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The chaos detector and commissioning result Kermani, Mohammad Arjomand 1993

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THE CHAOS DETECTOR AND COMMISSIONING RESULTSByMohammad Arjomand KermaniB.Sc., The University of British Columbia, 1991A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEINTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF PHYSICSWE ACCEPT THIS THESIS AS CONFORMINGTO THE REQUIRED STANDARTHE UNIVERSITY OF BRITISH COLUMBIADECEMBER 1993© M0HAMMAD ARJOMAND KERMANI, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)_________________________Department of______________The University of British ColumbiaVancouver, CanadaDate ) /7?] ,DE-6 (2/88)AbstractThe Canadian High Acceptance Orbit Spectrometer (CHAOS), which is a 360 degreemagnetic spectrometer designed for use in various 7rN experiments, is introduced. Thephysics program, constituent elements of the detector, analysis techniques, and commissioning results are discussed. In particular, 7r+p elastic scattering data acquired at anincident pion energy of 280 MeV with a singles trigger on a liquid hydrogen target arepresented.11AbstractList of TablesTable of ContentsIiviList of FiguresAcknowledgementsvi’xii1 Introduction1.1 The Physics Program1.1.1 The irp Program1.1.2 The (ir,2ir) program1.2 Theoretical Perspective1.2.1 Symmetries1.2.2 Spontaneous Symmetry Breaking1.2.3 Chiral Symmetry1.2.4 The irN sigma term12256789111315151819202 A Brief Description of CHAOS2.1 Monte Carlo2.2 The Magnet & Polarized Target2.3 Tracking Detectors2.4 Particle Identification & Multiplicity2.5 Trigger & Readout Systemsin3 Wire Chambers 1 & 2 213.1 Basic Operating Principles 213.2 Design & Construction 223.3 Performance 234 Wire Chamber 3 374.1 Basic Operating Principles 374.2 Description of WC3 384.3 Performance 445 Wire Chamber 4 475.1 Description & Construction 475.2 Charge Division 515.3 Performance 525.4 Induced Pulse Problem 586 CFT Counters, Trigger Systems and Readout Electronics 636.1 CFT Counters 636.2 First Level Trigger 666.3 Second Level Trigger 686.4 Readout Electronics 706.4.1 PCOS & 4290 TDC System 716.4.2 FASTBUS 737 Chamber Calibration 787.1 In-plane Calibration 787.2 Magnetic Field Corrections 827.3 Vertical Calibration 86iv8 Reconstruction 928.1 Momentum Reconstruction 928.2 The Interaction Vertex and Scattering Angle 958.3 Results 979 Conclusion 120Bibliography 122VList of Tables1.1 Table showing polarization definitions 38.2 Table showing beam calculation parameters for 396 MeV/c at 1.4 MHz. 117viList of Figures1.1 Figure showing the ratio of the various measured cross sections to theSM92 phase shifts near 67 MeV 42.2 Figure showing the CHAOS spectrometer. The corner post and the toppole tip have been removed to allow for a better view. For the same reason,a quadrant of the detectors is cutaway 142.3 Results of GEANT simulations are shown. This simulations were done fordetectors in helium surroundings 162.4 The CHAOS field map for 0.95 T central field setting is shown. The solidline shows the field value as a function of the distance from the center ofthe spectrometer, and the crosses denote the field uniformity 173.5 Plateau curves for WC1 and WC2 are shown. The data were acquired ata rate of < 50 kllz, for 225 MeV/c ir 253.6 The efficiency of WC1 and WC2 as a function of the incident beam rateis shown for operating voltages of 2450 V for WC1 and 2050 V for WC2,acquired with 225 MeV/c ir 263.7 The current drawn by WC1 and WC2 versus beam rate is shown. Thehigh voltage and beam conditions are the same as for figure 3.6. The solidcurves are straight line fits 273.8 Figure showing tracks in a proportional counter 283.9 Figure showing angular residuals for WC2 283.10 Figure showing calculated beam momentum using WC1 and WC2 31vu3.11 A typical target projection histogram in the x-y plane is shown 333.12 The number of activated cathode strips in WC2 for straight through beamis shown 343.13 Vertical target projections for beam rates of < 50 kllz and 1.8 MHz areshown 364.14 Figure showing the left-right ambiguity in a drift chamber. Drift times tothe central anode are identical for both tracks 394.15 Figure showing the WC3 cell structure. Thickness of the strips and wireshas been exaggerated in this figure for clarity 404.16 Drift electron trajectories for tracks with various angles of incidence, 8,are shown. The solid strips correspond to those used to resolve the left-right ambiguity. All dimensions shown are in cm. All cases are for B=1 Texcept the upper left figure which is at B=0. A and C denote the anodeand cathode wires respectively. The axes represent the cell dimensionsused in the simulation. For magnetic fields opposite in polarity to thatshown, the unshaded strips provide the best left-right resolution 424.17 Figure showing the normalized difference between diagonally opposed strips(a). The difference as a function of the drift time is also presented (b). Thenormalized difference scale has been expanded by a factor of 500. Longdrift times correspond to small TDC values. The data were acquired at amagnetic field setting of 1.2 T 434.18 Plateau curve for the WC3 anode bias is shown 444.19 WC3 drift time spectra along with their integrals (proportional to the driftdistance) for zero and nonzero field settings are shown. Increasing drifttime corresponds to smaller TDC channel number (1 ns/channel) 45viu5.20 Diagram showing a single cell of WC4. The letters A, G, and R denoteanode, guard and resistive wires, respectively. All dimension are in mm, 485.21 Figure illustrating the charge division method 515.22 WC4 plateau curve is shown 535.23 Graphs showing drift time spectra and their integrals for zero and 0.5 TOnce again, long drift times correspond to small TDC values 545.24 Illustration showing left and right tracks in a single cell of WC4 545.25 WC4 Left-right residual for a single wire along with the time centroids (it)of each peak are shown. The solid curve is a gaussian fit to the data. . 555.26 The CHAOS coordinate system is shown. The positive z-axis points outof the page, and the location of each of the anodes in each chamber is alsoshown 565.27 A sample track in WC4 is shown 575.28 Typical ADC spectrum from one end of a resistive wire is shown 585.29 Illustration of the induced pulse effect. Pulse heights and widths are justestimates and do not represent actual values 595.30 WC4 residuals prior to the implementation of the cancelation network areshown for events passing on the left of a cell 605.31 Schematic diagram of the cancelation network is shown 605.32 Spectra of WC4 residuals after instaflation of the cancelation network.Again, only tracks passing on the left of the cell were considered 626.33 Schematic diagram showing the first level trigger. For simplicity, only oneof the CFT counters is shown 676.34 Block diagram of the second level trigger. Control signals are not shown 696.35 Schematic diagram of the FASTBUS handshaking circuit 76ix6.36 Flow chart of the FASTBUS readout algorithm 777.37 Illustration of the incident track angle-y in WC3. A and C denote anodeand cathode wires respectively. Chamber cell is not drawn to scale. . . 807.38 Illustration of rotation offsets is shown. The offset has been exaggeratedfor clarity 827.39 X and Y residuals prior to and after the calibration along with positioncentriods () and standard deviations (a) for WC3 with B=0 are shown 837.40 WC3 x(t) residuals prior and after calibration for magnetic field setting of1.2 T 857.41 Graph of ratio versus displacement for the inner and the outer resistivewires. The solid lines are straight line fits to the data. The slopes shownare half of the electrical lengths 877.42 Z coordinate residuals for WC1, WC2, and WC4 before the calibrationprocess are shown (ie: with all offsets set to zero) 907.43 Z coordinate residuals for WC1, WC2, and WC4 after the calibrationprocess. The standard deviations (u) show the effective z resolution ofeach chamber 918.44 Scatter plot showing track momenta as a function of sum of pulse heightsin E1 and E2. The polygons are used to identify pions and protons. 988.45 Illustration of the target vessel in the X-Y plane 998.46 Reconstructed interaction vertex in the X-Y plane 998.47 The difference between pion and proton vertices in the X-Y plane areshown. The solid lines represent gaussian fits to the data. The vertexresolution per track is obtained by dividing the standard deviations shownabove by v’ 100x8.48 Illustration of the vertical picket fence target 1018.49 Vertical vertex reconstruction for the picket fence target. The three peakscorrespond to the three (2 mm diameter) rods 1018.50 Scattering angle versus momentum correlation for pions and protons at 280MeV pion incident energy prior to scaling the magnetic field are shown.The solid lines represent kinematic predictions 1038.51 Scattering angle versus momentum correlation for pions and protons afterscaling the magnetic field (by +5%) are shown. All other features are thesame as those for figure 8.50 1048.52 Pion versus proton scattering angle at 280 MeV incident pion energy. Thesolid line represents kinematic predictions 1068.53 Histogram showing the scattering angle resolution. The scattering angleresolution per track is obtained by dividing the standard deviation shownabove by 1068.54 Missing mass spectrum for elastic scattering at 280 MeV 1078.55 Missing mass spectrum versus sum of pulse heights in E1 and E2. . 1078.56 Region 3 of the missing mass histogram versus pion scattering angle. . 1098.57 Diagram showing the copper support disks around the target cell 1098.58 The vertical vertex for irp scattered pions (top) and decay events (bottom)are shown 1108.59 Region 2 of the missing mass spectrum on a magnified scale along withthe corresponding momentum distribution are shown 1128.60 Cross sections for irp elastic scattering at 280 MeV incident pion energy.The solid line represents the SM92 phase shift results 1148.61 Track angle in WC3 versus pion scattering angle 1148.62 Diustration of d(r) 118xAcknowledgementsThere are many people who deserve thanks, however to list them all would require abook in itself. I would like to say thanks to my supervisor of many years, Dr. GregSmith, for his help and guidance and the late nights he had to spend reading this thesis.In addition, I would like to thank my co-reader Dr. Garth Jones. I want to say a specialthanks to the following people whose help is greatly appreciated: Pierre Amaudruz, JeffBrack, Gertjan Hofman, Doug Maas, Martin Sevior, and Roman Tacik. I would alsolike to acknowledge the efforts of Faustino Bonutti, Paolo Camerini, Nevio Grion, DaveOttewell, and Rinaldo Rui during the running period, which at the time seemed to haveno end. I also want to thank my friends Chris K6nig, Alan Poon, and Dean Featherling.Finally I would like to thank my mother Salehe, my father Mehdi, and Sheila McFarlandfor their support through the years.xiiChapter 1IntroductionThe field of particle physics has made great advances in the past fifty years. The design and construction of new detectors and laboratories along with the development ofpowerful theories has allowed us to understand a great deal about the building blocksof nature. However an enormous amount is still unknown. To date the most completemodel of particle physics provides the following classification for the basic building blocksof nature:(e () ) ) (Leptom family)VT( ( (tI I I I I I (Quark family)d) s) b)All interactions studied in particle physics take place between the above families andare mediated by the strong, weak, electromagnetic, and gravitational forces. The stronginteractions take place between the quark constituents that make up the hadrons. Sincebefore the start of the meson factories the pion has been used as a probe to study thestrong force, and a great deal of physics has been learned from the interactions of pionswith nucleons. The Canadian High Acceptance Orbit Spectrometer (CHAOS) built atTRIUMF will study various irN reactions. This unique new device is a 360 degreemagnetic spectrometer capable of making simultaneous measurements over the entire1Chapter 1. Introduction 2angular region. The CHAOS physics program and detector will be described and recentcommissioning results will be presented in this thesis.1.1 The Physics ProgramThe major objective of CHAOS is to study the irN system. These measurements will beused to determine scattering amplitudes and scattering lengths which are needed to testQCD models. The physics program can be divided into two parts: the irp program andthe (ir, 2ir) program. Each of these programs will be discussed in this section.1.1.1 The irp ProgramThe aim of this program is to measure analysing powers for elastic lr±p scattering at lowincident pion energies. The analysing power for a given reaction on a spin 1/2 targetwith its spin polarized perpendicular to the reaction plane (along the unit vector F) anda spin zero projectile of a given momentum along the unit vector is defined as thefollowing:(1.1)where N,. and N1 represent the number of particles scattered to the right and the left ata given scattering angle 8 and P is the magnitude of the target polarization. In addition,left is defined along the vector pointing in the direction of F xIn the case of two identical detectors one would be able to make this measurement bysimply placing the two detectors on either side of the polarized target. However this is notan easy task since the measurement is extremely sensitive to instrumental asymmetries.Instead one can measure the analysing power by determining the differential cross sectionat a given scattering angle for positive and negative target spin polarizations. The latterapproach is much less prone to instrumental asymmetries.Chapter 1. Introduction 3Polarizations P (K1 x+ 1- -1Table 1.1: Table showing polarization definitionsPositive and negative polarizations are defined in table 1.1. In this table Ko represents the unit vector along the direction of momentum of the scattered particle. In thiscase the analysing power is given byA18 — .+() — o(O) 11 2In the above equation o+() and o(6) are the differential cross sections at positive andnegative target polarizations, and likewise p+ and p are the magnitudes of the positiveand negative polarizations. The analysing power is sensitive to the interference betweenthe spin flip and the non spin ffip components of the scattering amplitude, whereas thecross section is a measurement of the incoherent sum of the squares of these terms.It is true that irN scattering amplitudes can be extracted from the absolute differential cross section and spin-dependent measurements via partial wave analysis (PWA).However the existing cross section data below 100 MeV are not consistent and since thephase shifts are obtained by fitting the measured cross sections using a partial wave expansion it is clear that the phase shifts will be inconsistent as well. A brief review of lr±pscattering experiments is as follows. In 1953 H.L. Anderson and E.Fermi et. al. [1] werethe first to measure lr±p differential cross sections. The next thorough study did notoccur for another twenty years. In 1973 Bussey et. al. [2] made an extensive set of 7r±pmeasurements between 88 and 292 MeV; in 1976 data at energies below 100 MeVwere obtained by Bertin et. al. [3]. At this point different measurements seemed to beChapter 1. Introduction 41.50)CI)1.0I0.5Ratio of experiments to SM92 vs c.m. angle20 40 60 80 100 120 140 160 1800cm (Deg.)Figure 1.1: Figure showing the ratio of the various measured cross sections to the SM92phase shifts near 67 MeV.consistent with each other. In 1978 yet another study was done by E.Auld et. al. at 48MeV [4]; however the Auld data did not agree with the phase shifts that were extractedusing the previous two experiments. In the years that followed more data were obtainedby Frank [5], Ritchie [6], Brack [7] [8], and Joram [9] and further disagreement surfaced.An example of the discrepancy at 67 MeV is shown in figure 1.1. The absolute differentialcross section at a given scattering angle 8 can be obtained from the experimental datausing the following relation.— Yield(8)cos(8tt)df” “ N29d1e (1.3)Chapter 1. Introduction 5Where 6tgt is the target angle with respect to the incident beam, Ntgt is the numberof target particles per unit area. N represents the number of incident particles, dfZ isthe solid angle defined by the detector and e is the detection efficiency. In the case ofan absolute measurement all the above parameters must be known accurately and anysystematic errors will directly translate into an error in the cross sections. In an analysingpower measurement, most of these factors need not be known absolutely if one can relyon the fact that they stay the same for both target polarizations. Hence, an analysingpower measurement is not sensitive to the same normalization problems encounteredwhen making an absolute differential cross section measurement. Thus the ip analysingpowers measured with CHAOS will place an extra constraint on the partial wave analysis.This will be crucial in resolving the current impasse with the cross sections as well asproviding a more sensitive measure of the smaller partial waves. The amplitudes obtainedfrom the PWA can then be used to calculate the pion nucleon sigma term, discussed ina later section.1.1.2 The (ir,2ir) programThe aim of this program is to study irN —÷ lr7rN reactions for a wide range of energies andvarious nuclei. Further measurements of (ir, 2r) differential cross sections on nuclei willbe used to study effects arising from the nuclear medium. There has been some discussionregarding the enhancement of the cross section due to nuclear matter for complex nucleisuch as lead. The primary goal of this experiment is, however, to study the followingreactions at energies close to threshold for pion production:lr+p , 7r+7r+n7r+p 7r+lrOp7rp •—* 7r7r°pChapter 1. Introduction 6irp 4 lr+7rn(1.4)The amplitudes obtained from the above can then be related to the (lr7r) scatteringlengths. This will provide a good test of low energy QCD models. The theoreticalperspective is briefly discussed in the next section.1.2 Theoretical PerspectiveQuantum Electrodynamics (QED) is perhaps the most successful theory describing interactions between elementary particles. The success of QED is demonstrated, for example,by the very precise agreement between the theoretical and experimental values of theelectron and the muon anomalous magnetic moments. It seems logical to use QED techniques to study the strong force. The corresponding theory of the strong interactions isQuantum Chromo Dynamics (QCD); however, significant differences exist between thetwo theories. In QED the interactions are mediated by photons; in QCD this task isperformed by gluons. The photon is neutral and thus is not capable of self interactions.The gluon, on the other hand, although electrically neutral carries the strong color chargeand thus acts as a field source. In other words gluon-gluon vertices are allowed in QCD.The fact that gluons self interact makes QCD calculations difficult. The other majordifference is in the magnitude of the coupling constant. The strong coupling constant, a,9is dependent on the energy scale and the momentum transfer. To first order the strongcoupling constant can be written as [10]:= (33 — 2nf)ln() (1.5)where Q2 is the absolute value of the momentum transfer squared, flf is the number ofquark flavors involved in the interaction and A represents the energy scale, thought toChapter 1. Introduction 7be in the range of 50 to 500 MeV’. It is clear that as —* oo the coupling constantvanishes and thus perturbations in the coupling constant are acceptable. However in thelow energy region (E < 1GeV) the coupling constant is large and perturbation theory isno longer useful. This is why QCD symmetries have to be exploited.1.2.1 SymmetriesThe concept of symmetries is used widely in physics. It is a powerful tool that sometimesallows one to simplify and solve otherwise impossible problems. An entity is said to besymmetric under a given transformation if that entity is unchanged after the transformation has been performed. For example the Minkowski-space dot product is invariantunder a Lorentz transformation.To a given symmetry corresponds a conserved quantity. For example, in classical mechanics translational invariance results in conservation of momentum, and time translation symmetry yields conservation of energy. The concepts of symmetry and conservationalso hold in quantum field theory and this is manifested in the form of Noether’s theorem.Consider a lagrangian density £(5a(), 9,a(x)) and the following transformation:qsa(x)—* q’(x) + Sq(a) (1.6)where ç(x) is the field. The above transformation results in(1.7)where DIL is given by the equation 1.8.Dr = (()s + U(a)S(84)) (1.8)The theory described by £ is said to be invariant ifSS=fd4xDr=0 (1.9)1A is a renormalization group parameter.Chapter 1. Introduction 8where SS is the variation in the action. The above equation holds if= 8,1F (1.10)where F is a differentiable function. In this case, Noether’s theorem states that there areassociated conserved currents given by the following:= (llS —F) (1.11)where(1.12)Using equations 1.8 and 1.10 it can easily be shown that 8,1J’ vanishes. Therefore, Jis the conserved current.1.2.2 Spontaneous Symmetry BreakingThe best way to get an understanding of spontaneous symmetry breaking (SSB) is via anexample. A typical example is that of magnetic domains. The hamiltonian for a systemhaving spins S, is given by the following:(1.13)z,3It is clear that the above hamiltonian is symmetric under rotations and that the groundstate of the system occurs when all of the spins are aligned. Invariance of H underrotations implies that there exists an infinite number of ground states related to eachother by a rotation. However each of those states are not rotationally invariant; and thephysical ground state was chosen by some initial condition or interaction with the restof the universe. This is an example of SSB; the original hamiltonian displayed rotationalsymmetry but the ground state does not. The implications of SSB were studied byGoldstone, who suggested that massless particles (Goldstone bosons) appear when aChapter 1. Introduction 9continuous symmetry is spontaneously broken. In the case of the magnetic domainsexample, these are called spin waves. This is when the spins in each domain vary in awave like configuration with wave length A. As A —* co a rotation of all the spins in thesystem is performed; since the system has rotational symmetry this does not require anyenergy and for large A, E [12]. Here c is the speed of light. This corresponds to amassless particle as predicted by Goldstones’s theorem. At this point a valid questionis whether the Goldstone bosons seen in nature are massless. The answer is no; oftenthe original lagrangian does not have complete symmetry. In other words, there is asmall part that explicitly breaks the symmetry so that it is an approximate one. Thisphenomenon causes the Goldstone modes to acquire mass.1.2.3 Chiral SymmetryConsider the QCD lagrangian for the light quarks (ie: u, d, s) [11].£QCD = — iA,jq + Mq (1.14)where A is the gluon field, q is the column vector consisting of u, d and s, and M is a3 x 3 diagonal matrix consisting of the masses of the three quarks. Now consider thelimiting case of zero quark masses and define the following:rL,R = (1 +7) (1.15)qL = FLq (1.16)qR = 1’Rq (1.17)where the subscripts R, L correspond to the right and left handed quarks and projectionoperators. Using the above form for PL, R it is clear that the quark field, q can bewritten as q = qj + q. Thus in the limit of zero quark masses in equation 1.14 theright and the left handed quarks are decoupled; in other words there is a symmetry ofChapter 1. Introduction 10handedness. In the limit of zero quark masses the theory described by 1.14 exhibits chiralsymmetry 2•According to Noether’s theorem there are 8 conserved axial vector and 8 conservedvector currents. Chiral symmetry also indicates that there are many different possiblecombinations of left and right handed quarks of equal energy that form the ground stateof the system. In this case one would expect to observe particle multiplets (particles ofsame mass but opposite parity), however this does not appear in nature. The protondoes not have a partner of the same mass and opposite parity; this indicates that chiralsymmetry is spontaneously broken. Since SSB occurs there must exist Goldstone bosonsand these are (ir, K, ii). Clearly all of the Goldstone modes mentioned have mass. So, isthe chiral symmetry argument incorrect? Recall that 1.14 was chirally symmetric in thelimit of zero quark masses but in reality the nonzero quark masses explicitly break thissymmetry and as a result the Goldstone modes acquire mass.At low energies the constraints imposed by chiral symmetry are employed in termsof an effective theory. In the effective lagrangian, £eff, the concepts of chiral symmetryparity, unitarity and all other symmetries of the original lagrangian are manifest. Theexplicit symmetry breaking terms arising from the light quark masses are then treated ina perturbative fashion; this is the framework of chiral perturbation theory (CHFT).3 Inthe effective theory chiral symmetry is spontaneously broken and the Goldstone bosonsin the form of pions appear. In the framework of the effective lagrangian and CHPT theS wave isospin zero scattering length for (ir ir) scattering to leading lowest order is givenby equation 1.18 [11]:ao32F2 (1.18)2 is invariant under qj —+ Fq and q — FRqR.3The quark mass expansion is not the ordinary Taylor expansion. It also includes nonanalytic terms[11].Chapter 1. Introduction 11where m is the pion mass and F. is the pion decay constant. Since colliding pion beamsand meson targets do not exist one has to use reactions like ir + N —f irirN to obtain thisinformation. This is a major goal of the (ir, 2ir) program. Using this information, one canperform a good test of CHPT and the low energy effective theory of strong interactions.1.2.4 The irN sigma termThe o- term is a measure of the explicit breaking of chiral symmetry in the QCD lagrangian, and it is defined as [11]:(1.19)2mwhere p > is the single proton state, m is the proton mass and M = (m,. + md). Inorder to understand how this quantity is related to the irN scattering amplitudes, define[11]= 0,t = 2m) (1.20)where D is the irN scattering amplitude without the Born term, v = (s— u)/4m, and.s, t, u are the usual Mandelstam variables. This unphysical point (ie: choice of v andt) is called the Chang-Dashen point. The relation between E and o is a complex oneand will not be discussed here; it suffices to say that these two parameters are related atthe Chang-Dashen point via CHPT. Using the baryon mass spectrum the value of o hasbeen calculated to be [11]35+5MeV= .—y(1.21)where the variable y is given by= 2 <psp> (1.22)<pIu + ddp>In other words y determines the strange quark content of the proton. Work done byGasser, Leutwyler and Sainio has determined the value of D to be 60 MeV; this indicatesChapter 1. Introduction 12that a- = 45 MeV, thus making y 0.2 [11].The rN scattering amplitudes measured with CHAOS will be used to calculate y andtest yet another prediction of CHPT.Chapter 2A Brief Description of CHAOSThe CHAOS physics program was discussed in the last chapter. In this chapter, abrief description of the detector will be provided and some of the technical details will bediscussed. The CHAOS detector consists of a cylindrical dipole magnet, a solid, cryogenic,or polarized target located at the center, four cylindrical wire chambers (WC1, WC2,WC3, WC4) for particle tracking, and an array of scintillators and lead glass Cerenkovcounters. This is shown in figure 2.2.The design of the spectrometer was primarily driven by the physical constraints imposed by small cross sections, large backgrounds and the need to resolve nuclear finalstates.’ These factors combined require the momentum resolution of the detector to be(IXP/P <1%), and the incident beam rate capability 5 MHz.Since the majority of the reactions to be studied have small cross sections, it is crucialto maximize the angular coverage of the detector. The existence of large backgroundsnecessitates coincidence mode operation and the ability to perform fast hardware rejectionof unwanted events. These two factors are clearly seen in the following examples. Thez.±p reaction requires the use of a polarized target; however since liquid hydrogen cannot be polarized, one is forced to use molecules which contain other nuclei such as carbonand oxygen. This leads to high background in addition to that caused by the interactionof the pions with the target cryostat. All of the backgrounds mentioned can virtually beeliminated if the recoil proton is detected in coincidence with the scattered pion. In the‘Some of the proposed measurements are experiments whose goal is to study nuclear structure.13Chapter 2. A Brief Description of CHAOS 14Figure 2.2: Figure showing the CHAOS spectrometer. The corner post and the top poletip have been removed to allow for a better view. For the same reason, a quadrant of thedetectors is cutaway.Chapter 2. A Brief Description of CHAOS 15case of the (ir, 2ir) reaction a large source of background is elastic rp scattering. As aresult the detector must have the ability to perform hardware rejection of these events.All of the criteria mentioned have put constraints on the design of CHAOS.2.1 Monte CarloExtensive simulations using the CERN Monte Carlo program GEANT were done prior toconstruction of CHAOS. These studies indicated the best design for the various detectorsin the spectrometer given the physics constraints. Simulations provided information onchamber radii for optimum momentum resolution. The resolution was also studied fordifferent chamber materials. For example, figure 2.3 shows the momentum resolution asa function of the third wire chamber radius. GEANT simulations also aided in the designof the scintillator-Cerenkov counter arrays. Monte Carlo studies were done in order tostudy the interaction of the incoming pion beam with elements inside the spectrometer;pion decay inside CHAOS was also studied in detail. These two processes are of crucialimportance since they present a source of background.The first phase of simulations are now complete and the second phase has begun. Thisstage deals with the physics aspects. Simulations are required to obtain the effective solidangle for the spectrometer and assess the feasibility of future experiments given the designof CHAOS.2.2 The Magnet & Polarized TargetThe CHAOS physics program does not require 471- solid angle coverage, and the knowledgeof the incident beam is crucial during reconstruction; thus a cylindrical geometry orientedtransverse to the beam is ideal. In addition, large angular coverage and good momentumresolution at all angles rules out longitudinal magnetic field direction. Perhaps the mostChapter 2. A Brief Description of CHAOS 161 0op/p vs. WC3 radius from GEANT simulations100 200 300 400 500 600WC3 Radius (mm)Figure 2.3: Results of GEANT simulations are shown. This simulations were done fordetectors in helium surroundings.important factor in using the current magnet for CHAOS was cost. The magnet wasbuilt by upgrading an existing one. The CHAOS dipole magnet is capable of producingfields up to 1.6 T, and the field map for 0.95 T central field setting is shown in 2.4. Abore hole along the symmetry axis accommodates the cryogenic or polarized target. Themagnet must be capable of producing a uniform field up to and including the radius ofthe third wire chamber. This is important since in a uniform field the momentum of acharged particle can be obtained analytically using three points on its trajectory. Largeamounts of iron are required in order to reduce the fringe field which would otherwisecause difficulties with the operation of the photomultiplier tubes in the vicinity. Themagnet must be accessible and must have the ability to translate and rotate so that theChapter 2. A Brief Description of CHAOS 17-I Magnetic Field Profile10- Field Value 1.0o io 20 30 40 50 60 70 80 90 100 110Radius (cm)Figure 2.4: The CHAOS field map for 0.95 T central field setting is shown. The solid lineshows the field value as a function of the distance from the center of the spectrometer,and the crosses denote the field uniformity.incident beam hits the target located at the center.A major limitation placed on the polarized target is that it must fit through the borehole along the axis of the magnet. Since polarization requires an extremely uniform field,the target must be polarized outside of CHAOS and then lowered inside the spectrometer.The CHAOS field will then be used to operate it in frozen spin mode. The target ispresently in the construction stage.Chapter 2. A Brief Description of CHAOS 182.3 Tracking DetectorsThe trajectory of the charged particles inside the spectrometer is measured with fourindependent multiwire chambers. The major constraint imposed on the design of thechambers stems from the need for good momentum resolution. This means that thechambers must deliver good spatial resolution. To reduce the contribution of multiplescattering to the momentum resolution, they must also be thin and have low mass.Thus, low density materials must be used in the construction, and obstructions such assupporting posts must be avoided. Small cross sections require that CHAOS be capableof operating at an incident beam flux of up to 5 MHz. This requires that at least twoof the four chambers be able to operate at high rates. This is because two points on theincoming beam trajectory are needed for reconstruction purposes. As a result, the twoinner chambers are high rate proportional chambers. In order to perform fast hardwarerejection of unwanted events, at least three points are needed on the trajectory of anoutgoing particle. Since only two points are required for the incident beam track, a driftchamber (deadened in the region of entrance and exit of the beam) is a suitable choicefor the third CHAOS chamber. Note that this chamber must also be instrumented witha proportional chamber readout system to ensure the fast transfer of data between thechamber and the trigger electronics. Although a proportional chamber would also be asuitable candidate for the third chamber, the cost of instrumenting the device at such alarge radius is far too high.In principle, the information obtained from the three inner chambers is enough fortrack reconstruction. However, chamber inefficiencies may then cause the loss of manygood tracks, since two points are not enough for track reconstruction. This is overcome byintroduction of a vector drift chamber (jet chamber) as the outermost tracking detectorin CHAOS. Since this is the last tracking device, multiple scattering associated with aChapter 2. A Brief Description of CHAOS 19large volume is no longer a major concern. The large radius and good spatial resolutionof this chamber help constrain particle trajectories and thus improve the momentumresolution. This chamber will provide a vector along the direction of the track, which isessential for sorting ambiguous tracks.Three of the four chambers also provide information on the vertical coordinate of thetrack, which is useful in containing the events to the target region and providing a smallout-of-plane correction for the measured momentum.2.4 Particle Identification & MultiplicityAs mentioned before, large backgrounds are a major concern in nearly all CHAOS experiments and some of these backgrounds can be removed using coincidence detection; thusmultiplicity information (ie: the number of tracks in a given event) is essential. Thereis also a need for particle identification, primarily pions, protons, and electrons. Thisis demonstrated in the following example. Recall that some of the reactions studied inthe (ir, 2ir) program have neutral pion final states. The ir0 will decay almost immediately after its creation and the photons produced can cause pair production in the targetmaterial. The electron positron pair imitates a two pion final state. Hence, it is crucialto be able to resolve pions from electrons. The multiplicity and particle identificationinformation along with the track momentum can be used to perform offline rejection ofunwanted events. This information is obtained by using the array of scintillators andlead glass counters. These counter telescopes are referred to as the Chaos Fast Trigger(CFT) counters.Chapter 2. A Brief Description of CHAOS 202.5 Trigger & Readout SystemsAs stated before it is of great importance to perform fast hardware rejections. Thiscan be done in two stages; some of the unwanted events can be eliminated using onlythe multiplicity information from the CFT counters, where as the remainder must beeliminated using information obtained from the chambers. This requires the design oftwo levels of trigger for CHAOS. These will be referred to as the first and the secondlevel trigger systems.The readout system must be capable of fast data transfer between the detectors, thefirst and the second level triggers. For a given event, it must also be able to zero suppresschannels which do not carry any information, since there are 4500 channels in total. Aproportional chamber operating system (PCOS) is utilized for the first three chambers.The CFT counters are instrumented with both analog to digital converters (ADO’s) andtime to digital converters (TDC’s). It is clear that all drift chambers must be equippedwith TDC’s; all of the chambers are also equipped with ADC’s in order to obtain eithervertical coordinate information or for use in resolving the left-right ambiguities in W03.Chapter 3Wire Chambers 1 & 2In this chapter, the two inner proportional chambers used in CHAOS are discussed andsome recent commissioning results are presented. Before starting the discussion, it isappropriate to outline some basic concepts regarding the operation of multiwire proportional chambers (MWPC).3.1 Basic Operating PrinciplesThe first MWPC was built by Georges Charpak and his collaborators in 1967-68 [14].This marked one of the most important achievements in experimental particle physics.Today, multiwire proportional chambers are used in virtually all particle physics experiments. A charged particle traveffing in a gaseous medium will interact with the gas viaelectromagnetic interactions. The electromagnetic signature of the particle is exploitedin gaseous particle detectors.A charged particle traversing a gas will cause it to ionize, producing electrons andions. Consider a thin metal wire (in the gas) surrounded by an outer conducting cylinder;a potential difference applied between these two conductors will result in an electric field.If the polarity of the two electrodes is chosen such that the wire is at a positive potentialwith respect to the outer cylinder, the electrons produced by the ionization will drifttowards the anode wire, and the ions will drift towards the outer cylindrical cathode.Close to the wire (at distances on the order of several times the radius of the wire), theelectric field will be strong enough to cause avalanche multiplication of electrons. As a21Chapter 3. Wire Chambers 1 & 2 22result a pulse is observed on the wire; at the same time, an induced pulse of oppositecharge is produced on the surrounding cylinder. A multiwire proportional chamber hassimilar principles of operation but uses more than one wire. The wire spacing in thesechambers is usually on the order of a few millimeters, which allows for operation at highrates.3.2 Design & ConstructionAs mentioned before, low density materials must be used in the construction of CHAOSchambers. Various Monte Carlo studies using the simulation program GEANT wereperformed to obtain the momentum resolution for different chamber materials; thesestudies were also used to obtain the optimum chamber radii. In order to improve themomentum resolution it is necessary to obtain vertical as well as horizontal coordinateinformation; the two inner proportional chambers are designed to perform this task.WC1 and WC2 are located at radii of 114.59 and 229.18 mm respectively, and eachhas a (half) gap of 2 mm. WC1 consists of 720 anode wires with a pitch (separation) of 1mm, and WC2 also consists of 720 anode wires but has a pitch of 2 mm. This was doneso that each chamber has an angular pitch of 0.5°. The chambers are each instrumentedwith 360 cathode strips inclined at 30 degrees with respect to the anodes.Both chambers were built from two concentric cylinders of 1 mm thick rohacell heldin place by GlO rings.1 The inner cylinder consists of the anode wires and the innercathode wall. Because of the small wire spacing, the anodes were directly soldered tocylindrical circuit boards which provide the high voltage and carry the signals to thepreamplifier boards. The inner cathode wall was constructed by gluing a layer of 25 urnaluminized mylar, coated with graphite paint, on a 1 mm sheet of Rohacell. A layer of 121Rohacell is a low density material (p = 50 mg/cm3)similar to styrofoam.Chapter 3. Wire Chambers 1 & 2 23pm kapton forms the other side of this wall. The anode wires are 12 ,im diameter goldplated tungsten, and the wire tension of 10 grams is supported by the Rohacell frame.The outer cylinder was also constructed from 1 mm thick Rohacell supported by GlOrings. In this case, the Rohacell was sandwiched between layers of 12 um kapton and 251ttm Electro-Coated Nickel (ECN) foil, the latter one of which forms the cathode strips.2The strip pattern was etched on nickel plated kapton and glued onto the Rohacell. Thecathode strips were connected to the readout circuit boards using gold plated spring clips.The inner cylinder was then placed inside the outer one, and the gap was sealed using arubber tube. Two layers of 251Lm double sided aluminized mylar were used to constructthe flushing gas windows.The anode wires are instrumented with 16 channel preamplifiers, LeCroy 2735 PCamplifier/discriminator cards, and the LeCroy Proportional chamber Operating System(PCOS III). The cathode strips are connected to 8 channel preamplifiers, inverter/amplifiercards, and FASTBUS Analog to Digital Converters (ADC’s). The inverter circuit wasneeded in order to provide the ADC’s with a negative pulse. The gas used in both detectors is 80% CF4 and 20% isobutane. The performance of WC1 and WC2 along withsome results are discussed in the next section.3.3 PerformanceIn June 1993, the operation and performance of these two chambers were studied. Efficiencies as a function of voltage were studied to obtain the proper operating voltage.The efficiency of the chambers was calculated by analysing straight through beam events,and it is given by the following relation:i=2 N2=s-.. (3.23)L.i=O “:2The ECN foil is 25 .tm kapton covered with 1200 A copper and 300 A nickel.Chapter 3. Wire Chambers I & 2 24where N2 is the number of times i wires were activated. For a perfectly efficient chamber,two or more wires are activated in each event. Figure 3.5 shows the efficiency of eachchamber as a function of the operating voltage. The WC1 voltage was chosen to bea conservative value of 2450 V, which resulted in lower chamber efficiency and smallercathode strip pulse heights. WC2 was operated at 2050 volts, allowing for maximumefficiency. Rate studies were also performed at the nominal operating voltages. Figure3.6 shows the efficiency as a function of incident beam rate.The chamber efficiency will drop when the maximum operating rate is exceeded. Thisis due to the space charge effect. This phenomenon takes place when the number of ionsproduced around the wire becomes so large that it causes distortions in the electric field;consequently the chamber efficiency will decrease. Figure 3.7 shows the current drawnby each chamber as a function of the rate; the linear relation between the current andthe rate indicates that discharge does not occur at high incident beam rates.For a proportional counter, one can predict the optimum resolution the device iscapable of providing; this quantity is predetermined by the wire spacing. The positionof the hit in the chamber is quantized in terms of the wire closest to the track. In otherwords, no drift time information is used to obtain the coordinate of the hit. Let the wirespacing in a proportional chamber be 1. Now consider a track passing within a distanceof 1/2 on either side of the wire (see figure 3.8); the position of this hit in the chamberis going to be given as the location of the nearest wire. This is governed with a uniformprobability distribution given byf() (3.24)Using the standard definition of the variance, the resolution of the chamber is given by=(3.25)Thus a chamber with a pitch of 1 mm will have an optimum resolution of 288 ILm. TheChapter 3. Wire Chambers 1 & 2 25Plateau curve for WC110080C)I I I I I I I I2100 2200 2300 2400 2500 2600Voltage (V)Plateau curve for WC210090C.)a 80C.)706050ii 1li I ii i,IIiii I.iiil. ii1750 1800 1850 1900 1950 2000 2050 2100 2150Voltage (V)Figure 3.5: Plateau curves for WC1 and WC2 are shown. The data were acquired at arate of < 50 kllz, for 225 MeV/c ir.Chapter 3. Wire Chambers 1 & 2 26Efficiency vs rate for WC110096-92-80 I a I I I I1 2 3 4 5Rate (MHz)Efficiency vs rate for WC2100 •IIIII•IIIII•IIIII..96--80 - I I I a1 2 3 4 5Rate (MHz)Figure 3.6: The efficiency of WC1 and WC2 as a function of the incident beam rate isshown for operating voltages of 2450 V for WC1 and 2050 V for WC2, acquired with 225MeV/c ir.Chapter 3. Wire Chambers 1 & 2 27Current vs incident beam rate for WC112345Rate (MHz)Current vs incident beam rate for WC245004000 -— 350030002500 -Ci20001500 -1000 I I I1 2 3 4 5Rate (MHz)Figure 3.7: The current drawn by WC1 and WC2 versus beam rate is shown. The highvoltage and beam conditions are the same as for figure 3.6. The solid curves are straightline fits.Chapter 3. Wire Chambers 1 & 2 28Anodeso 0 0 0-t11/2 1/2Figure 3.8: Figure showing tracks in a proportional counter.WC2 angular residuals2000I15000210005000 I—1.0—0.5 0.0 0.5 1.0Angular deviation (deg.)Figure 3.9: Figure showing angular residuals for WC2.Chapter 3. Wire Chambers 1 t 2 29resolution of WC1 and WC2 is calculated by analysing straight tracks at zero magneticfield. All four chamber hits in WC1 and WC2 (two incoming and two outgoing) arefit to a straight line, and the intersection of the line with circles corresponding to thetwo chambers is obtained. The intersection points are the calculated positions of thehits. The angular deviation between the actual and calculated positions represents thechamber resolution. Figure 3.9 shows the angular resolution of WC2. For cases in whicha cluster containing an even number of wires has been activated, PCOS will register theposition of the hit to be half way between the two most central wires in the cluster. Thisis referred to as cluster mode operation, in which the effective angular and spatial pitchis half of the physical one. In figure 3.9, counts which correspond to angular deviations ofmore than ±0.125° occur when only one wire fired, and deviations smaller than half of theangular pitch (0.25°) are due to cluster mode operation. Counts appearing at deviationsgreater than 0.25° constitute less than 2% of the total number of events considered andare due to pion decay. Both the singles and the cluster mode residuals are consistentwith the angular spacing which is 0.5° for singles and 0.25° for cluster mode. In terms ofspatial resolution the chamber provides 577 pm for singles and 289 pm for cluster modeoperation.In-plane position reconstruction is a very easy task using a proportional chamber.PCOS will provide a given wire number for each hit; since the radius of the wire planeis known one can associate an angular coordinate with each wire. From this point itis trivial to work out the position of the hit in the Cartesian coordinate system. Anexcellent test of the performance of the chambers would be to perform momentum calculations using only the information from the two inner chambers. This can be most easilyaccomplished by considering events for which the beam passes through the spectrometerwithout interacting, with nonzero CHAOS magnetic field. One can then use three out ofthe four hits in the proportional chambers to reconstruct the beam momentum. This isChapter 3. Wire Chambers 1 & 2 30possible since, given a uniform magnetic field, the trajectory of a charged particle in thefield is a circle, which is completely defined by three points.Let the coordinates of three points on a given circle be denoted by: (x1,y),(x2,y),(xe, y). It is clear that the following equations hold:(x— a)2 + (yi — = R2 (3.26)(a2— a)2 + (y2 — = R2 (3.27)(x — a)2 + (y — b)2 = (3.28)where a and b are the coordinates of the center and 1? is the radius of the circle. Solvingthe above three equations simultaneously, the center of the circle is given in terms of thefollowing parameters:= ( + y) (i = 1,2,3) (3.29)= (R — R1) (i = 1,2) (3.30)= (x2 — x1) (i = 1,2) (3.31)=(y— yi+i) (i = 1,2) (3.32)(3.33)The coordinate of the center is given by- tXy1I R-tXy2I R334a—2(iyIx—ixiJ.y2)b =_-—aLx1] (3.35)The radius of the circle, R, is then obtained by using the calculated values of a andb along with one of the original three equations. The momentum of a charged particleChapter 3. Wire Chambers 1 & 2 31Reconstructed momentum using WCI and WC22500-= 229.5 MeV/c2000- o• = 4.0 MeV/c1500-0C.) 1000 -500 -0- I,.-160 180 200 220 240 260 280 300Momentum (MeV/c)Figure 3.10: Figure showing calculated beam momentum using WC1 and WC2.travelling in a uniform magnetic field is given byF = qBR (3.36)where q is the charge and B is the magnitude of the field. With B in Tesla and R inmm, the momentum for a particle of unit charge in MeV/c is given byF = 0.29979RB (3.37)Figure 3.10 shows the reconstructed momentum for a 230 MeV/c pion beam that exitsthe spectrometer without interacting. The agreement between the channel momentumand the reconstructed momentum is good. Using three out of the four hits recorded bythese two chambers only, the momentum resolution is 1.8%.The information obtained from WC1 and WC2 also allows one to reconstruct theincoming beam trajectory knowing its momentum and polarity along with the directionof the magnetic field. This is crucial for the reconstruction of the interaction vertex andChapter 3. Wire Chambers 1 & 2 32to the projection of the beam on the target. The procedure is discussed in the followingparagraph.Let the coordinates of the two incoming beam hits in WC1 and WC2 be denotedby (a1,y) and (x2,y). Furthermore, let P and q represent the beam momentum andpolarity respectively. The beam momentum is known to an accuracy which depends onthe slit settings used at the dispersed midplane focus of the channel. For all data acquiredthus far with CHAOS, the slits were closed such that < 0.5%.Given the field magnitude, the radius of curvature is obtained from equation 3.37.Since the two hits lie on a circle, the following equations hold:(x1— a)2 + (y — b)2 = R2 (3.38)(x2— a)2 + (y2 — = R2 (3.39)Again R is the radius of curvature and (a,b) is the center of the circle. Solving the aboveequations yields two possible solutions in terms of the following parameters:== Y2Y1ix2 + zy2a =2ZSya2—RThe solutions are given bya = z1 ++ /a2722+ 72) (3.40)1+7b= Yi + a + 7(ai — a) (3.41)3Uniform field assumption is once again used.Chapter 3. Wire Chambers 1 & 2 337000 —600050004000500020000——100 —50 0 50 100Distance (mm)Figure 3.11: A typical target projection histogram in the x-y plane is shown.Clearly there are two possible solutions; the correct one may be chosen knowing thebeam polarity and the direction of the spectrometer magnetic field. Let e denote theproduct of the field and the beam polarity. Rotating the solutions so that the angle ofthe hit in WC2 is zero (in the CHAOS coordinate system) results in one of the solutionshaving a positive center y coordinate and the other a negative one. In the case of theincoming beam, the correct solution is the one whose rotated center y coordinate has thesame sign as e . The beam projection onto the target is defined as the intersection ofthis circle and a line of a given slope (usually chosen to be perpendicular to the incomingbeam) through the origin, where the center of the target is situated.The target projection is of crucial importance. In an analysing power measurement,the beam spot on the target must not change between the two target polarizations sinceit can introduce fictitious asymmetries. A typical target projection spectrum is shownin figure 3.11. In this graph the distance from the intersection point to the center ofCHAOS is plotted, which corresponds to the horizontal profile of the incident beam on4This is opposite for the outgoing beam..11’J.Chapter 3. Wire Chambers 1 & 2 34100008000C’) 60000L) 400020000Figure 3.12: The number of activated cathode strips in WC2 for straight through beamis shown.a planar target oriented perpendicular to the beam.The vertical position of the hit is found by calculating the intersection of the chargecentroid of the cathode strips with the activated anode wire. Consider a track in whichn strips are associated with a given hit. The charge centroid is given byN qN (3.42)q2Here, q8 and N2 are the ADC value and the strip number for the ith strip respectively; Nrepresents the strip number corresponding to the charge centroid. Figure 3.12 shows ahistogram of the number of activated strips per event in WC2 for straight through beam.5 10 15Number of activated stripsChapter 3. Wire Chambers 1 & 2 35The vertical position of the track is obtained from the following equation:— 8(N)— 8hjt Rir 3 43Z— l8Otan(300)Where 8(N) is defined as the horizontal angle strip N has at z=0, and 8hjt is the angleof the associated PCOS hit from the anodes. All angles are in degrees. in addition, R isthe chamber radius. The vertical coordinate of the incoming beam track is used to obtainthe vertical projection of the beam onto the target. This is calculated by performing astraight line fit on the z-coordinate versus the distance in the x-y plane of the hit fromthe line defined for the horizontal target projection. The intercept obtained from the fitis the vertical coordinate of the projection of the beam on the target. Figure 3.13 showstypical spectra for high ( 1.8 MHz) and low ( 50 kllz) beam rates. This graph seemsto indicate that the beam profile changes with the rate; however, this is not the case.The broadening of the profile is due to the width of the ADO gate. Because of long drifttimes in W04, the ADO gate width had to be set to 500 ns. At high beam rates, thisallows for more than one incident pion to fall within the same ADO gate. As a result, theADO value obtained from the WOl and WC2 cathode strips corresponds to more thanone incoming beam particle. This is not a problem for the other chambers since they aredeadened at the entrance and exit of the beam. The wide gate causes an increase in thewidth of the spectrum, but the problem can be solved by providing a separate, shorterADO gate for the WC1 and WC2 cathode strips.4-I-)0.1-)0QChapter 3. Wire Chambers 1 & 2 361008060402020000010005000—100 —50 0 50 100Vertical target projection (mm)Figure 3.13: Vertical target projections for beam rates of < 50 kllz and 1.8 MHz areshown.Chapter 4Wire Chamber 3As stated previously, design considerations for CHAOS require the existence of a thirdtracking detector. This led to the design and construction of the inner CHAOS driftchamber, WC3, which is required to operate in a region of high magnetic field (ie: B1 T). Basic operating principles of drift chambers are discussed in the first section of thischapter. A brief description of the chamber and performance results are presented in theremaining.4.1 Basic Operating PrinciplesThe operation of drift chambers is similar to that of multiwire proportional chambers,described earlier. In this case, however, the drift time of the electrons from the ionizationregion to the anode wire is used to obtain position information. Electrons produced fromthe ionization drift towards the anode wire with an inverse velocity of approximately20 ns/mm, where avalanche multiplication occurs. If the electrons are liberated by thecharged particle at a time t0, and a signal from the wire is received at a later time, t, thespatial coordinate of the track with respect to the wire is given by the following:= Lv (4.44)where v is the velocity of the electrons in the drift space. Clearly the most convenientcase is that of a constant v, in which case, the space-time relation would be given by37Chapter 4. Wire Chamber 3 38= (t — to)v (4.45)In the absence of a magnetic field, the linearity of the space-time relation dependsmainly on the electric field uniformity in the drift region. In practice the time to isdetermined by placing a scintillation counter in front of the chamber.Multiwire drift chambers can not be constructed in the same way as proportionalcounters. In particular, adjacent anode wires are usually not used. This is because thespace-time relation becomes nonlinear in the low electric field region between the twoanodes. The problem is overcome by placing thick field shaping cathode wires betweensuccessive anodes.Drift chambers are less expensive to build and instrument than multiwire proportionalchambers; furthermore, they provide more accurate spatial information. However, somedisadvantages exist. The spacing between the sense wires in a drift chamber is muchlarger than that of a MWPC. Typical drift times are on the order of hundreds of nanoseconds; hence a drift chamber is not capable of operating at high rates. In a driftchamber, the coordinate information is obtained solely from the drift time and the anodewire location. As such, a particle passing at the same distance on either side of an anodewill result in identical drift times, making the location of the track ambiguous (see figure4.14). This is referred to as the left-right ambiguity problem and can be resolved invarious ways depending on the chamber geometry and environment.4.2 Description of WC3WC3 is a single plane cylindrical drift chamber located at a radius of 343.77 mm. Ithas a rectangular cell geometry consisting of alternating anodes and cathodes separatedby 7.5 mm. The chamber also uses alternating high voltage and signal cathode stripsChapter 4. Wire Chamber 3 39Left Right0 0 0Cathode Anode Cathode/TracksN CathodesFigure 4.14: Figure showing the left-right ambiguity in a drift chamber. Drift times tothe central anode are identical for both tracks.to achieve a more uniform electric field and resolve the left right ambiguity problem(see figure 4.15). WC3 contains a total of 144 anodes (angular pitch of 2.5°) and 576cathode signal strips. The half gap of the chamber is 3.75 mm and the vertical activearea is 90 mm. The design of WC3 is otherwise similar to that of WC1 and WC2. Twoconcentric cylinders of 1 mm thick rohacell placed in GlO rings support the wire tension.The anode and cathode wires are strung at tensions of 80 and 120 grams, respectively;they are mounted using crimp pins on the GlO ring which forms the frame of the innercylinder. Both the inner and the outer rohacell frames are sandwiched between layersof 12 m kapton and 25 m ECN foil. For each of the cylinders, the latter forms theChapter 4. Wire Chamber 3 40WC3 cell structure4.0 mm 3.0 mm, ( )Signal Signal H.V. Signal SignalI 0 • — 7.5 mm— 0Anode Cathode AnodeSignal Signal H.V. Signal Signal2.0 mm 1.0 mmFigure 4.15: Figure showing the WC3 cell structure. Thickness of the strips and wireshas been exaggerated in this figure for clarity.cathode strips, and the former prevents gas leakage through the rohacell. In addition,two layers of 25 pm double sided aluminized mylar form the flushing gas windows. Thecathode strip pattern was photo-chemically etched on 25 pm nickel plated kapton. Theanode and the cathode wires are 50 pm and 100 pm gold plated tungsten, respectively.Both the anodes and the readout strips are instrumented with 8-channel preamplifiers. As in the case of WC1 and WC2, the cathodes are also equipped with inverterpostamplifier electronics and the anodes with LeCroy 2735DC amplifier/discriminatorcards. The anode signal is split and fed to the LeCroy 4290 drift chamber chamber system as well as PCOS III, which is needed in order to provide the second level triggerwith the necessary information. Only the anode wire number and not the drift time information is used to form the second level trigger decision. The sections of the chamberlocated at the entrance and exit of the beam are deadened in groups of four adjacentcells by simply removing the anode bias to that group. This prevents damage caused bythe large incident flux. In the absence of a magnetic field, the drift electron trajectorieswould be straight. Consequently, one would be able to employ a variety of techniques toChapter 4. Wire Chamber 3 41resolve the left-right ambiguity problem, for example, using groups of two anodes separated by a small distance. However, since operation in a high field region is required,this approach is not practical [16]. Because the drift electron trajectories curve in thepresence of the field, the avalanche can occur in front of or behind the anode doublet. Insuch cases, left and right tracks are not resolved. This led the CHAOS group to develop anew method of resolving the left-right ambiguity [16]. It uses two pairs of readout stripson opposite sides of the anode to distinguish left from right. Figure 4.16 shows the driftelectron trajectories as calculated by Garfield.1 In this figure the difference in the pulseheights between the solid strips in a given cell is used to resolve the left-right ambiguity.In each case the upper right strip has a larger induced pulse height than the lower leftone. Figure 4.17(a) shows the normalized difference between diagonally opposed stripsnumbered 2 and 3 as shown in figure 4.16. The normalized difference between any twostrips, a and b, is defined as— Pb (4.46)Fa+Fbwhere Fa and Pb are the ADC values for strips a and b, respectively. Note that centroidsof the two peaks are not symmetric about zero. This is due to an offset resulting fromdifferent preamplifier, inverter and cathode strip gains, the latter of which is caused byimperfections in the positioning of the strips in the chamber. Graph 4.17(b) shows thisdifference as a function of the drift time.Tracks passing to the left and to the right of the wire are well resolved. Since theTDC’s were operated in common stop mode, increasing drift time is to the left in figure4.17(b).‘Garfield is a drift chamber simulation program [15]. It calculates various quantities such as electricfield and the drift electron trajectories for a given cell geometry. Figure from reference[16].Chapter 4. Wire Chamber 3 42Figure 4.16: Drift electron trajectories for tracks with various angles of incidence, 8, areshown. The solid strips correspond to those used to resolve the left-right ambiguity. Alldimensions shown are in cm. All cases are for B=1 T except the upper left figure whichis at B=O. A and C denote the anode and cathode wires respectively. The axes representthe cell dimensions used in the simulation. For magnetic fields opposite in polarity tothat shown, the unshaded strips provide the best left-right resolution. A1.0 1.0:1:i!400:1:.i0 i.o.Chapter 4. Wire Chamber 3 43.1Right Left2500•2000U)001000500 (a)0—200 —100 0 100 200 DINormalized difference.______________LeftU)C)200.U)U) ...-.. .0.Z-IQO.(b)Right—200.200 250 300 350 400 450 500Time (ne)Figure 4.17: Figure showing the normalized difference between diagonally opposed strips(a). The difference as a function of the drift time is also presented (b). The normalizeddifference scale has been expanded by a factor of 500. Long drift times correspond tosmall TDC values. The data were acquired at a magnetic field setting of 1.2 TChapter 4. Wire Chamber 3 44100 I I I I I I I I I Ia •. . ..-j—.. 8000 Itt I I I I I1900 2000 2100 2200 2300 2400Voltage (v)Figure 4.18: Plateau curve for the WC3 anode bias is shown.4.3 PerformanceThe operating voltage for the chamber was determined by means of a plateau curve asshown in figure 4.18. This was obtained at a rate of < 50 kHz. The operating voltageschosen for WC3 are an anode bias of 2250, a cathode strip bias of —600, and cathodewire bias of —300 volts. Chamber efficiency was computed using the same method as forWC1 and WC2. Typical drift time spectra for zero and nonzero magnetic field are shownin figure 4.19. The gas used in the chamber is a 50-50 mixture of argon and ethane; asmall amount of ethanol bubbled into the gas at 0°C is used as a cleaning agent.In the case of a uniformly distributed beam, a rough idea of the linearity of the spacetime relation can be obtained from the shape of the drift time spectra. The vertical axesin drift time spectra represent the number of counts, N, in a time bin I.t ; hence theChapter 4. Wire Chamber 3 45Figure 4.19: WC3 drift time spectra along with their integrals (proportional to the driftdistance) for zero and nonzero field settings are shown. Increasing drift time correspondsto smaller TDC channel number (1 ns/channel).counts represent 4J. Furthermore,dN — dN cisdt — ds dt (4.47)where s and t are the drift distance and time respectively. Given a uniform beam distribution, , a constant results in a linear time-distance relation.2 For zero magnetic2The time-distance relation determines the distance from the ionization point to the wire as a functionof the drift time.500400r8 20010005I- 4•0l_ 3100B=12,,,/)\•••100 200300400500 600TDC channel0 100 200 300 400 500 600TDC channelJ..../**..03000250020005000302510201015‘0105-0a100 200 300 400 500 600TDC channel100 200 300 400TDC channel500 600Chapter 4. Wire Chamber 3 46field setting, the drift spectrum is fairly flat, but this is not the case for nonzero magnetic field. This is because the drift electron trajectories curve in the field making thespace-time relation nonlinear. Figure 4.19 shows the integral of the time spectrum forzero magnetic field; the linearity of the time-distance relation is evident. The integral ofthe spectrum for nonzero field suggests a nonlinear time-distance relation. In order toobtain the coordinate of the track, the angle of incidence of the track with respect to thechamber midplane is needed. The process of obtaining the time-distance relation, theincident beam angle, and the coordinate of the hit in the CHAOS coordinate system isdiscussed in section 7.1. WC3 resolution is discussed in chapter 7.Chapter 5Wire Chamber 4The fourth and the outer most CHAOS chamber is a vector drift chamber, WC4, which iscapable of providing both horizontal and vertical coordinate information. The design andconstruction of this chamber along with performance data are discussed in this chapter.5.1 Description & ConstructionWC4 contains fourteen concentric cylindrical planes of wires separated radially by 0.5mm. Eight of the planes are anodes that provide horizontal spatial information, and twoplanes are resistive anode wires that are used to obtain vertical position data. The fourremaining anode wire planes are field shaping (“guard”) wires. The chamber consistsof one hundred cells, each spanning an angular arc of 3.6°. Figure 5.20 shows the cellgeometry. The first (innermost) resistive wire is located at a radius of 617.5 mm, and theradius of the first anode plane is 627.5 mm. To resolve the left-right ambiguity, the anodesin a given cell are alternately staggered by +0.25 mm in the direction perpendicular tothe radial line bisecting the cell. A major concern in the design of this chamber wasmechanical support. Several options were considered, one of which proposed the use of a“chamber box” that would provide support for WC4 as well as the three inner chambers.For repair purposes, this structure had to be breakable in the region between WC2 andWC3. However, it was realized that repairs would still be too difficult to perform, andthe design was abandoned.On each side of the cell there are nine cathode strips kept at a negative potential; these47Chapter 5. Wiie Chamber 4 48Back Wall Upper/lower plate boundry-HV______1< spine0.50ii T5.0I I I I Cathode Stripsii //H IIIIIi 11R II RibI IFront Window >‘ /—HV r612.5Figure 5.20: Diagram showing a single cell of WC4. The letters A, G, and R denoteanode, guard and resistive wires, respectively. All dimension are in mm.Chapter 5. Wire Chamber 4 49strips form the cell boundaries. Two cathode planes common to all cells and also kept ata negative potential form the front and the back walls of the cell. Due to its large radius,the chamber was constructed in eight separate sections. Four of the sections are each36° wide, and the other four each span 54°. The wires are strung and crimped at bothends to plates of Ultem, a rigid insulating material. The wire tension is supported byrohacell-GlO ribs, which also provide the cell boundaries as well as the surfaces on whichthe cathode strips are glued. The ribs are constructed by placing 2 mm thick rohacellwhich was compressed to 1.6 mm in a C shaped GlO frame in which the open part of theC faces the front of the chamber. The cathode strip pattern is photochemically etchedon 25 1um nickel plated kapton and glued on both sides of the rohacell. The shape of eachcell is a trapezoid; hence, to obtain a uniform electric field, the voltage on the cathodestrips at the narrow end of the cell must be less than that at the wide end. This wasaccomplished by means of a chain of 3.02 MQ resistors which dropped the voltage by 55V across successive strips, and then was grounded through a larger resistance.The resistor chain circuit pattern is etched on the GlO frame, and gold plated springclips are used to provide electrical contact between the high voltage circuit and thecathode strips. Various methods of achieving reliable electrical contact were studied.These included the use of conducting epoxy and low temperature solder paste. Neither ofthese two methods provided reliable contact. Conventional soldering was not an option,since high temperatures evaporated the metal from the kapton foil. The spring clipsproved to be the best option since one end could be soldered onto the GlO frame, whilethe other end provided contact to the fragile surface through spring tension.The inner (front) window of the chamber, which also forms one of the cell cathodeplanes, is constructed from 1 mm thick rohacell sandwiched between 25 m kapton and 25um aluminized mylar. The outer window (back wall) of the chamber provides the othercell cathode plane and is constructed from 250 itm thick GlO with one copper-coatedChapter 5. Wire Chamber 4 50side. The copper was nickel plated to protect against corrosion.Both the anode and resistive wires are connected to 8-channel preamplifier cards. Theanode signals are read into a 4290 TDC system and both ends of the resistive wires areinstrumented with FASTBUS ADC’s. As for WC3, cells located at the entrance or exitof the beam were deadened in groups of 2 ribs (3 cells) by removing the rib bias voltagevia a high voltage distribution panel located on top of the spectrometer.Extreme care was taken in the construction process. The rohacell ribs which formthe frame of the chamber are quite fragile and had to be handled with care. Each ofthe eight sections was constructed by gluing the rohacell-GlO ribs into grooves that weremachined into the top Ultem plate. The bottom plate was then glued to the other endof the ribs, which protruded through slots in the bottom plate so that the resistor chainand the high voltage connections were external. In each section, the end cells require aspecially made rib. The cathode strips on the end ribs appear on one side only, and thethickness of these ribs is haff that of others. The back cathode plane was also glued ontoboth the top and bottom plates. Thin GlO spines (1.6 mm) were glued on the outer sideof the back plane behind each rib to provide extra mechanical support. The chamber wasthen strung and the front window was fastened to the Ultem plates by means of screws.The edges of the window were taped to the end ribs with the use of kapton tape. A thinrubber gasket placed between the window and the plates proved to be helpful in makingthe chamber gas tight; however, a layer of electronic grade silicon RTV was also requiredon the outer seams of the window. The anode and resistive wires are 20gm gold platedtungsten and 20 1um Stablohm800, respectively [17]. The guard wires are made of either150 1ttm or 75 im gold plated tungsten. The anode and resistive wire tensions are 50 and10 grams respectively.Chapter 5. Wire Chamber 4 515.2 Charge DivisionThe method of charge division has been successfully used to obtain vertical coordinateinformation in drift chambers [18], [19]. The nominal resolution is 1% of the length ofthe wire. A brief description of the method is as follows. An amount of charge, Q, isinjected at a distance D from the center of a wire of length £ and resistance R (see figure5.21).L-;DI QA BFigure 5.21: Figure illustrating the charge division method.If the collected charge at the two ends of the wire is given by A and B, the distanceD is given by5482(A-j-B)The above is just a naive application of Ohm’s law and is valid if the integration time ismuch greater than the time constant of the wire [20]. This principle was used to obtainthe vertical coordinate of the track in WC4. The choice of wire resistance is crucialin the charge division method. The resistance must be large enough such that thermalnoise is kept low. However, if the wire is also used to obtain drift information, the timeconstant of the wire must be small. The smallest time constant is obtained when theChapter 5. Wire Chamber 4 52wire resistance is equal to the characteristic impedance of the wire, given byR=(5.49)where L and C are the inductance and the capacitance per unit length of the wire. InWC4, the resistive wires were not used to obtain drift time information. Furthermore,the integration times are on the order of 500 us. This is much greater than the time scaleof charge division, which is a function of the length of the wire (order of a few ns). As aresult, only noise considerations dictated the nominal wire resistance.The preamplifiers used must have an input impedance which is much less than theresistance of the wire. The wires used in WC4 are 25 cm long and have a resistanceof 1 K. The input impedance of the preamplifier is 75 1. Various wire materialswere examined in a prototype chamber, and Stablohm800 provided the best resolutionand linearity.5.3 PerformanceThe gas used in this chamber is a 50-50 mixture of argon and ethane; a small amountof ethanol bubbled into the gas at 0°C is used as a cleaning agent. Figure 5.22 shows theplateau curve for the chamber. Since this chamber has several wire planes, the efficiencyof a single wire is calculated using the following method. Consider three wires in a singlecell labelled 1, 2 and 3, where wire 2 is located between 1 and 3. The efficiency of 2 isgiven by= 12.3 (5.50)where 1 . 2 3 represents the number of times all three wires fired and 1 . 3 is the numberof times both 1 and 3 were activated. The efficiency of the anode wires was found to beindependent of the front/back plane voltage. However, the resistive wires were sensitiveChapter 5. Wire Chamber 4 53WC4 plateau curve100a90-80-C)70C.)5040 I4200 4400 4600 4800 5000 5200 5400Rib voltage (V)Figure 5.22: WC4 plateau curve is shown.to this voltage. As a result the back plane setting was chosen to provide maximumresistive wire efficiency without causing the preamplifiers to saturate. The cathode strip(rib) and front/back plane operating voltages are —5200 V and —2300 V respectively.Figure 5.23 shows typical drift time spectra and their integrals for zero and 0.5 Tcentral field settings. The field at WC4 is approximately 20% of the central value. Thetotal width of the spectrum is 400 ns. This corresponds to the average width of the cellwhich is 20 mm; hence a rough estimate of the time distance-relation is 0.05 . Theintegrals of the drift spectra show the linearity of the time-distance relation for zero andnonzero field settings. This is because the chamber is located in a low magnetic fieldregion.The left-right ambiguity problem is resolved using anode wire staggering. Figure 5.24shows the wire planes in a cell along with two sample tracks. The track passing on theleft side has shorter drift times to the even numbered wires than to the odd numberedChapter 5. Wire Chamber 4 54Figure 5.23: Graphs showing drift time spectra and their integrals for zero and 0.5 T.Once again, long drift times correspond to small TDC values.4.200ISO100500B=O T0 100 200 300 400 500 SCTime (tie)B—0.5 Tto 200 300 400 500 10Time (tie)0403020100110000I.5000;4000200005000040000(wacotzooootoOO0/4500to 200 300 400 500 I 00 200 300 400 500 500Time (us) Time (tie)Left RightTrackAnode0©©©00Figure 5.24: Illustration showing left and right tracks in a single cell of WC4.Chapter 5. Wiie Chamber 4 55500400Cl)0C) 2001000WC4 left—right residuals40Figure 5.25: WC4 Left-right residual for a single wire along with the time centroids (it)of each peak are shown. The solid curve is a gaussian fit to the data.ones. The situation is reversed for the track on the right. The difference in the drifttimes between the odd and even wires is used to distinguish left from right.The left-right residual for a given wire is defined by the following relation:R1=— t 2 i 7 (5.51)The sign of the residual depends on whether the track passed on the right or left sideof the wire. Figure 5.25 shows a typical residual histogram; left and right tracks arewell separated. Furthermore, the time separation between the centroids of the two peakscorresponds to a distance of 1.0 mm1. The time separation between the two peaks is‘This is just twice the staggering—40 —20 0 20Residual (ns)Chapter 5. Wire Chamber 4 565000—500Figure 5.26: The CHAOS coordinate system is shown. The positive z-axis points out ofthe page, and the location of each of the anodes in each chamber is also shown.20 ns. This confirms the 0.05 estimate for the time-distance relation obtained fromnsthe raw drift time spectrum.The CHAOS coordinate system is shown in figure 5.26. The polar angle is measuredcounter clockwise with respect to the positive x-axis. The coordinate of each WC4 anodein the CHAOS coordinate system is given by the following equations:= R cos(a) + d3 sin(180—a) (5.52)Yw = R sin(a) ± d3 cos(180 — a) (5.53)CHAOS coordinate systemYwhere a is the polar angle of the center line of the cell, d3 is the perpendicular distanceChapter 5. Wire Chamber 4 57between the wire and the center line (250 pm), and R is the radius of the wire plane(see figure 5.27). The sign of the second term in the above set of equations depends onthe wire staggering. The x-y coordinates of a track are given byXtrack X + Ddr:ft sin(180 — a) (5.54)Ytrack = Yw + Ddrifi cos(180 — a) (5.55)where Ddrift is the drift distance. The sign of the second term depends on whether thetrack passed on the left or the right side of the sense wire. The above equation is valid ifone assumes that the drift lines are perpendicular to the row of anodes. This is a goodassumption, except very close to the wire where the field becomes nonuniform. Thus, toobtain better resolution the angle of incidence of the track and the actual shape of thedrift lines must be considered.The vertical coordinate is obtained using the method of charge division. Figure 5.28shows a typical resistive wire ADO spectrum. Assuming that the preamp gains are theTrack..Figure 5.27: A sample track in WC4 is shown.Chapter 5. Wire Chamber 40ciTypical WC4 ADC spectrum58Figure 5.28: Typical ADC spectrum from one end of a resistive wire is shown.same for both ends of the wire, the vertical coordinate of the hit is given byt—bz= 2(t+b)l+Z0 (5.56)where t is the ADC value for the top of the wire, b is the ADC value for the bottom ofthe wire, 1 is its electrical length, and z0 is an offset. The constants in the above equationwere obtained from calibration data and are discussed in chapter 7.5.4 Induced Pulse ProblemWhen a negative pulse is produced in a given anode wire, at the same time a positivepulse is induced on the neighbouring anodes, resulting in a distortion of their signals.This effect is illustrated in figure 5.29.The induced signal substantially degrades the chamber resolution; it delays the directADC valueChapter 5. Wire Chamber 4 59Pulse Analysis for WC4zII)U,Figure 5.29: Illustration of the induced pulse effect. Pulse heights and widths are justestimates and do not represent actual values.signal and causes the measured drift time to be shorter than the physical one (see figure5.29). A series of tests were performed in which the tracks which passed only on the lefthaff of the cell were recorded. This was achieved by requiring a signal from a thin (1mm wide) scintillating fiber mounted vertically and positioned in front of the chamber.In this case the drift time to the even wires is longer than to the odd wires (see figure5.24). As a result, the pulse induced by the odd wires on their even neighbours will bepresent before the drift electrons arrive at the anode. This does not cause any distortionin the even wire signals; however, the induced pulse from the even wires will distort thesignal from the odd wires. In such a case, the resolution of the odd wires is much worsethan the even ones as shown in figure 5.30.The resistive wires are less susceptible to the induced pulse problem because a guardwire is located between each resistive wire and its closest anode.time [ns]Chapter 5. Wire Chamber 4 600C.)WC4 timing residuals prior to the cancelation networkFigure 5.30: WC4 residuals prior to the implementation of the cancelation network areshown for events passing on the left of a cell.20 20(T.÷ _)/2— T (ns)54RI. : 30K0R2 : 1.51(12R3 : 4700Figure 5.31: Schematic diagram of the cancelation network is shown.Chapter 5. Wire Chamber 4 61A resistor network shown in figure 5.31 is used to minimize this problem. The basicidea is to take a fraction of the signal from each anode and distribute it to its nearestneighbours. This negative signal will help compensate for the positive induced pulse.The values of the resistors in the cancellation network were varied while observing theinduced pulse height on an oscilloscope, using a source so that only one wire fired at atime. The values were chosen to minimize the induced pulse amplitude without distortingthe original signal. Figure 5.32 shows the residuals calculated after the implementationof the cancellation network. in this case again only tracks passing on the left werechosen. It is clear that the odd wire residuals have improved dramatically. The inducedpulse problem could have been entirely avoided if thick wires kept at ground were placedbetween successive anode planes. These wires would not cause an avalanche and wouldabsorb the induced pulse.The difference in the widths of the peaks shown in figures 5.32 and 5.25 is due to thefollowing. In the former, only tracks passing on one half of the cell, roughly parallel to therow of anodes were considered; hence, the drift time to all of the even wires is identical,and the same is true for the odd wires. Consequently the induced pulse problem isenhanced. In figure 5.25, tracks having different angles with respect to the row of anodeswere analysed, causing the induced pulse problem to be less pronounced. The intrinsicresolution of a given wire is 135 m, which is obtained by dividing the average of thestandard deviations of the peaks in figure 5.32 by ib/.22The factor of is needed since 3 wires are used to calculated the histogrammed quantities in 5.25.The estimate of 0.05 mm/ns was used.Chapter 5. Wire Chamber 4 621000- I I p I I I I -Residual from wires 2, 4, 6800- a = 3.67 nsU600•0400-200 -0— Iii—f———Ii—••••l 1111111 I[1IIII—Residual from wires 1, 3, 5500-= 5.70 ns400--I-,300-0200 -100 -0— I I I I I I I • I I I I ——60 —40 —20 0 20 40 60( t÷2 + t_2)/2 — t (ns)Figure 5.32: Spectra of WC4 residuals after installation of the cancelation network.Again, only tracks passing on the left of the cell were considered.Chapter 6CFT Counters, Trigger Systems and Readout Electronics6.1 CFT CountersThe outer most layer of detectors in the spectrometer are the CHAOS Fast Trigger (CFT)counters. Each of these counter telescopes consists of three layers. The first layer (E1)is a plastic scintillator 3.5 mm thick with an area of 25x25 cm2, and the second layer(/E2) is made up of two adjacent plastic scintillators, each of which is 13 mm thickwith a cross sectional area of 13x25 cm2. The third layer (C) consists of 3 adjacentlead glass Cerenkov counters each 12 cm thick with an area of 9.5x25 cm2. There are20 such counters (blocks) each of which covers 18°. The information from these blocksis used to make the fast (first level) trigger decision based on event multiplicity; hencethe name CHAOS Fast Trigger counters. Furthermore, the particle identification dataobtained are crucial in the analysis stage. Both LE1 and LE2 are equipped with TDC’sand ADC’s, and the Cerenkov counters are instrumented with ADC’s. Blocks positionedat the entrance and exit of the beam are removed.The CFT counters are required to identify pions, protons, and electrons over therange of momenta encountered in CHAOS experiments. Particle identification is basedon pulse heights, which are proportional to the energy deposited by different particlesin each layer. The energy lost by a heavy (with a mass much greater than that of theelectron) charged particle in a thin counter of thickness is given by the Bethe-Block63Chapter 6. CFT Counters, Trigger Systems and Readout Electronics 64relation. In natural units, this is written as4irNz2eZp ( f 2m13 ‘\ 21LE= m/32A 1n k.i(i — /32)) — /3 j (6.57)where 3 and z are the velocity and charge of the particle, m is the electron mass, N isAvagadro’s number and Z, A and p are the atomic number, atomic mass and densityof the counter material, respectively. In addition, I represents the medium’s effectiveionization potential. For a given material, the energy loss depends only on the velocityand charge of the particle. As a result, pions and electrons will deposit roughly thesame amount of energy if the pion velocity is similar to that of the electron. This occurswhen the pion kinetic energy is comparable to its mass. Consequently, E1 and zE2can distinguish pions from electrons over a limited range of lower pion momenta. Theprotons on the other hand are much heavier than both pions and the electrons; thus,LE1 and E2 are capable of separating protons from pions and electrons over the entiremomentum range encountered in CHAOS experiments. In practice, particle identificationin CHAOS is accomplished by selecting the appropriate particle group in scatter plots ofpulse height versus momentum.The third layer (C) is used to separate pions from electrons at higher momenta. Acharged particle traversing a medium at a speed higher than light in the medium emitsCerenkov radiation. The velocity of light in a material with index of refraction, n, is givenby c/n, where c is the speed of light in vacuum. Electrons resulting from r° decay insidethe spectrometer are highly relativistic and thus emit Cerenkov radiation in lead glass(n 1.7). The pions on the other hand, will radiate only if their momentum is greaterthan 100 MeV/c. Furthermore, due to their small mass, electrons emit bremsstrahlungradiation in the presence of the electric field produced by the lead nuclei in the glass.The bremsstrahlung photons will then produce electron-positron pairs which contributeto the Cerenkov light produced by the initial electron. The above process produces aChapter 6. OFT Counters, Trigger Systems and Readout Electronics 65shower of electrons that result in creation of a large number of Cerenkov photons. Thepions on the other hand are more massive and do not lose energy in the presence of thefield. As a result, the pulse height of the signals produced by electrons is much greaterthan those produced by pious.The CFT counters were calibrated with pions, protons, and electrons over a widerange of energies. In order to apply the same cut to all of the pulse height spectrafor each of the layers, it is important that all phototubes in a given layer have similargains. Each of the tubes was tested and those with similar gains were installed in thesame layer. Further adjustment of the gain was possible by changing the phototube highvoltage. However, the gain of each tube must still be monitored in order to account forthe fluctuations caused by factors such as changes in temperature. This can be done inseveral ways. One is to recalibrate the system with particles of known momenta at regularintervals during the course of an experiment. However, this option is not practical sinceit requires disruption of the experiment and loss of valuable time. The other is to supplyall of the tubes with exactly the same amount of light for calibration, but it is difficult toensure that the amount of light directed to each of the tubes is the same. Consequently,a new monitoring system was designed which operates in the following manner. A Xenonflasher system is used to produce flashes of light at precise time intervals. The light fromthe original spark is directed through a long helical acrylic cylinder. The helix is coveredwith reflective material, and a series of optical fibers are inserted over the circular regionat the end opposite the spark. Although the light intensity is not uniform over thisregion, the ratio of the intensities between the various points is a constant that dependson the geometry of the cylinder. In other words, the relative distribution of light tothe different fibers is constant and shows no memory of the spark. Hence, if one of thefibers is sent to a reference tube of constant gain and the remaining are each sent to aCFT tube, the ratio of each pulse height with respect to that of the reference can beChapter 6. OFT Counters, Trigger Systems and Readout Electronics 66monitored to look for changes in gain. The gain of the reference tube is surveyed usinga scintillating material that is connected to it and imbedded with a 207Bi source whichproduces 1.06 MeV electrons [21]. Both source and flasher events are recorded at regularintervals during an experiment.6.2 First Level TriggerThe CHAOS first level trigger (1LT) decision is based on multiplicity information provided by the CFT counters. The trigger is a fully programmable system that is flexibleand allows for quick changes to its configuration. The timing of the trigger decision iscrucial because it provides the gate for all the readout electronics. Some of the readoutsystems require the gate to arrive a short period of time before the data; thus, a long1LT decision time necessitates long delays for these signals. This is costly and increasesthe dead time of the detector. The first level trigger is capable of making a decision in100 us. The trigger electronics are based on Emitter Coupled Logic (ECL).A diagram depicting the first level trigger circuit is shown in figure 6.33. The signalsfrom each CFT block are fed into a programmable discriminator which accepts signalsabove a set threshold and produces an ECL signal. This particular discriminator alsohas an analog output, which is delayed and sent to Fast Encoding and Readout ADC’s(FERA). The ECL output is then sent to a delay/fanout unit to compensate for differentcable travel times. The signals from the delay unit are then directed to a programmablelookup unit (PLU), which outputs different logical combinations of its input. Some ofthese signals are used for scalers while others are fed into a programmable majority logicunit (MALU), which makes the multiplicity decision. The output of the MALU will openthe LAM gate which is a look-at-me signal produced if the first level trigger accepts theevent and the data acquisition computer is not busy. A positive decision from the 1LTChapter 6. CFT Counters, Trigger Systems and Readout Electronics 67Figure 6.33: Schematic diagram showing the first level trigger. For simplicity, only oneof the CFT counters is shown.AE1ScalersLcgTcal OR of PLU outputsSiSTOPs1EIEEEZJ ILReset Visual ScalerChapter 6. CFT Counters, Trigger Systems and Readout Electronics 68initiates the digitization of all chamber data and enables the second level trigger.Timing of the common start or stop signals for all the TDC’s is provided by the Sicounter, which is a plastic scintillator placed in the beam upstream of CHAOS. The stopsignal for the CFT blocks is taken after the delay unit and directed through long cableswhich further delay the signal for the length of time it takes the 1LT to make a decision.The rest of the circuitry shown in figure 6.33 forms the “BUSY” circuit, which ensuresthat a single event is processed in each cycle of the trigger. To avoid pileup of events,the LAM gate must be blocked as soon as possible. It remains blocked until the systemreceives either a computer “BUSY END” indicating that the event has been recorded ora REJECT from the second level trigger.6.3 Second Level TriggerThe second level trigger (2LT) is one of the most important parts of CHAOS. Itenables experimenters to perform a fast hardware rejection of unwanted events whichwould otherwise be recorded. The system has the ability to make a decision based onphysical quantities such as track momentum, polarity and interaction vertex. The 2LTis also based on ECL logic and is fully programmable.’The second level trigger uses the hit information from WC1, WC2 and WC3 to makeits decision. It works on the premise that the momentum of a given track is invariantunder rotations of the three chamber coordinates. The hit information is obtained fromthe ECL port of the PCOS III system, and is directed to two Memory Lookup Units(MLU’s) A and A’. These modules convert the PCOS information into angles in theCHAOS coordinate system and direct the data for each chamber into the proper datastack. From this point on, three nested DO loops are executed by the hardware. Consider‘For a detailed description of this system refer to [22].Chapter 6. CFT Counters, Trigger Systems and Readout Electronics= 03 —€3 ••‘ €3 +°ref0° < 03 63.750PCOS3 PCOS1, PCOS269WC35/4° -+ 1/4°To the nextTo the next stageTo the next stageFigure 6.34: Block diagram of the second level trigger. Control signals are not shown.Chapter 6. CFT Counters, Trigger Systems and Readout Electronics 70the case where there are I hits in WC1, J hits in WC2 and K hits in WC3. The firstWC2 hit is taken from the data stack and rotated to a predefined angle 9ref 32° in theCHAOS system. Thus, the angle of the hit in WC2 is now a known constant. However,to keep the track momentum unchanged the hits from the other two chambers must berotated by the same amount (ie: 02— 8ref). This is done by two Arithmetic Logic Units(ALU’s) F and F’ along with MLU’s I and J. Furthermore, MLU’s I and J decide whetherthe hits are within a 64° window about 02. If so, an acceptable track has been foundand the data are then passed to MLU21K. This unit calculates the track momentum,polarity, and the distance of closest approach to the center of CHAOS. It will then acceptor reject the event based on these calculations. In the latter case, the next set of hitsare examined. The process is repeated until either an acceptable track has been foundor all IxJxK possibilities have been exhausted. The above forms the first stage of theCHAOS second level trigger.There are two optional parts of the trigger not shown in figure 6.34. One makes ascattering angle versus momentum cut on single tracks; it is designed to help separate rpelastic scattering events from background reactions involving helium and carbon in theCHAOS target. The other section is a specialized (ir, 27r) trigger which helps separateinteresting events from the extensive rp background. It forces the 2LT to find two tracksthat pass the first section, calculates the momentum sum and applies an upper sum cut.In addition, it can compare the polarities of the tracks.6.4 Readout ElectronicsThe CHAOS readout electronics consist of 1696 ADC, 944 TDC and 1584 PCOS channels.Each of these systems is discussed in the following sections.Chapter 6. CFT Counters, Trigger Systems and Readout Electronics 716.4.1 PCOS £ 4290 TDC SystemThe three inner chambers are equipped with a LeCroy PCOS III system that is basedon ECL logic. It consists of a set of model 2731A 32 channel latches, three 2738 PCOScontrollers and two 4299 databus interfaces. In order to allow for cluster mode operation,there are two latch addresses corresponding to each chamber wire. Hence, 1440 channelsare allocated for each of WC1 and WC2. In addition, 288 channels are set aside for WC3.The signals from the preamplifiers are directed to LeCroy 2735PC cards, which outputan ECL signal if the analog input is above a certain threshold. This level is separatelyprogrammable through the latch modules. The output of the 2735PC cards is sent tothe 2731A units and sets the corresponding latches. After the system receives a gatefrom the first level trigger, it reads the latches and outputs the address of the wire(s)that fired. If two or more adjacent wires were activated, it will group them into a clusterwhose width is given by the number of wires that fired. In such cases, the output addresscorresponds to the average address of the activated channels. If a particle activates thefirst and the last wire in the chamber, the system will output two clusters of width one.Fast transfer of data to the second level trigger is made possible by the ECL ports ofthe 2738 PCOS controller. Data transfer is possible up to a rate of 10 MHz. The 4299databus interface buffer is used to readout the data through CAMAC. This occurs if andonly if the second level trigger has accepted the event. Otherwise the module is cleared.Wire chambers 3 and 4 are instrumented with the LeCroy 4290 Drift Chamber system.This consists of 2735DC preamplifier/discriminator cards, 4291B time digitizer modules,4298 TDC controllers and a 4299 databus interface module. Each 4291B TDC has 32front panel differential ECL inputs which accept chamber signals from the 2735DC cards.Unlike the PCOS III system, the threshold for the 2735DC cards is controlled manually.Normally, the 2735DC cards are mounted directly on the chamber, but lack of spaceChapter 6. CFT Counters, Trigger Systems and Readout Electronics 72inside the spectrometer does not allow for this. The chamber signals had to be brought tocrates containing the 2735DC cards via coaxial cables; the resulting attenuation requiredthe use of 8-channel preamplifiers, which resulted in the over-amplification of both thesignal and noise. As such, the thresholds on the 2735DC’s were often set near maximum.In WC3 the maximum threshold values were not sufficient to filter out the noise, Hence,a 17 Ku resistor to ground was connected to each input channel of the 2735DC cards.This had the effect of attenuating the input such that the noise was below the maximumthreshold.Each 4298 controls up to 23 time digitizer modules and rejects zero or full scale TDCvalues. The system can operate in either COMMON STOP or COMMON START mode.CHAOS operates in the former mode. This is so that the chamber signals need not bedelayed. The common stop is provided by a scintillator located at the entrance of thebeam into CHAOS. The TDC’s have an adjustable range between 500 ns and 2 1us, andthe conversion time for 9 bit accuracy is 35 is. The 512 ns range chosen for CHAOSresults in 1 ns time resolution and is near the longest drift times in WC4 ( 400 ns)The TDC controller is capable of producing accurate time marks. This feature allowsfor a stop signal to be produced at a precise interval of time after the start, which isuseful for calibration purposes. If all the preamplifiers are fired at the same time by anexternal pulse distribution system and a COMMON STOP signal is produced at a preciseinterval of time later, all the TDC values should be the same. However, this is not thecase because the wires carrying the signals from the preamps to the TDC’s have differentlengths. In the above scenario the system is capable of correcting for this if operated inAUTOTRIM mode.Chapter 6. OFT Counters, Trigger Systems and Readout Electronics 736.4.2 FASTBUSThe LeCroy FASTBUS ADC system is used to digitize the signals from the chambercathode strips and resistive wires. Although the faster FERA system could also beused, the cost of such a system is much greater than FASTBUS. The FASTBUS systemconsists of a single 1821 segment manager, nineteen 96 channel 1882F ADC’s, one 1810Calibration And Trigger module (CAT), one 1821/ECL auxiliary card, a single 1691A-PC interface card, two 4302 memory modules, and one 2891A FASTBUS port. Apartfrom the 4302’s, 1691A, and 2891A, all other modules are located in a Struck FASTBUScrate. The system is capable of pedestal subtraction, threshold comparison, and zerosuppression. This is required in order to eliminate the readout of unwanted information.The 1821 segment manager is a processor that controls all the ADC’s and the CAT.It configures the pedestal system and reads the ADC’s after the digitization process iscomplete. The pedestal system can be configured in one of the following ways.• No pedestal subtraction• Pedestal subtraction only• Pedestal subtraction and suppression of negative values to zero• Pedestal subtraction and suppression of negative values out of the memoryThis is done through writing the proper code in Register 3 of the 1821. CHAOS usesthe last of the above options. Another useful feature of the segment manager is thethreshold register which allows one to set a common (to all ADC channels ) thresholdthat is added to the pedestal value in each channel. The ADC data are readout onlyif they are greater than the sum of the pedestal and threshold in the correspondingchannel. This feature is used in CHAOS since the width of the pedestal distributionChapter 6. CFT Counters, Trigger Systems and Readout Electronics 74for each channel is not negligible. The source and the destination of the digitized dataare also configured through Register 3. The data can either be piped from the pedestalsystem to the segment manager memory or it can be sent to an auxiliary card located atthe rear of the unit. The latter option is more practical since it allows for faster readoutof data. The 32 bit data words from the auxiliary card are stored in two 4302 modules.Each 32 bit data word contains 16 bits of address and 16 bits of data. Since the 4302modules used to receive the FASTBUS data are 16 bit units, one was used to receive thedata and the other the address.Instruction words can be downloaded into the processor’s memory either throughCAMAC or through SONIC, which is a low level language developed by LeCroy. TheSONIC code is compiled and downloaded using the LeCroy Interactive FASTBUS Toolkitprogram (LIFT) running on a PC which uses the 1691A-PC card to communicate withthe 1821. A SONIC program is used to configure the ADC’s and read out the data. Twoinputs and a single output located on the front panel of the 1821 are used in the readoutsequence. For diagnosis and configuration purposes, a control program was developedwhich runs on a VAX system and allows for communications via CAMAC using the 2891AFASTBUS port. In practice, LIFT is used to download the instruction words requiredfor the readout procedure into the 1821 memory. The pedestal system and thresholdregister are configured with the VAX system.The 1882F’s are 96 channel ADC’s. The gate to the ADC can be provided eitherthrough the front panel or through the back plane using the 1810 CAT. The front orback panel options are configured via the Control Status Register (CSR) of the 1882Fthrough the segment manager at powerup. The 1882F requires the gate to arrive at least40 ns before the signal, thus all of the ADC signals had to be delayed for this period oftime plus the 100 ns required to make the 1LT decision. The conversion time for thismodule in 256 fts.Chapter 6. CFT Counters, Trigger Systems and Readout Electronics 75The 1810 CAT sends the gate and the clear to all the ADC’s through the back panel.The unit can also be used to inject specified amounts of charge into the ADO’s. Thisallows for the calibration of the AD C’s and location of faulty modules. A useful feature ofthe 1810 is the Measure Pause Interval (MPI). When this signal is held true, it preventsADC’s from commencing the digitization process. It can either be programmed into the1810 or input externally through the front panel. As soon as the gate is received by theCAT, it will start the MPI and set the BUSY output on its front panel to true. Duringthe MPI a clear signal will return the AD C’s to acquisition mode and set BUSY to false.If the clear signal is sent within the MPI, the ADO’s require 500 us to clear; otherwise 5s is needed. Hence, the MPI is set to the maximum second level trigger decision time.To calculate the ADC pedestals, a gate of the same width as the one generated by thefirst level trigger is sent to the modules. The ADC’s are then read out and recorded withthe VAX system. The above process is repeated a number of times and for each channel,the pedestal is set to the average of the recorded ADC values. Note that the above isdone when no beam is present in the area and all preamps are powered. Pedestals arecalculated at regular intervals during the course of an experiment.Readout ProcedureThe flow chart for the SONIC code used to readout the ADC data is shown in figure6.36, and the schematic diagram of the handshaking circuit is illustrated in figure 6.35.At powerup, the Control Status Registers of the ADC’s and CAT are configured so thatthe ADC gate is sent via the back plane through the 1810. The input (IN1) on the frontpanel of the 1821 is examined until it is set to true by the MPI output of the 1810. Theprocessor will wait the length of the MPI plus the period of time required for possibleclearing. It will then examine the BUSY output of the CAT via the front panel input(IN2). If BUSY is false the system is returned to acquisition mode, otherwise it willChapter 6. OFT Counters, Trigger Systems and Readout Electronics 76Figure 6.35: Schematic diagram of the FASTBUS handshaking circuit.wait for data conversion. The 1821 will then clear the 4302 memory via the front paneloutput (OUT1) and read the ADC’s. At this point, the data are sent to the 4302’s, andthe system is returned to acquisition mode.ADC gate C’ear from 2LTChapter 6. OFT Counters, Trigger Systems and Readout Electronics 77FalseInitialize ADC’s1,Initialize CATCheck IN1TrueWait for MPI to end1Wait for possible clearingCheck 1N2TrueWait for conversion1FalseClear 4302 memory with OUT1Read all ADC’sSend data to AUX. cardReturn the system to acquisition modeFigure 6.36: Flow chart of the FASTBUS readout algorithm.Chapter 7Chamber CalibrationIn order to determine the position of every hit for a given track two things must beknown. These are, the chamber positions and time distance relations. This chapterdeals with the procedures used for determination of these parameters. CHAOS chambercalibrations are divided into two parts. One is the in-plane calibration, and the otheris the vertical coordinate calibration. The software and techniques for the former weredeveloped by Gertjan Hofman [23].7.1 In-plane CalibrationThis task consists of calculating offsets and time-distance relations for the various chambers. Offsets are required in order to accurately determine the position of each chamberin the CHAOS coordinate system. Although great care was taken in installing the chambers, a more accurate knowledge of chamber positions is needed. The calibration of thetwo inner chambers requires determinations of position offsets only. WC3 and WC4 arehowever drift chambers; for these detectors, offsets as well as time-distance relations mustbe determined. Furthermore, space-time (x(t)) relations are needed for various magneticfield settings. In the calibration procedure, the x(t) relation for each chamber is a lookuptable that associates a distance with a given drift time. WC3 calibration is more difficultthan WC4, because it is located in a region of high magnetic field and has a single wireplane. As a result, the x(t) relations are nonlinear and internal consistency checks cannot be performed. WC4 on the other hand, is in a region of low field and has eight planes78Chapter 7. Chamber Calibration 79of wires.The chamber positions, rotation offsets and zero field x(t) relations are determinedby analysing straight tracks (B = 0) in which all 22 chamber hits (11 for beam in and11 for beam out) are present. The position and zero magnetic field x(t) determinationprocedure can be summarized as follows.• The positions of the hits in WC1, WC2, and WC4 are calculated using the initialguesses for the offsets and x(t) relations.• The position of the track in WC3 is determined. In polar coordinates, this is givenbyR = 347.55 mm9 = 8,, ± (7,tdrjft) (7.58)where R is radius of the chamber and 8,, is the angle of the activated wire in theCHAOS coordinate system. In addition, qS(y, tdrjft) is the angular distance of thehit from the wire. This is a function of the drift time, tdrjft, and the incident angleof the track with respect to the cell, y (see figure 7.37). The sign of q.y, tdr:ft)depends on whether the track passed on the right or the left of the sense wire. Thevalue of y is calculated through an iterative procedure. Initially, 7 is set to zerofor both the incoming and the outgoing hits and a linear regression is performedon all of the hits from WC1, WC2, WC3, and WC4. Using the slope of the fittedline a new value of y is obtained. Next, the WC3 track position is updated andanother fit is performed. The above procedure is repeated until the change is isnegligible.• A straight line is fit to the 22 sets of coordinates.Chapter 7. Chamber Calibration 80Figure 7.37: Illustration of the incident track angle 7 in WC3. A and C denote anodeand cathode wires respectively. Chamber cell is not drawn to scale.• The slope and the intercept of the line are transformed to a reference frame inwhich all the chambers are centered at (0,0).• Residuals representing corrections to the x(t) relations and offsets are calculatedusing the following equations:(t)new— x(t)old = 4cross — 1chamber xside (7.59)—6Xold = sin(9) x (q5chamber — lcross) X jRchamber (7.60)8Ynew— 6Yold = cos(6) x (&hamber — &ross) x Rcham&er (7.61)6new — 58o1d = (&hamber — ç’cross) (7.62)where 4cross is the angle of intersection of the line and the anode plane of each0Chapter 7. Chamber Calibration 81chamber in the transformed frame, and &hamber is the polar angle of the originalhit in the CHAOS system. SXL and SXold represent the improved and the initialestimates of the x offsets respectively, similarly for5Ynew and 5Yold. In addition, thu, isthe polar angle of the wire in the transformed frame, side is the left-right flag (+ 1),and Rchamr is the chamber radius. The initial estimates and the improved valuesof the rotational offsets are denoted by 8o(d and SOflew, respectively. For WC4, theequivalent of is obtained by calculating the intersection of the fitted line withthe electron drift trajectories which are assumed to be perpendicular to the radialvector passing through the activated anode.• A large number of tracks are analyzed and the above residuals are summed andaveraged over the contributing tracks. This yields corrections to the offsets and thespace-time relations. In order to determine the position offsets accurately, it wasnecessary to acquire data (straight tracks) at 0 and 900 in the CHAOS coordinatesystem.• Improved values of offsets are obtained and new x(t) look up tables are created. Inthe case of WC3, the x(t) relation is a 2 dimensional lookup table that associatesa drift distance with a given value of drift time and -y, at a given magnetic fieldsetting. In this table, the angle of incidence is specified to the nearest degree andthe drift time to the nearest ns.• The entire cycle is repeated with the same tracks.Several important points need to be stressed. First, once the residuals are addedall fictitious corrections will sum to zero. As an example, consider the case where achamber has no translational offsets and only a rotational offset is present (see figure7.38). Furthermore, assume that the x(t) relation is known. In this case, the X and YChapter 7. Chamber Calibration 82YOriginal trackFitFigure 7.38: Illustration of rotation offsets is shown. The offset has been exaggerated forclarity.residuals for the incoming and the outgoing hits are equal but have opposite signs. Assuch, they add up to zero. Similarly, corrections to the x(t) relation vanish, because,given a large number of tracks, as many pass to the left as right. Second, in the case ofWC1 and WC2 no x(t) relation is needed; only position and rotation offset correctionsare calculated. Figure 7.39 shows the X and Y residuals for WC3 before and after thecalibration procedure.7.2 Magnetic Field CorrectionsOnce chamber positions are known, WC3 x(t) relations for the various magnetic fieldvalues must be determined. Tracks with different momenta are analyzed to obtain awide range of incident angles. Using the Quintic Spline method outlined in section 8.1,an analytical form for the trajectory of the particle in the magnetic field is obtained ‘.‘The analytic form is presented in section 8.1Chapter 7. Chamber Calibration 83X—residuals before calibration Y—residuals before calibration;10X—re1duaI (mm) Y—residual (mm)X—residuals after calibration Y—residuals after calibrationiiX—reiiduel (mm) Y—resldual (mm)Figure 7.39: X and Y residuals prior to and after the calibration along with positioncentriods (it) and standard deviations (o) for WC3 with B=O are shown.The trajectory is calculated based on an initial estimate of the time-distance relation 2•The tangent to the trajectory at its intersection with the anode plane of WC3 providesa new value of y and results in a new position for the hit. The Quintic Spline method isapplied once again and the polar angle of the intersection of the track and the chamberin the CHAOS system, cbft, is found by simultaneously solving the system of equationsformed by the circle describing the WC3 anode plane and the analytic form of the track.2jnitiaj estimate of is zero.Chapter 7. Chamber Calibration 84The angular distance corresponding to a given drift time and incident angle, y, is givenby4(t,7)= çbt — I (7.63)where th, is the angle of the sense wire with respect to the CHAOS coordinate system.The procedure outlined above is repeated for a large number of tracks, illuminating a largenumber of cells. In practice, the actual data recorded in the acquisition phase of a givenexperiment can be and in fact are the best data to use in this procedure. Consequently,WC3 can be considered a “self calibrating” chamber. The values of q5(t, -y) for constantangles of incidence are summed and averaged over the contributing tracks. A third orderpolynomial fit is performed on the drift distance versus drift time at each value of,which is then used to create a new x(t) lookup table, and the same tracks are reanalysedusing the improved x(t) relations. The above procedure is repeated until the change inthe x(t) relation is negligible. Figure 7.40 shows time-distance (angular) residuals beforeand after calibration. The standard deviation of the time distance residual distributionis the effective chamber resolution. To date, magnetic field corrections are not appliedto WC4 time-distance relations where B is only 20% of the central value. This will beimplemented in the near future.Chapter 7. Chamber Calibration 85WC3 x(t) residuals before and after calibration250200Before calibration15000100500-0.3 -02 -Ci —0.0 0.1 02 0.3x(t) residual (deg.)250After calibration2004u=Oo=O.046200100500-0.3 -02 -CI -0.0 0.1 02 0.3x(t) residual (deg.)Figure 7.40: WC3 x(t) residuals prior and after calibration for magnetic field setting of1.2 T.Chapter 7. Chamber Calibration 867.3 Vertical CalibrationThe vertical position of a track, z, is determined from the hits in WC1, WC2, and WC4.The vertical position in chamber four is given byt—b 1ZbX+Zo (7.64)where t and b are the adc values for the top and the bottom of the resistive wire. Inaddition, 1 is the electrical length and z0 is the vertical offset. The vertical position inchambers one and two are corrected by means of an offset.= z + z (7.65)Z2 = z + zg (7.66)Here, z1 and z2 are the corrected z-positions in WC1 and WC2 respectively; similarly,z and z are the original z positions obtained from the chambers. Last, is the WC1vertical offset and z represents the vertical offset in WC2.The electrical lengths for the inner and outer resistive wires were obtained by directmeasurement. A single section of the chamber was placed on an Y-Z table and positionedin the beam. A thin scintillating fiber (1 x 1 mm2) mounted horizontally was placed incoincidence with two other large scintillator paddles to provide the trigger. The chamberwas moved vertically by precise amounts while keeping the fiber fixed. The ratio of thedifference to the sum of the adc values at ends of the wire was recorded for a large numberof tracks. Figure 7.41 shows the position of the chamber relative to an arbitrary fixedpoint in space as a function of this ratio. This graph shows a linear relation between theratio and chamber displacement; the electrical length is just twice the slope of this line.The electrical lengths for the inner and the outer wires were found to be 237.6 mm and248.8 mm respectively. In the above process two cells (4 resistive wires) were tested andChapter 7. Chamber Calibration 875030 Inner wire-10--10--0—30 --slope = 118.75 mmliii )iil 1111111111111 11111 I IOuter wire7E0z::e,:.a:m,0.6RatioFigure 7.41: Graph of ratio versus displacement for the inner and the outer resistivewires. The solid lines are straight line fits to the data. The slopes shown are half of theelectrical lengths.Chapter 7. Chamber Calibration 88the results were internally consistent. In each case, the inner and the outer wire werefound to have different electrical lengths; the reason for this is not clear. The lengthsobtained from each cell were the same to better than 0.5 mm. The electrical lengths areclose to the physical length of the wires which is 250 mm and were assumed to be thesame for all other sections of the chamber. Once the electrical lengths are determined, theoffsets for the three chambers can be determined by analysing tracks from a scatteringrun with zero magnetic field setting. The calibration algorithm is outlined below.• The interaction vertex in the X-Y plane is calculated using the anode informationfrom all four chambers.• All z offsets are initially set to zero and z-positions are calculated for each chamber.• The distance between the interaction vertex and the hit in WC1 (d1) and WC2(d2) in the X-Y plane is obtained. Similarly, the distance from the vertex to eachactivated resistive wire (d) is calculated.=— r)2 + (yi— yv)2 (7.67)=— x)2 + (y2— yv)2 (7.68)c1’ = — x)2 + (y — yv)2 (i = 1,2) (7.69)where (Xv,yv) denotes the interaction vertex point, and (x1,y), (r2,y) representthe position of the hit in WC1 and WC2, respectively. In addition, (4,y) is thelocation of the ith activated resistive wire in the CHAOS coordinate system.• A straight line fit is performed on z versus the distance from the vertex for thosetracks in which all 4 possible vertical coordinates are present.Chapter 7. Chamber Calibration 89• Residuals for WC1, WC2 and each hit wire in WC4 are calculated. These are givenbySZ Zj,— Zch (7.70)6z2 = Z— 4 (7.71)5z =— 4,j (7.72)Where 6z1, zh, 5z2, and Zh are the residuals and the original z-position for chambers one and two respectively. Similarly, 5z represents the residual for the ith wirein chamber four and is the vertical position of the hit as seen by the ith wirein the chamber. In addition z, z, and z are the z coordinates calculated fromthe fit.• A large number of tracks, distributed over all cells, are analysed.• The residuals are then summed and averaged over the tracks that contributed tothem, and new offsets are obtained.• The improved offsets ares stored and a new set of z-positions calculated.• The entire cycle is then repeated for the same tracks until corrections are negligible.In order to eliminate stray hits such as those produced by electromagnetic noise andparticle decay, tracks with large residuals were not considered. The residuals before andafter the calibration procedure are shown in figures 7.42 and 7.43. In these figures, WC4residual represents the corrections for all of the hit wires. The standard deviations ofthe distributions in figure 7.43 represent the effective vertical resolution of each chamber.The vertical resolutions obtained for WC2 and WC4 are reasonable; WC4 resolutionis better than 1% of the electrical length. It is expected that WC1 resolution will beimproved by increasing the chamber operating voltage.Chapter 7. Chamber Calibration 90Vertical residuals prior to calibration250020006000e1800040000__C.)100020005000 0—10 —5 0 5 10 —10 —5 0 5 10WCI reidua1 (mm) WC2 residual (mm)350300250200150100500—10 —5 0 5 10W04 residuals (mm)Figure 7.42: Z coordinate residuals for WC1, WC2, and WC4 before the calibrationprocess are shown (ie: with all offsets set to zero).Vertical residuals after calibration12000=—0.007 mm1:::3000200010000—10 —5 0 5 10WC4 ResiaualB (mm)Figure 7.43: Z coordinate residuals for WC1, WC2, and WC4 after the calibration process. The standard deviations (o-) show the effective z resolution of each chamber.Chapter 7. Chamber Calibration 91300025002000150010005000-10J4=0.004 mm•10W02 Residu1 (mm)—5 0 5WC1 Residual (mm)Chapter 8Reconstruction8.1 Momentum ReconstructionTo date, the momentum reconstruction algorithm is implemented in two dimensions only.The momentum calculation technique employs the Quintic Spline method developed byWind [24]. The software for this part was developed by Roman Tacik [25].The equations of motion in natural units for a charged particle with momentum F,moving in a magnetic field B are given by’cIF . -.—-=qvxB (8.73)where q and i are the charge and velocity of the particle, respectively.Given that the field points along the z direction, the above reduces tod2x— qBdy874dt2 — 7mctt (.d2y— —qBdx875dt2— 7mdtHere, B is the magnitude of the field at a point (x,y) and m is the mass of the particle.In addition, y (in natural units) is defined by equation 8.76,V1—v2(8.76)where v is the magnitude of the velocity.2 The first and second time derivatives can be‘The field is not uniform but is rather a function of x and y.27 is constant since the energy of the particle does not change with time.92Chapter 8. Reconstruction 93eliminated by successive application of the chain rule:d_— (8.77)22 &ydx d2xdy‘‘ Y— dt2 dt dt2 dt (8 78)(4)3Using the equations of motion the above expression can be written asd?y— —qB (()2+()2879)dx2ym ()3 (.Using relation 8.77, the above reduces to= ; (i+) (8.80)Now, the momentum P is defined asIdx dyP== 7m_ ( + (L)2) (8.81)Employing the results of 8.77, the momentum is given by the following:P = 7m/1 + ()2 (8.82)Combining the results of 8.80 and 8.82 yieldsP— = —qB (1 + ()2) (8.83)Equation 8.83 establishes a simple relation between the analytic form of the particle’strajectory and its momentum. From basic calculus, it is clear that1 a d2y=a+bx+f daf (P-4)dr (8.84)where a and b are integration constants. Hence, if the double integral is known, themomentum is obtained by fitting the coordinates of the track to equation 8.84.Chapter 8. Reconstruction 94The momentum calculation algorithm is summarized in the following.• The hits in WC1, WC2, and WC3 are used to obtain the 3 coefficients of the circlepassing through them.• From the equation of the circle two pseudo hits are generated. One is between WC1and WC2 and the other lies between WC2 and WC3.• A straight line fit is performed on the hits in WC4.• A cubic spline is used to generate pseudo hits between WC3 and WC4.• The analytic forms of the circle, spline and straight line are differentiated to obtainat all track and pseudo hit coordinates.• Given the polarity of the track (from the direction of curvature) and the magneticfield strength at each point, equation 8.83 provides the corresponding value ofpd2ydx2• A cubic spline fit is applied to the values of PJ.• The polynomial obtained from the cubic spline fit (above) is analytically integratedtwice and the value of the integral at each chamber hit is recorded. The doubleintegral yields a fifth order polynomial, hence the name Quintic Spline.• Once the double integral is known, an analytic form for the track in terms of a fifthorder polynomial is given by equation 8.84. A least square minimization betweenthe values of y obtained from 8.84 and the chamber hits yields the constants a, band . The pseudo hits are not used in the minimization.• is recalculated from the equation for the track, and the cycle is repeated oncemore to obtain a stable value of P.Chapter 8. Reconstruction 958.2 The Interaction Vertex and Scattering AngleOnce the track momentum has been found the interaction vertex can be calculated. Thevertex is defined to be the intersection of the incoming and scattered particle track. Thehorizontal and vertical coordinates of the vertex are computed separately.Consider the interaction vertex in the x-y plane. Assuming a uniform magnetic field inthe region of the target, the trajectory of the incoming beam is circular in that region andis obtained analytically using the two hits in WC1 and WC2, the known beam momentumand polarity along with the field direction and strength (as discussed in section 3.3). Thetrajectory of the scattered particle is traced back (starting from the chamber hit closestto the center of CHAOS), by solving the equations of motion based on the assumptionthat the field is constant over small intervals (ie: 0.5 mm). The vertex is then determinedby calculating the intersection of the scattered track and incoming beam trajectory.The equations of motion for a charged particle in a magnetic field are given by equation8.73. In the region of the target, B has no components in the x-y plane. Solving theabove system of equations given that the magnitude of B is constant over a small intervals, results inP(t) = Posin(w)+Pocos(w) (8.85)P(t) = Pocos(w)—Posin(w) (8.86)w = (8.87)7m= qBtvqBs (888)mv Pwhere P0 and P,o are the x and y components of the momentum at the starting point.q, F, and v are the charge and magnitude of the momentum and velocity of the outgoingparticle, respectively. In addition, B is the magnetic field strength at the starting point,which is obtained using the CHAOS magnetic field map. Integrating equations 8.85 andChapter 8. Reconstruction 968.86 with respect to time gives— cos(w)] + sin(w) + xo (8.89)y = — sin(w) — —-[1 — cos(w)] + yo (8.90)= (8.91)where (x, y) is the position of the particle calculated by taking a single step s from theinitial point (xo,yo).The above procedure determines the scattered particle trajectory in the region of thetarget. The following quantity is computed at each point on the traceback:d(x,y) = (x — a)2 + (y — b)2 — 1?2 (8.92)In the above, (a, b) and R are the center coordinates and radius of the circle that definesthe incoming beam track. The intersection of the two tracks occurs when d vanishes.Due to roundolf errors and the finite size of the step, d is often small but nonzero. Assuch, the vertex is the average of the points between which the sign of d changes.Once the horizontal vertex coordinates have been found, the vertical coordinate ofthe interaction point is obtained in the following manner. A straight line fit is performedon the z-coordinate versus the distance (in the x-y plane) from the interaction vertex tothe hits in WC1, WC2 and the activated resistive wires in WC4. The vertical coordinateof the vertex is the y-intercept of the fit line.The scattering angle is defined as follows:= cos’( • lC0t) (8.93)where km is the unit vector pointing along the tangent to the incoming beam track at thevertex. Similarly, the unit vector, points along the tangent to the scattered track atthe interaction point.3v is a constant.Chapter 8. Reconstruction 978.3 ResultsThe results presented in this section are primarily concerned with .+p reaction dataacquired at an incident pion energy of 280 MeV with 0.5 T field, a singles trigger and aliquid hydrogen target.Figure 8.44 shows the track momenta as a function of the sum of the pulse heights inIXE1 and E2. Pions and protons are well separated. The proton pulse heights displaya strong dependence on the momentum. This is to be expected since protons with lowermomenta produce a larger pulse height; however, at some point the proton momentumbecomes too small causing the particles to stop in the scintillator. As a result, a smallersignal is produced. The pions, on the other hand, have a much smaller mass and henceare minimum ionizing; thus, very little correlation between the pion pulse height andmomentum is seen. Placing a box cut on this scatter plot separates pions from protons.A diagram of the liquid hydrogen target is shown in figure 8.45; the radius of thetarget cell is 25.5 mm. Figure 8.46 shows the interaction vertex in the x-y plane. Thereconstructed vertex is consistent with the physical dimensions of the target vessel; thenon-circular shape in Y is due to the fact that the beam envelope is smaller than thetarget. The vertex resolution is obtained by calculating the difference between the verticesfor the pion and proton tracks in a given event. Figure 8.47 shows these values for x and ydimensions; both peaks are centered very close to zero. As expected, the resolution alongthe direction of the beam (in this case along the x-axis) is worse than that perpendicularto the beam direction. This is because the irp cross section is peaked at forward angles;hence often either the pion or the proton tracks emerge at small angles with respectto the incident beam. Due to the small angle, these tracks have a large overlap regionwith the incident beam trajectory which causes a broadening of the peak along the beamdirection (for a given spatial resolution, it is much harder to intersect two nearly parallelChapter 8. Reconstruction 98108ciC,’0x200 2000Figure 8.44: Scatter plot showing track momenta as a function of sum of pulse heightsin iE1 and E2. The polygons are used to identify pious and protons.lines than two perpendicular lines). The resolution for a single track is obtained bydividing each of the standard deviations in figure 8.47 by The vertex resolutionfor a single track along the direction of the beam is 1.54 mm and perpendicular to thebeam direction is 0.30 mm. The above technique could not be used to obtain the verticalvertex resolution, because at the current WC1 operating voltage, the cathode strips arehighly inefficient. in order to obtain vertical resolution of the vertex, data were acquiredwith a “picket fence” target which consists of three horizontally mounted thin ( 2mmdiameter) rods (see figure 8.48). Figure 8.49 shows the vertical proffle of the picket fencetarget. Althoughnot many counts are present, the three peaks corresponding to the rods500 1000 1500E1 + E2 Pulse heightChapter 8. Reconstruction 99..- Honeycomb0.007 mm Aluminum46.8 mmVacuum29.6 m37.6 mmLH20.125 mm MylarFigure 8.45: Illustration of the target vessel in the X-Y plane.Interaction vertex in the x—y plane10050 LH20 ....,...\....:-. Vessel—.—100 I I I—100—50 0 50 100Xvertex (mm)Figure 8.46: Reconstructed interaction vertex in the X-Y plane.Chapter 8. Reconstruction400350300250100501600140012001000400100Figure 8.47: The difference between pion and proton vertices in the X-Y plane are shown.The solid lines represent gaussian fits to the data. The vertex resolution per track isobtained by dividing the standard deviations shown above by200Figure 8.49: Vertical vertex reconstruction for the picket fence target. The three peakscorrespond to the three (2 mm diameter) rods.Chapter 8. Reconstruction 10111mm15 mmFigure 8.48: Illustration of the vertical picket fence target.108C,’+a0C.)20—40 —30 —20 —10 0Zvertex (i-nm)10Chapter 8. Reconstruction 102are seen and the separation between them is consistent with the physical dimensions ofthe target; for each peak, the mean (p) and standard deviation (cr) correspond to thestatistical ones and were not obtained via a gaussian fit to the data. Using the average ofthe standard deviations shown in 8.49, the vertical resolution is 2.26 mm. However, theresolution and efficiency will be improved by increasing the WC1 operating voltage. Inaddition to being inefficient, the WC1 cathode strip signal to noise ratio is too small atthe present voltage. Furthermore, the resolution of the vertical coordinate in WC1 andWC2 is related to the efficiency, because the technique used to obtain the z-coordlinateof the track relies on having two or more strips fire for optimum resolution.Figure 8.50 shows a plot of scattering angle versus momentum for elastically scatteredpions and coincident recoil protons at 280 MeV pion incident energy. A large fractionof the background due to the target vessel has been removed by placing a cut on thelocation of the interaction vertex. The solid line shows the kinematic predictions, whichare consistently high because the magnitude of the central field is not correct. Thefield value obtained from the NMR probe situated on the pole tip does not reflect thecentral value at which the field map was constructed. The disagreement between thedata and the kinematics is on the order of 5%. Increasing the field by this factor resultsin figure 8.51, in which scattering angle versus momentum correlations for both the pionsand protons are consistent with the kinematic predictions. All of the data points showncorrespond to events in which the scattered pion and the recoil proton were both detected.This is the reason for the limited kinematic range shown in figure 8.51. Both extremeforward and back angle scattered pions pass through the regions of the beam entrance andexit, where the CFT trigger blocks have been removed. Furthermore, the recoil protonscorresponding to forward scattered pions have low momenta; consequently they too willnot arrive at the CFT. Similarly, forward scattered protons exit through the region ofCHAOS where the blocks have been removed. The plots in figure 8.51 demonstrate thatChapter 8. Reconstruction 103100 200 300 400 500 600 700Proton momentum (Mev/c)180160 --140 -- H‘‘ 120 .U) ivPJd80 -. •i:•.-60 : .• ••;•-40 • :.••:-20--0 I I I I100 200 300 400 500 600 700Pion momentum (Mev/c)Figure 8.50: Scattering angle versus momentum correlation for pions and protons at 280MeV pion incident energy prior to scaling the magnetic field are shown. The solid linesrepresent kinematic predictions.Chapter 8. Reconstruction 104100100 200 300 400 500 600 700Proton momentum (MeV/c)180 ,....160140-‘ 120tJ)...Cl) 100 •. :‘-“ 80 .tz .... .t60 :.-.‘ i.:::4..40 • • :200I I I I I I100 200 300 400 500 600 700Pion momentum (MeV/c)Figure 8.51: Scattering angle versus momentum correlation for pions and protons afterscaling the magnetic field (by +5%) are shown. All other features are the same as thosefor figure 8.50.Chapter 8. Reconstruction 105the CHAOS detector is working as expected. Figure 8.52 shows the pion scattering angleas a function of the proton scattering angle. The solid line represents the kinematicpredictions, and there is good agreement between the data and kinematics.The scattering angle resolution is determined by calculating the difference betweenthe predicted and calculated scattering angle of the proton at a given pion angle, asshown in figure 8.53. The scattering angle resolution for a single track is obtained bydividing the standard deviation of the distribution in figure 8.53 by The calculatedscattering angle resolution for a single track is 0.510.Figure 8.54 shows the missing mass histogram for irp scattering; once again, a cutis placed on the location of the vertex. For the data presented in figure 8.54, the recoilproton and the scattered pion were not required simultaneously. The missing mass, I.m,is defined as= E2 + m — (8.94)where m is the proton mass and E1 is the total energy of the incident pion beam. Inaddition, E0 represents the total energy of the outgoing particle(s). The missing massshould be zero for events where both the pion and proton tracks were correctly identifiedand reconstructed. A nonzero missing mass is expected if either the pion or proton werenot detected.Figure 8.55 shows the missing mass spectra plotted against the sum of the pulseheights in LE1 and LE2. It is clear that region 1 in figure 8.54 corresponds to thoseevents in which the pion was not detected. The region starts at an energy greater than therest mass of the pion because the scattered pion kinetic energy is nonzero. Furthermore,the width of this interval does not violate kinematical constraints which limit the rangeof pion kinetic energy. The pions will not be detected if scattered at extreme forwardor back angles, where the CFT blocks are removed and WC4 is deadened. ChamberChapter 8. Reconstruction 10600468 1008. (deg.)Figure 8.52: Pion versus proton scattering angle at 280 MeV incident pion energy. Thesolid line represents kinematic predictions.I____________________________________M (deg.)Figure 8.53: Histogram showing the scattering angle resolution. The scattering angleresolution per track is obtained by dividing the standard deviation shown above byChapter 8. Reconstruction 107Missing mass spectrum for elastic scattering at 280 MeV2500 I V2000Region 1 Region 31500 Region 2 /I I!C)I . I—500 0 500 1000 1500Missing mass (Mev)Figure 8.54: Missing mass spectrum for-p elastic scattering at 280 MeV.15001000-Protons500-‘I—a •:Pions—500 I0 500 1000 1500 2000Sum of pulse heights in AE1 and E2Figure 8.55: Missing mass spectrum versus sum of pulse heights in /E1 and E2.Chapter 8. Reconstruction 108inefficiency, pion decay and reconstruction inefficiency also contribute to pion loss.Region 3 of the missing mass histogram is caused by those events in which the recoilproton was not detected. The large peak in region 3 corresponds to the recoil protonswhich did not have enough kinetic energy to arrive at one of the CFT blocks. Thisoccurs when the pion is scattered at forward angles. For example, consider a pion with300 MeV incident energy that is scattered at an angle of 300; the corresponding protonangle is 70°. At this angle, the proton energy is under 20 MeV and it will not arrive atany of the CFT blocks. Figure 8.56 shows a plot of pion scattering angle versus region3 of the missing mass spectrum, and evidently the large peak corresponds to small pionscattering angles. The centroid of this peak is located at 947 MeV, which is near theproton rest mass. The smaller peak in region 3 corresponds to events in which the pionis scattered at back angles causing the proton to exit through a missing block section atforward angles. The data points appearing between the extreme forward and back anglescorrespond to those events in which the recoil protons were missed due to chamber andreconstruction inefficiencies. The counts that appear in region 3 between ‘ 1100 and1300 MeV are muons from pion decay upstream of the target, and the momentum ofthese tracks is about 185 MeV/c. The CFT counters are not capable of separating pionsand muons; hence these particles were identified as pions. Several tests were done inan attempt to gain an understanding of these events, and various processes were ruledout. The momentum versus scattering angle correlation for these points is not consistentfor either j.+p protons or pions ( see figure 8.51). In addition, the momentum of thesetracks is too low to be due to pion scattering from heavier nuclei in the target vessel,which was not removed by the vertex cut. Figure 8.58 shows the vertical coordinate ofthe interaction vertex for these decay events as well as irp scattered pions. The peaksappearing in the vertex histogram of the decay events correspond to two copper disksthat provide support for the 0.125 mm mylar window (see figure 8.57). These peaks areChapter 8. Reconstruction 109MO0•13001200 •. . .... .-.. 21100 .‘. . . ..•j1ooo.:.....8 • • I •0 5 10 15(deg.)Figure 8.56: Region 3 of the missing mass histogram versus pion scattering angle.5.40 cmI .95cm0.125 mm My1r5.4 cm1’copperFigure 8.57: Diagram showing the copper support disks around the target cell.Chapter 8. Reconstruction 1101600140012001000800C) 6004002000—100161412—100—50 0 50Z (mm)vertex100—50 0 50Z (mm)vertex100Figure 8.58: The vertical vertex for irp scattered pion.s (top) and decay events (bottom)are shown.Chapter 8. Reconstruction 111caused by those events in which the incident pion decays upstream of the target and theresulting muon passes through the copper disk. The kinetic energy of a 185 MeV/c muonis 107 MeV, and the energy lost by a muon resulting from the decay of 396 MeV/c pionsin copper is less than 66 MeV “. The above suggests that the incident muon energy isless than 173 MeV, which is consistent with the kinematics describing pion decay at 396MeV/c. Consequently, it seems reasonable to attribute these counts to those incidentpions that decay before the target into muons whose trajectories pass through the disks.Region 2 corresponds to misidentified particles. Figure 8.59 shows region 2 of themissing mass spectrum on a magnified scale; the momentum spectrum corresponding tothese events is also shown. The spectrum shows two peaks which are centered around200 and 360 MeV/c. All of the counts in the momentum histogram were identified aspions (see figure 8.55). Calculating the missing mass based on this assumption yields avalue of 728 MeV, which is consistent with the centroid of the peak in region 2. Nowconsider the case in which one of the tracks (with momentum 200 MeV/c) was a protonbut was identified as a pion. If the proton mass and the second pion track (one withmomentum 360 MeV/c) are used in the calculation, the missing mass obtained is lessthan 15 MeV. Hence, particle misidentification seems to be a plausible explanation forthese events. The number of misidentified tracks is less than 1% of the total number ofcounts in the missing mass histogram. At this stage of the analysis the gain stabilizationof the OFT’s is still not optimized; however, this will be implemented in the near future.The histogram of the scattering angle is interesting because the number of counts ineach angular bin is proportional to the differential cross section at that scattering angle.The constant of proportionality, Jc, is given by15dcZEdENN1.8.94This is roughly constant over the entire range of allowed momentum.Chapter 8. Reconstruction 1120CiU)0C)Figure 8.59: Region 2 of the missing mass spectrum on a magnified scale along with thecorresponding momentum distribution are shown.Missing mass (Mev)200 400 600Momentum (Mev/c)Chapter 8. Reconstruction 113where df is the solid angle; e and Ed are the computer and detection efficiencies respectively . In addition, N is the number of target protons per unit area and N is thetotal number of incident pions. The accurate determination of some of these factors,such as the solid angle, is beyond the scope of this thesis; however, a rough estimate ofk can be made. Figure 8.60 shows the lr+p cross sections at 280 MeV obtained fromthe SM92 phase shifts plotted on top of the scattering angle histogram, in which thecounts obtained with CHAOS were scaled by a factor of 2.08 x 10_2 mb/sr.6 The scalingfactor was chosen so that the phase shift curve and the scattering angle distribution werein good visual agreement. The data shown in figure 8.60 were acquired with a singlestrigger, and the recoil proton detection was not required in the software. The shape ofthe distribution is consistent with the cross section curve. The absence of counts at theextreme forward angles (near 0° and 360°) is caused by those events in which the pionis scattered into the beam exit where the CFT block was removed. The lack of countsaround 180° is due to the missing block and the deadened sections of WC3 and WC4at the beam entrance. The disagreement around 320° and 40° is due to faulty wires inWC3. Figure 8.61 shows a plot of the pion track angle in WC3 versus scattering angle;the faulty wires are clearly visible, and the projection of the dead wire regions onto thescattering angle axis explains the dips in the scattering angle distribution. The effectof dead wires in WC3 on the scattering distribution is a complex one that depends onthe track momentum, the distribution of the beam over the target, and the number oftracks emerging from the target. If an outgoing track traverses a dead cell of WC3 anda second track is not present, the event will be rejected by the second level trigger. Near300° the distribution is higher than the SM92 phase shift results. This effect is caused by5The detection efficiency accounts for pion loss due to decay, reconstruction, and chamberinefficiencies.6To separate the two halves of the detector, the scattering angle has been plotted between 0 and360°.Chapter 8. Reconstruction 1143025 -2015C10rd50•••I I I0 100 200 300 4008 ir (deg.)Figure 8.60: Cross sections for elastic scattering at 280 MeV incident pion energy.The solid line represents the SM92 phase shift results.—>Faulty wires300-Q200-.øzJ.Faulty wirel0o-0100 200 300O (deg.)Figure 8.61: Track angle in WC3 versus pion scattering angle.Chapter 8. Reconstruction 115a defective CFT block which resulted in some of the proton tracks being misidentified aspions. Using separate particle identification cuts for this particular block minimized butdid not eliminate the problem. Implementation of the CFT gain stabilization in softwarein the analysis package will virtually eliminate particle misidentification.Now consider making a rough estimate of the constant k. The solid angle for a onedegree polar angle bin is given byf 180 dOf 180 sin()d = 0.00425 sr (8.96)The above equation is the expression for the solid angle given that the azimuthal angularacceptance of CHAOS is 14 degrees, as estimated from the width of the vertical positiondistribution in WC4 for events (fringe field effects were ignored). The combinedefficiency of the chambers and reconstruction along with scattered pion loss due to decayis obtained by considering a region in the proton scattering angle distribution for whichthe pion should have been detected. For this angular region, any counts appearingin the missing mass spectrum which correspond to missing pions are due to chamberinefficiency, reconstruction inefficiency or scattered pion decay. This method determinesthat the combined efficiency is 73%. The combined chamber efficiency expected from theplateau curves is 75%. In the calculation of this quantity, efficiencies of WC1 and WC2for both the incoming and scattered tracks must be taken into consideration, since thevertex reconstruction algorithm requires the presence of WC1 and WC2 hits for both theincoming and outgoing particles (WC4 was assumed to be 100% efficient). Comparisonof the combined efficiency with that of the chambers suggests that the reconstructionalgorithms are 99% efficient, accounting for an expected pion decay of ‘ 2%.The computer dead time is calculated from the following relation:c= TiT 7iT (8.97)‘‘pass — .LvCChapter 8. Reconstruction 116where N is the total number of events accepted by the first level trigger and Npassis the total number of events which were allowed through the computer busy circuitto the second level trigger. In addition, N represents the total number of calibrationevents. These do not correspond to physical interactions and are generated for calibrationpurposes only. Hence, they must be subtracted from both the denominator and thenumerator. For the data shown in figure 8.60 the computer efficiency was 1.7%.The number of incident pions is computed using the total counts obtained from aplastic scintillator mounted approximately 2 meters upstream from the target in whichan upper level discriminator setting removed the 20% proton contamination of the .+beam from the trigger. Let the number of counts from the scintillator be N8; the numberof incident pions is given byNirNs X f,t X (1+fd) X (lfdecay) X ftgt (8.98)where f is the pion fraction of the beam, fdeca is the fraction of pions that decay beforehitting the target and ftgt is the fraction of the beam which hits the target. In addition,fd is the doubles fraction of the beam, which represents the probability of having twopions in the target at the same time. In such cases, the beam counting scintillator wouldregister only one count.Since only a single in-beam scintillator was used, some of the above parameters,in particular ftgt, are estimates obtained from previous runs that employed an activescintillating target. The same momentum and magnetic field settings were used, and thescintillating target was roughly the same size as the liquid hydrogen one. In addition,a single in-beam counter causes N to be susceptible to fictitious counts produced byactivation of the scintillator and tube noise. Values of the above parameters for a 396MeV/c positive pion beam arriving at the in-beam scintillator at a rate of 1.4 MHz arelisted in table 8.3.Chapter 8. Reconstruction 117f,t 0.99fd 0.03fdecay 0.02ftgt 0.61N3 6.915 x iON,t 4.22 x iOTable 8.2: Table showing beam calculation parameters for 396 MeV/c at 1.4 MHz.In order to determine the number of target particles per unit area, the effective targetthickness must be known. Since the target cell was cylindrical, the beam profile is requiredto determine this quantity. The thickness of a cylinder of radius R, at a distance r fromthe center (see figure 8.62) is given byd(r) = 2V’R2— r2 (8.99)Assuming that the beam curvature is negligible over the target diameter, the effectivetarget thickness, t, is obtained from the following relation:— 8 100f°f(r)where f(r) is the beam profile as a function of the distance from the center of the target,and is obtained from the target projection histogram which represents the beam projection on a plane oriented perpendicular to the incident beam. The radius of the targetcell was 25.5 mm, resulting in an effective target thickness of 47.02 mm. The number ofprotons per unit area is given by= 2.0159 (8.101)Chapter 8. Reconstruction 118Figure 8.62: ]llustration of d(r).where p is the target density in grams per cubic centimeter and A is Avagadro’s number.The factor of 2 in the numerator is the number of protons in a hydrogen molecule and2.0159 in the denominator represents the atomic weight of the hydrogen molecule. Giventhe target density of 0.074 gm/cm3,the number of target particles per unit area wasdetermined to be 2.078 x 1023 cm2. Using the parameters mentioned, the value of k wasdetermined to be 2.16 x 102 mb/sr. There is a 2% discrepancy between the calculatedand estimated values of k. However, given the crude nature of this calculation and thenumerous simplifying assumptions, a relatively large uncertainty is associated with bothvalues of k.The aim of the above calculation is not to make a definitive absolute measurement of.+p differential cross sections; it is simply meant as a semi-quantitative approach to theproblem. Many parameters used in the calculation of k are rough estimates. For example,to completely eliminate scattering from the target vessel, background subtraction mustbe performed. Furthermore, accurate determination of the solid angle requires extensiveBeam directionChapter 8. Reconstruction 119Monte Carlo simulations, which are currently underway. Over all, the above results areencouraging and seem to indicate that the CHAOS spectrometer is operating as expected.Figure 8.60 indicates that there is reasonable symmetry between the two halves of thespectrometer, which is perhaps the most important result of the above calculation.It is impressive to note that the entire angular distribution shown in figure 8.60 wasacquired with CHAOS in a single 45 minute long period of data acquisition. Were itnot for the poor computer efficiency, the same data could have been acquired in about 1minute.Chapter 9ConclusionThe results presented in this thesis clearly indicate that the CHAOS spectrometer hasbeen a success. The preliminary momentum resolution as calculated for a 225 MeV/cbeam at a magnetic field setting of 1.2 T is 1% (o). Much has been learned from thecommissioning results which will help improve the momentum resolution. An increasein the operating voltage of WC1, the implementation of the three dimensional momentum reconstruction algorithm, the application of magnetic field corrections to WC4 x(t)relations, and the reduction of multiple scattering by placing helium bags between thechambers are thought to increase the resolution. The horizontal resolution of WC1 willalso be enhanced by raising the operating voltage since it will increase the fraction ofevents in which more than one wire per track is activated. Furthermore, the higher operating voltage will increase the cathode strip efficiency and signal to noise ratio, whichwill greatly enhance the vertical vertex resolution and efficiency.In order to obtain an accurate vertical projection of the beam onto the target, separateADC gates must be supplied to the FASTBUS system. This will be implemented in thenext CHAOS beam period in January of 1994. Clearly the computer live time of 1.7% isunacceptable. Improvement of the computer efficiency is one of the major goals targetedfor the next CHAOS running period, which we expect to accomplish by replacing theexisting CAMAC based data acquisition system with one based on VME.In future experiments, the number of incoming pions must be obtained using two inbeam scintillators in coincidence, which will virtually eliminate fictitious counts produced120Chapter 9. Conclusion 121by scintillator activation and tube noise. In addition, the fraction of the beam arrivingat the target can be calculated accurately if the second scintillator is placed closer tothe target. Although a cut placed on the location of the interaction vertex minimizesscattering from the target vessel, background runs with an empty target (only the vessel)are required to completely eliminate this problem. It is extremely difficult to correct thescattering angle distribution for dead wires in WC3; hence, in order to use the full angularcoverage of the spectrometer, it is crucial that these channels be repaired. However, itis thought that corrections can be applied if Monte Carlo studies of the problem areperformed. Furthermore, the implementation of the CFT gain stabilization software isessential for future analysis of experimental results.It must be stressed that the CHAOS detector is new and as such further analysisis required in order to fully understand the data acquired with CHAOS. For example,extensive Monte Carlo analysis is required to model pion decay inside the spectrometer,which is a source of background.The next set of CHAOS experiments are scheduled to begin in January of 1994 and willcontinue throughout the summer of that year. The first stage of the (ir, 2ir) experimentshas been completed and the analysis is currently underway. The second stage will beginin January 1994. The date for completion of the polarized target is the summer of 1994at which time measurements of the irp analysing powers will begin. In conclusion, theCHAOS detector at TRIUMF offers a unique new facility for studying irN interactionswhich are crucial in testing low energy predictions of QCD.Bibliography[1] H.L. Anderson, E. Fermi, R. Martin and D.E Nagle Phys. Rev. 91, 155 (1953).[2] P.J. Bussey, J.R. Carter, D.R. Dance, D.V. Bugg, A.A. Carter and A.M. Smith,Nuci. Phys. B58, 363 (1973).[3] P.Y. Bertin, B. Coupat, A. Hivernat, D.B. Isabelle, J.Duclos, A. Gerard, J. Miller,J. Morgenstern, J. Picard, P. Vernin, R. Powers, Nuci Phys. , B106, 341 (1976).[4] E.G Auld, D. Axen, J.Beveridge, C. Duesdieker, L. Felawaka, C.H.Q. Ingram, R.R.Johnson, G.Jones, D. LePatourel, R Orth, M. Salomon, W. Westlund, L. Robertson,Can. J. Phys. 57, 73, (1979).[5] J.S. Frank, A.A. Browman, P.A.M. Gram, R.H. Heffner, K.A. Kiare, R.E. Mischke,D.C. Moir, D.E. Nagle, J.M. Porter, R.P. Redwine, M.A. Yates, Phys. Rev. D, 28,1569, (1983).[6] B.G. Ritchie, R.S. Moore, B.M. Preedom, G. Das, R.C. Minehart, K.Gotow, W.J.Burger, H.J. Zoik, Phys. Rev. Lett. 125B, 128 (1983).[7] J.T. Brack, R.A. Ristinen, J.J. Kraushaar, R.A. Loveman, R.J. Peterson, G.R.Smith, D.R. Gill, D.F. Ottewell, M.E. Sevior, R.P. Trelle, E.L. Mathie, N.Grion,R.Rui, Phys. Rev. C, 41, 2202, (1989).[8] J.T. Brack, J.J. Kraushaar, R.J. Peterson, R.A. Ristinen, D.R. Gill, R.R. Johnson,D.F. Ottewell, F.M. Rozon, M.E. Sevior, G.R. Smith, F. Tervisidis, R.P. Trelle, E.L.Mathie, Phys. Rev. C, 34, 1771, (1986).[9] Data obtained from the SAID data base on the TRIUMF computer cluster.[10] Renton, Peter, Electroweak Interactions Cambridge University Press, Cambridge, (1990).[11] Ulf-G. Meissner, Chiral Perturbation Theory With Nucleons, Lectures givenat summer school on Nucleaons and Nuclear Structure, Institute of Nuclear theory,University of Washington, Seattle, USA, (1991).[12] Donoghue, John F., Chiral Symmetry As an Experimental Science, Lecturespresented at the International School of Low-Energy Antiprotons, Erice, (1990).122Bibliography 123[13] Sauli, F., Principles of Operation of Multi Wire Proportional and DriftChambers, Lectures given in the Academic Training Programme of CERN, (1975-76).[14] G. Charpak, R. Boucier, T. Bressani, J. Favier, C. Zupancic, Nuci. Instr. Meth.,62, 235, (1968).[15] R. Veenhof, Garfield: a drift vhamber simulation program, v.3.0, CERNprogram library entry W5050, (1991).[16] G.J. Hofman, J.T. Brack, P.A. Amaudruz, G.R. Smith, Nuci. Instr. Meth., A325,384, (1993).[17] This is an alloy of Ni obtained from California Fine Wire Company.[18] G.C. Barbarino, L. Cerrito, G. Paternoster, S. Particeffi, Nuci. Instr. Meth. ,179,353, (1981).[19] C. Bino, R. Mussa, S. Palestini, N. Pastrone, L. Pesando, Nuci. Instr. Meth., A271,417, (1988).[20] A. Fainberg, N. Horwitz, I. Liriscott, C. Montei, Nuci. Instr. Meth., 141, 277, (1976).[21] P. Camerini et. al., paper submitted to Nuci. Instr. Meth., (1993).[22] S.J. McFarland, M.Sc. thesis, UBC, (1993).[23] G.J. Hofman, Internal CHAOS document, (1992).[24] H. Wind, Nuci. Instr. Meth., 115, 431, (1974).[25] R. Tacik, Internal CHAOS document, (1992).


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