS 12 These parameters are possibly related to the strange quark content of the proton. Theoretical calculations based on chiral symmetry predict that 35 MeV 2 < plsslp > y — — i l l — = < p\uu + dd\p > where p = pi = Ps {t=0, case of soft scattering process), y is thus a direct measure of the strange quark content of the proton. Latest results yield S = 60 MeV and therefore (7 = 45 MeV, from which one finds y ~ 0.2. This results in a 10% strange quark content for the proton [6]. In the past, the standard process of determining S in 7rp —» irp scattering has been the following. Experimental physicists perform experiments to measure the relevant differential cross sections over some range of angle and energy. Phase shift analysis is then performed to yield a function for the total scattering amplitude that is energy dependent. The amplitude for the unphysical Cheng-Dashen point, where q^ = 2/i^, can then be determined by extrapolation. Also, the irp even ^ S and P scattering lengths, ao"+ and af^, that are required for the calculation of S can be extracted. Finally, S can be determined, from which <r and the strange content of the proton can be calculated. The problem has been that there is much discrepancy among 4 ^ results from various sources. The reason for this is that the cross sections must be properly normalized - all sources of error must be properly accounted for. There are many possible sources of error, from background reactions to uncertainty in the thickness of the target. Consequently, the value for S is uncertain. One of the main goals of the CHAOS physics program is to improve the data used to determine the phase shifts upon which the calculation of this parameter is based. ^Even denotes that it is a combination of the lengths for I = 1 + | and I = 1 - | states that keeps the same sign undei an isospin transfoimation. Chapter 1. Theoretical Motivation Behind CHAOS 13 The CHAOS group proposes to make low energy analyzing power measurements for Tr^p scattering. Consider an elastic scattering experiment that uses a target made of spin | particles (such as protons). The analyzing power is defined as da_^ _ dffi Ay = ^ ^ r (1.5) Pi^' + P^^' The I denotes that the target (source of protons) is polarized in the direction parallel to the vector fc,„ x kout (up)j where kin and kout are unit vectors along the incoming and outgoing pion beams, respectively. Similarly, the | denotes that the target is polarized in the direction antiparaUel to fe,„ X kout (down). P | is the percentage of the target that is polarized up. The advantage is that the absolute normalization of the cross sections has no effect on the results because the normalization factor cancels out in the numerator and denominator of Ay. The values for Ay put an extra constraint on the phase shift analysis and together with differential cross section measurements, accurate and reproducible scattering amplitudes can be calculated. The final result is an improvement in the value of S . Both the (7r,27r) and irp experiments present various challenges. They involve low cross sections and a wide coverage of angles and energies. In addition, they require a good momentum resolution on the order of 1%. These challenges motivated the group to build CHAOS, a unique spectrometer for use in various pion studies. Chapter 2 Overview of the Des ign of C H A O S 2.1 Des ign Mot ivat ion After having established that interesting pion physics investigations still remained to be done at TRIUMF, the CHAOS researchers considered the problem of how to gather the necessary data. The only spectrometer that existed at TRIUMF for such work was the QQD, with a solid angle of less than 20 msr and an upper limit on momentum mea-surements of 150 MeV^  jjj addition, the primary TRIUMF proton beams used to create the pion beams are seven times less intense than those at SIN or LAMPF. Motivated by these constraints, the CHAOS group set out to design a pion spectrometer that would make the fuUest use of the beams at TRIUMF in order to keep the facility competitive with other similar ones. The detector has a full 360° azimuthal angular acceptance and a vertical acceptance of ±7° (giving it a solid angle more than 100 times that of QQD), and there is no upper limit to the energies it can measure. Indeed, it could be used as a high energy spectrometer in the KAON factory if it is built in the future. In order that CHAOS be suited to the Trp and (TT, 27r) experimental programs, certain requirements were imposed on the spectrometer: Ability to measure very low cross sections Ability to utilize an incident beam flux > 5MHz Extensive range of angle and energy Must use cryogenic or polarized targets Ability to detect charged particles in coincidence Momentum resolution on the order of 1% 14 Chapter 2. Overview of the Design of CHAOS 15 The problems associated with the requirement that CHAOS be able to measure small cross sections are exacerbated by the relatively low beam intensity at TRIUMF, as well as the nature of the reactions the group proposes to study. In particular, the spectrometer must be able to identify relatively scarce (7r,27r) events from amongst a large background of elastic irp scattering. The large angtdar range and energy range that can be studied at one time using the spectrometer again allows for the optimization of data collection. All of the experiments which have been proposed require the use of special targets, and CHAOS has been designed to accommodate these within its center. A cryogenic LH2/LD2 target has been built and used with CHAOS already. The polarized proton target is presently being built. In addition, a system for maneuvering these targets in and out of the spectrometer has been designed. The ability to detect charged particles in coincidence is very important. AU the reactions which will be studied have final states with two charged particles. Multiplicity is one of the first tests performed in hardware to determine whether an event may be of interest. Coincidence mode operation wiU allow researchers to easily separate good events from a high singles background due to pions scattering off helium, carbon and oxygen in the polarized target. In addition, pion interactions with the target cryostat walls contribute to the singles background rate. Finally, the momentum resolution is of great importance. In order to gain information that will allow for a good test of chiral symmetry parameters such as the S term and the (7r,27r) scattering lengths, the momentum resolution must be at least ^w- < 1% (cr), if not better. Without this accuracy, the error bars will be too large to be able to draw any useful conclusions. Chapter 2. Overview of the Design of CHAOS 16 2.2 Various C o m p o n e n t s in Brief This chapter provides a brief technical description of the CHAOS spectrometer. Al-though there are many interesting facets to the project, a detailed discussion is beyond the scope of this thesis. Rather, the next few pages wUl outline some of the important points in order to provide an idea of how the spectrometer works. 2.2.1 Sagane Magne t The spectrometer detects charged particles and as such is built upon a large cylindrical dipole magnet called the Sagane. The 55 ton magnet is composed of two poles measuring 95 cm in diameter that are supported by an iron framework with dimensions of 173 x 224 X 224 cm^. The poles are separated by a 47 cm gap. Several changes were made to the magnet to tailor it to the needs of CHAOS. The addition of tapered iron pole tips and small ring shims to the poles increased both the field and the field uniformity in the gap region where the three inner wire chambers sit. The pole tips reduce the gap to 20 cm. Figure 2.2 illustrates a plot of the CHAOS magnetic field as a function of radius [7]. Evidently, the field value remains relatively constant over the region of W C l , WC2 and WC3; thus the second level trigger (2LT) algorithm assumes the field is constant and fits circular tracks to hit combinations from the three inner wire chambers. Another major change involved raising the field saturation point from 0.8T to 1.6T by adding iron to the top and bottom segments of the magnet as well as the return yokes in the four corners, thereby increasing the area of the iron return path to match the area of the poles. Chapter 2. Overview of the Design of CHAOS 17 Magnetic Field Profile (43.8 a / c m ) 10 CJ) 8 ; ^ 4 O .^ 2 -Field Value Uniformity 1.0 0.8 1-0.6 0.4 0.2 o *c Z) —f 1 1 1 1 1 1 1 — ^ r 0 10 20 30 40 50 60 70 80 90 100 110 Radius (cm) Magnetic Field Profile (43.8 a / c m ) Radius (cm) Figure 2.2: CHAOS radial magnetic field profile. The upper plot illustrates the field over a broad range (solid line) as well as the field uniformity (crosses). The lower left corner of the plot corresponds to the center of CHAOS, and the remaining lines illustrate a side view of magnet components in a quadrant. The lower graph shows a closeup of the field over the region of the three inner chambers. Chapter 2. Overview of the Design of CHAOS 18 2.2.2 C H A O S T a r g e t s CHAOS experiments will make use of either a cryogenic target or a polarized target. Each must fit into the 100 mm wide open bore down the cylindrical axis of the Sagane. The cryogenic target is a relatively straightforward addition to CHAOS. Essentially the only requirements are that it is not too big for the bore hole and that it it can be ma-neuvered into the spectrometer. The polarized target is more costly and labor intensive to build. The design of the target includes a cryostat and a large volume dilution refrig-erator. There are some important limitations placed on the design of the target. First, it must be polarized outside the magnet because the CHAOS field is too inhomogeneous to be used for this purpose. Once it is polarized, it must maintain a frozen spin config-uration (FS) while it is lowered into the spectrometer. Even the lowering mechanism is complicated since it must allow for over 1 m of vertical movement. The CHAOS target wiU be polarized outside of the spectrometer using a 2.5T solenoid which already exists at TRIUMF. After the polarization is complete, a small supercon-ducting coil inside the target cryostat will be turned on to maintain the FS configuration for the short time during which the apparatus is lowered into the bore in the Sagane. Once the target is situated at the center of the beam plane, the superconducting solenoid is no longer required because the CHAOS central field can hold the spin configuration. Once the desired CHAOS target is chosen and put in place, it is necessary to ensure that the incoming beam intersects the target. Since the beam curvature wiU vary with the CHAOS field strength and the TRIUMF channel momentum, the spectrometer must be translated perpendicular to the 0° beamline. This is performed using a straight rail assembly over which the Sagane is pushed or puUed using a hydraulic mechanism. Above the rail system is a circular bearing assembly that allows for rotational motion to further optimize the beam path within the spectrometer. Chapter 2. Overview of the Design of CHAOS 19 2.2.3 W i r e Chamber Des ign A major part of CHAOS planning involved Monte Carlo studies and momentum re-construction calculations for determining the optimum design of the four cylindrical wire chambers. In these tests, different sets of chamber geometry and materials specifications were defined in detail in the CERN Monte Carlo program GEANT and the software was then used to simulate actual physical processes as expected to be seen in CHAOS for each set. 7r~p elastic scattering was simulated with an incoming beam momentum of 250 MsY^ at a CHAOS field strength of 1.4T. Incoming tracks that hit the target were elastically scattered in the simulation; the scattered pion angle was chosen at random between 0° and 180° since the kinematics of the reaction is symmetric about TT. The scattered pion, the associated recoil proton and the outgoing beam track were traced through all cham-bers by GEANT. The events were made as realistic as possible by considering processes such as energy loss and multiple scattering, and effects due to a magnetic field that varies slightly and then quickly falls off at a radius of approximately 35 cm. The program collected precise information regarding the intersection of each track with all the chambers for every event. The next step was to replay the events and reconstruct what occurred according to how CHAOS would see it. Various configurations of cathode and anode wires were considered for each chamber. For each simulation, the pieces of track information were converted into the same form they would have as CHAOS output from the readout electronics; at this point in the tests, the chamber resolutions were the variable parameters. Finally, the simulated CHAOS output was input to reconstruction programs, and the associated track momenta for each event were calculated. For each set of chamber specifications, one could get an idea of how well the spectrometer would be able to function. These studies allowed the group to decide on the optimum radius, materials construction and number of channels (ie: number of wires) Chapter 2. Overview of the Design of CHAOS 20 for each of the four chambers. Mult i -Wire Proport ional Chambers The two innermost CHAOS chambers, W C l and WC2, are multiwire proportional chambers (MWPC's) used for tracking charged particles. The first chamber of this type was built in 1967-1968 by Georges Charpak and colleagues [8]. The development of MWPC's continued rapidly and soon it became the favorite type of detector in experi-mental particle physics. Among its good points are excellent time resolution on the order of a few ns, and simple readout consisting of the list of wires which were hit. The typical design of a MWPC involves two planar cathode walls placed parallel to each other with respect to a plane half way between them (henceforth referred to as the PC plane). These walls could be flat, or they could be cylindrical and thus concentric. The cathode walls are joined at the top and bottom by two walls of insulating material perpendicular to the PC plane. A gas is pumped through this sealed environment, and a set of parallel anode wires are strung under tension in the PC plane between the two cathode planes. The wires collect the negative charge that creates a fast signal when a particle passes through, while the cathode planes are kept at a constant negative potential and collect the corresponding positive ions that create a slower signal. When a charged particle travels through a MWPC, it undergoes electromagnetic interactions with the gaseous medium. Excitation and ionization of the gas molecules are the main processes that occur, and all others are negligible. The particle undergoes a particular number of primary ionizing collisions to create electron and positive ion pairs. The primary electrons then go on to create other secondary electron and ion pairs. The total number of pairs can be determined given the total energy lost by the particle into the detector through the creation of pairs and the average energy required to create one pair in the gaseous medium. Chapter 2. Overview of the Design of CHAOS 21 If the anode wires were held at a very low positive voltage, the charge of the primary and secondary electrons would be aU that makes up the signal induced on the wires. However, by holding the anodes at a substantial voltage, one can create an avalanche effect. This process occurs when a primary electron arrives to within a few anode radii from the wire. At this point it enters a very high electric field due to the ^ rule. The electron suddenly starts to undergo numerous ionizing collisions and electron multiplica-tion occurs as a chain reaction starts. A drop-like mass of electrons quickly surrounds the anode wire and is collected, creating a pulse of risetime ~ 1 ns. The positive ions, on the other hand, are slower moving and they drift towards the cathodes to create a slower pulse of risetime ~ 30 ns. W C l and W C 2 W C l and WC2 are cylindrical MWPC's with radii of 114.59 and 229.18 mm respec-tively. In both chambers, the anode wires are strung under tension between two GIO rings. The rings are supported by two concentric rohacell walls re-enforced with kapton foUs. The inside surface of the outer wall is covered with cathode strips, rather than a single cathode plane, that are inclined to the anode wires by 30°. Thus, there is a grid system and by intersecting the signal from the anodes with that from the cathodes, one can determine the (x,y,z) point through which a particle passed. Both chambers have a . 1 ° half gap (anode-cathode distance) of 2 mm and an anode spacing of A (1 mm pitch for W C l and 2 mm pitch for WC2). The W C l cathode strip pitch is 2 mm, whereas the pitch for WC2 is 4 mm. The anode wires are read using the LeCroy Multiwire Proportional Counter Operating System (PCOS III) ^, to be discussed later. The cathodes are read out with the LeCroy FASTBUS Analog to Digital Converter (ADC) system. The two chambers have identical proportions and similar construction. However, they ^The latest veision of the system is PCOS III, which will also be referred to simply as PCOS. Chapter 2. Overview of the Design of CHAOS 22 could not be combined into a single MWPC with two planes. There is very little room inside the spectrometer once all pieces are installed; working with a bi-planar chamber would be quite difficult in this environment. Also, because the anode wires are separated by only 1 mm (WCl) or 2mm (WC2), the group had to solder them in place between the two GIO rings, rather than crimp them. A bi-planar chamber cannot be constructed in this manner. The purpose of W C l and WC2 is to help define incoming and outgoing beam tracks as well as any tracks belonging to scattered particles. They can withstand a pion flux of up to 5 MHz without being damaged and, as such, can provide two incoming beam points. WC3 is deadened at the beam spots to avoid damage. This has no eff^ ect on beam track definition because the incident pion track in each event can be accurately determined using the W C l and WC2 points as well as the channel momentum. It is essential to know the incoming beam track in order to determine the reaction vertex of an outgoing track. Drift Chambers Drift chambers measure the drift times of electrons produced by ionization when a charged particle traverses the chamber. This information can then be used to determine the positions of the ionizing events. In its most basic form, a drift chamber consists of a single cell in which there is a uniform electric field and a proportional counter. As usual, a charged particle traverses the chamber and ionizes the gas inside. The electrons liberated from the gas at time to drift towards the nearest anode wire with velocity v and, as in a MWPC, an electron avalanche occurs at time ti near the wire, and a pulse is created for readout. The position of the ionizing track with respect to the wire is given Chapter 2. Overview of the Design of CHAOS 23 by x= r vdt (2.6) J to In the simplest case of a uniform electric field in the absence of a magnetic field, the resulting time-distance relation is simply x = {t\ — tQ)v. At first glance it appears as though a MWPC can be used as a drift chamber. However, this would not be desirable because there is a low field region between the anode wires in the former; the nonuniform field would result in a complicated time-distance relationship. Drift chambers have field shaping electrodes, wires or strips that ensure a uniform electric field. The need for such devices result in a tendency for drift chambers to be thicker than MWPC's . In addition, typical drift times are on the order of 200 ns, so this type of chamber cannot tolerate high rates. However, this is offset by the fact that drift chambers provide highly accurate position information once the time-distance relation is determined. Also, in a cylindrical spectrometer such as CHAOS, it is impractical to have a MWPC at a large radius; the proportional chamber has a small anode spacing and as such the number of readout channels increases linearly with radius given the same spacing. Instrumenting this many channels becomes very costly and so drift chambers, with their larger anode spacing, are desirable at larger radii. W C 3 WC3 is a thin drift chamber that is similar in construction to W C l and WC2. It has only 144 wires and, as such, has a much larger anode pitch of 15 mm and a half-gap of 3.5 mm. It is located at a radius of 343.77 mm, just before the sharp magnetic field drop off (refer to Figure 2.2). Therefore, not only are the anode wires instrumented with Time to Digital Converters (TDC's) , but they are also connected to a PCOS III system so that the angular hit information can be input to the second level trigger. The anode Chapter 2. Overview of the Design of CHAOS 24 wires are strung and crimped under tension from two GIO rings that are supported by two concentric walls made of rohacell re-enforced with glue and kapton. The cathode walls are covered with vertical cathode strips that are not inclined to the anode wires as in W C l and WC2. There is a group of four cathode strips read out for each anode wire. On either of the inner or outer cylindrical walls, every third cathode strip is not read out, but rather its purpose is to provide field shaping. With a drift time ~ 150 ns, WC3 is a much slower chamber than the inner pro-portional chambers, W C l and WC2. Thus, the second level trigger must wait for the WC3 PCOS system to no longer be busy before starting to process angular hit informa-tion. Furthermore, as stated previously, WC3 must be deadened at the incident beam spot because it cannot keep up with the beam rate; the current draw would damage the chamber. WC4 WC4 is a vector drift chamber that sits beyond the region of uniform magnetic field. The relatively deep chamber contains eight anode planes separated radially by 5 mm; the radius of the innermost plane is 627.5 mm, and at this distance from the center of CHAOS, |B| is always less than 0.5T. The chamber is divided into trapezoidal cells 3.6° wide, with one ray of wires in each cell. In every cell, each of the two walls parallel to the anode plane are covered with 9 cathode strips that are 7.4 mm wide and separated by 1.0 mm. The half-gap is half the cell width, or 1.8°. The anodes are instrumented with a TDC system only. It would be of no use to read out the wires with PCOS for input to the second level trigger, since WC4 lies in a region of varying magnetic field, and the 2LT algorithm assumes a uniform B. Moreover, accurate WC4 position information is available only through the ofiline analysis of TDC spectra. On either side of the group of eight anodes, there is also one resistive anode wire. Chapter 2. Overview of the Design of CHAOS 25 These are instrumented at both ends with LeCroy FASTBUS ADC's, allowing one to use the method of charge division to calculate z-position information. When the electrons in the gas avalanche onto the wire, the charge will be collected at both ends of the anode. By considering the difference in the ADC pulse heights at the ends of each anode, one can approximate the z-position of the particle track. In WC4 one must be able to determine on which side of a cell the track passed; this is termed the left-right ambiguity problem. This problem was solved by staggering the wires by ±250 ^m in the L-R direction (every second wire staggered in the same direction). The result is that a track passing through a ceU wiU have shorter drift times, on average, to one set of wires, depending on which side of the cell it traversed. It should be noted that in addition to the 10 anode wires, there are also two thicker field shaping wires at either end of each cell. As was discussed earlier, these wires ensure that the electric field is uniform in the region of the anode wires. Since WC4 is so large, it had to be constructed in multicell sections: four 36° sections and four 54° sections. The wires are connected to two wide arc-shaped plates of rigid insulator called Ultem. These plates are separated by ribs made of rohacel, GIO and nickel-plated kapton on which the cathode strips are etched. The inner window is a cathode plane made of rohaceU covered with aluminized mylar (conductor) on the inside and kapton (insulator) on the outside. The outer window is also a cathode plane, and is made of thin GIO coated with nickel plated copper on the inside. 2.2.4 C F T Blocks The CHAOS Fast Trigger Telescopes (CFT's) provide information that is used to determine event multiplicity and to mass identify charged particles (namely pions, elec-trons, protons and deuterons). CFT pulse height information for good events is written to tape for offline mass identification of particles. In addition, various signals are fed to Chapter 2. Overview of the Design of CHAOS 26 the first level trigger (ILT), which makes a fast decision based on the minimum number of particles the researchers wish to see (event multiplicity threshold). If the proper con-ditions are not m.et, the first level trigger clears all spectrometer electronics; otherwise, it sends a gate signal to the 2LT to enable further tests. Note that the data regarding particle id and multiplicity that are provided by the CFT's are not available to the 2LT, as this would have complicated all levels of the CHAOS trigger and been very costly. Each of the eighteen CFT blocks is 18° wide and is made of three layers termed AEi, AE2 and C. AEi is a differential energy counter in the form of an NEllO scintillator with dimensions 25 x 25 x 0.35 cm^. AE2 is also a differential energy counter, made up of two adjacent NEllO scintillators measuring 13 X 25 x 1.3 cm^ each. The C layer is made up of three adjacent Cerenkov detectors. Each Cerenkov counter is a block of lead glass (index of refraction = 1.6-1.7) measuring 9.5 X 25 x 12 cm^. From 50 to 800 ^ ^ , the CFT signals can be used in offline analysis to mass separate pions, protons and deuterons by considering pulse height information from the A ^ i counter in the CFT blocks. When a particle traverses a counter, it loses energy through electromagnetic interactions with the material; the deposited energy produces a pulse out of the counter, the height of which is dependent upon various parameters. In particular, the pulse height out of a thin counter, such as one of the AE counters, is proportional to the differential energy lost by the particle in the detector. With some manipulation of equations, it is found that there is a definite relationship between the E and AE of a particle that varies depending on its mass. Thus, one can use A ^ i to distinguish between the pions, protons and deuterons on the basis of pulse height. The second differential energy counter, AE2, is used to double the amount of information available for mass identification of particles and to provide a AEi • AE2 coincidence in the first level trigger Programmable Lookup Units (PLU's). The coincidence ensures the track indeed radiates into or from the center of CHAOS. Chapter 2. Overview of the Design of CHAOS 27 At energies of up to 50 MeV, pions can similarly be mass separated from electrons using the pulse height information from the A ^ counters. However, at higher energies the pulse heights are indistinguishable and the C layer is essential. The theory behind the use of this counter setup is that relativistic electrons produce lajge amounts of bremsstrahlung radiation when they travel past a high Z material like the lead atoms in the C layer. The radiation produces electron-positron pairs which then contribute to the Cerenkov light cone through the creation of additional photons. In contrast, pions produce very little bremsstrahlung radiation. This allows the two types of particles to be separated since the pulse height for electrons is much larger than that of pions at the same momentum. 2.2.5 E l e c t r o n i c s Part of what made CHAOS so challenging to build and commission is the vast array of electronics that manipulate over 4500 channels of information. For instance, a LeCroy fast encoding and readout (FERA) system of ADC's is used to read out the pulse height information from the CFT blocks. A 4290 drift chamber time digitizing system, also from LeCroy, is used to measure the drift times to WC3 and WC4 anodes. A LeCroy FASTBUS ADC system reads out the WC4 resistive wires, as well as the cathode information from the three inner chambers. The PCOS III system, also developed by LeCroy, is used to record hits on anode wires in W C l , WC2 and WC3. Additional information from the CFT blocks is fed to the first level trigger electronics, which make a fast decision regarding the merit of an event based on event multiplicity. If the event passes this stage, the first level trigger enables the second level trigger; the 2LT then takes in PCOS hit information for processing and makes a final hardware decision as to whether to send a 'Look At Me' (LAM) ^ to the data acquisition computer. One could go into much detail on each of these electronics systems, but the scope of this thesis is limited to a brief A LAM is the signal that tells the data acquisition computer to write the event to tape. Chapter 2. Overview of the Design of CHAOS 28 description of the first level trigger and the PCOS readout system. Subsequent chapters will provide the details of the design and testing of the second level trigger. First Level Trigger The first level trigger decision is made using information read from the CFT scintil-lator blocks and Cerenkov detectors. The CFT signals are discriminated, and delays are added so that all signals arrive simultaneously at the input of the coincidence modules. Upon making its decision, the ILT will then clear all readout electronics in the case of a poor event. If the event passes this stage, the first level trigger enables the 2LT and also opens the gate for the ADC's so they can be ready for possible transfer to tape once the 2LT has finished making its decision. After being discriminated and delayed, every signal from the CFT blocks is fed to a corresponding channel in one of several FLU's. The user programs each PLU to accept only certain input coincidences. Typically the PLU's are programmed to look for a A ^ i • AE2 coincidence within any block. If the required coincidences are present in an event, the PLU will output a flag to indicate this is so. The final stage of the ILT is the Majority Logic Unit (MajLU), which produces an output if the number of PLU coincidences is greater than the programmed threshold multiplicity. The programmed logic follows from where one expects to see signals from different types of particles. For instance, if one expects that a particle belonging to a background reaction will not have enough energy to reach a particular detector layer in the CFT blocks, whereas the particles of interest will, the chosen coincidences will include the appropriate signals. The PLU's will reject all other patterns of signals from the CFT blocks. Chapter 2. Overview of the Design of CHAOS 29 P C O S Readout Although the chambers provide much more information than simply addresses of hit wires, this is the only data that the 2LT takes in. These data are provided by the PCOS III system which is connected to the three inner chambers. In short, each wire of the chambers is connected via 2735PC amplifier/discriminator cards to 2731A delay and latch modules which sit in dedicated CAMAC crates that have special 2738 PCOS controllers rather than the normal type of crate controller. PCOS can handle input rates in excess of 10 MHz, which is well above the maximum rate at which W C l and WC2 can be operated (~ 5 MHz). In CHAOS the PCOS systems are operated in cluster mode in order to optimize the resolution of the chambers. This process is as foUows. A particle activates several wires in the chambers as it traverses the spectrometer. Each wire that produces a signal over the preset threshold wiU set its corresponding latch in a dedicated PCOS crate. Upon receiving an enable signal from the first level trigger, the 2738 controller for each PCOS crate will survey all of its latch modules. If it sees that adjacent wires fired, it wiU group these together into a cluster. It can group together up to 15 wires in a cluster. Otherwise it wiU break the set in half (or as close to half as possible) into two smaller clusters; however, large groups do not occur in CHAOS unless a test system is being used to create artificial data. Once the controller has grouped the hits, it calculates the address of the cluster. If the group includes an odd number of wires, the address wiU be the middle wire. However, if the group includes an even number of wires, the address will be expressed as a particular "wire and a half", or equivalently, the corresponding PCOS "channel and a half". The controller then outputs information for all the clusterized hits for the event in question. It outputs the data in pairs of words. The first word contains the width of the cluster, while the second word contains the address in terms of Chapter 2. Overview of the Design of CHAOS 30 channels. In the address word, the first bit ^ is the half bit that is set if the cluster is an even number of wires wide. One can see that clusterizing has the effect of doubling the 1 0 resolution of the chambers; for example, the wire spacing in W C l and WC2 is J , but PCOS can determine addresses between the wires and so the actual resolution presented to the 2LT is ^ ° . One can preassign 9-bit logical addresses to each 2731A module through CAMAC, and in CHAOS those chosen are as follows: W C l 2731A's have addresses 0-22, WC2 2731A's have addresses 32-54 and WC3 2731A's have addresses 64-68. These values were chosen to conveniently separate the wire addresses in any of the three inner chambers from those in the other two. In addition, it allows for easy conversion from W C l and WC2 PCOS words to angular data. The format of the PCOS data output for each cluster word is shown in Figure 2.3: address word 0 S9 SB S7 Se S5 S4 S3 s. s, L5 L4 L3 L2 Li h ! f MSB LSB X width word x 1 0 0 0 0 0 0 0 0 0 0 0 W4 W3 W2 W, Figure 2.3: PCOS clusterized data output format For completeness, the width word is shown, in which W indicates the number of wires in the cluster, up to 15. S is the logical address of the corresponding 2731A module, and the L bits plus h in the LSB specify the address of the center of the cluster in terms of 32 latch channels in the given 2731A module, h is a 'half channel" bit from the cluster centroid calculation. For example, if two wires fire and these are input to latch channels ^Thioughout this thesis the least significant bit (LSB) in a binary woid is teimed bit 1, and the most significant bit (MSB) is labelled by the width of the word. Chapter 2. Overview of the Design of CHAOS 31 16 and 17 in the 2731A with logical address S, PCOS would calculate the address of the centroid to be 16.5 channels and output an address word with the least significant bits as follows: plus 0.5 1 0 0 0 ' 1 ^ ^ V ' channel 16 For both W C l and WC2, PCOS channel 0 in the S=0 2731A corresponds to 0° and so on. Thus, this setup ensures that the PCOS addresses for the two inner chambers are simply 1 ° . the center of the cluster in -r units plus a base value of 2048 in the case of WC2 only. WC3 addresses are slightly more complicated because the cabling to this chamber was accidently offset during the commissioning run. The WC3 PCOS address 0 corresponds to an angle of 2.5° and will probably remain so due to the difficulty of repositioning the CO chamber. Thus, the address words are the angle of the cluster centroid in f units (recall WC3 has a larger anode pitch), minus 2.5°, plus a base of 4096. Each 2738 PCOS controller has both input and output databus ports, as well as ECL ports for both input and output. The databus port sends information to a databus buffer and interface module (LeCroy 4299) that acts as a CAMAC interface between the PCOS system and the data acqtdsition computer. A special delimiting word is tacked on at the end of the data out of the databus port. Using ECL logic, the ECL port transmits the same data without the terminator word to the CHAOS second level trigger, which determines the merit of the track based on any combination of the following: momentum, distance of closest approach to the origin, polarity, momentum versus scattering angle correlation, and sum of momentum and/or comparison of polarities in cases where two tracks are searched for and found. The PCOS readout time can be dramatically improved if the ports of the controllers are daisychained. Up to 16 PCOS controllers can be daisychained at one time; they are given sequential controller numbers starting with 0, and the zeroeth controller is Chapter 2. Overview of the Design of CHAOS 32 designated MASTER, while the last is designated TERMINAL. In the CHAOS readout system, the W C l and WC2 controllers (called PCOSl AND P C 0 S 2 , respectively) are daisychained, and the WC3 controller (called PC0S3) belongs to an entirely separate system. In the original setup all three controllers were connected. A common gate was sent to the controllers to tell them when to survey the 2731A latches in their corre-sponding crates. However, due to the fundamentally different designs of the chambers, the signals on the wires in the W C l and WC2 were ready long before the signals on the wires in WC3. Recall that W C l and WC2 are MWPC's with identical proportions, whereas WC3 is a drift chamber that is also operated in proportional mode. As such, the electrons in WC3 take much longer to drift to the anodes than they do in the two inner chambers because they must drift over a relatively far distance. As such, PCOSl and P C 0 S 2 could not be enabled with the same gate as P C 0 S 3 . The group then tried to send two different gates, while leaving the controllers daisychained with PCOSl still being the MASTER. Again PCOSl had difficulty communicating with P C 0 S 3 , and most of the time data were lost from WC3. The final solution to the timing problems was to daisychain only PC0S2 and PCOSl and leave P C 0 S 3 by itself with its own databus, thus improving the efficiency of the anode wire readout. Chapter 3 Introduct ion to the Second Level Trigger The second level trigger makes a fast rejection of events based on several different tests. The first section of the trigger performs general tests that wiU be used in every experiment. Here aU hit combinations from W C l , WC2 and WC3 are considered until an acceptable track can be constructed through them. Acceptable means that the tracks have a proper momentum and polarity as defined by the user, and they also have a dis-tance of closest approach to the origin of CHAOS that lies within a defined target region. After a good track is found, it can be subjected to further tests in three other sections that can be used together or one at a time. One group of trigger electronics calculates the scattering angle of a track and does a cut on the momentum versus scattering angle correlation. Another group performs the rejection of events in which a pion in the beam has decayed to a muon. Here the trigger checks to see that there is at least one incoming beam hit in both W C l and WC2 in the regions through which the pion beam is expected to pass. Yet a third group of electronics looks for a second good track in a set of hits and then performs a cut on the momentum sum and compares the polarities of the tracks. Even in its most simple form, the second level trigger is crucial to the operation of CHAOS. H the trigger were not present, LAMs would be issued to the data acquisition computer for millions of uninteresting events. Since no calculations would have been done to filter the data, the vast majority of information written to tape would be of no use. In addition, the maximum rate at which the computer can read in events is 100 Hz. If a LAM was generated for most events, the result would be an enormous dead time and 33 Chapter 3. Introduction to the Second Level Trigger 34 a corresponding increase in the amount of beam time required to collect enough events of interest. With the trigger present, the detector can run at beam rates of up to 5 MHz and nearly all of the data collected wiU belong to the reaction the researchers are studjring. It is especially important that the trigger be able to reconstruct an approximate distance of closest approach to ensure that the tracks indeed came from inside the target and not from scattering events outside of it. The momentum and polarity cuts can also be quite important depending on the experiment. For instance, a momentum cut that requires a track to have P > 500 ^ ^ would effectively eliminate all other reactions in a resonance energy absorption experiment. The polarity cut option aids in TT"*" —> 7r~ DCX experiments, which involve very low cross sections compared to the TT"*" scattering background. One can reject nearly all other sources of events with a polarity cut that requires a negatively charged final state particle to be present. The only other source of events that would pass the test would be the ir'^n —> Tr+Tr"^ reaction. However, since it has a low cross section that is comparable in magnitude to that for a DCX reaction, the two types of events can be easily separated offline through the use of missing mass information. In addition, the track momentum and polarity are required for the more extensive hardware tests performed in the remaining optional sections of the trigger. 3.1 P u r p o s e of M o m e n t u m S u m Cut and Polarity Comparison The first section of the 2LT is not sufficient to distinguish (TT, 27r) reactions from the far more numerous vp elastic scattering events. Figure 3.4 illustrates the momentum distribution for outgoing charged particles in two separate Monte Carlo simulations: one for a (TT, 2ir) reaction TT'^P -^ 7r"'"7r"*'n Chapter 3. Introduction to the Second Level Trigger 35 and one for irp scattering. Each simulation used an incident TT"*" beam with a momentum of 396 ^ ^ . The data sets are the same size because the simulations were done separately, and thus the plots do not indicate the relative cross sections. Each outgoing charged particle has been accounted for in the histogram, since one does not know which the 2LT will find first. Evidently, the single particle distributions for each reaction overlap and together with the fact that ivp scattering has a much larger cross section, this would result in the inability of the 2LT to separate the events based on single particle momentum alone. However, the momentum sum of the two outgoing charged particles provides a way of separating the data. Figure 3.5 illustrates the momentum sum of the two final state charged particles in the same Monte Carlo simulations used to generate the data in Figure 3.4. Evidently, the irp plot differs substantially from that for the (TT, 27r) reaction. The peak for irp scattering is higher and there is no overlap of the two distributions. This tends to be the case for all (TT, 27r) reactions with two outgoing charged particles. In this case illustrated, an upper cut on the momentum sum of approximately 400 ^^^ would eliminate the irp elastic scattering events from the data. The momentum sum/polarity comparison section of the 2LT is an optional section that performs such a cut. It makes the trigger loop back and search for a second track that passes the tests in the first section. Upon finding two good tracks, it can determine the momentum sum and compare the polarities of the tracks. It will then make a decision based on the residts of the tests, according to what the user programmed into the trigger. This section of the 2LT is crucial to the (TT, 2ir) experimental program. Without these electronics, researchers would not be able to separate the (TT, 27r) events from the extensive irp elastic scattering background. Tables 3.1 and 3.2 show the expected first level trigger acceptance rates (ie: rate at which 2LT is being enabled) for the major reactions which will be observable with CHAOS [5]. For each table, the incident pion beam has T^ = 300 MeV and a rate of 2 x 10^ Hz. The first level trigger is the coincidence between either Chapter 3. IntToduction to the Second Level Trigger 36 200 400 600 800 1000 M o m e n t u i n (MeV/c) Figure 3.4: Momentum histogram for outgoing charged particles in a (TT, 27r) reaction, ir'^p —^ ir'^ir'^n, as well as irp elastic scattering in P,r = 396 —^— Monte Carlo examples. The momentum of each charged particle (both TT'^'S or both the TT"*" and p in the (7r,27r) and irp cases, respectively) was accounted for in the histogram, since the 2LT can not distinguish the particles. Note that the data sets are equal in size for both reactions, and therefore do not reflect the fact that the irp scattering has the larger cross section by several orders of magnitude. 4000 V) 3000-o 2000 2 1000 (TT^IT) Momentum Sum 100 200 300 400 500 600 Momentum (MeV/c) Trp Momentum Sum 200 400 600 600 1000 Momentum. (MeV/o) Figure 3.5: Monte Carlo results for momentum sum of final state charged particles in both a (7r,27r) reaction, ir'^p -^ Tr+Tr+n, as well as Trp elastic scattering with a beam momentum of P,^ = 396 ^ ^ . Ciap te r 3. Introduction to the Second Level Trigger 37 Reaction TT+p —> TT+p 1st Level Rate (s ^) 1.4 3.6 4800 Table 3.1: Rates for selected reactions involving incident TT''". Reaction 7r~p —»7r~7r°p •K~p —> 7r'^7r~7i ir~p —> 7r~p 1st Level Rate (s ^) 4.4 12.0 840 Table 3.2: Rates for selected reactions involving incident TT . two charged pions or a charged pion and a proton. Evidently, if an experiment were run with only the general 2LT that simply makes a momentum, distance of closest approach and polarity cut each time it is enabled by the ILT, the data acquisition would be saturated with irp elastic scattering events. Because the (7r,27r) reaction rate is far outweighed by that for irp scattering, the (7r,27r) program would not be possible if this section of the trigger were not present. 3.2 Purpose of M o m e n t u m versus Scattering Angle Cut Another important section of the 2LT performs a momentum versus scattering angle {9s) cut on single tracks passed by the first stage of the 2LT. Using the PCOS hit in-formation and the calculated momentum from the first section, this group of electronics calculates an approximation to the scattering angle. Note that because the second level trigger receives only a fraction of the information available in CHAOS, it cannot make a highly accurate evaluation of the momentum or the scattering angle. In particular, it Chapter 3. IntToduction to the Second Level Trigger 38 cannot reconstruct incoming tracks, and thus it makes the assumption that the interac-tion vertex within the target is approximately equal to the point of closest approach of the outgoing track to the origin. In particular, the momentum versus 9a cut is important for separating the pion elastic scattering data from the events in which the pion scatters off helium, oxygen and carbon in the polarized target. Figure 3.6 illustrates the pion momentum versus 9s for a 100 MeV TT"*" scattering from protons as well as helium and carbon: T„ = 100 MeV Trp K i n e m a t i c s ^,-^ 225 I ' ' " ' ' ' ' L O > CD e 200-0 20 40 60 80 100 120 140 160 180 pion Og (degrees ) Figure 3.6: Illustration of momentum versus 9s points for 100 MeV TT+'S scattering from protons as well as helium and carbon. The error bars indicate the ±5% bands on the momenta. Except for angles less than 50°, the irp pion momenta normally lie below those for pions that scatter from the heavier elements. The fact that the pion momenta for background scattering is virtually independent of angle can be used to cut out many of the unwanted Chapter 3. Introduction to the Second Level Trigger 39 events in the second level trigger. A cut on the scattering angle of the pion that reflects the pattern for irp events can be programmed into the trigger. The second level trigger cannot know if it is considering the scattered pion or another charged final state such as the proton. However, it is expected that every good event will have a pion present in the final state, but it is not necessarily true that a proton will always be present. Tracks are therefore tested for the pion momentum versus scattering angle correlation until a satisfactory one is found or all possibilities have been considered. It should be noted that this test would be used after a preliminary momentum cut in the first section of the 2LT. The irp elastic scattering data are kinematically bound. For example, in the graph shown the momentum of the pion is bound by 120 and 205 —^. The first section of the 2LT would find tracks and discard them if the momentum was not in this region, and only after an acceptable track was found would the momentum versus scattering angle cut be applied. 3.3 N e e d for M u o n Reject ion During the first experiment in the summer of 1993, it was determined that a sub-stantial background resulted from pions that decayed into muons between the beam-line production target and the CHAOS target. It was originally thought that if a pion decayed, it would be most likely to do so at the production target. The momentum-selecting beamline magnets would ensure that the muons entering CHAOS had the same momentum and initial trajectory as the incident pions. In addition, muons are weakly interacting and would thus travel right through the target along the same trajectory as the incident pions that do not interact. Recalling that WC3 is deadened at the incoming and outgoing beam spots, it is evident that neither the incoming or outgoing muon track would be reconstructed by the 2LT. It was thus thought that the majority of the muons Gbaptei 3. Introduction to the Second Level Trigger 40 would not cause data to be written to tape. However, it was found that a significant number of muons were produced by pion decays between the momentum-selecting magnets and the CHAOS target. The resulting muons do not travel on the same trajectory as the incoming pions. The reason for this is that a pion decays into a muon plus a neutrino; thus the muon does not have the same momentum as the original pion. Some of the muons were rejected by the ILT because their trajectories missed the incoming beam counter. However, most entered the counter at an odd angle to its face, and then continued on to pass through the CFT block next to the one removed for the incoming beam passage. The tracks continued on through the inner wire chambers on trajectories different from the pion beam, passed through the target and continued on out of CHAOS. The second level trigger then mistook the muon trajectories for two outgoing tracks in its momentum reconstruction. Figure 3.7 illustrates an example of this type of problem event. The axes indicate distance away from the center of CHAOS in units of mm. W C l and WC2 are shown as the solid circles and WC3 as the dotted circle. WC4 is the circle made of hash marks at a radius of ~ 650 mm. The remaining block components of the schematic are the CFT's . The shaded CFT blocks are those physically removed to permit the entry and exit of the pion beam, which would travel from left to right in the figure, passing through the centers of the absent blocks. In this case, the incident pion decayed to a muon some time before reaching CHAOS. The second level trigger reconstructed the muon trajectory as two separate outgoing tracks, labelled 1 and 2. In reality, the muon travels into the target along Track 1 and out along Track 2. The tracks passed the tests of the 2LT, and the event was written to tape. Fortunately, the fact that the muon has a different trajectory means a test is possible to veto these events. W C l and WC2 are not deadened at the incoming beam areas in order to provide points to define the pion beam. One can go a step further and require Chapter 3. IntTodnction to the Second Level Trigger 41 X ( m m ) Figure 3.7: Example of a muon trajectory reconstructed as two outgoing tracks. that the incident particle in every event passes through the areas where it is expected to if it is indeed a pion. This check has been incorporated into the second level trigger in a relatively simple manner. While the other sections of the 2LT are trying to find suitable tracks, a parallel branch of electronics makes certain that at least one W C l PCOS hit and one WC2 hit lies in the expected beam path as defined by the user. The final trigger decision is the AND of the incident particle check and the test results from the original trigger. Chapter 3. Introduction to the Second Level Trigger 42 3.4 Basic Des ign Phi losophy Upon first considering the complete second level trigger schematic in Figure 4.16 on page 61, an obvious question comes to mind: W h y must the design be so complicated? The design of the trigger has been carefully thought out; in the beginning stages, six different algorithms for reconstructing tracks were simulated with Monte Carlo software. The simplest, least expensive and most accurate algorithm was chosen. Further devel-opment took place, even as late as during the commissioning run in June 1993, and a streamlined version was the final result. However, there are two basic requirements that make the trigger inherently complicated. First, the trigger must be able to loop through chamber hit combinations until it finds a track that passes certain conditions and only then can the track be put through further tests. Second, in each iteration of the looping sequence, the trigger must consider 31 bits of angular PCOS information. If there existed a module with this many inputs that could perform the tests, much of the electronics in the first section of the 2LT would not be necessary. 3.4.1 U s e of D O Loops Many data are read into the 2LT by PCOS for each event. The first two memory lookup units (MLU's) shown in Figure 3.8 reject the clusterized width words, convert the 1 o wire addresses into angular hits with the proper units of ^ , and steer the data into the proper data stacks. The trigger must then consider all possible combinations of chamber hits. The first section of the 2LT includes handshaking logic that makes it try different combinations until it finds a good track. The electronics are set up as if they were doing calculations using three nested FORTRAN DO loops in a computer program, except that Chapter 3. IntToduction to the Second Level Trigger 43 the tests are performed by means of lookup tables in preloaded MLU's. In short, the user inputs an address to the MLU which specifies a physical quantity or combination of quantities. The module then "looks up" and outputs the value contained in its memory at that address, which is simply the result of previous calculations done by the user to load the module ^. The DO loops that are implemented in the second level trigger are as follows: do i = 1, # W C 2 hits do j = 1, # W C 1 hits do k = 1, # W C 3 hits enddo enddo enddo The use of data stacks makes this internal looping possible. As discussed in Section A. l , these are simply queues that operate according to the First In First Out (FIFO) principle. Information is not lost after it is used once because the stacks keep the data until they are reset after the final 2LT decision has been made. Thus, a chamber hit can be grouped with successive angular words from both the other chambers until a good track is found, or until all hits in the three chambers have been considered. In addition, the stacks are operated in an automatic looping mode. If a stack reaches the end of its queue and the trigger attempts to read another word from it, the stack wiU return to the beginning and once again output the first word. In order for the trigger to be able to loop until it finds a good track, it must generate a NEXT signal in the case of a bad track to tell the electronics to get another combination of angles. In addition, the use of three nested DO loops means that the trigger must ^For moie infoimation, refer to Section A.7.1. Chapter 3. Introduction to the Second Level Trigger 44 MLU A' 6-. y WC3 Stack B' d-. A ALU F' MLU A e. \f ¥C2 Stack C 9^ 6. 1. WCl Stack B 6. ALU F ye; = 9 , - ^ 2 6: \L MLU J 0° ^ e^ s: 63.75° ^3'V 0-\l MLU I 0° s e ; s: 63.75° 1. MLU21 K momentum, polarity and target cuts V ^i ' Figure 3.8: Block diagram of the first section of the 2LT. Gbapter 3. Introduction to the Second Level Trigger 45 know at what times it should get another word from a particular data stack. It gets the next WC3 word in each iteration. When it arrives at the end of all WC3 data the 2LT gets the next W C l word, and when it arrives simultaneously at the end of W C l and WC3 data, it finally looks at the next value from WC2. As one wiU see in Chapter 4, the purpose of the majority of the logic circuitry in the 2LT is to create the NEXT signals and teU the trigger what combination to consider next. 3.4.2 R o t a t i o n A l g o r i t h m Although it is now evident that data stacks and extensive circuitry are required to provide a looping mechanism, it is stiU not clear why a given angular combination cannot simply be input from the stacks into a module that wiU determine the track and output the accept or reject decision. The explanation is that there are too many bits of information in the raw data words. MLU21 K essentially constructs circular tracks through any set of angles given to it; the only exception is if they lie on a straight line, in which case the combination is rejected because in a magnetic field this would imply a particle with infinite momentum. It will then determine the goodness of the track. In order to reconstruct tracks, the module requires information regarding hits from aU 1 ° three chambers. Given that the PCOS data for W C l and WC2 are each in j units and CO the PCOS data for WC3 are in £ units, the combined input word to MLU21 K would be 31 bits in length. The MLU can not have an input word this large and furthermore, the maximum input word can be only 18 bits if it is to output the 8 bits of information that are required for subsequent use in the trigger. Fortunately, CHAOS is cylindrically symmetric, and the second level trigger algorithm exploits this in a rotation algorithm designed to compress the data. Referring again to Figure 3.8, the algorithm is as follows. Using the arithmetic logic units (ALU's) ^ as well as MLU's I and J, the track is rotated •^  Refer to Section A.3 for a technical overview of ALU's. Chapter 3. Introduction to the Second Level Trigger 46 so that 02 -> 32° = Oref. First the ALU's calculate e\ = Oi - 62 and 6'^ = 63 - 62, and then the MLU's add 32° to 9[ and B^. The result is that the track is rotated so that the WC2 hit coincides with 9ref- I and J then ensure that 6[ and 6^ can each be . . 1 ° expressed as an 8-bit word in units of 4 by passing only those angles which lie between 0° and 63.75°. As such, the rotational invariance of CHAOS allows one variable to be eliminated (^2 -^ ^ref) and the remaining information to be compressed without loss of angular resolution. At this point, two questions may come to mind: does the ±32° cut limit the data CHAOS wiU write to tape, and why is the angular data compressed to 16 bits in total when 18 are available? The answer to the first question is no. It is true that the angular cut places a minimum momentum cut on the tracks that can be reconstructed by the 2LT, as shown in Figure 3.9. However, one must consider the geometry of this track inside CHAOS. Figure 3.10 illustrates the track corresponding to the minimum momentum, which intersects the target and WC3 along the (^2 —^re/) ray. This geometry is independent of the magnetic field value and as such defines the lowest-momentum track that is reconstructible by the 2LT at aU settings. Pmm is then directly proportional to the field setting, since momentum is proportional to \B\. Simulations were performed and it was found that the 2LT minimum momentum track becomes trapped in CHAOS because its radius of curvature is too small. Tracks with this momentum never reach WC4 and so become lost. As such, they are never reconstructed in offline analysis; they are not tracks the researchers are looking for. The angular cut in the 2LT therefore does not cause a rejection of interesting data. In fact, the ±32° cut even allows some events to be accepted due to the outcome of tests on these trapped tracks, rather than tests on tracks that are reconstructible in offline analysis. This is unavoidable because to decrease the cut to ±16° would cause valid data to be rejected. The answer is now evident as to why the number of bits used to represent the angidar information is not increased to 18 Ghaptei 3. Introduction to the Second Level Trigger 47 Pnjjjj as a Funct ion of Magnetic Field 90 8 0 -7 0 -5 60-S 5 0 -I 40-3 0 -2 0 -10 Target Radius 20 m m 10 m m 0.2 1 1 0.7 1.2 iMagnetic Field| (T) 1.7 Figure 3.9: Lower momentum limits in second level trigger momentum reconstruction. WC3 Figure 3.10: Trajectory of minimum momentum track for 2LT. Chapter 3. Introduction to the Second Level Trigger 48 bits. This would allow 9i and ^3 to be within ±64° of 62. Pmin is decreased further, and an even larger fraction of acceptable 2LT tracks would correspond to those which can not be reconstructed ofiline. 3.4.3 O t h e r C o n s i d e r a t i o n s In designing the complete trigger, cost, simplicity and physical space were overall concerns. With this in mind, the vast number of readout channels made ECL logic the natural choice for the trigger. ECL modules are quite compact and cabling between the modules is much neater than with NIM based ones. These two factors made it possible for the group to situate the trigger electronics in crates above the Sagane alongside the readout electronics, thus avoiding the use of what would be a spider's web of cables trailing into the counting room. In addition, ECL modules have a lower per channel cost than NIM modules. When the decision to use ECL logic in the 2LT was made and work was begun on the trigger, the CHAOS group was aware that suitable MLU's were not available to make the decisions regarding track merit in the first section of the 2LT as well as in the momentum versus scattering angle cut. The LeCroy modules did not offer the required input/output word size combinations for use in the 2LT. As such, two CHAOS 21-bit MLU's were built. Recently, LeCroy introduced a new MLU that could be used in the first section of the trigger. However, the unit was not available in time for the testing of the trigger, and furthermore, the momentum versus scattering angle cut is stiU not possible without a CHAOS 21-bit MLU. Further information regarding this module can be found in Section A.7.2. Another general requirement for the second level trigger is that the electronics must be fast. As explained earlier, CHAOS has been designed to have a high rate of data collection which makes up for the lower beam intensity at TRIUMF. Normally, the trigger Chapter 3. Introduction to the Second Level Trigger 49 2LT YES T iming v s N u m b e r of C l u s t e r s 25 <D •+-> m 3 f—1 « H o 0) XJ a 3 ^: 20 15 10 5 -• -. -. -1 .1 i ) - i mm nil _J I I I - J ] I 1_ _J I I l_ : . .• t. ••...-, •••'J li-.-'fl-i-.-lJ. ••: i: j!ae!i:r:**i-ajiii)".' : i". . ; 'Umiii iMii i ' ' . ' l iM IR I I I I I IV icisrni' I I I -- I — r — I — I — I — I — I — 1 — I — f - T I F - I — I — I — I — I — I — ] — I — r -0 2 4 6 8 10 T ime t o Make 2LT YES Decis ion (//s) Figure 3.11: Time for 2LT to make a YES decision as a function of the number of clusters (hits). wiU be expected to run at rates of ~ 100 KHz, although this varies depending on factors such as the beam rate and the experimental cross section. ECL modules provide fast processing and the rate at which decisions are made is quite satisfactory. During the 1993 commissioning run, it was determined that the trigger can make a decision regarding a particular combination of angles every 207 ns. In addition, rate tests were performed with TDC's to determine the amount of time the trigger took to make a YES decision as a function of the number of clusters (ie: hits). The results are illustrated in Figure 3.11. Evidently, the majority of 2LT YES decisions are made in under 6 fis, and the average time is between 2 and 4 fis. A further major consideration in the design of the trigger was the need for flexibility. The 2LT modules are programmable via CAMAC; this task is made even simpler by a Chapter 3. Introduction to the Second Level Trigger 50 menu-driven program called ECL (refer to Section B . l ) . Through ECL, the user is able to quickly change the tests that an event must pass before it is labelled as good. Chapter 4 First Sect ion of the Second Level Trigger 4.1 Descr ipt ion The purpose of the first section of the second level trigger is to simply find circular tracks as defined by PCOS hit information and decide if the tracks are acceptable based on their momentum, polarity and distance of closest approach to the origin of CHAOS. If a track passes these tests, this section outputs the track momentum and polarity for use in the remainder of the trigger; otherwise, it issues a second level trigger R E J E C T . The first section wiU try to find only one track each time it is accessed. There is no handshaking logic that forces it to look for another acceptable track in a group of PCOS hits. Three nested DO loops that correspond to each of W C l , WC2 and WC3 are implemented in hardware and these allow the trigger to consider different combinations of chamber hits. If the event is acceptable, the trigger will output the proper information for the first good track it finds and remain at the same point in the DO loops until it is either 'told' to find another good track by a latter section or it is cleared and ready to consider another group of hits. 4.1.1 T h e General Flow of D a t a A full schematic of the first section of the 2LT is shown in Figure 4.16. However, the discussion to follow will refer to the much simpler schematic in Figure 4.12, which illustrates only the flow of data and none of the handshaking signals. The PCOSl 51 Chapter 4. First Section of the Second Level Trigger 52 2738/ECLport PC0S3 2738/ECLport PC0S1, PC0S2 WC3 5/4° -» 1/4° MLU A' input loiolololoioioixixixixixixixixixl output loioioioloixixixixixixixixTxIxIxl 1/4° units F low o f D a t a To Stack P (jj. Rejection .r-1 sort WC1, WC2 MLU A V input WC1 loiojojoioixixixixixixixixixlxTxl WC2 lOIOIOIOIIIXIXIXIXIXIXIXIXIXlxIxl output WC1 |0|0|OIOlOIXIXIX|X|XlXlXlXlXlxI)<] WC2 ion lOIOiOiXIXIXIXIXiXiXIXIXlXlXl WC3 s t a c k B input lOIOIOiOIOIXIXIXIXIXIXiXIXIXiXiXl output loioiolojoixixixixixlxIxlxTxTxTxl 1/4° units WC2 Stack C Input lOMiOIOlOIXIXiXiXIXIXiXiXiXiXIXI output Id 1|0|0|0|X|X|X|XlXlXlXlXlXlXlXl Two's ComplementX _ , 1/4° units WCl s t a c k B input loioioioioixixlxixjxlxixlxlxlxixi output lolololololxixixixixixixixixixixl To MLU21 L Two's Complement e,' = 6 , - ^ 2 ,ALU F 9 / - 63' + «r.f 0° ^ 83 ^ 63.75° input |X|1|0|0|0|X|X|X|X|X|X|X|X|X|X|X| output loiololololoioioixixixixixixixixl 0° ^ e ; ^ 63.75° MLU I input ixi iioioioixixixixixlxlxlxT3(1xlx] output ioioioioioiojoioixixixixixlxlxlxl MLU21 K momentum, polarity and target cuts input I2'l2'l2'bi2'l2i2l2ii1rlvlrlrlrlrlrl output IGIDIPIPIPIPIPIPI I To MLU21 L ,To MLU21 L and MLU M Figure 4.12: Simple schematic of the first section of the 2LT. Chapter 4. First Section of the Second Level Trigger 53 controller transports data for W C l and WC2 out of its ECL port and into MLU A; the information for WC2 is supplied to PCOSl by the P C 0 S 2 controller, and the information for W C l comes directly from the PCOSl crate. MLU A is programmed to see only 12 bits of input data and to output a 16-bit data word. It is enabled by the DATA READY signal from the PCOSl controller and the inverted most significant bit (MSB) in the PCOSl ECL port data. Referring back to Figure 2.3, one can see that only address words (MSB=0) and not width words (MSB = 1) wiU be input to the MLU. 1 ° The purpose of MLU A is to output the wire chamber cluster addresses in units of 4 and to make certain the data for W C l and WC2 go to Data Stacks B and C respectively. Recall that there is no angular offset in the cabling for the two inner chambers. In addition, the logical addresses are chosen so that the PCOS address words are simply 1 ° the angle of the cluster centroid in -j units, plus a base value of 2048 for WC2 only. If the word is < 2048, MLU A recognizes that it is already in the proper angular units; otherwise it will subtract the base value of 2048 from the word to extract the WC2 chamber coordinate. In order to transfer the data from the two chambers into the proper data stacks, MLU A also sets the 15th bit of all WC2 words to TRUE to act as a flag. Words with most significant bits 000 (WCl) and 010 (WC2) are then collected by Data Stacks B and C respectively. The fact that the 15th bit is set in all WC2 words does not affect subsequent calculations in the trigger; potential problems were overcome by programming the next level of MLU's to see only 12 bits of input, thus encompassing all possible angular hits while neglecting the steering flag that is no longer required. MLU A' is involved in a similar process. It is fed with information from the ECL port of the P C 0 S 3 controller and, again, width words are not input to the MLU. Since this MLU supplies data only to Data Stack B' , no flags are set. However, due to the angular offset described in Section 2.2.5, MLU A' must subtract a base of 4096 from the Gbaptei 4. First Section of the Second Level Trigger 54 PCOS word to get the 'apparent ' angle in j units, and add 2.5° to the result to get the actual WC3 angle. The MLU then converts the data to units of ^ and outputs the WC3 angular coordinate to Stack B' . The trigger is finally ready to find good tracks 1 ° using W C l , WC2 and WC3 coordinates that have common units of ^ . The remaining modules perform the rotation discussed in Section 3.4.2 and the second level trigger tests. To reiterate, the angular information that is input to MLU21 K must be compressed into a 16-bit word without loss of angular resolution. First the track is rotated so that 62 —> 32° = 6ref' ALU F calculates 6[ = 61 — 62 and MLU I determines e\ = e'^-\- 32°, while ALU F ' and MLU J do the same for $3 to yield 6^. MLU's I and J 1 ° also pass only angles that can be expressed as an 8-bit word in units of j by rejecting all rotated angles that do not lie between 0° and 63.75° (the rejection method is explained in Section 4.1.4). The filtered information for acceptable tracks is combined into a word of the form 00 unused all bits m)-of ei •m) my ^ - V all bits m) of e[ that is finally passed to MLU21 K. 4.1.2 M o m e n t u m , Dis tance of Closest Approach and Polarity Determinat ion The first section of the second level trigger can now determine the goodness of the track. For any address in the possible range from 0 to 65535, MLU21 K has been programmed with the final answer of several calculations performed on the track defined by the address. The offline loading program TRIG2, which is described in Section B.2, does the calculations for each of the possible 65536 tracks. It extracts the rotated and filtered W C l and WC3 angles from the address and assumes the rotated WC2 angle is 32°. The program then further rotates the track so that 62 coincides with 0°, as illustrated in Figure 4.13. This ensures that tracks with positive curvature (curves towards positive Chapter 4. First Section of the Second Level Trigger 55 Actual Track y ¥C3 Rota te so 62 -» O' WC3 Figure 4.13: Illustration of the rotation algorithm for determining polarity. Cbaptei 4. First Section of the Second Level Trigger 56 angles) wiU be rotated into a new track that has a positive center y-coordinate (3/^), while tracks with negative curvature will correspond to a negative {Vc)-yl can never equal zero because of the ±32° angle cut on the W C l and WC3 hits. Since the y-coordinate of both the center and WC2 hit of the rotated track equals zero, a radius of the track must necessarily lie on the CHAOS x-axis. Only two types of tracks with zero j / ^ are geometrically possible given that they must lie within a 64° cone about 62] examples of the largest track of each type are shown in Figure 4.14: WC3 Figure 4.14: Illustration that y^ can never equal 0. Tracks 1, 2 and 3 are the largest geometrically possible tracks that lie within a 64° cone about 62. The saving factor is that tracks of this sort will never be considered by this stage of the 2LT because either a W C l point or a WC3 point is missing (or if the track is small enough, both coidd be missing). Thus, valid tracks wiU have only positive or negative center y-coordinates when rotated. Chapter 4. First Section of the Second Level Trigger 57 The MLU21 K loading program then solves for the center and radius of curvature {x[,y^, p) of the circle defined by the three points using the following algorithm: a i = »? + J/i , "2 = 352 + 2/2 > «3 = aJ3 + yl hi = X2OL1 — xiOLi — X3{ax — 0L2) — a3{x2 — xi) 62 = 213(^1 - 2/2) + 22/3(3:2 - xx) - 2{yiX2 - y2Xi) '^ - T2 a 2 - a i - 263(2/1 - 2/2) a i = — 02 2(x i — X2) Xia2 - X2ai - 263(2/1X2 - y2Xi) {X2 —xi) where P = \J(i\ + 6 3 - ^ 2 , aJc = - t t i , 2/c = - ^3 (a5i,yi) = (aJi.aii) ; (^2,2/2) = {Rwc2,^) ; (a!3,2/3) = ( « 3 . 4 ) The momentum and distance of closest approach to the origin are then calculated as foUows ^ : Momentum = p x 0.29979 x Magnetic Field (4.7) Distance = \p- ^(a;^)^ + (y^y \ (4.8) Lengths are measured in units of mm and the magnetic field has units of Tesla. The last quantity the loading program calculates for MLU21 K is the polarity of the track. A simple rule aids in determining the charge of outgoing tracks: Charge = — 1 x Magnetic Field Direction x sign of yl ^The momentum is calculated in natuial units. Chapter 4. First Section of the Second Level Trigger 58 The charge calculation for incoming tracks differs by a sign when using the rotation method because these tracks travel in the opposite direction to outgoing tracks when they are rotated. However, this is not a problem because, once the incoming muon events have been rejected, the CHAOS trigger is unable to reconstruct incident beam tracks because the pions pass through the deadened WC3 region. Thus, incoming WC3 points are never detected through PCOS, and as such all reconstructed tracks will be outgoing tracks and the polarity calculation will be valid. Finally the MLU21 K loading software makes the decision regarding the merit of the track. First the momentum must be in the proper range defined by the user. Second, the track must have originated within the target (distance of closest approach is less than the radius of the target). Third, it must have the proper polarity as defined by the user, who can choose it to be opposite to the beam, with the beam or either. In any case, the offline software determines what the answer should be for a particular set of angles and the result is loaded into MLU21 K at the corresponding address. If the track is poor, the program determines that the MLU output for this address is simply 00000000. On the other hand, if the track is acceptable then the program will determine an output answer composed of three parts: polarity G POL P(6) P(5) P(4) P(3) P(2) P ( l ) ^ ' •' ' J'^9 momentum The six least significant bits represent the momentum (P( l ) -P(6 ) ) , which is simply a linear function of the bits: Momentum = Pmin + Momentum, Increment per Bit x ^bits (4.9) Momentum Increm,ent per Bit — """^ ^^^ (4-10) 63 or equivalently one could write NINT(Momentum - P„ ,„ ) # 6 i i 5 = "77 ^  ^ Mom-entum Increment per Bit Cbaptei 4. First Section of the Second Level Trigger 59 where Pmin aJid Pmax are the momentum limits defined by the CHAOS user, and #b i t s is the value which is output from MLU21 K in bits P ( l ) through P(6). Although a linear momentum function results in an increasing ^w- as P decreases, this is not of concern because it is more desirable in CHAOS experiments to have a constant and minimized A P . The 7th bit of output is a flag that indicates the polaxity of the track; 0 represents a negative y^ for the final rotated track and 1 represents a positive center coordinate. The last bit of the output for a good track is a flag set to 1 to indicate that the track was acceptable, and it is used to make further control signals. 4.1.3 T h e Start of 2LT Process ing BUSY PCOSl BUSY indicates PCOSl finished reset i LATCH PC0S3 iv^ PC0S3 BUSY indicates PC0S3 finished reset | L_ LATCH ADI Figure 4.15: Illustration of how the ADI signal is created. Figure 4.15 illustrates the ALL DATA IN (ADI) signal, which teUs the second level trigger to begin processing data. This signal is not issued until both the PCOSl and P C 0 S 3 controllers have finished transporting data through their ECL ports. The NIM electronics that create this signal are illustrated in Figure 4.15. Quite simply, a latch is set when the PCOSl BUSY goes FALSE, and another is set when P C 0 S 3 is no longer busy. The latches axe input into a quad coincidence unit and are AND'd together to Ciapter 4. First Section of the Second Level Trigger 60 create a logical TRUE pulse, which is the ADI signal. Once the ADI tells the 2LT to begin processing angular data, the first section of the trigger can m.ake three different types of decisions: a fast rejection due to a lack of data, a pass after finding a good track, and a rejection after trying all possible chamber hit combinations. Referring to Figure 4.16, the corresponding logic will now be discussed in detail. Note that the AND/OR gate and delay module labelling convention used in this discussion is as follows: < channel number > < module name > where module name refers to a particular module in the 2LT by name and channel number specifies the channel address within the modiJe. D l and D2 are names of the two delay modules, while G l and G2 refer to AND/OR modules set in modes [A-B-C] and [(A'B)+C], respectively. Information regarding the AND/OR gates and the delay units can be found in Sections A.4 and A.6, respectively. The simplest decision is the fast rejection, and for this the trigger makes use of Latch LI , the READ READY (RR) signals from the data stacks and the ADI signal. Upon clearing the trigger at the end of the previous event or at the beginning of a run, all latches are reset with Signal 4 (CLEAR) and are placed in a configuration where Q = 0 (FALSE), Q = 1 (TRUE). Also, all stack RR's are set to FALSE. The data stacks are built to automatically read the first word they receive without requiring a READ ENABLE (RE) signal. As such, the RR goes TRUE as soon as a stack gets any data. The RR signals from the three stacks are AND'd by Gate 1 G l to create a signal that is TRUE only if hits were present in all three chambers. This signal is then AND'd with the ADI by Gate 1 G2 at some time later when this signal arrives; a TRUE result will set Latch LI so Q —> 1, while a FALSE result will leave the latch in the reset configuration with Q = 1. In other words, LI is set if each chamber registered a hit and all data have Chapter 4. First Section of the Second Level Trigger 61 Width Bit 2738/DataRDY All Data In {ADI PULSE) 2738/ECLport PC0S3 tl±^^ Width Bit 2738/DataRDY 2738/ECLport PC0S1, PC0S2 © MLU A' @ to Slock P © CLEAR '° '^""=1" P T To Stack P Oi Rejection) 16 16 MLU A My '16 IK g S <" i WC3 Data Stack r^ ®-held TRUE 2LT NEXT —(3 G2 optional NEXT 16 * i 9 " » WC2 Data Stack T To Stack P 16 - i Sci Data Stack ALU F' \ OR DiA > a 16 MLU J {a G2B rB^'""^ Good track based on momentum, target and polarity cuts Figure 4.16: FuU schematic of the first section of the 2LT. Chapter 4. First Section of the Second Level Trigger 62 been input to the trigger. Another equivalent ADI is delayed and AND'd by Gate 2 G2 with LI Q. The delay is set so that the ADI arrives just a few ns after the possible LI Q FALSE -^ TRUE transition occurs at Gate 2 G2-Input B. The output of this gate is therefore FALSE upon startup of the trigger, but will go TRUE if LI still has not been set by the time the delayed ADI reaches the gate. In other words, if one or more chambers did not register any hits by the time all the data have been transferred from PCOS, a fast rejection signal wiU be generated by Gate 2 G2. If aU three chambers do have hit information, LI will be set by the leading edge of the ADI signal. LI Q will flip to FALSE, but the ADI signal into 2 G2 is delayed to come after the output of the latch has settled. 2 G2 will then always remain FALSE and this line wiU not generate a REJECT. Rather, the trigger wiU begin to look for a good track amongst all possible hit combinations. MLU's I and J are enabled by two signals: the DATA READY (DR) out of the ALU's and the Q output from Latch LI . Thus, upon resetting the trigger, the MLU's are disabled by LI . Once all information is in and it is known that there is enough data, LI no longer disables the modules and the trigger is ready to begin processing. 4.1.4 Looping Sequence As discussed previously, the first section of the 2LT wiU loop through chamber hits in a particular order. It operates in three nested DO loops, with WC2 as the outer loop, W C l as the middle loop and WC3 as the inner loop. This algorithm is implemented through the use of read overflow signals (ROF's) from the stacks, as well as NEXT signals produced by the MLU's. The ROF is a level that is normally FALSE, goes TRUE a few ns after the last word is read in a data stack and stays TRUE until the stack automatically loops back to the beginning of its queue and reads the first word again. The NEXT signal is a little more complicated in that it is created through the use of Gbaptei 4. First Section of the Second Level Trigger 63 logic gates. Each MLU either enables the next MLU in the line or creates a NEXT signal that makes the trigger consider another combination of hits. MLU's I and J axe loaded to output either the rotated and filtered angle in the first 8 bits with the remaining bits being zero, or else the rejection word COOO. In both cases, the output is latched until the next iteration of the 2LT. In addition, they output a READY (RDY) signal for each word they process. The RDY is a level that is normally TRUE, goes FALSE some time after the module is enabled, and goes TRUE again 25 ns later, approximately 5 ns after the output is valid. However, for reasons that will be explained, the level is converted to a RDY pulse. As illustrated in Figure 4.17, this is accomplished for MLU J by inverting m l u EN m l u RDY ex: m l u o u t p u t b i t RDY RDY pulse 50 n s T F F F Figure 4.17: How the MLU RDY pulses are created. the RDY and delaying the signal by its width of 25 ns using 5 D2. This has the effect of leaving the leading edge stationary, which is crucial in defining the time at which the MLU output is valid. The RDY pulse is then used to create further control signals. The most significant bit of MLU I or J output is AND'd with the RDY pulse from MLU J in Gate 4 G2 and 3 G2, respectively, to create a NEXT pulse in the case of a rejection word. If the hit combination is accepted at this level, the outputs of these gates wiU remain Chapter 4. First Section of the Second Level Trigger 64 FALSE due to the latched output from the MLU's. In order to simplify the wiring in the trigger and reduce the required number of delay channels and logic channels each by 1, only the RDY from MLU J was used to create the NEXT. This is possible because the timing (<m/u RDY ~ tatack RE) with respect to leading edges is nearly identical through the two branches of the 2LT, and a J RDY is present Avith every iteration since a new WC3 word is considered each time. Equivalently, the individual RDY signals could have been used. The second most significant bit (which is identical to the MSB) of output from I and J is inverted and AND'd with a RDY level from the corresponding module to create an ENABLE for MLU21 K in the case of an acceptable angular word. Similarly, MLU21 K outputs either an 8-bit data word with the MSB=1 (TRUE) for good events, or else an 8-bit word composed of zeros. However, the RDY for this module is already a pulse. The MSB is fanned out, and one output is AND'd with the RDY by Gate 9 G2 to create a pulse in the case of an acceptable event. This signal can be used either as a 2LT YES if the main stage of the trigger is used alone, or as an enable for whatever section of the 2LT is next in the line of processing. Another output is inverted and AND'd with the RDY by Gate 8 G2 to create a NEXT signal in the case of a bad event. Throughout the 2LT, any RDY's that have a part in generating the NEXT signal are converted to pulses if they are output as levels. The reason for this is as follows. As illustrated in Figure 4.16, the final NEXT is the result of an OR network (3 G2, 4 G2, 8 G2) in which signals are input at various stages (MLU I and J stage, MLU21 K stage, and latter sections of the 2LT). The OR gates are not edge-triggered, nor do they have pulsed output. Rather, the value of any output channel continually changes depending on the corresponding inputs and the programmed logic. To see how this poses a problem, consider what would happen if RDY levels were used. If a module after I and J rejects a combination and generates a RDY that is a level rather than a pulse, the NEXT signal Chapter 4. First Section of the Second Level Trigger 65 wiU identically foUow the corresponding input to the OR network: it will go FALSE for some time, then go TRUE and remain so until the next word is processed at the same stage in the trigger. Suppose the subsequent combination does not reach this level, but is rejected by MLU I or J . The signal generated by I or J to indicate a rejection occurred will have no effect on the OR network because the input further down the line is holding the NEXT stationary at TRUE. As such, a leading edge is not created to read enable the data stacks and the trigger wiU stop. To summarize, the problem with using RDY levels is that when one level of decision-making generates a NEXT upon rejecting a combination, it will inhibit aU levels above it from generating a NEXT in the subsequent iteration of the trigger. When a level of decision-making accepts an iteration, there is no inhibition effect on other levels because the corresponding input to the NEXT OR network is set to FALSE. The RDY levels from MLU's I and J do not have this effect on the trigger because they are the first level of decision-making. However, to be consistent and to make timing tests easier from an esthetic point of view, the RDY's from MLU's I and J were also converted to pulses. Once a NEXT is generated, the looping sequence begins. The simplest way to see how the looping works is to consider an example in which each chamber has two hits labelled 1 and 2. The trigger will try at most 8 combinations, and the order in which it considers the combinations is WC2_1, WC1_1, WC3_1 WC2_1, WC1_1, WC3_2 WC2_1, WC1_2, WC3_1 WC2_1, WC1_2, WC3_2 WC2_2, WC1_1, WC3_1 WC2_2, WC1_1, WC3_2 WC2_2, WC1_2, WC3_1 WC2_2, WC1_2, WC3_2 First take note of the RE inputs of the data stacks. The NEXT signal is AND'd by Chapter 4. First Section of the Second Level Trigger 66 Gate 4 G l with the Q output of Latch L2. This latch is set only when aU possible combinations have been tried. Thus after all rejected combinations except the last, Gate 4 G l generates a pulse that is fanned out to the RE's of all three data stacks. Stack B' is in the innermost loop and has only one RE input; thus, everytime Gate 4 G l generates a NEXT, B ' presents a new WC3 word. Stack B is in the middle loop and has two requirements for an RE condition, the NEXT and a delayed B ' ROF. Stack C is in the outermost loop and is enabled by a NEXT and the delayed B and B ' ROF signals. If the trigger tries the first combination and finds it to be poor, a NEXT pulse is presented at the RE's of all the stacks. B ' reads WC3_2 and its ROF level -> TRUE. However, the ROF is delayed and arrives well after the NEXT pulse does at Stack B, so B is not enabled because the ROF is stiU FALSE. This timing is a crucial feature of the 2LT: to determine the RE condition of Stacks B and C, the NEXT that gets combination i from the stacks is always compared to the relevant ROF that resulted from combination i — 1. In other words, when the ROF that is connected to a particular stack RE becomes TRUE on a particular iteration, the stack will not be enabled until the following iteration, given that another NEXT pulse is generated. Thus, coming back to the example, one sees that B remains at WC1_1. In addition. Stack C remains at WC2_1 because B has not read-overflowed. Thus, the second combination is tried. If another NEXT is generated. Stack B ' loops back and reads WC3_1 again, and its ROF —> FALSE. But recall that the ROF is delayed substantially so when the leading edge of the NEXT reaches Stack B, it still sees a TRUE ROF signal; it is enabled and reads out WC1_2. B ROF -^ TRUE, but this signal does not reach Stack C until well after the NEXT pulse has passed. The trigger still looks at WC2_1, and the third combination is tried. Say another NEXT is generated; B ' reads out WC3_2 and its ROF -^ TRUE. Again, the ROF = TRUE misses the NEXT at the enable of Stack B, and the trigger still looks at WC1_2. Since the ROF is also delayed into Stack C, here it also misses the NEXT and the trigger remains at Chapter 4. First Section of the Second Level Trigger 67 WC2_1. At this point, the fourth combination is tried. Note that while the fourth combination is going through the trigger, both Stack B' and B ROF's are TRUE at the enable input to Stack C. If the fourth combination fails and a NEXT is generated. Stack C finally reads WC2_2 upon the leading edge of the signal. The B' ROF is TRUE on the enable input to Stack B, and WC1_1 is read out upon B receiving a NEXT. Stack B' as always is enabled and reads WC3_1 out again. As such, the trigger is back in the configuration in which WC1_1 is paired with WC3_1 and the cycle continues as described above. This time, however, the value for Chamber 2 is WC2_2. The value for Chamber 2 remains at WC2_2 for the rest of the looping. It would be able to change back to WC2_1 only if a B ROF, a B' ROF and a NEXT signal are simultaneously TRUE at the enable of Stack C, and this never occurs again. If the trigger gets to the eighth combination and rejects it, the following occurs. First of all, the trigger was considering the combination (WC2_2, WCl-2, WC3_2) and as such, the ROF's of all three data stacks have been TRUE from the time these words were read. Through AND Gate 3 Gl, the ROF's set Latch L2, which tells the trigger that all combinations have gone through the trigger. L2 Q —> FALSE, and recall that this signal is input to Gate 4 Gl along with the NEXT. If the eighth combination is rejected, the trigger tries to get another combination, but a NEXT cannot be generated by 4 Gl because all data have been considered. In the REJECT circuit, L2 Q=TRUE keeps one input to Gate 5 Gl high. When the other input sees a leading edge from the eighth NEXT pulse, a second level trigger REJECT pulse is finally issued. Chapter 4. First Section of the Second Level Trigger 68 4.2 Reso lut ion and Accuracy Only the anode wire numbers of hits in the three inner chambers are input to the trigger. Thus the resolution of the 2LT cannot be expected to be nearly as good as that of offline event reconstruction, which uses aU of the information the spectrometer provides. In particular, the drift time information from WC3 and WC4 is not available to the 2LT. Since the decision whether to write an event to tape is ultimately determined by the second level trigger, it is important to know how accurate its calculations are. The user must know how tight the limits in tests can be set so as not to cut out too many good events, while at the same time not taking in an unacceptable amount of unwanted data. 2LTRES.F0R ^ is a relatively straightforward program that has been written to simulate the resolution of the trigger. Recall from Figure 2.2 in Section 2.2.1 that the magnetic field profile deviates less than 1% where the three inner chambers sit. Thus the program assumes that the field is constant and that circular trajectories can be fit to angular hits. The user inputs the momentum of the particle, the radius of the target and the magnetic field strength. Using the FORTRAN random number generator RAN, the program generates an exact WC2 angle, as well as an exact W C l angle within ±32° of the WC2 value. Using the momentum and the two angles, an exact WC3 angle is solved for algebraically. These angles mimic the actual path of a particle through the chambers. Before continuing, the program determines whether the track originated within the target region. If so, the distance of closest approach to the origin is saved for output to a file. In addition, the polarity of the track is determined using the rotation algorithm described in Section 4.1.2. On the other hand, if the track does not come from inside the target, the simulated event is discarded, and the program generates a new one. 1 0 The angles are then rounded off to the nearest j for W C l and WC2, and to the ^Written by Sheila McFarland with some routines by Greg Smith Chapter 4. First Section of the Second Level Trigger 69 CO nearest ^ for WC3. This is equivalent to the situation in an actual experiment, in which the wires closest to the track fire and PCOS clusterizes the data. For example, recall that if a track passes close to the midpoint between two wires in W C l , both wires will fire, and PCOS wiU clusterize the data and output a hit address of X.25° or X.75°. If the particle passes close to one wire, only that wire will fire and PCOS will output an address of X.0° or X.5°. The rounded-off data are the same as those which PCOS would output to the second level trigger for the track. Now the program simulates the trigger identically. First it uses the same equations as those used by the MLU21 K loading software to fit a circular trajectory to the three angular hits and calculate the radius of curvature and center of the track (refer to Sec-tion 4.1.2). It then determines the reconstructed momentum and distance of closest approach to the origin using Equations 4.7 and 4.8. Finally, the program calculates the polarity of the reconstructed track using the rotation algorithm. The exact momentum, distance from the origin and polarity are output to a file along with the corresponding reconstructed values. One should note that this is a very rough simulation. The results for momentum resolution, in particular, strongly depend on how one mimics the conversion of an exact track to PCOS information. It is not yet known what proportion of tracks fire only one wire in the inner chambers, when they actually should have fired two because they pass close to the midpoint between the two wires. Effectively, the angular resolution of the chambers decreases by a factor of 2 for tracks that fall into this category, because the actual track coordinate is 'rounded off' to the nearest wire, rather than the nearest half wire. Because WC3 has such a large pitch compared to W C l and WC2, it is thought that this effect is mostly due to a reduced angular resolution (in the 2LT) out of this chamber, although the other two chambers do contribute to the problem to a lesser extent. The Chapter 4. First Section of the Second Level Trigger 70 final result is that the resolution of the 2LT (for any quantity it calcidates) decreases because it performs calculations only with PCOS data. Judging by data seen with online SUSIYBOS (CHAOS analysis package) momentum reconstruction using the second level trigger algorithm, there is certainly a proportion of tracks that do not fire two wires in every chamber when they theoretically should have. Figure 4.18(A) illustrates the online SUSIYBOS momentum reconstruction according to the 2LT algorithm for a 225 ^^^ particle in a +0.5T magnetic field (pointing up along axis of CHAOS). Plots (B) and (C) illustrate the simulated momentum resolution as seen by the 2LT assuming that WC3 has an effective angular resolution in the 2LT of ^ and 2 , respectively. Evidently, both plots have some similar features to the actual momentum distribution, but neither simulates it exactly. Approximately 40% of the counts in (A) lie outside the FWHM of the distribution in (B), and ~ 26% lie beyond the endpoints. If one combines the two cases, the result is a distribution that has a roughly C 0 similar shape to the proper distribution. Plots (D) and (E) illustrate the results for § : w resolution ratios of 70:30 and 75:25, respectively. For this example, the combination seems to be somewhere in between these two cases. Evidently, it is very difficult to Monte Carlo the 2LT exactly. At this point it is only possible to simulate it by combining different distributions in select proportions, and these proportions vary with momentum and magnetic field, since tracks are less likely to fire two wires at a time as they get stiffer. Since the results are stiU very approximate, simulations were done for only the best case scenario, in which the effective resolution of the chambers in the 2LT is as good as it can be. The results presented in the remainder of this chapter are intended only as a rough guideline, and it is best to always do two quick test runs with straight-through beam at the momenta that define the limits of the region in which one expects to see outgoing scattering data. The online SUSIYBOS 2LT histograms will provide the best idea of how good the resolution actually is. Chapter 4. First Section of the Second Level Trigger 71 ( A ) YBOS 2LT Momentum Beconstruction woo-no 200 300 400 Momentum (MeV/c) 500 S i m u l a t i o n R e s u l t s f o r V a r i o u s S i t u a t i o n s 5/4* Effective ¥C3 Hesolution (C) 5 /2 ' Effective ¥03 Resolution 200 300 400 Momentum (MeV/c) 5/4':5/2" Ratio = 7030 SOO woo-m o BOO-d b E l 600-0 ^ 400-^ H a 200-z 0-1 1 1 1 . . ,1 U.I lUui , fWUlLj .1 T^liUlMlii, / ^'"'*fl«.. (E) 100 200 300 400 Momentum (MeV/c) 5/4*:5/2" Ratio = 75:25 500 200 300 Momentum (MeV/c) 500 no 200 sdo 400 sdo Momentum (MeV/c) Figure 4.18: Actual and simulated 2LT momentum histograms for a 225 ^ ^ particle in a 0.5T magnetic field. (A) illustrates the SUSIYBOS online histogram of what the 2LT sees. (B) and (C) illustrate the simulation for both good and poor WC3 effective resolution in the 2LT. (D) and (E) are plots of two simulation data sets combined in two different ratios. Chapter 4. First Section of the Second Level Trigger 72 4.2.1 M o m e n t u m Resolut ion Using 2LTRES.F0R, a rough estimate of the second level trigger momentum resolu-tion can be known ahead of time for any value of particle momentum and magnetic field strength. Figure 4.19 illustrates how the best case resolution varies with momentum for three different magnetic field settings: 300 250 200-150 KM) 50' C B = 0.5 T 1 I • • • • • « • ) 50 100 150 200 250 3C Selected P (MeV/c) 0 FWHU as a 200 ^ 150-% a - 1 0 0 -•* 50-0-C Function of Selected Uomentum B = 1.0 T I 1 1 1 1 • ^nrt • . ' U.U wo 1^  80 a 60 1 *°-20-rt. B = 15 T • I 1 I • 1 • - ' 50 100 150 200 250 300 350 *'0 50 100 150 200 250 300 350 Selected P (UeV/c) Selected P (UeV/c) Figure 4.19: Illustration of momentum resolution of first section of second level trigger. FWHM values were quoted because the momentum distributions are not gaussian. Un-fortunately, as the momentum of a track increases, the trigger is increasingly worse at reconstructing momentum. This is an unavoidable effect that is exacerbated by the large pitch of WC3. It was known when the chamber was designed that the anode pitch would cause the momentum reconstruction in the trigger to be poor. Unfortunately, the oiJy solution is to build another chamber with a greatly reduced anode spacing, which is far too expensive and time-consuming. The reason for the poor resolution with increasing momentum is as follows. Consider a track that passes through WC3 and causes PCOS to readout an angle of 30° for this chamber. Together the chamber wires and PCOS 'rounded off' the actual angle of the track to this value. Thus, it could have actually been at an angle of anything from 28.75° and 31.25°. This may not appear to be much of an uncertainty, but the large radius of WC3 means that the length of the arc the Chapter 4. First Section of the Second Level Trigger 73 track point could lie on is 7.5 mm. A track with a large momentum has a correspond-ingly large radius of curvature, p. For such a track, a change in the WC3 point of a few mm in any direction causes a large increase in p. Thus, the large pitch of WC3 has an effect that increases with momentum and in fact becomes quite unacceptable at large momenta and/or small magnetic field. In a like manner but to a smaller degree, W C l and WC2 also have an effect on the 2LT momentum resolution that increases with increasing momentum and decreasing magnetic field strength. 4.2.2 Simulated Accuracy in Determin ing Dis tance of Closest Approach The simidation program also outputs the dg — dr values, where the e subscript denotes the exact distance of closest approach of the simulated track to the origin of CHAOS, and r denotes the 2LT reconstructed distance. These differences were then histogrammed and plotted to determine the standard deviation (a) of the dg — dr distributions for var-ious momenta and magnetic field strengths. Again these are for the best case effective chamber resolution in the 2LT. Figure 4.20 illustrates the results. Evidently, the second level trigger can determine the distance of closest approach to better than ±2.5 mm using only the PCOS information that it is provided with. Although this is relatively poor, the results for the target cut are much better. In Figure 4.21, sample graphs of the reconstructed distances of closest approach indicate approximately how many events are discarded when a tight target radius cut of 15 mm is applied. The top graph is a histogram of the exact distance of closest approach for each case. It is a relatively uniform distribution of 25000 events, as it should be since the simulation employs a ran-dom number generator. The reconstructed distances are quantized because only PCOS information (discrete anode wire numbers) is used. In addition, the distributions have tails that extend past the 15 mm target radius; events in the tails would be lost if a tight target cut of 15 mm were part of the 2LT rejection condition. The percentage of lost Chapter 4. First Section of the Second Level Trigger 74 a vs Momentum for 0.5T, LOT and 1.5T 3.0-J 1 ' 1-350 Momentum (MeV/c) Figure 4.20: Standard deviation of the error in the 2LT distance of closest approach determination. events for 0.5T, LOT and 1.5T as well as 6 values of track momentum are summarized in Table 4.3: Percentage of Reconstructed Tracks Outside Target Track Momentum ( ^ ) 100 140 180 220 260 300 [Magnetic Field (T) 0.5 1.0 1.5 6.6% 5.0% 3.5% 4.8 5.3 5.3 4.8 6.6 6.5 4.6 6.7 6.0 4.9 5.5 6.7 4.9 4.7 6.6 Table 4.3: Percentage of simulated events for which 2LT improperly determines point of closest approach to be outside a target radius of 15 mm. Regardless of field setting and momentum, the values are relatively constant in the 5-7% range. If a smaller false rejection value is desired, one need only increase the target cutoff by 2-3 mm. However, note that the second level trigger will also accept a similarly small Chapter 4. First Section of the Second Level Trigger 75 Exact Distance of Closest Approach to Origin 10 20 d. (mm) 2LT Reconstructed Distance of Closest Approach to Origin Momentum = 100 MeV/c B = 0.5 T B = 1.0 T B = 1.5 T 10 20 d, (mm) Momentum = 260 MeV/c 30 10 20 d, (mm) Figure 4.21: Plots of 2LT dr values for 0.5T, LOT and L5T at track momenta of both 100 and 260 ^^^, with a target radius of 15 mm. Chapter 4. First Section of the Second Level Trigger 76 percentage of events whose tracks lie outside the cutoff due to the uncertainty in the reconstruction from PCOS information. 4.2.3 S imulated Accuracy in Polarity Determinat ion As explained previously, 2LTRES.F0R also outputs the polarity of the exact gen-erated track and the corresponding reconstructed track. The only way that the trigger can give a wrong answer for the polarity is if the track changes polarity in the process of PCOS "rounding off" actual coordinates to the nearest channel in the chamber readout. Intuition teUs one that this would be a rare event. The actual and reconstructed polar-ities were compared, and it was indeed found that the 2LT determines this parameter quite reliably. For magnetic fields of 0.5T, LOT and 1.5T, 25000 events were generated and reconstructed for each of twelve momenta, from 80 - 300 ^^^ in 20 ^ ^ steps, to yield a total data set of 300000 events at each magnetic field setting. The results were very satisfactory, and Table 4.4 lists the percentage of events for which the trigger recon-structed the polarity improperly: jMagnetic Field| (T) 0.5 1.0 1.5 % of Wrong Events 0.020 0.002 0.001 Table 4.4: Accuracy of 2LT in determining polarity. Again the values quoted are for the best case effective chamber resolution in the sec-ond level trigger. As expected, the percentage gets worse as the magnetic field drops in magnitude. For a given momentum, the particle track is not bent as much at lower magnetic fields. In rounding off the coordinates to the nearest channel number, there is a higher probability of the polarity changing for straighter tracks. Thus, the percentage Chapter 4. First Section of the Second Level Trigger 77 gets worse for lower magnetic fields or higher momenta. For almost all realistic tracks, however, the 2LT is still quite reliable in determining polarity. 4.3 Success of Operat ion In order to test the operation of the electronics setup, the exact second level trigger algorithm was placed into online SUSIYBOS routines. When the first section of the 2LT was tested in an actual experimental setup, it was not connected to the LAM circuit. Thus, every event that was passed by the first level trigger was written to tape, along with the corresponding 2LT decision. For each event, the online routines calculated what the decision should have been. This information was recorded, and a histogram called Reconstructed Equals Experiment (REQE) was also updated depending on whether the second level trigger hardware decision was correct or incorrect. These tests proved that the first section of the 2LT was quite successful. Numerous test runs were performed using various momentum, point of closest approach and polarity cuts. In each, the fraction of events in which there was a disagreement between the software answer and the 2LT answer was normally on the order of 0.001% and 0.01%, although at times it fluctuated as high as 0.4%. It is believed that the minor disagreement is due to some intermittent timing problems related to the begin of run signal and the CLEAR for the trigger. These conclusions are based on the fact that many of the events in which there was a disagreement occurred within the first few seconds of a run, as well as the fact that changing the width of the CLEAR appeared to have an effect on the REQE histogram. Further work wiQ be done to investigate these potential explanations of the problem. For instance, disagreement rate tests wiU be done to determine a possible relationship between the width of the CLEAR and the disagreement rate, and also offline analysis tests win be done to monitor the disagreement rate as a function of the number of events Chapter 4. First Section of the Second Level Trigger 78 that have been processed. An example of the successful operation of this section of the trigger is provided in Figure 4.22, which illustrates the results for a run in which the 2LT was programmed to accept a momentum range from 200 to 400 M Y^^  ^j^^ incident ;r~ beam of momentum _ ggg MeV ^^^ used, there was no target and the magnetic field was +0.5T. There was no polarity cut, and tracks with a distance of closest approach anywhere from 0 to 1000 mm were accepted as long as they passed the momentum cut. The upper diagram illustrates the momentum spectrum of the good events as decided by the 2LT, while the lower diagram illustrates the spectrum for events that the online software decided were acceptable by the same criteria. For this run, the REQE histogram indicated that the 2LT was incorrect 6 times out of a total of 79494 decisions (both YES and NO), 0.008% of the time. In the momentum region from 200 to 400 ^^^ , the two spectra are virtually identical; there were two bins in which the 2LT missed 1 event, out of a total of 25222 events which the software determined were good. Thus, the 2LT collected 99.99% of the events that should have passed the tests. The remaining disagreements were 4 bad events between 60 and 200 ^ that the 2LT accepted. Figure 4.23 provides another example of the successful operation of the 2LT, in which the results are shown for a run that employed a cut on the point of closest approach. Again an incident ir~ beam of momentum = 396 ^^~ was used, and the magnetic field was +0.5T. This time there was a CH2 target perpendicular to the beam. There was no polarity cut, and tracks with momenta anywhere from 25.2 to 5000 ^^^ were accepted as long as they passed the target cut. The events were required to pass through a target region with a radius of 20 mm centered about the origin of CHAOS. Again, the upper diagram illustrates the histogram of the distance of closest approach for good events as decided by the 2LT, while the lower diagram shows the results for the software decision. For this run, the REQE histogram indicated that the trigger was wrong only 1 time out Chapter 4. First Section of the Second Level Trigger 79 Run 383 - Momentum Cut Results 0 zoo 400 600 800 1000 Hi 17 Good Hardware 2LT Momentum (MeV/c) 0 200 400 600 800 1000 Hi 16 Good Software 2LT Momentum (MeV/c) Figure 4.22: Example - Results of a 200 to 400 ^^^ momentum cut. The upper histogram illustrates 2LT acceptance spectrum, while the lower one illustrates the corresponding online analysis results. Ciap te r 4. First Section of the Second Level Trigger 80 of a total of 44553 decisions (again, both YES and NO), to give a disagreement rate of only 0.002%. Looking at the illustrations of the radius spectra for good events, one can see that the agreement is excellent. The differ by only 1 bin in which the trigger missed a count, out of a total of 3956 YES decisions; thus, in this case the 2LT collected 99.975% of the events which should have passed the tests. As there was only one disagreement, the trigger evidently did not accept data that it should have rejected. In addition, two runs were done to test the polarity cut. In both, the beam was ir~ with an incident momentum of 396 M Y^^  ^^^^ j^^ g magnetic field was +0.5T. The target was CH2 mounted perpendicular to the beam path. When the polarity was chosen to be the same as the incoming beam, the percentage of disagreement was 0.08%, while it was 0.003% when the polarity was chosen to be opposite to the incoming beam. Chapter 4. First Section of the Second Level Trigger 81 Run 388 - Target Cut Results 0 K) 20 Hi 20 Good Hardware 2LT Distance of Closest Approach (mm) 1000-800-m 600-d o O 400-200-1 1 1 1 1 1 1 1 1 10 c 1 1 r 1 1 1 1 1 1 1 -1 } -h ' 1 1 1 1 1 20 30 Hi 21 Good Software 2LT Distance of Closest Approach (mm) Figure 4.23: Example - Results of a 20 mm target cut. The upper histogram illus-trates 2LT acceptance spectrum, while the lower one illustrates the corresponding online analysis spectrum. Chapter 5 M o m e n t u m Addit ion and Polarity Comparison Once the first section of the 2LT finds a good track and outputs the corresponding momentum and polarity, the momentum addition/polarity comparison section forces the trigger to find a second acceptable track. The 2LT will start from where it left off in the list of W C l , WC2 and WC3 angle combinations and again output the momentum and polarity if it finds a good trajectory. After two such tracks are found, the electronics in this section read in both momenta and polarities, and further tests can be done on these variables. Most importantly, the trigger can determine if the momentum sum lies below the cutoff that indicates a (TT, 27r) reaction occurred. In addition, the user can program the trigger to perform useful polarity comparisons and use the result to determine the goodness of the event. This was the case in the trigger setup for the first CHAOS (7r,27r) experiment in the summer of 1993. The 2LT searched for two charged particles of either polarity that came from the target. If two such particles were found in the final state and either of them had negative polarity, the event was accepted as GOOD. The reason for this was that since the incident beam was TT+j there were only two mechanisms that could lead to a negatively charged final state. First, it could correspond to an event from one of the (TT, 27r) reactions TT"*" + n —* TT"*" + 7r~ + p Second, it could have resulted from a double charge exchange (DCX) reaction when carbon, calcium and lead targets were used. The DCX reaction has a low cross section 82 Chapter 5. Momentum Addition and Polarity Comparison 83 on the same order of magnitude as the (TT, 2%) reaction, and therefore the two types of events can be easily sorted offline through the use of missing mass information. Because DCX data are scarce, it is actually desirable to coUect such events, given that they do not interfere with the acquisition of (TT, 2X) data. The only other result of the polarity comparison that can occur is that both tracks correspond to positively charged final states. In this case, the trigger for the (7r,27r) experiment was programmed to perform the momentum sum cut. As discussed in Chapter 3, most of these events are 7rp scattering, and the (TT, 27r) data must be quickly sifted out in hardware. Recall from the phase space momentum sums illustrated once again in Figure 5.25 (first column) that 400 ^ ^ appears to be a suitable cutoff for these events. However, one must consider how good the trigger resolution is by performing simulations before any limits can be set in hardware. 5.1 Descr ipt ion of Electronics Referring to Figure 5.24 one can see that the electronics setup is relatively straight-forward for this section. Recall that MLU21 K outputs an 8-bit word made up of 6 bits of momentum (bits 1-6), 1 bit to indicate polarity (bit 7) and a 1-bit flag to indicate that the track was acceptable thus far. The flag is AND'd with the MLU21 K RDY to produce an ENABLE (EN) signal for the rest of the trigger. The EN is fanned out to produce three equivalent signals. One is input to the STROBE (STB) of a data register R; the other is connected to one of the EN inputs of a LeCroy 16-bit MLU, labelled M, that performs the tests of this section. The momentum and polarity word (P,pol) from MLU21 K is fed into two places: the lowest 7 bits of Data Register R input, and bits 8 through 14 of MLU M input. The first 7 bits of the register output are connected to bits 1 through 7 of input to MLU M. The mode of M is set such that it sees only 14 bits of Chapter 5. Momentum Addition and Polarity Comparison 84 MLU21 K outputs 7 bits of momentum plus 1 bit (most significant) indicating polarity of track (n. 2n) NEXT Momentum end polarity of second good track 11 D2 : ENABLE pulse fan—out Indicates that MLU21 K found a track that passed the polarity, momentum and target cuts Momentum and polarity of first good track MLU M Out Sat Reset Latch Q i3 L4 If first 2 tracks do not pass tests and there is a third good track accept the events and sort out in offline analysis Second Level Trigger YES Figure 5.24: Schematic of momentum sum/polarity comparison section. Chapter 5. Momentum Addition and Polarity Comparison 85 input and can output 4 bits of data. Upon clearing the trigger, the two latches are reset. Latch 3 Q = 0 is input to one EN of MLU M, and Latch 4 Q = 1 is input to another EN; in other words, M has one EN at FALSE and one at TRUE. Latch 3 Q output (also TRUE) is connected to the W E of the data register. When the first section of the 2LT finds an acceptable track, the (P,pol) is passed to R and M. The EN pulse is fanned out and arrives at both modules; however, since the MLU is disabled by Latch 3, only R accepts the data when it receives the EN on its STB input. The register simply latches the data on its output (INQ —> O U T Q ) , and issues two READ READY (RR) signals. One RR is used in the NEXT circuit, and as such is inverted to create a RDY pulse so as not to inhibit the proper operation of the trigger (as described in Section 4.1.4). Note that the RR is not delayed by its width to keep the leading edge stationary in time. This is not necessary because the RR is not AND'd with any of the output data bits from Register R, and the leading edge is only useful in defining when data are valid. When the NEXT is generated, the trigger begins to look for the second good track. The other register RR output sets Latch 3, thus setting another EN of MLU M to TRUE and disabling R for the remainder of the trigger processing. R keeps the information for the first track stationary on the lower inputs of M. If a second good track is passed from MLU21 K, the (P,pol) data are presented to the upper inputs of MLU M. M is finally enabled when the corresponding EN pulse arrives through the fan-out. The input word is a combination of the (P,pol) of the first and second acceptable tracks in the lower 7 bits and the next 7 bits, respectively. M determines the two momenta and polarities from the address, performs the test based on the polarities and does the momentum sum if required. It then outputs two identical bits, each with value 1 if the event passes and 0 otherwise. As per usual, the MLU RDY level is converted to a RDY pulse with the same leading edge; the result is fanned-out Chapter 5. Momentum Addition and Polarity Comparison 86 to create two equivalent signals. One of the signals is AND'd with the first output from the MLU by Gate 12 0 2 to create a TRUE signal in the case of a good event, which subsequently generates a 2LT YES at the output of OR Gate 12 0 2 . The second bit of MLU output is inverted and AND'd by Gate 10 0 2 with the other RDY pulse; this circuit will generate a NEXT signal if the tracks did not pass the tests. The trigger will at tempt to find a third track that is accepted by the first section. One of the first two tracks could have been reconstructed partially from noise, and thus the valid track pair may not have been found yet. If a third good track is reconstructed, the event is automatically accepted because the electronics to test it with each of the first two tracks would be much too complicated. These events, of which there are on average ~ 20%, are sorted out using offline analysis routines. The circuit that accepts these cases is fairly straightforward. Another MLU RDY signal sets Latch 4, which in turn disables M and sets Input B of AND Gate 11 0 2 to TRUE. If a third good track is passed from MLU21 K, the EN pulse sets Input A of the gate to TRUE. A signal is generated, which in turn produces a 2LT YES pulse from OR gate 12 0 2 . Otherwise, the trigger arrives at the end of all possible chamber hit combinations and generates a 2LT NO through the circuit described in Section 4.1.4. 5.2 Simulat ing Resolut ion of M o m e n t u m Sum The momentum sum resolution of the second level trigger was simulated in much the same way as was the resolution for single momenta. For the incident beam energy in the (TT, 27r) experiment this past summer, a data set of the momenta of the outgoing charged particle pairs was generated using a Monte Carlo program (see first column in Figure 5.25). For each pair, the simulation takes the mom.entum of the first particle and generates a random exact track originating from the target region. As described Chapter 5. Momentum Addition and Polarity Comparison 87 in Section 4.2.1, it then rounds off the track coordinates to mimic PCOS digitization, determines the track according to the 2LT algorithm and reconstructs the momentum. The program repeats this for the second particle in the data pair. Note that the track coordinates were rounded off under the assumption that the effective angular resolution of each chamber in the 2LT is as good as it could be: 4 for W C l and WC2, and j for WC3. A second rounding off must then be performed in order for the simulation program to mimic the hardware setup. Recall that MLU21 K calculates the momentum of each particle and rounds the values off for output in a 6-bit word based on a linear scale, as given by Equations 4.9 and 4.10. Likewise, the simulation calculates the rounded value of each momentum as it would be seen in the 2LT and then adds these together to mimic the operation of MLU M. The result is the reconstructed momentum sum. This process is repeated several times for each pair of particles in the phase space data set in order to simulate an actual experiment. 5.2.1 Resu l t s of Simulation Although the momentum resolution of a single particle is relatively poor in the second level trigger, the momentum sum for two particles provides a reasonably good (TT, 27r) filter. The first column of diagrams in Figure 5.25 illustrates the phase space momentum sums for both a (TT, 27r) reaction, x+p —* ir'^ir'^n, and irp elastic scattering, while the third column shows plots of the reconstructed sums assuming the best angular resolution for each chamber in the 2LT. The diagrams in the middle column illustrate how the sums would appear if the momenta could be left unrounded. As one can see, the rounding off operation has the effect of making the reconstructed sum discrete rather than continuous since only certain values of momentum are obtainable in the representation given by Equations 4.9 and 4.10. However, the momentum rounding does not introduce much error into the total number of points under the curves over different momentum ranges. Chapter 5. Momentum Addition and Polarity Comparison 88 Homeutum Sum of (7r,2Tr) Charged Particle Final States at 396 UeV/c Phase Space Calcillation 0 wo 200 300 400 SCO 600 Momentum (IleV/o) Reconstruction — no P Roundoff 2000 i 0 n o 200 300 400 500 SOD Uomentum (UeV/c) Reconstruction - P Roundoff 20000-6000-UOOO' 5000-0' 1 1 l  lllllllll,... WO 200 300 400 SCO BOO IComentum (UeV/o) Uomentum Sum of irp Charged Particle Final States at 396 MeV/c Phase Space Calculation Reconstruction — no P Roundoff BOOH a S S woo-a 200 400 600 800 WOO Uomentum (tIeV/c) Jiik.^ ,... 500 1000 1SQ0 2000 Uomentum (UeV/c) Reconstruction — P Roundoff GOOOH 500 WOO 1500 2000 Uomentum (UeV/c) Figure 5.25: Exact and reconstructed charged particle momentum sums for the ir"^p —> 7r''"7r''"7i reaction and irp elastic scattering at an incident pion momentum of 396 ^^~- The first column illustrates the phase space sums, while the third column il-lustrates the 2LT reconstructed sums. The middle column illustrates the reconstructed sums before the momenta are rounded off to mimic the binary representation in the 2LT. For example, the percentage of (TT, 2ir) counts above 340 ^^^ (the phase space sum cutoff) is ~ 6% in both the rounded and unrounded sums. In comparing the (TT, 27r) phase space sum with the reconstructed sum, it is evident the two are fairly close. The only major difference is that the reconstructed sum has a drawn out tail on the high momentum side. The vp momentum sum curve is distorted to a great extent because there is much more error introduced in the momentum determination from the first section of the 2LT at higher momenta. The (7r,27r) phase space sum ranges from Chapter 5. Momentum Addition and Polarity Comparison 89 95 to 340 ^^£^, while the irp phase space sum has limits of approximately 407 and 833 ^^^ . Some statistics for the number of counts in the reconstructed curves outside these c limits aje given in the Tables 5.5 and 5.6: Momentum Range (MeV/c) 0-95 340-500 500-2000 Percentage of Counts 0.06 6.2 0.09 Table 5.5: Statistics for (TT, 27r) reconstructed momentum sum. Momentum Range (MeV/c) 0-407 833-2000 Percentage of Counts 4.1 25.6 Table 5.6: Statistics for xp reconstructed momentum sum. As stated previously only ~ 6% of the (TT, 27r) data points are placed outside the phase space limits by the trigger reconstruction. Due to the higher momenta of the individual charged particles, ~ 30% of the irp points are placed outside the phase space limits. The reason for the relatively good agreement for (TT, 27r) data is as follows. Using the trigger to look at track pairs and reconstruct the momentum sum using the PCOS information has the effect of taking each region of the real momentum sum and convoluting it. Just as the trigger adds width to any particular momentum, it takes each region of the phase space curve and spreads it out. This effect can be seen in Figure 5.26, where each composite figure shows the 2LT convolution of each phase space region without momentum rounding (the convolution is easier to see in this case, and the only difference is that the spectra are not discrete). The plots start with 50-100 ^^^ and continue in 50 ^^^ steps. Although the momentum determination of the trigger is stiU increasingly inaccurate with increasing momentum, the value of the reconstructed momentum sum normally lies within the Chapter 5. Momentum Addition and Polarity Comparison 90 M o m e n t u m S u m s of B o t h O u t g o i n g C h a r g e d (7r,2Tr) P a r t i c l e s ^ •g 90-p< o (0-V • ^ 3 0 . a m B 20-o a, o 1-0-50 t o 100 U e V / c Fhan Space , -. . 2LT RecooB il I ^ | 3 D 0 . £ 2 5 0 ^ 2 0 0 -| 1 0 0 . 3 50-2 e so-o 0. 40' 4-1 O 30-^ 20-1 "• Oi 100 t o 150 U e V / c II Phaaa Space -1 • • II • ' 2LT Recons i Julii A ^moo-'s ». BOO-^ 600-| 4 0 0 -§ 200-o 0. 400-O 300-I200-1 wo-0-150 t o 200 U e V / c Phase Space II lilU in pfl'i . 2LT Reoons / 1 50 70 90 i n 130 150 U o m e n t u m S u m (MeV/c) 50 WO ISO 200 Momentum S u m ( U e V / c ) I 150 200 250 U o m e n t u m Sum (UeV/c) 3000-2500-2000-1500-1000-500-1500-1000-500-0-200 ; to 250 ilk if f 1 1 f\ ' \ MeV/c Phase Spaoe -----2LT Reoons -^ - - ^ . 250 t o 300 U e V / c 300 t o 350 U e V / c 0 150 200 250 300 350 400 U o m e n t u m S u m (UeV/o) ZOO 300 400 500 U o m e n t u m S u m (UeV/c ) BOO CL. O 4 0 0 "a zoo a o a. 200 V a Phase Space 2LT Recona too 200 300 400 500 600 U o m e n t u m Sum (UeV/c) Figure 5.26: Illustration of how the 2LT momentum sum reconstruction convolutes each region of the phase space distribution. Chapter 5. Momentum Addition and Polarity Comparison 91 boundaries of the phase space curve. Thus, the reconstructed curve looks very similar to the real one. 5.2.2 Us ing Simulation t o Choose Set t ings The simulation program is required to choose a reasonable maximum momentum cutoiF for the (7r,27r) trigger. Without knowledge of how the phase space curves are distorted by the momentum reconstruction, one may choose a setting that contaminates the data with a large number of irp events or ignores an unacceptable percentage of interesting data. The phase space sums do not overlap at all, so a cutoif of 350 ^ ^ would be suitable if the trigger could reconstruct momenta to great accuracy using the PCOS information. However, this is not the case, and the spectra for the (TT, 27r) reconstructed momentum sum are drawn out to a high limit of 480 Me_^ jf one then chooses this value to be the cutoff without considering the reconstructed irp curve, the resulting data will contain approximately 13% of the irp events. Since the cross section for the latter process is two orders of magnitude larger, this is entirely unacceptable. However, using the simulated reconstructions, one can determine the goodness of other cuts. For instance, only ~ 1% of (7r,27r) data fall above 400 ^eV^ ^^^^ ^jjy. 3 ^ Q£ ^^ events fall below this momentum. This is much more acceptable and was chosen as the cutoff for the trigger in the first (7r,27r) experiment. 5.3 Success of Operat ion The operation of this section of the second level trigger was tested in the same manner as the first section. AU events that passed the first level trigger were written to tape, regardless of whether the 2LT made a YES or NO decision. The algorithm for the momentum sum and polarity comparison was added to the online analysis routines. Chapter 5. Momentum Addition and Polarity Comparison 92 and the hardware decision was compared to the corresponding software decision. Again, the REQE histogram kept track of how many agreements and disagreements there were. These tests indicated that this section of the 2LT is working quite well. In these tests, the fraction of events for which the hardware decision was wrong was never greater than 0.4%. As in the first section of the second level trigger, it is believed that the minor disagreement is due to timing problems related to the Begin Run signal and the CLEAR for the trigger, and more work wiU be done in this area. Figure 5.27 illustrates the results for a run in which the beam was TT''" with momentum _ ggg M^^ and the magnetic field was +0.5T. The maximum allowable momentum sum was 500 Me_^ a^ j^ jj ^he polarity comparison described in the first part of this chapter was implemented. The upper diagram illustrates the momentum sum spectrum for the good events as decided by the 2LT, while the lower diagram illustrates the spectrum for events that the online software determined were acceptable. These spectra are very similar. The spectra for cases in which 3 good tracks were found are identical in each plot, and those sections below 490 ^^ —^ differ only by one count that was missed by the 2LT around 60 ^^^ . There is some discrepancy between the two spectra around the momentum cutoff. The reason for this is believed to be as follows. When the momentum sum routine was added to the online YBOS analysis, it was forgotten that the momenta calculated by the previous routines required rounding off in order to mimic MLU21 K binary output. This most likely explains why some counts are missing from the 2LT spectrum below 500 ^ ^ ; if the 2LT had rounded up either one or both of the momenta in a pair, it could have caused the sum to be too large and the event to be rejected, whereas the YBOS routines could likely have accepted it. In addition, the 2LT spectrum has some counts as high as 506 MeV^ which probably reflects the error when the 2LT rounded down the momenta in a pair. In this run, the momentum increment per bit out of MLU21 K was ~ 6 Miv^ so if both momenta were rounded down, the result would be an error of approximately Chapter 5. Momentum Addition and Polarity Comparison 93 2 x 3 MsY^ Regardless, the overall performance of the trigger in this run was excellent, as reflected in a disagreement rate of 0.4% for all events considered (both YES and NO decisions by the 2LT). Chapter 5. Momentum Addition and Polarity Comparison 94 R\m 410 Momentum S u m / P o l a r i t y Comparison Resul ts • • I I — I — 1 — sum for 2 good grades based on p. sum/pol. comp. sum for 3 good tracks based on first 2LT section 507 1I.V/C / . \ . pftfiili^^niiLjJilipinflftryilXiiiyiii^iii[i lyl 500 1000 1500 2000 Hi 25 - Good Hardware 2LT P Sum (MeV/c) 50 40 •» 30 •!-> a 0 o " 20 10 • ' sum for 2 good graeks based on p. sum/pol. comp. JV-4 sum for 3 good tracks based on first 2LT section 501 MeV/c ^ ^ / 500 1000 i4m[yiii^iii[i l y i 0 1500 2000 Hi 24 - Good Software P Sum (MeV/c) Figure 5.27: Example - Results of a momentum sum/polarity comparison cut. The momentum sum limit was 500 ^ ^ and the polarity comparison test was as described in this section. The upper histogram illustrates the momentum sum spectrum for tracks that the 2LT accepted, while the lower plot shows the spectrum corresponding to the online analysis. Chapter 6 M o m e n t u m versus Scattering Angle Cut As described in Chapter 3, the momentum versus scattering angle cut is important in the wp program for separating Tp elastic scattering data from events in which the pions scatter from helium, carbon and oxygen in the polarized target. This major source of background in the scattering experiments can be greatly reduced by calculating Og for each track found acceptable by the first stage of the 2LT, and then rejecting the event if the track momentum is greater than that allowed by irp kinematics. As illustrated in the T^ = 100 ^^^ example in Figure 6.28, there is a distinct correlation between momentum and 6s for pions in vp scattering, as well as background scattering reactions. In this plot, the irp limit is also shown as a double line, and the dotted vertical lines indicate the 6a regions that the x-axis has been divided into in defining the irp cut with line segments. Note that the cut is slightly above the irp data to allow for uncertainties in the 2LT calculations. The momentum of irp pions is a kinematically bound, decreasing function of 6s', on the other hand, the momentum function for pions that scatter from helium, carbon or oxygen is relatively independent of angle and overlaps with the irp data only at forward angles. By placing a cut on the correlated momentum and scattering angle of the final state pions, the irp data can be separated from background data to a large extent. The second level trigger can not tell if a track it finds belongs to a pion or some other final state charged particle; however, since a pion is always present in an elastic scattering event, the trigger will search for tracks until it finds one that satisfies the irp 95 Chapter 6. Momentum versus Scattering Angle Gut 96 > B B o 100 MeV 7rp Kinemat ics J I I I I L 0 20 40 60 80 100 120 140 160 180 pion 6g (degrees) Figure 6.28: Illustration of pion momentum versus 9a cut for irp elastic scattering. The error bars indicate the ± 5 % bands on the momenta. pion momentum versus ds cut. The first section of the second level trigger is programmed to find a track with a momentum between the bounds for a %p pion. Once a track is found, the present section is enabled and performs the cut for pions. The definition of scattering angle is the angle between the tangents to the incident and outgoing tracks at the reaction vertex. However, the 2LT cannot calculate the reaction vertex in the same manner as the analysis software does. The software first determines the W C l and WC2 points in the incoming beam track as well as the three inner chamber hits in the outgoing track. It then reconstructs the beam track by using the known beam momentum and polarity, as well as the incoming hits, and calculates the intersection of this trajectory with the outgoing track. At present, it is impossible to implement this in hardware. It is true that one could design a circuit that looks for hits in the incoming beam regions of W C l and WC2 (like the muon rejection section) and Chapter 6. Momentum versus Scattering Angle Cut 97 reconstructs tracks until it finds the incoming beam. The W C l and WC2 points could be input to data registers and 'stored' as latched output from these modules. However, the section of the 2LT that searches for outgoing tracks and calculates 6a must know which two hits were used for the incoming beam so that it does not reuse them for the outgoing track reconstruction. A theoretical solution is to let the 2LT loop through all hit combinations, and for each iteration, input to an MLU the W C l and WC2 beam hits along with the angular combination data. If there was no duplication of W C l and WC2 data, the reaction vertex and scattering angle could be computed and the result of the test could be output. However, this can not be done because, to reiterate, no MLU is available that has enough inputs to read in this much data (for 4 angular hits). As such, the trigger must approximate the reaction vertex in a consistent manner. The approximation chosen was the point of closest approach to the origin, a quantity which the 2LT reconstructs fairly reliably, as was shown in Section 4.2.2. In addition, the 2LT approximates the angle of the tangent to the beam at the reaction vertex to be the average angle of the beam at the center of CHAOS, which is a constant for each setting of magnetic field and beam momentum. An example of an approximate scattering angle is illustrated in Figure 6.29. The exact 9^ is the angle between the tangents to the incoming and outgoing tracks at the reaction vertex, P i . However, the 2LT approximates the reaction vertex by the point of closest approach, P2, of the outgoing track to the origin, and it then calculates 63 to be ^ minus the angle of the beam at the origin. 6.1 E l e c t r o n i c s The electronics for this section are illustrated in Figure 6.30. Noting that MLU21 K is redrawn in this schematic for clarity, one can see that the addition to the trigger is quite straightforward. The decision maker is the 21-bit MLU21 L, which must receive four Chaptei 6. Momentum versus Scattering Angle Gut 98 1 incident pion target perimeter tangent to outgoing track at point of closest approach to origin of CHAOS tracli V X -^-^^outgolng charged ^ - " " ^ particle track ^ \ ) center of outgoing track Figure 6.29: An example of the approximation to Qg as defined by the 2LT. In this example, the estimate of Bg would be <^  minus the angle of the beam at the center of CHAOS. pieces of information that uniquely define the track in order to calculate the scattering angle and perform the cut. The input data includes the momentum as well as two angles, of which at least one must be the original, unrotated coordinate. In addition, L requires the polarity in order to pick from the two possible tracks through the coordinates. MLU21 L receives this information in a 21-bit input word configured as follows: momentum upper 6 bits of 0^ POL P ( 6 ) - P ( l ) g2( l l ) -g2(4) 0[{8)-e[{Z) polarity ^^pper 8 bits of 62 where 62 is the WC2 angular data from Data Stack C (the original, unrotated coordinate), and 6\ is the rotated and filtered (recall the ±32° cone about 62) W C l angular data from Chapter 6. Momentum versus Scattering Angle Cut 99 MLU21 K outputs 6 bits of momentum plus 1 bit indicating the polarity of the trock (it also outputs an 8th bit indicating the pass/fail status of the track at this stage for use as a control signal) From MLU I 6 bits of e,-fl2 units of 1° NEXT input to 2LT main stage NEXT from any further 2LT sections (optional) Good Result Passed Momentum vs 6^ Cut Figure 6.30: Electronics schematic for momentum versus scattering angle cut. Chapter 6. Momentum versus Scattering Angle Cut 100 MLU I. Recall tha t MLU21 K outputs 1 bit to indicate polarity and 6 bits representing momentum on a linear scale. This 7-bit word is input to MLU21 L, which is set to accept a 21-bit word. The remaining bits must then be divided between the 8-bit W C l angle from MLU I and the 11-bit WC2 angle from Stack C, both of which are in 4 units. This is accomplished by taking the 8 most significant bits of 62 and the 6 most significant bits of 6[ data, thus truncating 62 and 0[ to units of 2° and 1°, respectively. Although it is unfortunate that the angles must be truncated, it is somewhat comforting to note that this section of the trigger would not be feasible at all without the 21-bit MLU. Recall that the LeCroy MLU's do not have an input word size that is large enough to be used in this section of the trigger, and as such, the CHAOS 21-bit MLU is essential (as discussed in Section A.7.2). The 21-bit input to MLU21 L specifies an address in its Random Access Memory (RAM). As per usual, offline calculations have been done with the information contained in each possible input word to determine the scattering angle and perform the cut. The address is then loaded with a flag that indicates the result of the test: 1 for a good track and 0 for a rejected track. The 1-bit output is fanned out to create two flag signals. One flag is inverted and AND'd by Gate 14 G2 with an MLU21 L RDY pulse (which is fanned out since only one is available); this process creates a NEXT signal in the case of an unacceptable track. The other flag is directly AND'd with another RDY pulse in Gate 15 G2 to create a 2LT ACCEPT pulse. If the trigger considers all possible hit combinations without finding a good track, a 2LT REJECT pulse will be created in the main stage of the 2LT, as described in Section 4.1.4. Chapter 6. Momentum versus Scattering Angle Cut 101 6.2 Loading Program Algori thm The loading program (again TRIG2) first asks the user to input the (P , \da\) ^ points that define the angle cut as a function of momentum. Referring back to the example in Figure 6.28, this would be the irp limit, shown by a double line. In this case, the cut designates tracks with a (P , |5g|) under the Hmit as being acceptable, since this would mean an outgoing pion from a irp scattering event has been found. Alternatively, there may be other applications in which the user wants to define a lower limit on the correlated momentum and ds points, which is also allowed. Depending on the kinematic momentum bounds and the CHAOS magnetic field strength, one can determine approximately how good the momentum resolution will be, and as such decide how close to put the cut to the theoretical data. It is true that there is also some uncertainty associated with MLU21 K rounding off the momentum into a 6-bit binary word, but this effect is usually small. For the example given, MLU21 K would only accept 100 < P < 225 ^ (approximately), corresponding to a increment of 2 ^^^ per bit, or equivalently an uncertainty of ± 1 M^ Y After the cut has been decided upon, the user simply approximates the curve by as many as 30 line segments and defines the endpoints of each one. In Figure 6.28, the line segments are separated by vertical dotted lines. The loading program then stores the slope, y-intercept and endpoint angle values of each line segment, all of which define the P versus 6^ cut for later use. Whenever a 6^ is calculated, the program determines which endpoint angle values the absolute value lies between and then uses the corresponding line segment definition to determine if the track momentum lies within the cut. MLU21 L has a 21-bit input word, and thus any of 2,097,152 addresses may be accessed for each event passed to this section. The loading program considers each address, extracts the track information, calculates an approximate 9^, performs the angle ^Recall that the kinematics of all reactions aie symmetric about 180°. Chapter 6. Momentum versus Scattering Angle Gut 102 cut and loads the address with 1 if the track passes or 0 otherwise. Recall that the 21-bit address contains all the information to uniquely define the rotated track (polarity, momentum and 6[), given that 6^ = 32°. As in the first section of the 2LT, the track is rotated further so that 62 —> 0°; the center of this new track is {x[,y^). Recall that the rotation implies a direct correspondence between the polarity of the original track and the sign of 1/^ , which depends on whether the CHAOS magnetic field points up or down. The momentum and two chamber coordinates define two tracks of opposite polarity, and the rotation allows MLU21 L to pick the proper track. Furthermore, the loading program can simply determine the rotated scattering angle, 6^, add the original 62 to it (rotate the track back) and calculate 6a. 6.2.1 Determin ing t h e Center of t h e R o t a t e d Track To simplify the mathematics for determining the center of the rotated track, it is translated in the negative x-direction by the WC2 radius so that the WC2 hit coincides with the origin. The rotation and translation process is illustrated in Figure 6.31. The program calculates the radius of curvature, p, of the track from the momentum and magnetic field strength. It can then easily determine the center of the rotated and translated track, (a, 6), by solving the equations p2 = a^ + b'^ , at (0,0) p' = {x[-ar + {y[-bY,^.t{x[,y[) to yield ^ = 2^ a = Cl-C2y[ Chapter 6. Momentum versus Scattering Angle Cut 103 (A) Actual Track (B) Rotated Track WC3 Rotate so 02 "* 0 (C) WC3 Translate so WC2 (x,y) -* (0,0) Translated Track WC3 Figure 6.31: Illustration of the rotation/translation algorithm used in the calculation of scattering angle in the 2LT. Gbaptei 6. Momentum versus Scattering Angle Gut 104 where CI = V / 2a!'i C2 = ^ a = l-\-C2^ /3 = -2C1C2 7 = Cl^-p^ Finally the program solves for (s^, y^) = (a + R2,6) (essentially translates the track back) to yield two solutions corresponding to each sign oiy^. The proper solution can be chosen depending on the polarity and the direction of the magnetic field. 6.2.2 Determining the Point of Closest Approach Once (a5c>3/c) ^^  found, the program must then calculate the point of closest approach (A,B) of the rotated track to the origin. If JC^  = 0? the solution is simply (0, d), where Otherwise, A and B must be determined from the following two equations: yT ^ B d? = A^ + B^ The solution of this set of equations yields A = ± (6.11) B = ^ A (6.12) Cba,ptei 6. Momentum versus Scattering Angle Cut 105 The solutions for (A,B) are then sorted graphically due to the ambiguity in the sign of A. The three possible cases for polarity = 0 (y^ < 0) tracks are illustrated in Figure 6.32. There are also three corresponding diagrams for polarity = 1 (y^ > 0) tracks, generated simply by letting JB'" —> —a;'" for the tracks shown. Thus, evidently six different cases exist, and if one considers the sign of A in each situation, a simple ride emerges: Sign of A = —1 X Sign of d x Sign of x^ qjr The sign of B then follows from Equation 6.12 and depends on that of both A and ^ . 6.2.3 Determining the Rotated Scattering Angle Lastly, the tangent line can be parametrized and 6^ can be determined. The slope of the tangent is required: n^r = y'\x=A,y=B where y = r y-Vc is obtained by differentiating the equation of the circle that defines the track. Once the mr is known, the two cases of polarity can be considered separately. Figure 6.33(A) illustrates the polarity 0 case while (B) illustrates the polarity 1 case. Using the relation and some simple trigonometry, one arrives at the following equations for the rotated scattering angle in each case: polarity = 0 e: = sin-'\- " '^ ' y/i^+m^T) Chapter 6. Momentum versus Scattering Angle Cut 106 y \ wciV^ WC2\ y ^ \ / 3 2 ' ' ^ ^ I 0-^ / ^ - 3 2 ° xj line y ^ X / S l " 5^ =^^ —J 0' u / ^ - 3 2 ° xj line y VwciV^ WC2\^^ ^ v / 3 2 " j(^Ai—.1 0" ^ / ^ - 3 2 ' " V X,, line d p o s i t i v e X,. n e g a t i v e y^ n e g a t i v e A p o s i t i v e B p o s i t i v e d p o s i t i v e xj p o s i t i v e y / n e g a t i v e A n e g a t i v e B p o s i t i v e d n e g a t i v e x / p o s i t i v e y^ n e g a t i v e A p o s i t i v e B n e g a t i v e Figure 6.32: Signs of point of closest approach coordinates (A,B) for all possible cases with polajity = 0 and x^ ^ 0. Chapter 6. Momentum versus Scattering Angle Cut 107 A B (A.B)-(A.B) Tangent to Track at (A,B) . I / ^ < \ / (A+1/mT, B+1) Particle Track 1 1/m, '/•"' X'' J ( \ ^ " " 1 Particle Track (A+l/niT, B-1) Tangent to Track at (A,B) Figure 6.33: Trigonometric diagrams for calculating Q\. This figure illustrates the dia-grams for polarity = 0 (A) and polarity = 1 (B) that are used in the calculation of the scattering angle of the rotated final state track. Chapter 6. Momentum versus Scattering Angle Cut 108 polarity = 1 e: = -sin-^\ m-j' v/a+mf,) where the solutions are defined such that —180° < 6^ < 180°. 6.2.4 Determining the Scattering Angle Finally, the loading program must determine the actual scattering angle. First, the angle of the tangent to the beam at the center of CHAOS is determined using the curve in Figure 6.34: Angle of I n c i d e n t B e a m a t C e n t e r of CHAOS 200-J L 200 600 1000 1400 1800 B e a m R a d i u s of C u r v a t u r e , r ( m m ) Figure 6.34: Average angle of beam at center of CHAOS This graph shows the absolute value of the average angle as a function of beam radius of curvature. The sign of the angle is given by the product, q x f, where q is the Chapter 6. Momentum versus Scattering Angle Cut 109 beam polarity and / is the field direction ( + l = u p , - l = d o w n ) . The center angle is an approximation to the angle of the incident pion track at the reaction vertex. It is the reference angle for all scattering angle measurements, and thus is subtracted from d^. The loading program then adds 62 to the rotated scattering angle in order to rotate the track back to its original position in CHAOS. The final result is the approximation to the scattering angle of the track as determined by the 2LT algorithm. 6.3 Current Progress Unfortunately, this section of the second level trigger has not yet been implemented. Development work during the 1993 commissioning run was geared to fulfiU the immediate requirements for the (TT, 2ir) experiment of that summer. The first section of the second level trigger as well as the momentum sum/polarity comparison section were successfully implemented, leaving no time for the testing of the scattering angle section. This is expected to be done during the setup period before the second (7r,27r) experiment in January 1994. Chapter 7 M u o n Reject ion As discussed in Section 3.3, the first (TT, 27r) experiment indicated that an unacceptable proportion of data written to tape in fact belonged to events in which pions decayed to muons along the beam before reaching the CHAOS target. The muon must share the total initial momentum with a neutrino, and as such does not have the same momentum or trajectory as the original pion. Although some of the muons were rejected by the first level trigger because they followed trajectories that missed the incoming beam counter that is external to CHAOS, many were detected by the scintillator. A significant number of these muons then travelled through the CFT block next to the one removed for the beam entry, passed through the target region ^ and continued on out of the spectrometer on a path that missed the CFT block removed for beam exit. Thus, they satisfied the further ILT condition that two CFT blocks must fire, and they were passed to the 2LT by the ILT. Furthermore, many of the muons followed trajectories that missed the deadened region of WC3, and thus registered both incoming and outgoing hits in each of the three inner chambers. The result was that the 2LT was able to reconstruct the muon track as two outgoing tracks. As illustrated in Figure 7.35, when the incoming and outgoing muon tracks are rotated so that the WC2 angular coordinate —> 0, the result is two tracks of opposite polarity. Thus, a track that appeared to correspond to a negative outgoing particle was always present in these events. Recall that the 2LT was programmed to look for two tracks of any polarity that passed the target and momentum cuts, and then ^Recall that the muons aie not affected by the taiget because they are not stiongly inteiacting. 110 Chapter 7. Muon Rejection 111 ( A ) Original Incoming aind Outgoing Muon Tracks 0' X (mm) ( B ) Rotated Incoming and Outgoing Muon Tracks -500 X (mm) Figure 7.35: Illustration of rotation algorithm performed on muon track. The two inner solid circles are WCl and WC2, and the dotted circle is WC3. In addition, the black CFT blocks are those removed for pion beam entry (left) and exit (right). Figure (A) shows the original muon track, incoming along portion 1 and outgoing along portion 2. (B) illustrates the track portions after they have been treated as separate outgoing tracks and rotated so their 62 values —> 0°. Evidently, the result is two tracks of opposite polarity. Chapter 7. Muon Rejection 112 accept the event if either corresponded to a negative particle. Consequently, if the muon had an acceptable momentum and passed through the target, the event would be written to tape. The fact that the muons do not follow the same trajectory as the incident pions is the basis of a section of electronics that runs in parallel with the other parts already described. This section requires that at least one hit in both W C l and WC2 lie in the regions that the incident pions are expected to pass through. The event can not be accepted unless it passes both this test, as well as the momentum, polarity and target cuts of the first section, and any tests in the optional sections the user may choose to employ. 7.1 E l e c t r o n i c s Although this section is not yet implemented, it has been designed. The electronics for the muon rejection, as illustrated in Figure 7.36, are relatively straightforward. First the angtdar hit addresses are input to this section. The ECL port output of W C l and WC2 from the PCOSl 2738 Controller is input to a new data stack, labelled P, and then daisychained to MLU A for input to the first section of the 2LT. Stack P is set so that it will not accept words with a 1 in the 16th bit position, and thus width words are not written to it . Stack P receives the same ADI and MRST signals as the stacks in the main stage of the 2LT. There are four important signal lines in this section: muon rejection (MuRJT) , suf-ficient W C l and WC2 data (S12D), all data processed (ADP), and NEXT. The ADP is the Latch 7 Q level that is FALSE at the start of the trigger processing and goes TRUE if all data in Stack P has been read and processed. At this point, P generates a ROF (since its ADI latch was previously set), which is delayed before setting Latch 7 to allow Chapter 7. Muon Rejection 113 2738 DataRDY 273B/ECLport Note: All inputs to Stock P PC0S1. PC0S2 are doisychained to MLU A and so these inputs are not terminated Selector bits set so that stack will not see words with 1 in the 16th bit position (will not see width words in clusterized data) Sat Reut Latch 0 Q S12D Latch Q a L5 held high s<t R M M Latch 0 Q Found Sufficient WC2 Data L6 Found Sufficient WC1 Data L7 © All Data ^ Processed (ADP) ra -•MuRJT (reject) S12D Sufficient WC1/WC2 Data (S12D) Figure 7.36: Electronics schematic of muon rejection section. Chapter 7. Muon Rejection 114 for the time required to process the last word and possibly generate an S12D signal. By the time the ADP goes TRUE, aJl processing is complete. A NEXT signal is created whenever S12D is still FALSE in order to generate the readout of the next word in the stack. Before an event readout, the trigger is reset and a MRST pulse is input to Stack P. Also, the three latches in this section are reset, setting both ADP and S12D to FALSE. When the stack receives its first word, it automatically reads it and issues a RR signal. This wiU. enable MLU MU, which reads in the PCOS word and checks to see if it lies in the desired range for either W C l or WC2. MLU MU outputs a 2-bit word that indicates the result of this test: 01 if the word is the W C l range, 10 if it is in the WC2 range, and 00 if it falls in neither range. The first bit is connected to the SET input of Latch 5 and, if the bit is TRUE, it wiU set the latch to indicate that there is sufficient W C l data. Similarly, the second bit wiU set Latch 6 if it is TRUE, indicating that at least one good WC2 point is in the data set. If a 00 is output from MLU MU, neither latch will be set. Also, note that once a latch is set, it remains so until it receives a RESET signal, regardless of the value of the SET input. S12D is the AND of L5 and L6 Q outputs and wiU remain FALSE until sufficient data have been found in both inner chambers. Recall that the gates used in the trigger are not edge-triggered and do not have pulsed output, but simply reflect the values on their inputs and the programmed logic. Similarly, the outputs of the delay/fan-out modules simply reflect their inputs. Thus, one can see that S12D and S12D are latched because they are created from latch outputs. MLU MU generates a RDY level, which is inverted to create a RDY pulse. The delay shown is not employed to keep the leading edge stationary (since it is not AND'd with any MLU output data bits), but rather has another purpose. The RDY pulse is AND'd with the latched S12D signal by Gate 6 G l , which wiU create a NEXT pulse until sufficient Cbaptei 7. Muon Rejection 115 data are found. The RDY pulse is delayed to ensure that it arrives at 6 G l after any possible S12D transition due to the word it corresponds to. Along with ADP the NEXT generates a RE for Stack P. Thus, this section wiU continue testing data until either all the data have been processed or sufficient data have been found. If the last word is read &om Stack P and there is still insufficient data, S12D wiU remain FALSE. After the word has been processed, ADP wiU become TRUE to indicate processing is complete. Further reading of data from Stack P is disabled. The ADP is then AND'd with S12D by Gate 7 G l to create a MuRJT for use in the CHAOS FAST CLEAR circuit. It should be emphasized that MuRJT is latched because the AND gate only reflects the inputs, which are also latched. If sufficient data are found, S12D will become latched at TRUE, thus disabling the MuRJT line and the NEXT circuit. S12D is output for use in the YES circuit of the 2LT. To reiterate the timing for the last word, if this is the data that causes S12D -» TRUE, the ADP will -> TRUE, but will do so after the S12D transition due to the delayed stack ROF. Thus, by the time the ADP = TRUE arrives at Gate 7 G l , the latched S12D is already holding one of the inputs FALSE, and as such MuRJT remains FALSE. 7.2 Final Second Level Trigger Dec is ion The S12D and MuRJT signals are combined with the preliminary 2LT YES and NO signals from the remainder of the trigger as shown in Figure 7.37. First the preliminary 2LT YES pulse must be converted to a level (using Latch 7) because the signal is AND'd with S12D, and the timing between the two signals varies with each event. Recall that S12D is already a level. Then all four signals are converted to NIM logic, simply because there was a lack of space in the 2LT crate, and also because the final decision electronics are easier to see and understand when they are labelled clearly and placed in NIM crates. Chapter 7. Muon Rejection 116 Preliminary Accept Event passes 2LT cuts: polarity, P, target, P vs 0„ polarity comparison/ P sum S12D (data besides /z's are present) 1 2 QUAD COINC. Preliminary Reject Event does not satisfy 2LT cuts Latch Second Level Trigger YES to LAM circuit •NIM-ECL 'Conv MuRJT (no incoming data besides fj,'s are present) IN 1 IN 2 DISCRIM 1 acts as an OR gate Second Level Trigger NO CHAOS Fast Clear Figure 7.37: Electronics for the final 2LT decision. Chapter 7. Muon Rejection 117 Understandably, the 2LT crate is quite cluttered with well over 150 twisted pair wires. The final 2LT decision is quite straightforward. A final 2LT YES to enable the transfer of data to tape is created as foUows. The preliminary 2LT YES is AND'd with the S12D in a quad coincidence unit; if both of these are TRUE, indicating that an incident pion was present and the event passed the cuts, a second level trigger YES pulse is generated. This is input to the LAM circuit to tell the data acquisition computer to record the event. Otherwise, the coincidence output will remain FALSE. In this case, either the MuRJT level is TRUE, or a preliminary 2LT NO pulse has been generated, or both may have occurred. If any of these conditions exist, a final second level trigger NO pulse wiU be generated by Discriminator 1, which essentially acts as an OR gate. This pulse is the FAST CLEAR for the spectrometer electronics. Chapter 8 Conclusion The importance of the second level trigger is evident from the discussion that has been presented. Without the 2LT, one could not gather useful information with CHAOS. The main stage of the 2LT is crucial for any experiment to reconstruct circular tracks in the region of the three inner chambers, and then perform general tests of the momentum and polarity of the associated particle. In addition, this section wiU determine if the track originated in the target region. A further test can be done on the correlation between the particle momentum and scattering angle, which is particularly useful for separating irp elastic scattering events from those in which an incident pion scatters from other atoms. Also, the 2LT can be run in a doubles mode in which it searches for two acceptable tracks based on whatever tests the user chooses. It wiU then perform a cut that depends on the momentum sum and/or the polarities of the tracks. This section is crucial for the successful collection of (TT, 27r) data, which must be separated from a irp scattering background that is many orders of magnitude larger. The main stage can be used alone or with one or both of the optional sections to create a preliminary 2LT YES or NO decision. The final 2LT decision takes into consideration the result of a test which rejects events in which the incident pion decayed to a muon before reaching the CHAOS target. The muon rejection electronics process data in parallel with the other sections of the trigger. Section 7.2 outlined how the decision from the muon rejection section is combined with that from the remainder of the trigger. However, the manner in which the main stage 118 Chapter 8. Conclusion 119 wUl be combined with one or both of the optional stages has not yet been discussed. At present, not all sections of the trigger are operational, but the way in which they will be connected has been determined. At all times, every section of the 2LT wiU be wired up in the following order: main stage, then the P versus Os cut, and finally the P sum/polarity comparison section. AU NEXT lines wiU be connected as shown in Figure 8.38. Note that these lines can be connected like this because they are normally held at FALSE unless a NEXT pulse is generated by one section or another. Inputs to the NEXT OR gate network from unused sections wiU simply remain FALSE and will not effect the operation of the trigger. When optional sections are put in use in the second level trigger, the preliminary 2LT REJECT output does not change. It is still generated by OR Gate 2 G2 in Figure 4.16 on page 61, to signal either that one or more of the inner chambers did not receive a hit or that the event failed the tests of the 2LT. Whenever an optional section of the 2LT is put in use, only one change occurs: what was previously a preliminary 2LT YES (does not include the test for muons) now becomes an ENABLE for the next section. Instead of tapping off the preliminary 2LT YES at a particular point, one simply connects the enable line for the next section to that point and takes the YES from the end of the next section. Figure 8.38 also illustrates the ENABLE and ACCEPT lines for the main stage, the momentum versus 6^ cut, and the momentum sum/polarity comparison section. It was necessary to design a method of connecting these lines in the manner described so that one or both of the optional sections could be operational. The main concerns were that the method be quick and easy, and also that the users do not disconnect any twisted pair cables inside the trigger. With this in mind, a method involving a ECL-NIM-ECL converter (whose channels can be easily labelled) was chosen. As illustrated in the two examples shown in Figures 8.39 and 8.40, the 3 ACCEPT lines in the 2LT are converted to NIM pulses, while the 2 ENABLE lines for the optional sections are connected to the Chapter 8. Conclusion 120 Inside Tr igger 2LT NEXT t 2LT MAIN STAGE AND Gate 9 G2 NEXT ENABLE of MLU21 L ^ MOMENTUM VERSUS 9, CUT AND Gate 15 G2 NEXT Delay 13 02 MOMENTUM SUM/ POLARITY COMPARISON OR Gate 12 G2 <r Outside Trigger passed main stage -^ enable P vs e„ cut passed P vs 0, cut enable P sum/pol comp ^ passed P sum/pol comp Figure 8.38: Diagram illustrating the order of the 2LT sections, as well as a condensed NEXT OR gate network. Chapter 8. Conclusion 121 output of NIM-ECL channels. In addition, another NIM-ECL channel is connected to the preliminary 2LT YES line in the trigger, which is input to the latch shown in Figure 7.37. The user then simply has to connect the proper channels in the ECL-NIM-ECL converter (straightforward plugging in of cables). Figure 8.39 illustrates the connections for implementing the P versus 9a cut: passed main stage TRIGGER SIGNALS enable P vs B, cut passed P vs 0, cut preliminary 2LT YES (ECL) A T ECL in ECL out ECL-NDl-ECL ch. NIU In/out ECL in ECL out ECL-NIM-ECL ch. NM in/out :i A ECL in ECL out ECL-NIM-ECL ch. NIM in/out ECL in ECL out ECL-NIM-ECL ch. MM in/out preliminary 2LT YES (NIM) Figure 8.39: Illustration of how the momentum versus 6s cut is implemented. Similarly, one can implement only the momentum sum/polarity comparison section with the main stage. Figure 8.40 shows how aU three sections would be used together. It may seem odd that the preliminary 2LT YES is converted to an ECL signal and sent back into the trigger electronics. Recall from Section 7.2 that the preliminary YES must be latched. However, NIM latch modules are scarce at TRIUMF, and furthermore, CHAOS has a surplus of ECL latch channels. The conversion of the signal to ECL and then back to NIM adds only w 10 ns to the 2LT decision (a negligible amount of time), and as such, the proposed setup is quite satisfactory. If a NIM module could be obtained, the only resulting change to this setup would be that the preliminary 2LT YES NIM signal would be input to the latch, and the output of this module would then be AND'd with the MuRJT NIM signal (as in Figure 7.37). Chapter 8. Conclusion 122 TRIGGER SIGNALS main stage enable P TS 0, cut passed P vs 8, cut enable P s u m / polarity comp A t ECL in ECL out ECL-NQl-ECL ch. NIll in/out ECL in ECL out ECL-NOf-ECL ch. NIIC in/out TRIGGER SIGNALS passed P s u m / preliminary polarity comp 2LT YES (ECL) 1. A ECL in ECL out ECL-KDf-ECL ch. NIIC in/out ECL in ECL oui ECL-NIM-ECL ch. Nnf in/out y A ECL in ECL out EC3,-NIM-ECL ch. mu in/out ECL in ECL out ECL-NM-ECL ch. NIU in/out preliminary 2LT YES (NIM) t h e s a m e ECL-NIM-ECL c o n v e r t e r Figure 8.40: Illustration of how to implement both optional sections. Chapter 8. Conclusion 123 The second level trigger electronics setup has not yet been completely tested. Due to time constraints during the commissioning run in the summer of 1993, only the main stage and the momentum sum/polarity comparison section were tested before the start of the first (TT, 2X) experiment. Several different cuts were tested under many different experimental conditions, and the trigger performed very well. Although the resolution of various quantities in the 2LT is limited by the fact that it processes only PCOS data, it still does its job well. CHAOS users must simply be aware of the resolution limits when specifying limits in the 2LT tests. Some work stiU remains to be done on the second level trigger. The muon rejection electronics, as well as the momentum versus scattering angle electronics are currently wired up and wiU soon be tested in December 1993. Also, the NIM setup to allow the enabling and disabling of the optional sections wiU be installed. Overall, the building and testing of the 2LT has been quite challenging. In particular, the constraints imposed by limited MLU input word sizes resulted in some innovative trigger features. These limitations necessitated the development of an elegant rotation algorithm to compress data without loss of angular resolution, and they also motivated the design of a CHAOS 21-bit MLU. In short, the final result of the work that has been put into the second level trigger is an excellent setup that wiU allow CHAOS users to perform interesting irN interaction studies with the aim of measuring various fundamental parameters as predicted by chiral symmetry and Chiral Perturbation Theory. A p p e n d i x A Basics of the Second Level Trigger Module s There are several different modules in the second level trigger setup. As explained in Section 3.4.3, they are all based on ECL logic due to the speed requirements, the lower cost per channel and the ease of programming them. The following is a short introduction to each module. A . l D a t a Stacks - LeCroy 2375 A data stack is simply a memory queue that operates on the First In First Out (FIFO) principle. It has 256 16-bit memory locations labelled 0 to 255. The user can set the read and write pointers (RP and W P ) to any of these 256 values through CAMAC and then read or write to these locations, incrementing the corresponding pointer by 1 in each case. In addition, read and write operations can be performed through the front panel, in which the memory access is sequential. The length of a write cycle is not more than 50 ns, and the length of a read cycle is not more than 35 ns. Once a stack is full, further write operations are inhibited until it is reset. An important front panel input is the ALL DATA IN (ADI) signal. If this input is used, it is kept FALSE while data are written to the stack and then pulsed TRUE after all the data are in, thus setting an internal ADI latch. When using the front panel, the first write function results in the readout of the first word. If reading continues until the R P equals the WP, two results can occur. If the ADI latch has not been set (or equivalently, is not being used), the stack will inhibit reading 124 Appendix A. Basics of the Second Level Trigger Modules 125 until the W P is > RP. If the ADI latch has been set, the stack READ OVERFLOW (ROF) level -> TRUE, and the RP -> 0. The ROF wiU -^ FALSE once the first word is read again. A useful feature of the LeCroy 2375 is the set of selector bit switches on the side panel. These allow the user to specify the values of the four most significant bits (bits 13-16) that the stack can see. Words with any other combination wiU not be written into the queue. One can make 2^ = 16 different combinations involving four bits, and as such there are 16 corresponding switches. The user can select any number of these combinations as allowed input to the stack. One should note that the data stacks must sit in the 8025 LeCroy high current CAMAC crate. In the second level trigger, there are three data stacks, one for each chamber, which store the addresses of hit wires for each event. Along with the logic units, the stacks allow the 2LT to consider aU possible hit combinations in a set of nested FORTRAN DO loops (one loop for each chamber). • Inputs Master R e s e t ( M R S T ) Sets RP and W P to 0. There are two bridged inputs to enable daisychaining to other stacks. Write Enable ( W E ) Initiates the writing of data to the memory location spec-ified by the WP. There are two separate inputs that are internally AND'd to create the W E condition. R e a d Enable ( R E ) Initiates the reading of data from the memory location spec-ified by the RP. There are two separate inputs that are internally AND'd to create the RE condition. All D a t a In ( A D I ) Sets an internal latch that indicates no more data wiU be written into the stack through the front panel. Sets the logical end-of-data Appendix A. Basics of the Second Level Trigger Modules 126 marker to the current W P value and forces the stack to loop back to memory location 0 whenever the last data word is read out. • Outputs W r i t e R e a d y ( W R ) A level indicating that a write operation is complete and the data are valid (steady) in the memory location. Also indicates that the W P has been incremented. R e a d R e a d y ( R R ) A level indicating that a read operation is complete and the data are valid on the output channels. Also indicates that the RP has been incremented. W r i t e Overflow ( W O F ) A level that indicates the memory is full. R e a d Overflow (ROF) A level that indicates the last word has been read out. If ADI signal was input to set ADI latch, the ROF will cause the RP to be reset to 0. The ROF wiU —+ FALSE when the first word is read again. Figure A.41 is a timing diagram for the data stacks in which write and read cycles are illustrated. The timing is as it would be in the second level trigger, which employs the ADI latch in the stacks. Appendix A. Basics of the Second Level Trigger Modules 127 READ cycle ADI in u s e a u t o -m a t i c looping 50 ns _J last irord read cycle begins first word read cycle begins old word last irord last vord valid T F first -word first word valid F T F T F WRITE cycle 1 wordl word1 Is input wordl is in memory word2 •word2 is input wordZ is in memory T F T F T F Figure A.41: Example of stack timing for both a write and read cycle. With regard to the write cycle, the ADI latch has previously been set; therefore, the stack automatically reads the first word in its queue when it is read enabled and the last word has been read. As can be seen, the time for a write cycle (leading edge of WE —»• leading edge of WR) is ~ 50 ns, whereas the time for a read cycle (leading edge of RE —> leading edge of RR) is ~ 30 ns. Appendix A. Basics of the Second Level Trigger Modtdes 128 A.2 Data Registers - LeCroy 2371 A data register, which is used in the momentum sum/polarity comparison section, is a simple module that takes a 16-bit input word and distributes it on two parallel 16-bit outputs in approximately 10 ns. It latches the input on its two output words each time it receives simultaneous STROBE and ENABLE signals. It should be noted that unused data inputs are seen as TRUE. The propagation delay through the module is adjustable from 30 to 90 ns, and the minimum value is used in the 2LT. • Inputs Input Enable (EN) Enables the STROBE input. The EN is automatically held TRUE if it is unconnected. Strobe (ST) Initiates the reading of the input word, but only if the EN is TRUE. • Outputs Data Ready (DR) A level indicating that an input word has been distributed on the outputs and that the output is valid. It is identical to the RR output of a data stack, except that the position of the leading edge is user-adjustable. A.3 Arithmetic Logic Units - LeCroy 2378 An arithmetic logic unit (ALU) performs arithmetic and logical operations on two 16-bit input words, A and B, and outputs the result on a 16-bit data word, C. The entire cycle takes approximately 50 ns. The module can do simple arithmetic sums and differences, such as C = A - B C = P rev iousC-B Appendix A. Basics of the Second Level Trigger Modules 129 and the logical operations C = A - B C = A + B C = AXORB The operations are initiated by STROBE (ST) signals, and the user also has some choice in programming the module to perform the operation on the leading edge of ST A, ST B or (ST A • ST B). The operation and manner of enabling the module are normally programmed through CAMAC by setting the OP-CODE within the module. The two ALU's that are included in the 2LT (F and F') are set to perform C = A — B on the leading edge defined by ST B, which is connected to the Q output of a latch that is set when data from aU three stacks are vaJid. The input word B is the WC2 angle, while A is the WCl angle and the WC3 angle for ALU F and F', respectively. These modules are necessary for the implementation of the rotation algorithm used to compress the angular data into a 16-bit word. • Inputs Strobes (ST A, ST B) There is one ST signal associated with each data input word. Strobes A and B indicate that data words A and B, respectively, are valid on the inputs and can be read in. Depending on the OP-CODE choosen by the user, the ALU wiU initiate an operation cycle when either ST A, ST B or (ST A . ST B) -> TRUE. • Outputs Data Ready (DR) A 20 ns wide pulse that indicates that the output data are valid. Appendix A. Basics of the Second Level Trigger Modules 130 A.4 Logic Gates - LeCroy 4516 The LeCroy 4516 is a ftdly programmable 3-fold AND/OR logic unit that performs operations quickly within 10 ns. The modules are not edge-triggered and do not have pulsed output, but simply reflect the inputs and programmed logic. It has 16 channels, each of which has 3 inputs. A, B and C. Every channel performs the same type of operation on its corresponding inputs. There are four possible outputs A B C (A -^  B) • C (A . B) + C (A -F B) -F C which are choosen by means of switches on the rear-panel or through CAMAC. The CHAOS second level trigger includes two 4516's, called 01 and 02. They are set to output [A'B-C] and [(A-B)-|-C] respectively, and are used to create numerous control signals (ex: enables, disables, NEXT pulses) as well as the 2LT ACCEPT and REJECT. A.5 Latches The latch module was built by the TRIUMF electronics division. It contains two sets of 16 output channels, labelled Q and Q. Each output pair is separately set (Q = 1, Q=0) by their corresponding SET (S) input. The pair will remain in this configuration until the module is reset (all Q's —^  0, all Q's —> 1) by one common RESET (R) input. Appendix A. Basics of the Second Level Trigger Modules 131 A . 6 Logic D e l a y / F a n - O u t Module s - LeCroy 4418 The programmable LeCroy 4418 modules have 16 delay lines, each of which has one input and three equivalent outputs, for use as a fan-out. The modules are not edge-triggered and do not have pulsed output, but simply reflect the inputs. Every line has a common minimum delay, but they can be individually programmed to have more delay. The mininum delay value and the delay increment depend on the 4418 submodel number. For those modides used in the second level trigger, the minimum delay is 13 ns and the increment is 2 ns. A . 7 M e m o r y Lookup Uni t s Both LeCroy memory lookup units (MLU's) and CHAOS MLU21's comprise an inte-gral part of the 2LT. Without these modules, the tests to determine the merit of a track could not be carried out. An MLU works in a relatively simple manner, as illustrated in the example of MLU A' in Figure A.42. The user inputs an address to the MLU which is actually a physical quantity or combination of quantities. The MLU then "looks up" the address contents, which indicate the results of previous calculations done by the user to program the module. The MLU then outputs this value along with a READY (RDY) signal for further use. A.7 .1 LeCroy M e m o r y Lookup Uni t - 2372 16x12 LeCroy 2372 MLU's are used in the second level trigger. The first dimension indicates the size of the maximum input word the module can read, while the second dimension specifies the number of Random Access Memory (RAM) chips that are within the module. Thus, 2372's have a maximum of 16 bits input with 12 RAM chips of memory to allow for the five choices of dimensionality ( input/output size combinations) Appendix A. Basics of the Second Level Trigger Modules 132 input an address which is actually physical quantity or combination of physical quantities Output contents of address, which is the proper answer based on previous calculations done to load the MLU Example - MLU A' addr : 00001111 u n i t s of 5/4° t h e t a 18.75" MLU conver t s to u n i t s of 1/4° (ou tpu t= inputx5) MLU(15) = 75 Output is 75 Figure A.42: Dlustration of how MLU A' works. Appendix A. Basics of the Second Level Trigger Modules 133 that are outlined below in Table A.7: Dimensionality 0 1 2 3 4 # Input Bits 16 15 14 13 12 # Output Bits 1 2 4 8 16 Table A.7: Dimensionality of the LeCroy 2372. The 2372 has three modes of operation: transparent, inhibit and strobed. Inhibit mode turns off the front panel inputs and enables CAMAC programming of the module (used to load the memory). In strobed mode the input word is latched upon the leading edge of an ENABLE (EN) signal, and the module begins to look up the corresponding output. In tranparent mode the input word is not latched, so it must remain steady untu the module has performed its operation cycle and the resulting output is valid. The normal mode of operation is strobed mode, which is used in the second level trigger. The 2372 has three equivalent READY (RDY) signals; in strobed mode, the RDY is normally TRUE, then goes FALSE shortly after the leading edge of the EN and goes TRUE again a few ns after the output data are valid (as was shown in Figure 4.17). It is useful to note that if any data inputs are unconnected in a particular mode (ex: one uses only 10 bits of input when the mode allows for 12), the unused inputs are seen as TRUE. The 2372 has a CAMAC Control Register (CCR) into which the user writes a code to set the mode and dimensionality. In addition, it has a CAMAC address register (CAR) that stores the MLU address pointer. The user can read the CAR in order to determine the present address, and also write to it to change the value of the pointer. In addition, each 2372 has a backup battery that keeps the contents of the memory intact for up to 15 minutes when the module is not powered. It should be noted that if Appendix A. Basics of the Second Level Trigger Modules 134 the battery begins to wear down, it will affect the voltages on the MLU circuit boards when it is in use, and as such eratic output will result. • Inputs Enable (EN) Latches the input and starts the lookup cycle in strobed mode. There are four separate inputs that are AND'd to create the EN condition; unused inputs are seen as TRUE. • Outputs Ready (RDY) There are four RDY level outputs that indicate the lookup cycle is complete and the output data are valid. A.7.2 21-Bit Memory Lookup Unit In addition to the LeCroy MLU's, two 21-bit MLU's are also used to perform the momentum, target and polarity cuts in the main stage of the 2LT, as well as the momen-tum versus scattering angle cut in an optional section. These were designed by Pierre Amaudruz, and modified and built by the author. Motivation for Design When the work on the CHAOS second level trigger began, only two types of MLU's were available. One was the LeCroy CAMAC ECLine 4508 with independent 8-bit input and output words. The other was the 12x16 LeCroy ECLine 2372 described previously. However, these did not offer the dimensionalities that CHAOS required. The 2LT called for an MLU that could have 21 bits of input/ 1 bit of output for the first section, as well as 16 bits of input/8 bits of output for the scattering angle cut. Unfortunately, there Appendix A. Basics of the Second Level Trigger Modules 135 were no immediate plans for LeCroy to introduce an MLU to suit the group's needs. As such, two 21x8 MLU's were built for use in the second level trigger. It should be noted LeCroy has since created a new ECLine 2373 MLU that has an independent 16-bit input and output words, which it made available in 1993. However, although this module could be used in the second level trigger where the required mode was 16 bits input and 8 bits output, it stiU does not have the option of 21 bits of input required in one section of the trigger. Furthermore, this module was not available in time for the testing and development of the trigger. Also, the building of a second 21-bit MLU was straightforward, fast, and economically feasible since all design changes and testing routines had been worked out during the development of the first MLU. Descr ipt ion of 21-Bit M L U To reiterate, the dimension of the CHAOS MLU's is 21x8 . This means that it has a maximum input word size of 21 bits and there are 8 RAM chips. The four dimensionalities that are available are outlined in Table A.8: Dimensionality 0 1 2 3 # Input Bits 21 20 19 18 # Output Bits 1 2 4 8 Table A.8: Dimensionality of the CHAOS 21-Bit MLU. The 21 Bit MLU has no CAMAC Control Register and as such the dimensionality is choosen with jumpers on the circuit board. Through CAMAC the user can choose from two modes of operation. Program Mode (to load memory) and Work Mode (to allow read and write access through the front panel only). Like the LeCroy modules, the MLU21 Appendix A. Basics of the Second Level Trigger Modules 136 begins to process information a few ns after it receives the leading edge of an EN signal that is the AND of three separate inputs. Unused EN inputs are automatically held TRUE. Unlike the LeCroy MLU, the CHAOS module has only one RDY and it is a pulse. The signal is FALSE normally, goes TRUE a few ns after the output data are valid, and then goes FALSE again after a specified width. The width of the RDY is adjustable from 30 to 110 ns via a pot in the circuitry. Again, unconnected data inputs are automatically held TRUE. Unfortunately there is no battery for memory backup, so the contents are lost when the unit is powered down. • Inputs Enable (EN) Latches the input and starts the lookup cycle when the module is in work mode. There are three separate inputs that are AND'd together to create the EN condition. • Outputs Ready (RDY) One pulse output of user-adjustable width that indicates the lookup cycle is complete and the output data are valid. A p p e n d i x B ECL Program and T R I G 2 Program Each of the modules found in the second level trigger are programmable through CAMAC. In particular, the RAM chips of the memory lookup units must be loaded in order to perform the numerous second level trigger cuts. This necessitated the develop-ment of two programs called ECL ^ and TRIG2 ^. ECL is a CAMAC interface program that allows for easy communication with any module in the 2LT, and TRIG2 calculates the values that must be loaded into each MLU based on the user's choice of trigger parameters. B . l ECL Program ECL is a user-friendly program that lets CHAOS users program the trigger without having to know CAMAC commands. The applications in the program actually extend beyond the second level trigger. The PCOS system and first level trigger system (includ-ing the Fast Encoding and Readout ADC's) are fully programmable using ECL menus. Furthermore, it is hoped that menus for initializing the FastBus ADC's wiU soon be added. ECL is window-driven and menu-driven, with each screen consisting of three windows. A large window shows the current crate the user has accessed, with the crate number and optional name at the top. Another sizeable window contains the present menu. The ^Majority written in C by Kelvin Ray wood, with several routines written in FORTRAN by Sheila McFarland ^Written in FORTRAN by Sheila McFarland and Kelvin Raywood 137 Appendix B. ECL Program and TRIG2 Program 138 third window is a small one for the current command line as well as the three previous ones. There are two levels of menus: the main menu and a submenu for each individual module. The main menu window is illustrated in Figure B.43(A). The purpose of ECL is to allow the user to perform all CAMAC functions that are defined for any module. The most commonly used commands for each module are listed in its corresponding submenu. In addition, the main menu includes a general purpose command that prompts the user for the CAMAC code parameters and executes the function. AH commands in the ECL menus prompt for any required information. Once the user starts ECL, the main menu appears. Different crates can then be configured (drawn on the screen). The Configure command draws a picture of the empty crate, whose number the user specifies, and presents a menu of aU the possible modules that can be drawn in the crate. The user can than specify the contents of the crate as it looks in reality. An example of a configuration sub-window is shown in Figure B.43(B). Once the users are finished configuring the crate, they can then exit the Configure menu and access it by keying in "CR cratenumber". The crate picture will be redrawn, and the user can then access any modide by simply entering the slot number or label. When configuring a crate, one can give each module an optional label, such as a letter of the alphabet, to reflect any labels in the corresponding electronics diagrams. Once the module has been accessed, commands can then be chosen from its submenu to initialize or change module settings. Any sequence of commands issued in ECL can be written into an ECL Command Macro (ECM) and qiuckly executed with the @ command in the main menu. ECM files have been created to initialize the PCOS system, the first level trigger and the second level trigger. An important command in ECL is PCOS-TEST, which was used extensively in the setup of the PCOS system and the debugging of the 2LT. This command allows the user to simulate wire chamber hits by setting bits on the PCOS 2731A latch inputs. A submenu asks for the number of wires that fired in a particular cluster as weU as the Appendix B. ECL Program and TRIG2 Program 139 (A) Main Menu Window Crate 2 TEST 1 lau A 2 9 ALU B 4 5 STACK C ft 7 • » » 11 e B u s » 17 V 20 21 22 23 ECL Control Datinad Grata Valid Command* 2 TEST • CQntif CRate PCna LOad SAva REfreah quit ]>CDa_Uat TOg_|iooa EElp <alot_liam1>Hr> <ali>t_labal> > (B) Submenu Window Crate 2 TEST 1 lau A 2 3 ALU B 4 9 STACK C 6 7 8 « n It e s u E « 17 S B 20 21 22 23 Crate Configuration 1£LU Hemory Lookup Unit ALU AriUimaUe Lo(ic Us l t PLU ProBrajnmable Lookup Unit UALU lta}orlty Logia Unit COREG 4A-Input Coinotdanoe Latok DELAT Delay/Fan-Out LOGIC AND/OS Logic Unit STACK Data Staok DISCRDI FrogrammaUa Dlacrlmlnator DREG Data Register PCOS FCOS 2731a Delay and Latch I1LU21 21-Bit ULU FERA Faat Encoding k Readout ADC FEHA-DRV FEBA Driver TOC_PS FbilUps ScientiJic TDC ENTER: <Slot> <Uodiila> 'labal" » DO 2 last » 1 mlu a » 3 aitt ta » S ataok o Figure B.43: Illustration of the ECL main menu, as well as a "configuration" submenu. Appendix B. EGL Program and TRIG2 Program 140 center angle of the cluster for any number of clusters. After this information in entered, ECL latches the proper channels in PCOS, and they can then be read out in trigger tests, B.2 T R I G 2 Program TRIG2 creates the data sets that are loaded into the MLU's of the second level trigger. Among some of the data it prompts the user for are the maximum acceptable momentum, the target radius, the polarity acceptance and the magnitude of the magnetic field. It wiU geometrically calculate the minimum momentum the trigger could see based on the target radius and the fact that only angles within ±32° of the WC2 hit will be accepted. The user can then choose this to be the minimum acceptable momentum or can specify a tighter cut. If the momentum versus scattering angle cut is to be used, the program prompts for the beam momentum and the direction of the magnetic field in order to calculate the average angle of the beam at the center of CHAOS. It wiU also ask for the cut parameters. If the momentum sum section is employed, the user must input the maximum momentum sum. Finally, the program asks for the range of PCOS addresses that at least one hit in W C l and WC2 must lie in, so as to reject pions that decay to muons before reaching the CHAOS target. TRIG2 asks the user for a suitable name and creates the files for all 2LT MLU's. It assigns file names in a standard manner, giving them the proper extensions to indicate the module. For example, if the user keyed in "RUN400" when prompted for the filename, TRIG2 would create the file RUN400.MLU21K to load the MLU21 K. The researcher then simply has to run ECL, choose the proper MLU menu and choose the LOAD command specifying the file name. Bibliography [1] J . F . Donoghue. Chiral Symmetry as an Experimental Science. Lectures presented at the International School of Low-Energy Antiprotons in Erice. CERN-TH.5667 No. 1696, (January 1990). [2] J . Gasser. Strange Quarks in the Nucleon. TNewsletter, N o . 2, 72, (May 1990). [3] J . Gasser and H. Leutwyler. Quark Masses. Physics Reports, 87C, 77, (1982). [4] K. S. Krane. Introductory Nuclear Physics. John Wiley and Sons, New York, Chap-ter 4, (1987). [5] M. E. Sevior. "The wp —> TTTriV^  reactions with the CHAOS detector. An update," TRIUMF research proposal for E568 submitted to TRIUMF EEC, (November 1991). [6] G. R. Smith. "The CHAOS Physics Program and Detector," an appendix to the CHAOS major equipment grant submitted to NSERC, (September 1991). [7] R. Tacik. Information regarding the field profile as a function of radius in CHAOS has been supplied by Roman Tacik (1993). [8] F . Sauli. "Principles of Operation of Multiwire Proportional and Drift Chambers", lectures given in the Academic Training Programme of CERN, 1975-1976, (1977). 141 

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