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Development of a high magnetic field drift chamber for the chaos spectrometer Hofman, Gertjan J. 1991

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DEVELOPMENT OF A HIGH MAGNETIC FIELD DRIFT CHAMBERFOR THE CHAOS SPECTROMETERByGertjan J. HofmanBSc.A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF SCIENCEDEPARTMENT OF PHYSICSWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIASeptember 1991© Gertjan J. Hofman, 1991In 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- Dec- ? DE-6 (2/88)AbstractDesign considerations for the Canadian High Acceptance Orbit Spectrometer (CHAOS)led to a set of apparently mutually inconsistent requirements for the inner (WC3) driftchamber. This detector chamber has to be cylindrical, of low mass, have excellentspatial resolution (<200 pm) and operate in a variable magnetic field of up to 1.6 T.This thesis describes the investigations which culminated in the testing of a unique newdrift chamber which satisfies all the requirements for the CHAOS WC3.An overview is given of present drift chamber technology and its application inhigh magnetic fields. Methods to obtain the space-time relationship are reviewed. Inparticular, the integral, displacement and trackfitting methods have been applied toprototype chambers. A trackfitting algorithm developed to calibrate a set of wirechambers and correct systematic wire position offsets is presented.Three types of prototype chambers were designed and constructed. Tests werecarried out in beams at TRIUMF to measure the spatial resolution of these chambersin a 1 T magnetic field. The results indicate that a resolution of as 150 pm can beachieved.A simplified model of electron transport through gasses is used to explain electrondrift properties in high magnetic field chambers. A method to resolve the usual left-right ambiguity, proposed within the framework of this model, involves the comparisonof the charge induced on diagonally opposed cathode strips mounted parallel to thepotential wires. After extensive simulations using the Garfield drift chamber program,a final, unique prototype was designed on which the WC3 chamber to be built forCHAOS is now based. A final beam test in a 1.6 T magnetic field showed that theleft-right problem is resolved for track angles between —45° and +45°.iiTable of ContentsAbstract^ iiList of Tables^ viList of Figures^ viiAcknowledgements^ xi1 Thesis overview and the CHAOS spectrometer^1.1^Introduction ^1.2^The CHAOS spectrometer ^1121.2.1^Physics goals 21.2.2^Energy and momentum resolution^ 31.2.3^The Sagane magnet ^ 31.2.4^Detector description 42 Drift Chambers 92.1 Introduction to chamber principles ^ 92.2 The electron avalanche ^ 122.3 The Garfield program 143 Properties of Electron Drift through Gasses 173.1 Introduction ^ 173.2 Drift equations 17iii43.3^Electron Diffusion ^The Left-Right Ambiguity21224.1 Introduction^ 224.2 The application of induced signals ^ 234.3 Solution for the WC3 Chamber 234.4 Position error resulting from the left-right ambiguity ^ 265 Drift Chambers in Magnetic Fields 275.1 Introduction^ 275.2 Implication for the CHAOS chamber ^ 305.3 Chamber positioning ^ 326 Space-time Relationships and Resolution Measurements 366.1 Introduction^ 366.2 Displacement method ^ 386.3 Trackfitting method 396.4 Chamber Resolution Measurements ^ 436.4.1^Introduction ^ 436.4.2^Measurement of the intrinsic resolution ^ 436.4.3^Track reconstruction resolution ^ 467 Description of the Chambers 497.1 First prototype and Dcal chambers ^ 497.2 WC3-prototype ^ 527.2.1^Motivation behind designing a new prototype ^ 527.2.2^Construction ^ 54iv7.2.3 Choice of drift gas ^  607.3 Chamber Electronics  627.3.1 Introduction ^  627.3.2 Wire chamber pre-amplifiers ^  627.3.3 Cathode inverters ^  648 Results^ 678.1 Bench testing the first prototype ^  678.2 November test ^  698.2.1 Description of the experimental setup ^  698.2.2 Results ^  708.3 March and August tests with magnetic field. ^  748.3.1 Description of the experimental setup  748.3.2 Momentum dispersion in the Sagane magnet ^ 778.3.3 March beam test results ^  798.3.4 August test results  859 Trackfitting^ 939.1 Introduction  939.2 Algorithm ^  939.3 Application to real data ^  989.4 Obtaining the track coordinates in CHAOS^  10010 Summary and conclusions^ 103Bibliography^ 106vList of Tables7.1 Cell parameters of the first prototype and calibration chambers. ^ 497.2 Cell parameters of the last prototype chamber. ^ 578.3 High voltages applied to the prototype and Dcal chambers. ^ 678.4 Measured and expected chamber efficiencies at high incidence rates. 74viList of Figures1.1 The z-component of the magnetic field as a function of radius.  ^41.2 The radial component of the magnetic field as a function of radius andheight for a 1 T vertical field ^51.3 The CHAOS detectors inside the Sagane magnet^  62.4 Adjustable field chamber. ^  112.5 A comparison of the Lorentz angle as calculated by Garfield versus mea-surements [44]. ^  153.6 Electron drift paths from a straight particle track for (a) B z =0 and (b)B z =1 T. Angle 0 is discussed in section 8  3 4^   204.7 Drift lines for Bz = 1 T at various angles of incidence. ^ 255.8 Isochrones separated by 20 ns for a 1 x 1cm cell, B=1.5 T, calculated byGarfield. The lines spiraling in towards the anode are drift trajectories.Two tracks at +45° are also shown. ^  285.9 Effect of high voltage variations on drift time, calculated using Garfieldat 1 T. ^  325.10 The Lorentz angles 0, a in the presence of 13,, Br . Paths d and d' as wellas d" and d' are coplanar. ^  335.11 The x(t) relation from Garfield for different radial components of themagnetic field. The error shown is x(t)B4O — x(t)Broo.^35vii6.12 TDC spectrum (counts versus time) of the last prototype (B=1.6 T) andits integral (drift distance versus time). ^  376.13 A comparison of the x(t) relation obtained by integration (solid line) andusing the displacement method (triangles) for the first WC3 prototype.^386.14 A comparison between the x(t) relations obtained using Garfield and byfitting cosmic particle tracks, in the absence of a magnetic field. ^ 406.15 Uncorrected and corrected residuals per TDC bin obtained in the Dcalchambers for cosmic rays without magnetic field. ^  427.16 Structures of the prototype and Dcal chamber showing the front end andside view. The aluminium frames are not shown. ^  507.17 Proposed new cell designs, showing which wires/strips are read out.^547.18 Potential contours of the proposed new cell designs. ^ 557.19 Contours of the electric field (top) and a vector plot of the electric fieldfor a rectangular version of the last WC3 prototype. Electric field unitsare in V/cm. In these calculation, Vanode = 2300 V, V_,athode = —600 V,Vstrips = —300 V^  567.20 Top and side view of the WC3 prototype showing the cathode foils,chamber frame and cell configuration. ^  597.21 Normalized cathode signals inverted using the SL560 (top) and the LeCroy 428F fan-in fan-out (bottom). ^  657.22 Inverter amplifier circuitry. ^  668.23 The prototype plateau curve showing the anode and cathode efficiencyversus chamber voltage. No cathode voltage was applied. ^ 68^8.24 Typical ADC spectrum showing induced signals on cathode strips.   698.25 Dot plot of the cathode signal amplitude versus drift time. ^ 70viii8.26 Dot plot of the left-right difference signal versus cathode signal amplitude(bottom) and normalized signal difference ANI, versus signal amplitude(top).   718.27 Measured x(t) relation at 0° and 48° and the left-right separation ANI,against drift distance for the first prototype. ^  728.28 Schematic diagram of the March and August setup. Distances are notto scale and scintillator S3 is not shown^  758.29 Photograph showing the chambers mounted inside the magnet. Theprototype chamber is the second from the left. ^  768.30 Schematic of the hardware trigger used in the March and August beamtests. Actual delays and reshaping discriminators are not shown^ 788.31 Typical drift time (ns) spectra of the prototype (a) and Dcal chambers(b).  ^808.32 Time distance spectra for four separate collimation windows showingthe peaks that were fitted to obtain the time resolution a t for the firstprototype in the 1 T field  828.33 Resolution measurements of the Dcal (a) and first prototype (b). Graph(a) also shows the raw a r 's, before subtracting the contribution of theother chambers (see equation 6.15)  838.34 Left-right signal (AN/,) as a function of drift time from the adjacent(left) and diagonal (right) strips at B z =0 (top) B z =0.7 (middle) andB z=1.0 T (bottom).   848.35 Time to distance relation for the prototype chamber and a dot plot ofthe ADCs in the Dcal chambers. Shown are the software cuts. ^ 858.36 Typical ADC spectrum of a cathode strip in the last prototype for twodifferent cuts (B=1.6 T). ^  86ix8.37 ADC pulse on a strip against drift (TDC) value for tracks that passoutside the physical boundary of the cell. ^  888.38 Left-right separation without magnetic field for adjacent strips (left) anda diagonal combination (right)^  898.39 A.Nir against TDC time in ns for all four combination of the strips.Straight tracks in a 1.6 T field. ^  908.40 Drift lines from a straight track in high magnetic field in a cell of theWC3 chamber. ^  918.41 A Arir obtained from the combination D1 at +45° (left) and —45° (right)in the 1.6 T field. ^  928.42 Drift lines from tracks at 45° (a) and —45° (b) in the WC3 cell^ 929.43 Flowchart showing the order of the main tasks performed by the programTRACKFIT. ^ 949.44 Monte Carlo results for wire offsets and TDC relations before and afteriteration.   979.45 Residuals summed per chamber obtained from cosmic ray tracks at B=0 T. 999.46 Definition of the angle 0 and distances r, x.   101xAcknowledgementsThe word 'acknowledgement' takes on a completely different meaning in a subject suchas nuclear physics. It is impossible to achieve anything by oneself because no one canbecome a physicist, electronical engineer and machinist in the available time. Eventhose small pieces of this project that I could call almost mine would not have beensuccesful without the help of the staff at TRIUMF, especially those of the detectorfacility.Above all I would like to thank Greg Smith who showed undiminishing enthusiasmfor this project and whose 'outer office' is always open for discussion and guidance. Itis a pleasure to work with an engineer like Pierre who can design anything in half thetime and make it work in even less. I would like to thank Jeff for being continuously onshift during the beam tests as well as for correcting this thesis, and Martin for writingsoftware when things got very hectic.Finally, I want to thank my parents. Regardless of my geographical escapades theycontinue to support and encourage me in every way they can.xiChapter 1Thesis overview and the CHAOS spectrometer1.1 IntroductionThe purpose of this thesis is to provide an overview of the development process thatled to the final design of the inner drift chamber (WC3) for the CHAOS spectrometer.Various prototypes were built, bench tested and evaluated in tests using pion beamsat TRIUMF. Chamber resolution, behaviour in a strong magnetic field, and a solutionto the so-called left-right ambiguity were investigated and are evaluated. The firstfive chapters give a review of chamber technology and physics. Understanding theprocesses involved will help to justify the choices made in defining the final chambercharacteristics. Methods to obtain the time distance relationship are presented inChapter 6. Chapter 9 briefly discusses a simple trackfitting method and examines thecoordinate information obtained from a chamber.During the development process a total of five new chambers were constructed. Thefirst prototype proved unsuitable for the spectrometer but provided much experiencewith the chamber electronics and the operation in a real particle beam (December90). A further three identical chambers, referred to here as the Dcal chambers werebuilt to overcome the lack of available calibration chambers at TRIUMF as well as toinvestigate the effect of a different cell geometry. The results from a beam test and atest using cosmic rays in March (91) motivated the design of a third (final) prototypeon which the planned CHAOS WC3 chamber is now based. A final beam test was1Chapter 1. Thesis overview and the CHAOS spectrometer^ 2carried out in August (91) with this final prototype.Suggestions are provided throughout that will help commission the chamber. Thisthesis should also be useful as reference material for anyone designing magnetic fieldchambers at TRIUMF or elsewhere.1.2 The CHAOS spectrometer1.2.1 Physics goalsThe CHAOS detector is being built at TRIUMF to fulfill the need for a spectrometerwith a complete 27r angular acceptance. This will allow a nearly 100% coincidenceefficiency for coplanar events and is especially important for the detection of recoilparticles from the experimental target. Proposed experiments include (7, 27) reactionswhose cross sections will provide information on the N*77N coupling constants andprovide a test for chiral symmetry QCD models. The measurements will determinethe isospin 0 and 2 77r scattering lengths using reactions such as 7+p 7+7+n and7 -p 7r- r+n in which both outgoing pions must be detected. Since total cross sectionsare less than 100 itb, measurements at single angle pairs of both outgoing pions wouldrequire vast amounts of beam time.Another CHAOS experiment will measure 7rIp polarized scattering asymmetry(analysing powers) at low energies to complete the existing 7-nucleon phase shiftdatabase and resolve discrepancies between existing differential cross section measure-ments. Especially interesting is the `7rN sigma' term which can be obtained from thesemeasurements and related to the strange quark content of the proton. Recent data givea 10% strange quark content but measurement accuracy is insufficient to give definiteanswers.Chapter 1. Thesis overview and the CHAOS spectrometer^ 31.2.2 Energy and momentum resolution.The accuracy of any spectrometer at TRIUMF is limited by the channel resolution un-less the detector can measure the energy/momentum of the incoming beam. Howeverthe drift chambers in CHAOS have a drift (dead) time much longer than the 43 nsbeam cycle and they can not handle the full beam intensity of up to 40 MHz. Thespectrometer therefore aims at achieving a 0.5% APIP (detector) momentum resolu-tion. This gives an energy resolution sufficient to resolve nuclear levels of the order ofa few Mev and is close to the upper limit of the beam channel resolution.1.2.3 The Sagane magnetThe Sagane magnet chosen for the CHAOS spectrometer is a cylindrical dipole with the27r angular acceptance required. The pole diameter (95 cm) and a maximum field of 1.6T gives the 5 B • dl needed for high (400 MeV/c) momentum particles. Furthermore,the open central bore allows easy access to the target. The pole gap is only 20 cm whichseverely restricts the space available for the chambers and requires the design of verycompact high density electronic boards. Modifications to the magnet have includednew pole tips to improve the field homogeneity and larger return yokes to allow higherfields. A field map [3] is shown on figure 1.1. The coordinate system used has the z-axisalong the major component of the magnetic field and perpendicular to the plane of theincoming beam. All chamber wires are parallel to this axis. Figure 1.2 shows the radialcomponent as a function of the radius and height. The varying radial field componentinfluences the positioning of the drift chamber, discussed in detail in section 5.3. Itshould be noted that Sagane will be operated with weak and strong magnetic fieldsof both polarities. This places further constraints on the design solutions of the WC3chamber.1=43.8 A/cm2Field ValueUniformityxxx.x—x'"N„x^x. ..xxxxxCoil1 1 1 1 10.21.00.21 .0^VChapter 1. Thesis overview and the CHAOS spectrometer^ 4^I ^I^10^10^20^30^40^50^60^70^80^90^100^110Radius (cm)Figure 1.1: The z-component of the magnetic field as a function of radius.1.2.4 Detector descriptionFigure 1.3 [6] shows an overview of the target, the inner detectors (PC1, PC2, WC3),the vector chamber (WC4) and the surrounding scintillating and Cerenkov calorimetersinside the magnet. At the centre of the magnet is the target, surrounded by twoproportional chambers (PC1 and PC2) which handle incoming and outgoing beamreconstruction and determine the reaction vertex. Due to their small wire spacing andgap (1-2 mm) and consequent short dead time (< 40 ns) these proportional chambersare fast and it is expected that they can handle beam intensities of up to 10 MHz. The0.5% momentum resolution also forces the use of low density materials. The chambersare constructed using Rohacell and very thin (25 pm) Kapton sheets. Extensive MonteChapter 1. Thesis overview and the CHAOS spectrometer^ 5Radial Distance [cm]Figure 1.2: The radial component of the magnetic field as a function of radius andheight for a 1 T vertical field.Carlo simulations have been performed to evaluate the effect of material thicknesses onmultiple scattering and momentum resolution. The PC1 chamber has a wire spacing(pitch) of only 1 mm and thus a spatial resolution a of 300 pm i . The second chamberhas a larger, 2 mm pitch, the limitation being readout costs. The angular resolution inthe x-y plane of both chambers is 1/4°. The wire signals are amplified, discriminatedand fed into the PCOS readout electronics. There are no cathode wires in PC1 andPC2.The out of plane acceptance of the spectrometer is approximately ±7° and some1 Quite generally, these resolution parameters are calculated as v 22 = f ///2 2 (x — x) 2dx 3002 pmtwhere 1 is the pitch (1 mm in this case) and x the distance from the wire.Chapter 1. Thesis overview and the CHAOS spectrometer^ 6Figure 1.3: The CHAOS detectors inside the Sagane magnet.z-coordinate information is needed to make the vertical momentum correction, and asan additional aid in determining whether the track originated from the target. For thispurpose both PC1 and PC2 have inclined cathode strips, made of copper coated Kaptonfoils with conductive strips of nickel. In conjunction with the anode information, theinduced pulses on these strips describe the z-coordinate of the track. They are amplifiedthrough pre-amps, inverted and digitized using the Le Croy FASTBUS analogue todigital converters (ADCs).Chapter 1. Thesis overview and the CHAOS spectrometer^ 7The original spectrometer design intended to implement three proportional cham-bers. The three hit wire coordinates unambiguously define a circular arc, allowing ahardware (2' level) trigger to select particles of the right momentum and polarity .GEANT Monte Carlo showed that the extra mass of this third proportional cham-ber gives a noticeable increase in the multiple scattering. Secondly, space requirementswould force the inner drift chamber to be located outside the pole tips, in an inhomoge-neous fringe field that introduces complications that are discussed in section 5.3. It wastherefore decided to incorporate the WC3 drift chamber in the 2n d level trigger by split-ting the anode signal, thus eliminating the third chamber. Part of the discriminatedsignal is fed into the logic units while the remainder stops the time-to-digital converters(TDCs) for drift time information. The trigger has been simulated in software [4].The outer chamber (DC4) is a vector chamber of the type built by the RMC [2]collaboration. It consists of 10 wires per cell, eight being read out for drift time infor-mation and two optionally used for charge division readout [7,34] to provide additionalz-coordinate information. Field calculations were performed using the Garfield pro-gram [5] to investigate the uniformity and the effect of the fringe magnetic field as wellas to determine the cathode high voltage distribution.Lastly, the spectrometer will need accurate particle identification. For this pur-pose the outer layer consists of a combination of dE/dx and Cerenkov counters. Massidentification of p, d, ir particles from 50 ---+ 280 MeV is achieved using two layers ofNE110 scintillators. Pion-electron separation is more difficult because e+ parti-cles from 7r° decay (7r ° 2 y —> e+e- ) can emulate pions over a large momentumrange. The Cerenkov counter is based on the light intensity difference between highmomentum electrons creating a shower of secondary radiating electrons via photon(Bremsstrahlung) conversion, and pions producing little further radiation. The infor-mation from these detectors forms the first level trigger, selecting particles of the rightChapter 1. Thesis overview and the CHAOS spectrometer^ 8type and events with the right multiplicity. The trigger will operate at 25 MHz and isimplemented in ECL logic. A fast first level trigger is essential to gate the ADCs asquickly as possible — any delays require long delay cables on all the analogue signalsfrom the spectrometer.Chapter 2Drift Chambers2.1 Introduction to chamber principlesDrift chambers were developed as an extension of the work carried out on proportionalchambers and other gas ionization detectors. The latter were in operation as early as1908 [8]. The early versions of gaseous detectors were chambers with charged conduct-ing plates. Proportional counters containing many anode wires were not built until1967 when it was realized by Charpak and co-workers that the expected capacitiveeffects (cross talk) of multiwires would not interfere with the ability to distinguish in-dividual particles. It is somewhat surprising that drift chambers were not designeduntil 1968 (Charpak and co-workers) because extensive research on electron and iontransport through gasses had been carried out in the 1920's (Townsend [9]) in thestudy of weakly ionized plasmas. Corresponding electron drift velocities had also beenmeasured.The philosophy behind the drift chamber is that the coordinates of a charged particlecan be measured to a precision much greater than the spacing between the anode wireswithout significantly altering the trajectory. Ionization electrons (and ions) created ina gas when the particle traverses the chamber drift towards (or away) from a positivelycharged anode wire. If the electric field created near the anode is strong enough, theelectrons multiply (avalanche) via collisions and an electric pulse is observed on thewire (see section 2.2). Details on the ionization process and radiation losses due to9Chapter 2. Drift Chambers^ 10charged particles can be found elsewhere [10]. To summarize, in the most commonlyused chamber gasses one can expect a primary ionisation of approximately 30 ion-electron pairs per cm of track length. Because the ionization process is a collection ofindependent events, it follows Poisson-like statistics. If one assumes no losses duringdrift (such as recombinations), the inefficiency (1 — e) of the detector is simply theprobability that no ionization occurs. Thus 1 — e = Pon = e' , where P is the Poissonprobability function and n the total number of ionizations. Good efficiency is thereforeachieved for detectors only 1 mm thick. The released electrons may have absorbedenough energy to ionize further electron-ion pairs thus creating lumps of charge, orclusters. Very high energy (keV) knock-out electrons are referred to as S electrons andcan travel a long distance from a track before establishing thermal equilibrium throughinelastic collisions.Early work also indicated that for a certain range of electron multiplication nearthe anode wire the measured pulse height is a function of the energy loss of the particlein the chamber region. The Bethe-Bloch equation shows that this loss is a function ofparticle )3 at lower energies and of particle mass at higher energies. Chambers usingthese properties, proportional chambers, have found extensive use in nuclear physics.Note that although PC1 and PC2 are referred to as proportional chambers, they arein fact only position detectors since the anode signal height is not analyzed.The desire to increase particle tracking accuracy in large volume detectors led tothe design of drift chambers [12]. The basic principle is to measure the time it takesfor the ionized electron cluster to reach the anode wire. The timer is triggered by thepassage of the particle through a scintillator close to the chamber and stopped by thesignal on the anode wire. Knowledge of the drift velocity then determines the positionof the particle track. Accuracy is only limited by electron diffusion, ionization statisticsand knowledge of the space-time x(t) relation.Chapter 2. Drift Chambers^ 11Cathode plane0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 AnodeCathodes0 0 0^0 0 0 0 0 0 0 0^  -H.V.Figure 2.4: Adjustable field chamber.Drift chamber designs are extremely varied. In general, any configuration thatprovides a sufficiently high drift field will work. Parameters such as readout cost,multiple track resolution, magnetic fields and mechanical stability determine the design.Initially, drift chambers were seen as a low cost alternative to proportional chambersbecause of the reduced number of wires per detection area to read out electronically.Much effort went into chambers of the type shown in figure 2.4, with a drift path lengthof up to 50 cm [10] and overall sizes of 4 x 4 m2 [15]. As will be discussed in greaterdetail (Chapter 6), the track reconstruction accuracy finally depends on the knowledgeof the time-distance relation. Chamber designs such as the one above aim to provide aconstant drift field and thus a linear x(t) relationship. This simplifies calibration and,if the chamber is operated in a region where the gas velocity is saturated, makes thedrift time less sensitive to variations in temperature and voltage.Chapter 2. Drift Chambers^ 12Given a strong electric field, the electrons drift towards the anode. The field herenecessarily follows a 1/r behaviour and close (100 -- 200 pm) [11] to the wire theelectron avalanche begins resulting in charge gains (multiplication) of up to 10 5 . Theobserved pulse on the wire is not due to the electrons but due to the ions created duringthe avalanche. Since the pulse height dV oc q • dr, where q is the total charge and drthe drift distance, the 200 pm that the electrons drift to the wire surface contributerelatively little to the total pulse and are generally neglected when calculating thecharge collected on the anode.2.2 The electron avalancheThe avalanche process deserves a more detailed discussion because the CHAOS detectormakes direct use of its geometrical properties. When the electric field exceeds somethreshold value, the kinetic energy the electron gains between successive collisions canbe sufficient to cause further ionization. The first Townsend coefficient (a) is defined asthe inverse of the mean free path an electron has to travel before secondary ionizationoccurs. Typical values are 700 cm -1 at fields of 106 V/cm. Such fields are readilyobtained close to the surface of a potential wire. It was initially assumed that dueto the small wire radius and diffusion that the avalanche completely surrounds theanode wire in the azimuthal direction. This was supported by the fact that inducedpulses are observed on all surrounding cathodes. Fischer et al. [13] first designedexperiments to determine the extent of avalanche localization. One method consistedof measuring the charge induced by the slowly drifting ions from the anode to thecathode. A clear asymmetry was observed between the pulse height on a cathode wireon the side of the initial ionization and another on the opposite side. Ion drift velocitiesare low (v -1 ,=..--.. 50 ps/mm versus 20 ns/mm for electrons) thus long integration timesChapter 2. Drift Chambers^ 13and low rates are needed for such a measurement. In normal drift chamber operation,the ion pulse on the cathodes is not detected. A second method measured the fastinduced pulses on the surrounding cathodes produced by the electron avalanche thusdetermining a charge centre-of-gravity. Asymmetries were again observed.With the low noise electronics and high gain amplifiers presently available, extensiveuse is made of the induced chamber pulses. The CHAOS proportional chambers detectthe induced pulses on strips inclined at 30° with respect to the anode wire. Stripnumber combined with the hit wire number will then give z-coordinate information.The ambiguity that arises from not knowing on which side of the anode wire the trackpassed, or 'left-right' problem (see Chapter 4) is resolved in the WC3 chamber byreading pulses from strips parallel to the wires. Recently, Roderburg et al. [14] havebuild an induction chamber in which the particle track is localized using only inducedsignals, making use of the special field geometry near closely spaced wires. Each trackposition leads to a slightly different azimuthal position of the avalanche. They reportaccuracies of better than a = 30 pm.Recent computer modelling of avalanches has produced results in agreement withFischer's measurements. Groh et al. [11] simulated the path of electrons in argon-ethane mixtures by tracking individual electrons released 1 mm from the anode wire.The vast amount of computing time normally needed was reduced by treating Coulombeffects using plasma physics matrix techniques to avoid calculating the contribution ofsingle electron-ion pairs. They concluded that the avalanche starts at 100 pm from a10µm anode wire and has an azimuthal spread of no more than 50°, depending on wireradius but with little dependence on the gain in the investigated range. Furthermore,they concluded that in certain mixtures not one but several avalanches may be created,resulting from chance ionizations as far as 500 pm away from the wire. This results ina spread in arrival time of the order of nanoseconds, placing an additional upper limitChapter 2. Drift Chambers^ 14to the intrinsic accuracy of drift chambers.Two other aspects of avalanche formation are relevant to this discussion. When therate of incident charged particles is high, the slow moving ions created in the avalancheregion significantly reduce the electric field around the wire. This space charge effectforces the avalanche further out to larger radii. Groh and co-workers observed such achange in radial behaviour.Increasing the anode voltage increases the pulse height which might seem to improvethe signal to noise ratio. However at some electron kinetic energy, another physicalprocess begins to play a role. Photons from excited argon atoms can induce furtherionization of surrounding atoms. In the absence of any polarization, photon emissionis isotropic and the effect increases the azimuthal spread of the avalanche. This effectmay have been observed in our bench tests while investigating the difference in cathodesignals at very high gas gains. Photons released from argon atoms can also liberatephotoelectrons from the cathodes which will then indefinitely sustain an avalanche.Most drift chamber gasses therefore contain quenchers — polyatomic molecules thatabsorb the electromagnetic energy but de-excite through rotational and vibrationalchannels.2.3 The Garfield programThe Garfield program played an essential role in the development of the CHAOS driftchambers. Garfield, written and updated by Rob Veenhof at CERN, is a drift chambersimulation program that performs electric field map calculations, signal simulation, drifttime calculations and field optimization. The accuracy of the program is limited only bythe somewhat primitive physical model underlying the electron transport calculations.The program can be used with magnetic fields but for reasons that will be described, theChapter 2. Drift Chambers^ 150.6^0.8^1.0^1.2^1.4^1.6^1.8Electric Field kV/cmFigure 2.5: A comparison of the Lorentz angle as calculated by Garfield versus mea-surements [44].Lorentz angle (defined in Chapter 3) predictions are generally too low. A comparisonbetween Garfield's predictions and recent data is shown in figure 2.5.The great advantage of Garfield is its ability to handle periodic structures thatoften occur in drift chambers. The program was mainly used to obtain field maps anda visual image of the electron drift under magnetic fields to give some intuitive insightinto the process through which signals are induced on the cathodes.The program is divided into several sections. The chamber and cell geometry aredefined in the cell section. Only wires and infinite planes are allowed — cathode stripshave to be simulated by rows of closely spaced wires. The field section calculatesChapter 2. Drift Chambers^ 16the electric fields using the thin wire approximation. Garfield will display the surfacecharge of a wire in the chamber, thus allowing the calculation of the surface fields.This was verified against data [10] for some simple geometries. The surface fields areessential to determine the minimum diameter of a cathode wire since electron emissionis expected at fields over 30 kV/cm. In the field optimization section the program willtry to match a user specified form of the electric field but the results often requireunrealistic voltages. It was used to obtain a rough estimate of what the necessarypotentials should be but proved very helpful for field calculation in the cells of theWC4 vector chamber. The chamber gas is specified in the gas section. Garfield onlyknows the drift velocities and diffusion coefficients for a few standard mixtures. Dataon argon-isobutane gas mixtures were added using results from Mea et al. [16]. Themost commonly used program routines are called from the drift section. It calculatestime-distance relations (see Chapter 6), draws drift lines from specified particle tracksand plots and stores isochrones (contours of equal arrival time). Examples are shownin figures 5.8 and 4.7.Chapter 3Properties of Electron Drift through Gasses3.1 IntroductionThe widespread application of drift chambers renewed interest in the theory of electrontransport through weakly ionized plasmas. Electronic computers have enabled the so-lution of the Boltzmann transport equation with a reduced number of approximations.Rigorous solutions (to second order in the distribution function) have achieved [20]good agreement with experimental data for unmixed gasses in low magnetic fields.The essential weak point in this approach is that the elastic and inelastic electronscattering cross sections have been measured over a wide energy range only for a fewgasses. Standard drift gasses use polyatomic molecules for their quenching proper-ties. These molecules have complex rotational and vibrational excitation spectra thatmake any approximations unreliable. A simplified treatment, based on the approachby Townsend [9] and Palladino [20], adequate to discuss the operation of a chamber ina magnetic field, is presented in this chapter.3.2 Drift equationsRather than use the Boltzmann equation, programs such as Garfield calculate the tra-jectories using much simpler equations of motion, relying only on data for the drift ve-locity as a function of the electric field. The underlying approximations being made are17Chapter 3. Properties of Electron Drift through Gasses^ 18that the mean free path is constant over the electron energy spectrum and that the col-lision intervals are independent of the scattering angle. Especially relevant for CHAOSis the drift velocity in a magnetic field and the resulting Lorentz angle. Garfield'spredictions do not compare well with experimental data as was shown on figure 2.5.Discussing the equations of motion will explain how some simple parameterizations [29]may be able to aid calibration of the CHAOS drift chambers.Under the influence of a magnetic field in the y direction and an electric field in thez direction,= wz^where w = -63 Lmf—wx^and f= eEIntegrating twice giveswx^vzo(1 — cos(wt)) + ft + (vzo — f /w) sin(wt)wz^vzo sin(wt) (vxo — f 14.0)(cos(wt) — 1)where the average starting velocities (v.., vxo), assuming isotropic scattering, will bezero. These equations are valid for a time t, between two collisions. The mean collisiontime < t, > over the whole energy spectrum is T. To average over n collisions onemust integrate the terms sin(wt) and cos(cot) over the Poisson like probability that acollision takes place between time t o and t, dt. For example [9],< sin(wt) >fo°°^e--t/x•sm(wt)^dtnun-1 + L0 2 7- 2Thus the mean distance travelled after n collisions isf nun-< wx > = ^ nfco (1 + 44; 2 7 2 )n fun-31 + w27-2dxdtdidt<x>Chapter 3. Properties of Electron Drift through Gasses^ 19and similarly< z > -1 + co 2r 2The drift velocities are therefore< x > f w72^eE wr 2= ^nr^1 + w2T2 — m (1 + w 27-2)< Z > fr^eE^Tn7^1 +w2.7-2^m (1 + w 2 1-2)The same simple model gives for vz in the absence of a magnetic fieldeErvz = f7. =^= µEmwhich defines it, the electron mobility. Thus the velocity is reduced by the factor(1 + w 2 72 ) which, measurement shows, can be as large as 3/2. The Garfield equationsare essentially those of equations 3.1, 3.2, extended to three dimensions. The Lorentzangle, defined by tan(0 / ) = vs /vy is simply equal to0i = arctan(wr) = arctanavIB/E)^ (3.4)where v is the drift velocity at B = 0. For a typical electric field of 1 kV/cm, a 0.5 Tmagnetic field setting, electrons drifting in an argon-ethane mixture (v = 5.3 cm/µs)drift at a 15° angle.The model's main shortcoming is the above mentioned approximation that T(E) andl(e) (the mean free path) are both taken to be constant over the whole energy spectrum.If the equations of motion up to first order in awe [20] are calculated then the moregeneral results below are obtained.1^2 eE l(v)) 1 eE al(v)VIu'll = vz = ( 1 w 2 12 (v)/v2) [3 m \ v^+ 3 m \ av J J^(3.5)1^1 eEch) / 12 (v)) 2 eEw^Ol(v)\1(3.6)= vx =( 1 w 2 1 2 (v)/ v 2) 13 m \^+ 3 m \nf 72vx =-vz =(3.1)(3.2)(3.3)TRACK—DRIFT LINE PLOTParticle LI. Electron0., 0) =Arlon SOX Ethane 50%:^C(b)^x—axis [cm]0Ao.ro.1^00.0Chapter 3. Properties of Electron Drift through Gasses^ 20TRACK —DRIFT LINE PLOTParticle ID= ElectronGas W =Avon 50% Ethane 10%(a)^x—axis [cm]Figure 3.6: Electron drift paths from a straight particle track for (a) B z =0 and (b)B z=1 T. Angle # is discussed in section 8.3.4.This result is in fact identical to that obtained using the Boltzmann transport equationto second order in the distribution function. If a, = T then equation (3.6) reducesto the Townsend results. Programs such as Garfield derive T and p from the drift dataand can therefore be expected to produce good results in the absence of a magneticfield.Some typical drift paths for straight tracks are shown on figure 3.6 for electronswith and without magnetic field (1 T) for the 1 cm drift space prototype cell. Thebasic configuration is an anode wire (A), a cathode wire (C) and cathode walls at 1 cmbehind and in front of the wires (forming the axes in the above figure). These pictureswere generated assuming that thirty equally spaced clusters were generated along theparticle track. The electric field in this cell is almost cylindrically symmetric and is aslow as 500 V/cm at the centre of the drift space. Thus the drift angle (6,/ on figure 3.6(b)) near the mid plane, the line through the chamber wires, is large forcing the electronChapter 3. Properties of Electron Drift through Gasses^ 21towards the back cathode wall. Near the anode wire the electric field increases, theLorentz angle is reduced and the path follows the electric field vectors more closely.Even for perpendicular tracks one would expect adjacent cells to trigger (in the B=1T case) since the Lorentz force sweeps the electrons across the cell boundary.3.3 Electron DiffusionAn important limit to the intrinsic resolution of a drift chamber is given by the diffusioncoefficient. The classical diffusion equationanat DV 2ncan be integrated by parts to givea < x2 >=2Dat (3.7)and similarlya < x 2 >2D=ax^ w^(3.8)Thus (7 2 -2D is a measure of the lateral spread the electron swarm undergoes per unitwdrift distance. Equation 3.7 can be integrated over the total drift time or equation 3.8over the drift space to calculate the uncertainty in the arrival time. For the 1 cm pitchprototype chamber using an argon-ethane (50:50) mixture, the integrated diffusioncoefficient is approximately 3 ns for a single cluster which corresponds to a positionuncertainty of 160 pm. Although this seems large, discriminators are generally sensitiveto the pulse generated by several avalanching electrons and the mean arrival timespread is some fraction of the number mentioned above. In addition, measurements[21] indicate that the longitudinal diffusion (in the direction of the electric field) is fielddependent and substantially smaller than the transverse diffusion coefficient D quotedin the result above.Chapter 4The Left-Right Ambiguity4.1 IntroductionThe left-right ambiguity arises from the inherent symmetry between the tracks to theleft and right of the anode wire. Without additional information there is no way ofdetermining on which side the initial ionization took place. This chapter discussesa number of conventional solutions used in low magnetic fields as well as the novelapproach developed for use in the WC3 chamber at high fields.The simplest way to avoid the ambiguity is to use an additional plane of wires (asecond chamber) staggered by half the anode wire spacing. This has the additionaladvantage that the sum of the drift times t = t i t2 for the hits in the two layers isconstant in a uniform electric field, allowing a continuous check on the stability of thechambers. Several other methods to determine left from right have been developed,usually involving more than one anode wire per cell. One of the first drift chambers everdesigned used two anode sense wires spaced by 1 mm [18]. Tracks traversing the cellfired only one of the two, except when passing in between the wire pair. Later Breskinet al. [34] showed that two very closely spaced (200 ,um) anodes provide unambiguousinformation. Even for inclined tracks only one wire would fire at any given time,presumably due to space charge effects — the electron avalanche around the first wirereduces the effective field around the second. For this technique no timing informationis obtained for tracks passing in between the wires.22Chapter 4. The Left-Right Ambiguity^ 234.2 The application of induced signalsIn 1977 A.H. Walenta [36] wrote a classic paper on the use of induced signals to resolvethe left-right ambiguity. In fact, Walenta first commented on possible application ofcathode signals in an article published five years earlier but did not develop the ideafurther. J. Fischer [13] had shown that the avalanche is indeed localized for moderategains and therefore the ion cloud which drifts away from the anode is not symmetricalin the azimuthal direction. The mirror charge induced in surrounding conductors thuscontains information on the direction of the avalanche. In his drift cell, on which ourfirst prototype is based, Walenta was able to resolve left from right for tracks furtherthan 1 mm from the wire using very long charge integration times on the order of ,us.He concluded that the slow ion drift caused the slowly increasing difference betweenthe induced signals on either side of the wire. By contrast, all of our chambers reada fast, differentiated induced pulse achieving equally good separation between left andright.Further systematic study by Breskin et al. [35] showed that reading out adjacent fieldshaping wires on both sides of the anode wire (figure 2.4) through blocking capacitorsproduced the same results. Coupling together more wires on one side of the anodeincreased the pulse height, improving the signal to noise ratio. After combining morethan four cathode wires, the increased capacitance negated this advantage. The ratioof the left-to-right signal was independent of the distance between the cathode fieldwire being read and the anode wire.4.3 Solution for the WC3 ChamberResolving the left-right ambiguity using multiple planes for the large, variable angletracks in the CHAOS spectrometer requires a large number of chambers. This increasesChapter 4. The Left-Right Ambiguity^ 24the readout cost and, more relevant to the spectrometer, chamber mass. In the simpletrackfitting algorithm described in Chapter 9 it was found that even the four planesavailable during the cosmic ray test did not fully resolve the ambiguity.The double anode wire approach has several drawbacks for the CHAOS spectrom-eter. The chamber wires will be crimped for ease of construction and repair, requiringa minimum wire spacing of 2.5 mm. The double wires would leave a large fraction ofthe cell unuseable. No reference was found to any group having used this approach ina drift cell without electric field shaping in a strong magnetic field. Garfield simula-tion indicates that unless the electric field is strong enough, the electron drift path iscurved to the extent that the avalanche reaches the wires from the back or front ratherthan from the side, possibly triggering both wires or the wrong one. Finally, the largeelectrostatic forces between the wire doublet frequently requires additional support,usually a drop of epoxy glue, to ensure even separation over the height of the chamber.Our results (Chapter 8) indicate good left-right separation by reading either cathodewires or strips, thus confirming Walenta's work. The pulse difference on the adjacentcathode wires in the plane of the anodes can be empirically described as follows [22]DP = k • q • cos(a) (4.9)where AP is the signal difference, k a cell-geometrical constant, q the total inducedcharge and a the angle between the line joining the centre of the avalanche to theanode wire and a line joining the anode and cathode wires. For angled tracks the firstelectron no longer arrives from the cell midplane but along a geometrically shorterpath at some angle to the midplane. Therefore a is increased and AP decreased. Athigh magnetic fields the drift lines shown in figure 4.7 are expected, and thus AP willbe zero or even reverse sign as the avalanche arrives from the other side. Garfieldsimulation suggests that for a wide range of track angles and magnetic fields (of the13, 1 Tback rightCEChapter 4. The Left-Right Ambiguity^ 25Figure 4.7: Drift lines for B, = 1 T at various angles of incidence.same polarity), the cathode strips indicated on figure 4.7 (shaded areas back right andfront left) should pick up a large pulse difference. A novel solution to the left-rightambiguity would therefore be to use the induced pulses of the diagonally opposedstrips. Since the azimuthal coordinate of the avalanche is largely determined by theelectric and the magnetic fields this method is less sensitive to the angle of incidence.Given the symmetry of the cell, reading these strips should be as efficient as readingadjacent strips for the low magnetic field or field off situations. Digitizing only twochannels of analogue signal per cell for a given magnetic field polarity maintains thereadout cost at the same level as before. No useful information is expected from theChapter 4. The Left-Right Ambiguity^ 26other diagonal strip pair although these would of course be required when the polarityof the magnetic field is reversed.4.4 Position error resulting from the left-right ambiguityIdeally, the contribution of the unresolved left-right assignments to the chamber inac-curacy is much less than all other contributing factors. Since the region of ambiguityxmax that remains after digitizing the induced pulses is of the order of 1 mm or less(see Chapter 8), a large cell size would be advantageous. Relatively fewer events wouldfall in this region close to the anode wire.On reconstructing the event two strategies can be taken. The position of the trackfor some Ix' < xmax is approximated by the wire position itself or else one blindly truststhe information from the induced pulse down to x 0 with the accompanying risk ofdoubling the error. In the first case, over a region 2 x xmax , the chamber acts like theproportional chambers PC1 and PC2 for which no drift time information is obtained.The corresponding error contribution is cr?,. = 1/3 xmax , the standard deviation of auniform distribution. The remainder of the chamber has the normal uncertainty inthe position. Thus the contribution of the 'dead zone' for a 1 cm cell is no more thanoIr xx,„„. 60,um.cell—sizeChapter 5Drift Chambers in Magnetic Fields5.1 IntroductionSince most particle physics experiments employ a magnetic field to measure the particlemomentum, drift chambers are often operated inside a magnet or near a fringe field.It was shown in the Chapter 3 that electrons drifting in crossed E and B fields drift atan angle 0/ to the electric field vector where 9/ is given approximately by tan(0/) = WT.At low E fields (<500 V/cm) and high B fields (>1 T) the Lorentz angle can exceed60°. This leads to large drift paths, increasing electron losses to recombination. Driftvelocity along the electric field is also reduced by the factor 1+,,12 ,2 (see equation 3.2).This is not necessarily a disadvantage. Towsend [9] argued that since the drift pathsare curved but still of average length A, the random walk diffusion perpendicular tothe magnetic field should be reduced by the same factor, in principle increasing theintrinsic resolution of the chamber.The time-distance relation becomes highly non-linear under these conditions anddifficult to calculate as seen by the incorrect estimate given by the Garfield program.Moreover, as is demonstrated in figure 5.8, there is an asymmetry between tracksat opposite angles of incidence. In one case, there is a drift along the direction ofthe Lorentz force, in the other case away from it, resulting in the isochrones shown.Isochrones are lines connecting those points in the chamber where drift electrons haveequal arrival time at the anode.27D....4,1.. In— c.f.-4...N...Chapter 5. Drift Chambers in Magnetic Fields^ 28WIRE DRIFT LINE PLOTx—axis  c mFigure 5.8: Isochrones separated by 20 ns for a 1 x 1 cm cell, B=1.5 T, calculated byGarfield. The lines spiraling in towards the anode are drift trajectories. Two tracks at±45° are also shown.For small magnetic fields one solution is simply to increase the electric field. Inthe RMC [2] vector chamber (B = 0.27 T, E -,z..-1 2 kV/cm) the measured Lorentzangle is only 7° — 8° and no special design features have been incorporated. In 1973Charpak et al. [25] showed that relatively simple chambers could be constructed inwhich the electric field is adjusted to compensate for the Lorentz force. The chamberis similar to that shown in figure 2.4 but the potentials are modified to give a slantedelectric field at an angle a = arctan(Bv/E), symmetric around the anode. Thoughapproximately calculable, in practice the high voltage angle is adjusted until the arrivalChapter 5. Drift Chambers in Magnetic Fields^ 29time is minimized for a given track distance. Reported accuracies are of the order ofa = 150 pm at 1.5 T. Chiavassa [26] et al. built smaller drift chambers of the same typeand used the double wire method to resolve the left-right ambiguity. As discussed inChapter 4, if two anode sense wires are placed close together (on the order of 500 pm)then only one will fire depending on which side the particle traversed the pair of sensewires [24]. There is a resulting 'dead zone' in between the two anodes, hence the desireto have the wires as close as possible. However, the results of this method during their1.5 T field test were not described.Mechanical simplicity stimulated research into drift chamber designs without com-plex field shaping. Sadoulet et al. [28] constructed a small chamber of the `Walenta'type: one anode wire, one field wire separated by a 7.5 mm drift path and groundedcathode planes 7.5 mm from the anode. They measured the expected non-linear time-distance relation but no loss of efficiency or accuracy at 1.5 T except for large angledtracks close to the field (cathode) wire. Drift velocity saturation (see section 7.2.3)was not observed. De Boer et al. [29] built similar chambers and confirmed Sadoulet'sresults. They also showed that the drift velocity could be parameterized with twofree parameters which allowed extrapolation of the measured space-time relations todifferent magnetic fields. From equation 3.2 one can writevo vII(B) = 1 + (kB/Evo ) 2where vo is the drift velocity without field, v 11 is the velocity along the electric field andk is a parameter depending only on gas constants: k = r/(m,u). A second parameter7 is inserted in equation 3.4 to correct the Lorentz angle0/ = arctan(7wr)(5.10)The drift velocity v o was known from previous measurement and the velocity v11 wasdetermined for several field strengths. It was found that the time distance relationChapter 5. Drift Chambers in Magnetic Fields^ 30constructed using equation 5.10 agreed with those measured directly. Using trackfit-ting techniques it was verified that time-distance relations for other magnetic fieldsand angles of incidence could be predicted using to an accuracy comparable to otherreconstruction errors. Such a parameterization may be applied to calibrate the CHAOSchamber. Improved resolution was observed for B=1 T but this was attributed to thereduced relative contribution of electronic error for longer drift times. No attempt hasyet been made to measure the reduced diffusion coefficient.Ever higher accelerator energies have required stronger magnetic fields for particlemomentum determination. Sanders et al. [27] tested the slanted electric field driftchamber up to 4.5 T and concluded that electric fields of 5 KV/cm were necessary tocompensate the Lorentz angle. The highest field measurements, up to 10 T, have beenperformed by Becker [32] et al.5.2 Implication for the CHAOS chamberThe important constraints on the CHAOS drift chamber are: a small pitch for shortdrift times and an accurate second level trigger, low mass materials to reduce multiplescattering, high spatial resolution for track reconstruction and the ability to operatein varying magnetic fields and incident track angles. Over the course of the studydemands changed somewhat depending on developments of other parts of the detector.For example, to reduce the multiple scattering it was suggested that one 'chamber box'supported only at the corners of the magnet would provide the support for WC3 andWC4, effectively eliminating the chamber walls. Many field calculations were performedto design a chamber with a minimum number of wires in order to reduce the torqueon the proposed chamber box. In the end it was concluded that the combined tensionof over 1000 wires would unacceptably deflect the top and bottom of the chamber boxChapter 5. Drift Chambers in Magnetic Fields^ 31unless unacceptably thick support walls were used. The preferred design is now an`independent' free standing chamber with Rohacell walls, thin foils, and Noryl rings forcrimp pin support.The slanted electric field approach does not seem suitable for CHAOS. To shapethe electric field, electrostatic considerations show that the ratio of cell width to fullgap must be at least 1:2 (unlike the 1:1 geometries used in the calibration chambers).A minimum of three cathode wires must be used on each side of the anode to obtain asomewhat homogeneous slanted field. Given a crimp pin spacing of 2.5 mm the smallestpossible cell size is 1 cm, which reduces the resolution of the second level trigger. AsCHAOS will be operated at fields ranging between zero and 1.5 T of both polarities,(almost) every cathode wire within one cell would need a separate high voltage cableand a complicated system of bussing between cells to allow a reversal of the electricfield angle.The cell type considered to be most appropriate for CHAOS is a simple Walenta typewith the addition of cathode strips for left-right determination and field shaping. Thecell configuration is shown in figure 7.20. The main disadvantage of this design is thatsince the electric field will be inhomogeneous and the magnetic field high, a constant,saturated drift velocity can not be obtained. The time-distance relations will be non-linear and dependent on the high voltage stability and mechanical inaccuracies. Someorder-of-magnitude calculations using the Garfield program are shown in figure 5.9.The error contribution is insignificant (less than 100pm) in the 1 cm cell if the stabilityis better than +10 V.10Garfield B=1 TAV 50 VAV 10 V8 —a6 —a.)4 —4-)^2 —0—2Chapter 5. Drift Chambers in Magnetic Fields^ 320^2^4^6^8^10distance from anode wire [mm]Figure 5.9: Effect of high voltage variations on drift time, calculated using Garfield at1 T.5.3 Chamber positioningThe previous discussion shows that it is clearly possible to operate high accuracy drift-chambers in strong magnetic fields. Complications arise when the field is inhomoge-neous as is the case in the Sagane fringe field. Figure 1.2 shows the radial componentof the magnetic field as a function of height (z) and distance from the pole centre (r).It would be convenient to place the chamber outside the pole tips to reduce the spaceconstraints and thus simplify construction. GEANT Monte Carlo studies shows thatsuch a position is near the optimum for momentum resolution. However, at this radiusof 40 cm the radial component of the magnetic field varies between 0 and 1.0 T overthe full gap of the magnet poles. The question arises of what variation of the field cantrack 11d = drift path, no fieldd'= drift path, konlyd"= drift path, B, and B,(Br)(By)Chapter 5. Drift Chambers in Magnetic Fields^ 33Figure 5.10: The Lorentz angles 9, a in the presence of .13,, Br . Paths d and d' as wellas d" and d' are coplanar.be tolerated before the uncorrected systematic changes in the drift velocity introduceerror of the order of the chamber resolution. In principle some z-coordinate informationis available from the two proportional chambers and thus corrections could be madeoff-line. Calibrating the chamber at different fields and angles of incidence is sufficientlycomplicated however without having to allow for yet additional parameters.The drift path is affected in two ways. First, the radial component of the B fieldinduces a Lorentz angle along the direction of the wire. Second the magnitude of themagnetic field increases as the radial component is added, decreasing the drift velocity.An upper limit on the allowable radial component can be estimated as follows. The pathd' followed by a drift electron in a homogeneous magnetic field is shown in figure 5.10.The only change to the arrival time is in the component Vy . SinceChapter 5. Drift Chambers in Magnetic Fields^ 34pEyV =Y 1 + w2 T 2a B field of different magnitude gives a relative change ofV^wt2T2- =^Vyl^1 + W 2 T2making the approximation that the collision time is not a strong function of the mag-netic field. The position reconstruction would then be off by Ad = tLV orAd^1 -I- W2 7-2^d = (1 + w'27-2^1)If it is desired to keep such systematic errors below 100pm, then, for a 1 cm cell Ad/dPsse,0.01. Collision times 7 have been measured by Breskin et al. [31] for argon-isobutane.Taking a nominal B field of 0.8 T one obtains AT" = 0.2 T for Ex = 0.5 kV/cm andB iT" = 0.25 T for Ex = 1.0 kV/cm. This is only half the strength of the Saganeradial field at r = 45 cm. To verify the above estimates, the x(t) relations for a 1 cmcell with different magnetic field components were calculated using Garfield. As seenin figure 5.11, errors of 100 pm are made when B,. exceeds 0.2 T. For angled tracksthe error reduces proportionally because the path length is geometrically shorter. Inconclusion, it was decided to place the chamber inside the pole tips at r = 35 cm, wherethe field is strong but uniform over the active region of the chamber (+4.5 cm).1.0= 10,041B = 10,0.1,11B = 10,0.2M=0.0^iI^I0^80^160 240 320 400TDC (ns)^cell size 1 cm0 0.80.6 -7/ 0.4ro 0.2 -B=00^80^160 240 320 400TDC (ns)Chapter 5. Drift Chambers in Magnetic Fields^ 35Figure 5.11: The x(t) relation from Garfield for different radial components of themagnetic field. The error shown is x(t)B4O — x(i)Broo•Chapter 6Space-time Relationships and Resolution Measurements6.1 IntroductionUltimately, the position accuracy of any chamber will depend on the precise knowledgeof the time-to-distance relationship needed to reconstruct the particle track throughthe detector. All other sources of uncertainty such as electronic jitter, diffusion andmechanics should dominate the spatial resolution.There are several methods available. The simplest and least accurate is to integratethe drift-time spectrum such as the one shown in figure 6.12. One observes thatdn dn dxdt^dx • dt^k v(t)where do/dt is proportional to the number of particles in time bin t, . Integration gives,1^dnx(t) = k Jo Tit dtif the assumption can be made that do/dx is indeed constant over the drift spaceof the cell. Given the size of the beam relative to the cell size this approximationis usually justified. The equation also implies a constant efficiency over the wholedrift cell. If this is not the case, in principle the varying efficiency can be correctedfor. The largest contribution to the uncertainty comes from the determination of theconstant k. A drift time (TDC) spectrum and its integral is shown in figure 6.12. Theintegral is normalized by noting that the full width of the spectrum must equal thefull width of the chamber cell. It is clear, however, that both the TDC pedestal and36Chapter 6. Space-time Relationships and Resolution Measurements^37100^200^300^400^500^600drift time (tdc) [ns]Figure 6.12: TDC spectrum (counts versus time) of the last prototype (B=1.6 T) andits integral (drift distance versus time).the endpoint of the spectrum are not well defined. In fact, if the angle of incidenceof the particle is not exactly normal to the cell then the width of the spectrum willvary since the geometrical path for electrons from angled tracks is always shorter. Inaddition, care must be taken to eliminate those hits that also trigger neighbouring cellsby allowing only those counts for which the TDC time in the cell under investigation isshorter than that of the neighbouring cell. As Djilkibaev et al. [17] have pointed out,substantial numbers of 6' -electrons may trigger bordering cells even if the track didnot pass through them, thus contributing to the data in the histogram. The integralmethod gives a good first guess but no more than that. Figure 6.13 shows the x(t)relation obtained by the integral method, normalized by information obtained from thedisplacement method (discussed in the next section), compared to the displacementmethod for the first prototype in the absence of a magnetic field.Chapter 6. Space-time Relationships and Resolution Measurements^380 ^400 600^800^1000^1200^1400TDC value Ch-6Figure 6.13: A comparison of the x(t) relation obtained by integration (solid line) andusing the displacement method (triangles) for the first WC3 prototype.6.2 Displacement methodIn the displacement method [34] the chamber under investigation is mounted on somemechanical device whose accuracy is better than the resolution of the chamber. Thechamber is then scanned with a collimated beam. Plotting the displacement against theTDC value one can deduce the TDC offset from the intercept of the curves obtainedin the left and right halves of the drift cell. This method will work at all anglesand in all magnetic fields. Beam collimation can be achieved simply by using smallscintillating fibers, as was done in the first beam test (November 90), or by using twoor more additional chambers. A pencil beam can be selected by requiring a coincidencebetween two narrow time windows in two chambers. Given the left-right ambiguity,Chapter 6. Space-time Relationships and Resolution Measurements^39each time gate will define two possible track positions in the cell, one on each side of thewire. Thus four possible trajectories are selected, some of which are usually eliminatedby the beam geometry. No knowledge of the chambers in use is needed except a roughestimate of the drift velocity in order to calculate the approximate width of the definedbeam. If performed in hardware, the tight coincidence vastly reduces the amount ofdata written to tape. During the March beam test, all events were written to tapegiving the advantage that software coincidence gates could be applied to several partsof the TDC spectrum, in effect providing several simultaneous measurements of thex(t) relation of the chamber under study.6.3 Trackfitting methodRegardless of the method used to obtain an initial measurement of the space time rela-tion, iterative trackfitting must be used to optimize the resolution of the chamber. Evenan accurate knowledge of the drift velocity and electric field are not enough becausemechanical tolerance (crimp pin sizes, wire sagging, wall deformation) will contributeto the position uncertainty. Given a sufficient number of coordinate measurements(n > 3 for straight lines) a track is fitted using some first estimate of the space timerelation. The difference (residual(t i)) between measured drift distance using the x(t)relation and calculated drift distance using trackfitting (see chapter 9) is recorded andaveraged for each hit in each TDC bin t i . A new polynomial fit f(t) is performed tothe data points x i = f(ti) residual(t i ) and the process is iterated until the residualsare minimized. An example is given in figure 6.14 which compares the results given bythe Garfield program and iterations on relatively few tracks per cell, (less than 300/cellgood hits of cosmic particles) without a magnetic field. The large deviation near theedge of the cell is probably due to the small number of hits — a result of a software cut.Chapter 6. Space-time Relationships and Resolution Measurements^400^1 ^1^1^i^1^1^1^1^i0^20^30^40^50^60^70^80^90^100TDC time in nsFigure 6.14: A comparison between the x(t) relations obtained using Garfield and byfitting cosmic particle tracks, in the absence of a magnetic field.Further description of the trackfitting algorithm is given in chapter 9.A more sophisticated approach was suggested by Dellacussa et al. [19] which re-duces the number of iterations needed to obtain the correct x(t) relation. Rather thancalculating the drift velocity as a function of x or t and integrating it over the driftspace, they writex = (to — T) x W (to , T)where to is a TDC offset, T is the measured TDC drift time and W(to , T) the averagevelocity over the interval t o —4 T. Instead of merely iterating, use is made of the shapeof the residual curve.Let X f be the fitted coordinate. If the average residual has no systematic error then,= X f (to — T) x W(to ,T) =-543024)10Chapter 6. Space-time Relationships and Resolution Measurements^41Introducing systematic deviations in the TDC offset ( At o ) and in the average velocityA Wo , thenOx = X f — (t — At 0 — 7') x (W — AW)X f (to — T)W + At OW + AW (tO T)Thus the average residual for many data points isAx = At oW + (to — T)AWFitting an Tit th order polynomial EZ_ c, 1),Tn to W givesmAx = E bnTn to .Ab raTn — bn Tn+1^(6.11)n=0= E(Atobn + to Abn )Tn — bn Tn+ 1^(6.12)n=0If a polynomial fit of (m 1) th order is performed to Ax, comparing the coefficients ofTn to those in equation 6.12 gives in +1 equations that can be solved for Ab n , the onlyremaining unknowns. During the next iteration, one substitutes bn —4 1),,,-1-.Abn and thetrackfitting is repeated. The great advantage is that the number of iterations is greatlyreduced, to perhaps one or two. Such a procedure has not yet been implemented inthe trackfitting routine discussed in Chapter 9. Figure 6.15 shows the type of residualdot plot which would have to be fitted in the above method. This example is takenfrom the Dcal chambers using the simpler method described in Chapter 9 before andafter iterations. A large asymmetric spread is observed (the projection of which on theresidual axis gives the resolution histograms of figure 9.45). A dot plot with zero averageresidual indicates a fully corrected time distance relationship. Wire misalignments,electronics jitter and diffusion are the remaining causes for the width of the residual.0.20.0 -Xc4 —0.20Tr —0.4—0.6 ——0.80Chapter 6. Space-time Relationships and Resolution Measurements^42II^I,^1^1,, ^ 1^1^1^1^1^1^1^1^1^111^11^11^1 11111111111150^100^150^200tdc no. 12 [ns]1^11^II^11^11^11^11^1^I^1^1^1^1-44-+ * + + 4+ +77+ + 7-4-474--111 F+ * . 141-++44.61,441--1174.^41.2,-+^T 14++41"111111111111111110^50^100^150^200tdc no. 12 [ns]0.40.2—0.8 — 0.0Figure 6.15: Uncorrected and corrected residuals per TDC bin obtained in the Dcalchambers for cosmic rays without magnetic field.Chapter 6. Space-time Relationships and Resolution Measurements^436.4 Chamber Resolution Measurements6.4.1 IntroductionMonte Carlo simulations indicate that the position resolution of the WC3 chamberis critical to the overall momentum resolution of CHAOS. It is hoped to achieve aQ, < 150 pm at any magnetic field setting. Various authors have shown that thereis no resolution degradation in high fields [10,25], even for chambers without fieldshaping [28,29,30], We have measured the resolution of the Dcal chambers and the firstprototype at a 1 T field. Two types of measurements should be distinguished. Theintrinsic resolution gives the best possible chamber accuracy limited only by physicalprocesses such as diffusion, fluctuation in primary ionization and by electronic andtiming errors. The reconstruction resolution is a measure of how well the detector canreproduce the track coordinates. The additional constraining parameters are knowledgeof the wire positions and the time-to-distance relation.This section discusses all of the methods used to determine whether the drift cham-bers are capable of the resolution needed for CHAOS.6.4.2 Measurement of the intrinsic resolutionSince there are no devices capable of resolution substantially better than drift chambers,they themselves have to be used in the measurement as their own 'rulers'.The simplest approach is to create a finely collimated beam of width much less than2 x ax and to observe the width of the TDC spectrum a t of the chamber under study.The spatial resolution ax is given byax = at x v(t)where v(t) is the drift velocity corresponding to TDC bin t. The collimation can mostChapter 6. Space-time Relationships and Resolution Measurements^44easily be achieved using an identical set of chambers, either in hardware by requiringnarrow time coincidences in the trigger, or in software by applying gates in the TDChistograms in two of the chambers. Since one expects ares < 200 pm, these gates mustbe no more than 2 or 3 ns wide. In our case, software gates were used and consequently,large amounts of data (over 10' hits ) had to be stored on tape.If three equidistant chambers are available and two are used to define a track, thecoordinate at the centre chamber is1 ,x 2 = —2^+ x3 )The resulting peak in the centre chamber due to tracks passing through points x l , x3has a width that is a weighted sum of the uncertainties in these coordinates. Thereforewoes = 0.2(x2 )^u2(xi)^0.2(x3) (6.13)2 0.2(x) (6.14)where the last simplification is justified only if the chambers are identical and a istaken to be constant over the drift space. This method is simple and gives a resolutionaveraged over the drift space. We however, wanted to measure the resolution as afunction of distance from the anode wire to investigate whether it decreases near theedges of the drift cell. In addition the collimation did not occur at the same distancefrom the anode in the drift cells of the collimating chambers due to beam focussingand curvature.The resolution calculation for the prototype chamber is performed in two steps.Ideally a gate set in chamber 1 and 3 at position xi produces a peak at position x i inchamber 2. This is not the case for the reasons discussed above. Thus, the cell wasdivided into n sections (typically 5 or 6) within each of which the resolution is assumedconstant. A narrow TDC gate was set at or close to the centre of one section in each ofChapter 6. Space-time Relationships and Resolution Measurements^45the collimating chambers such that the resulting peak in the middle chamber occurrednear the centre of a section. One then obtains equations of the form:2^,.2^1 r 2^2jobs./ =^ 4"deal i^— k.Crelcal.rn + Dcal.1)' 2^ ( 2^„r2Cr obs.j^ad^1cal.j iladcal.k^" Dcal.j)(6.15)(6.16)where {i,j,...m} refer to the section of the cell. The width of the peak in the middlechamber is the sum of the width due to that chamber plus the width due to theresolution of the other chambers in cell section n. One needs only to set up sufficientequations by going through the rather tedious process of setting software gates andobserving where the peak forms in the middle chamber. A mathematical problem-solving program such as MathCad is then used to solve the set of n equations. Theactual coefficients used are different from the ones above because the chambers werenot equidistant as in this example.There are two sources of error in the above procedure. The track curvature in themagnetic field has been ignored. However, the curvature over the chamber spacing15 cm) is small and the only error thus introduced is that of the momentum dis-persion. Two measured points on the track do not necessarily predict the coordinatein the third chamber unless the momentum of the particles is constant. This effect isanalyzed in detail in section 8.3.2. One also needs to have a good knowledge of thedrift velocity before being able to calculate as , the spatial resolution. Therefore sometime-to-distance calibration has to be performed. Results and errors are discussed inchapter 8.Chapter 6. Space-time Relationships and Resolution Measurements^466.4.3 Track reconstruction resolutionAlthough the intrinsic resolution of the chamber may be sufficient, reconstruction ofthe event might not be feasible to that level of accuracy. In the CHAOS spectrometer,the chamber positions will (initially) not be very well known as they are independentlymounted inside the magnet. Other large particle detectors may have gravitational orelectrostatic wire sagging that limit the knowledge of the wire coordinate. Trackfittingis therefore a much better approach since it directly provides the resolution that canbe expected in an actual experiment. This section discusses a method to extract theactual resolution of a single chamber from fits in a set of chambersThree or more layers must be available and a best track is fit for each set of hitsusing an algorithm such as the one described in section 6.3 and Chapter 9. All points,including the one of the chamber under study are included. The residuals between thefitted track distance and drift position provided by the chamber are histogrammed foreach wire or chamber layer. Fitting a Gaussian to the residuals gives a o -x resolution foreach layer directly. This width will be smaller than the actual resolution of the planebecause the track fit has been weighted by that plane itself. The following solutionis only applicable to straight tracks, a useful case because even in a magnetic fieldhigh energy cosmic ray tracks may have insignificant curvature. The actual chamberresolution can be extracted as follows. The chamber planes are parallel to the x-z planewith y-coordinate yi . To avoid the infinite slopes, the track fit will be parameterizedin the formx=mxy-l-bA possible z-component of the track will not be observed in the chambers. The residualis therefore,xesp — x fit = xesp — m X yi + b^(6.17)Chapter 6. Space-time Relationships and Resolution Measurements^47where x fit is the fitted (predicted) x-coordinate at plane y i and x exp the measured valuefrom the chamber using the x(t) relation. Thus2^2 /(robs = Crobsk rn x yi^b X esP) (6.18)In other words, the observed residual is a function of the slope, intercept and x exp fromthe chamber. The aim is to isolate the cr(x exp ) for one specific chamber. This variancewill be denoted by o -res.i for chamber i. The coefficients m, b are calculated using a ,(2minimization:b =^E x i _ E yi E yi x i )E yix i — E yi x i )whereA = NEY (Ey.) 2and the x i 's are given by the time-distance relation for each hit cell. One can substitutethese forms into equation 6.18. The results are greatly simplified if one requires thatyi = n = 0 [49] which is always possible by an appropriate transformation. Onefinally obtainsares.iaobs.2 — nYj Yi + 1) 2 +(, + 1 - n) 2j#i(6.19)As previously, this equation holds only if the chambers are identical. To obtainthe resolution as a function of distance, one would have to group the tracks per TDCbin as discussed previously. Equation 6.19 has been tested using Monte Carlo data bygenerating drift distances with a given standard deviation for four equidistant chamberplanes and reconstructing the events (see Chapter 9). In this example, with n = 4 andChapter 6. Space-time Relationships and Resolution Measurements^48Y1 = —Y4 / Y2 = — 1J3 givesa068.2^Crobs.3 = '10 Crres-2,3andCrobs.1 = aobs.4 = 0.3 ores-1,4 •The measured width of the residual curve corrected by the above factors reproducedexactly the standard deviation with which the drift times were generated.Chapter 7Description of the Chambers7.1 First prototype and Dcal chambersThe first prototype chamber was designed [33] with the aim of investigating the left-right ambiguity according to specifications in a paper by A.H. Walenta [36]. As spatialresolution measurements in a magnetic field were needed and no appropriate calibrationdetectors were available at TRIUMF, three more identical drift chambers, the 'Deal'chambers, were built. All the chambers are fiat, planar chambers with an active areaof approximately 20 x 20 cm 2 and the wires soldered on a G10 midplane circuit board.Figure 7.16 shows the general features of these chambers. Dimensioning details aregiven in table 7.1.The G10 wire midplane contains all the decoupling circuitry and, for the first pro-totype, the pre-amplifier circuitry. Two rectangular frames of G10 on either side ofthis plane set the chamber gap. A further pair of 1/4" G10 frames have the cathodeTable 7.1: Cell parameters of the first prototype and calibration chambers.first prototype Dcalanode wire 0 (pm) 20 20cathode wire 0 (pm) 100 100cathode strip width (mm) 9 4half-gap (mm) 5 ch anged to 10-- 5pitch (drift space) (mm) 10 549kzcathode strip® <^pitch^ spacer layeriSOwireswire soldering padChapter 7. Description of the Chambers^ 50Figure 7.16: Structures of the prototype and Dcal chamber showing the front end andside view. The aluminium frames are not shown.strip foils glued on one side and an aluminized-Mylar foil on the other. Gas tight-ness is ensured by using rubber 0-rings and two aluminium frames to bolt the layerstogether. Only positive anode voltages were applied. The aluminium foil and outeraluminium frames act as a grounded shielding plane to reduce interference from outsidehigh frequency sources. Care was taken to interconnect all metallic parts of the cham-ber. Copper braid or tape was used to improve the contact between parts of the circuitboard and chamber body. To avoid ground loops the whole chamber was connected toonly one external ground, the pre-amplifier power supply. Inside the Sagane magnet,trial and error showed that it is necessary to connect the high voltage supply groundto the chamber as well.Gas flows in and out through two lines in the corners of the active area. It alsopasses through the space between the cathode foils and the shielding foil. This avoidsa possible pressure difference between the two layers that would cause a bulging of thecathode readout foil with respect to the anode wires.Chapter 7. Description of the Chambers^ 51The cathode foils were made from a 18 pm copper laminate on 25 pm Mylar. Thefoil patterns were designed using the AutoCad program, the negative and positivefilms were then produced off-site [37]. Substantial effort was put into the developingprocess because the quality of the cathode signal depends on the quality of the foils.The production process begins by stretching a length of clean foil on a vacuum tableand transferring it onto a temporary G10 frame using double sided tape. This ensuresconstant tension during the development process. The basic photo-chemical processsteps are: coating the foils with a photoresist, exposure to ultra-violet light, develop-ment to harden the resist and finally etching to remove the unwanted copper from thesurface. Parameters such as the method of applying the photoresist, the strength of theetchant and exposure times all affect the result. Air-brush spraying was one of severaltechniques used to apply an even layer of photoresist but best results were obtained bysimply brush painting a single thick coating and allowing it to dry for several hours.Exposure times with the ultra-violet varied with the thickness of the resist layer. Thepositive developing process in which the resist reacts on copper areas is relatively easybecause one can actually observe the change of colour on the area that is protected.When making thick windows such as laminated copper on Mylar, concentrated andwarmed ferricchloride (FeCl3) should be used but for the very thin layer of depositednickel on Kapton it is essential to dilute the etchant with water to less than 20% of itsoriginal concentration. Etching of the nickel foil is still almost instantaneous. Furtherdetails can be found elsewhere [39]. Finally, the foils are glued onto the G10 chamberframes using epoxy and the electrical contacts are soldered to them.Several modifications were made to the first prototype during the initial stages ofthis study. The half-gap (see figure 7.16) was increased to 1 cm to obtain a better fielddistribution. The cathode and anode wire pre-amp boards were redesigned to reducethe pick-up noise. Originally, the cathode planes were made of aluminium depositedChapter 7. Description of the Chambers^ 52on Mylar but after difficulties with the soldering of contacts onto this thin foil theywere replaced with laminated copper on Mylar. All the signals were to be amplifiedby a modified version of the Brookhaven DF1001 chip (see section 7.3). Subsequently,the new Fujitsu MB43458 boards became available [45] during production of the newcathode planes and were mounted instead.The drift-space of the three Dcal chambers is only 5 mm. These new chambersincorporate many of the improved features of the first prototype such as a solid alu-minium support frame and plug-in pre-amp boards (Fujitsu MB43458 chip) for all thereadouts. To resolve the left-right ambiguity, cathode strip readout is available on bothsides of the cells. The cathode wires are simply grounded.7.2 WC3-prototype7.2.1 Motivation behind designing a new prototypeThe result from the second beam test (Chapter 8) in a 1 T magnetic field indicatedthat the Dcal chambers performed satisfactorily. However, the electric field in the 1 cmpitch first prototype was too low. The Lorentz force drives the electrons to the far sideof the wire resulting in very long (> 400 ns) drift times and no left-right separation isobserved on the cathode strips. With this information in hand, it was decided to builda new prototype, which would also provide experience in building a curved chamberusing crimped wires. Designs were made for both a chamber consisting of wires only(to be used in conjunction with the 'chamber box' idea) and one with foil strips. Theaim was to obtain an improved electric field by applying a negative voltage on cathodewires or strips yet have a large cathode strip surface to read, preferably without the useof high voltage blocking capacitors. A proposed change from the Le Croy FERA adcacquisition system to the Le Croy FASTBUS system significantly reduced the readoutChapter 7. Description of the Chambers^ 53cost per channel and a slightly smaller pitch became affordable.The linearity of the time-distance relation was another concern in the new design.Calculation with the Garfield program showed that this goal is difficult to achieve giventhe small cell dimensions employed. The 1/r behaviour of the field around the anodewire dominates a large fraction of the cell. Different magnetic field settings will changethe minimum electric field needed to obtain a saturated drift velocity (see section 7.2.3).Furthermore, angled tracks will result in a non-linear time-distance relation unless thereis complete azimuthal symmetry in the electric field. A box type cell design with acentral anode wire surrounded by four or more cathode wires would give concentricisochrones except in the far corners of the cell, but as figure 5.8 indicates, this is neverthe case for high magnetic fields. Tests showed that the drift time spectrum of the newchamber for straight tracks without magnetic field is indeed more flat than that of thefirst prototype, resulting in a more linear x(t) relationship.Figures 7.17 and 7.18 show some of the proposed cell structures and their associatedelectric potential contour maps. Initially, a wire-only version was planned with eachside of the cell having two or more cathode wires to read out and one wire for fieldshaping. Only a thin gas-tight foil would enclose the cells. In the cathode-strip versionchosen for the design of the final WC3 prototype, (top left portions of figures 7.17 and7.18) a relatively uniform field exceeding 1 kV/cm is achieved by splitting the cathodestrip into a readout section and a high voltage section, separated by 1 mm. Tests weredone in air to investigate the maximum potential difference that can be applied acrosstwo strips. Sparking did not occur until the potential difference was raised to 1000 V,with this threshold expected to increase in the much drier drift gas mixture.Figures 7.19 (top) shows an informative map of the electric field contours for thechosen prototype. The bottom picture shows the direction of the field vector which,in the absence of a magnetic field is identical to the direction of the electron drift. AllShaped Field I a: anode^c: cathodeStrips Version1=t tina tDcal — lire VersionH.V.I=.6 cmCS etShaped fieldChapter 7. Description of the Chambers^ 54Figure 7.17: Proposed new cell designs, showing which wires/strips are read out.the calculations were performed with 2300 V applied to the 50pm anode wire, -600 Vto the 20 ium cathode wire and -300 V applied to the cathode strips.7.2.2 ConstructionThe last prototype design is substantially different from the previous chambers andmore similar to that chosen for the final CHAOS design. Figure 7.20 shows the basiccomponents and the cathode strip foil. In order to test two different wire pitches, onehalf of the chamber was built with a 7.5 mm anode-cathode spacing, the other halfwith a 5 mm pitch. The use of crimp pins to string the wires simplifies the structures.Two curved Noryl bars supported by steel rods form the frame of chamber. Noryl isCONTOURS OF V•10Cathode strips CONTOURS OF Deal Wire VersionVIgNNIISIIII oLx—oxis ern-7,1k^0 0 0 0 0,•••••,....._ ^*___---%^------!-.......4, ..... .,.-.. '-----1 - ii i a i i . i i iys-asis [ern](100000 .po;IChapter 7. Description of the Chambers^ 55CONTOURS OF V^Shaped Field Ix—axis - CmCONTOURS OF V Shaped Field IIFigure 7.18: Potential contours of the proposed new cell designs.used because it is difficult to drill crimp pin holes in the abrasive G10 with the requiredconsistency. In the absence of a computerized numerically controlled drilling machine atTRIUMF, the drilling was carried out off-site [38]. The requested positioning tolerancewas 50 ,um. Note that the actual crimp pin hole diameter is 100 ,um, thus for 25 pmanode wires the crimping misalignment can be as large as 38 ,um. Gas lines were madeof thin copper tubes soldered through holes in the copper laminated G10 side walls.The foils were developed as described above for the first prototypes. A serious designflaw resulted from the incorrect assumption that the difference between the inner andouter radii could be neglected. The back wall foil was therefore made too large, thef15001250, 000nan^060000 0 00000\ \ C\•^/ /^000Chapter 7. Description of the Chambers^ 56ELECTRIC FIELD CONTOURSx—axis [cm]VECTOR PLOT OF EX,E'Y^0 o0ON^ jr op0pOo0000. ocyoozOo\oo\ oO__.^ipocipo<\^\^\^I^/^/^/^/^/^/^/^/^ __ — 7 /^/^I^I- \^\^\^I^I^/^/^/^/^/^/^/ --^ /^/\ \ \ 1 I I / / / / / —^/ / 1 \- \^\^\^I^I^/^/^/^/^/^7^--  ^\- \ \ \ / / / / 7 7\^\^I^I^/^/^ 7 ^- \^\^I^I^/^/ 7 ^^N \^\^I^/^N \ ^/^/ N^/ / //^1^\- / \ N/^/^/^I^\^\^N/^/ \^\ N- /^/^/^/^1^1^\^\^\^_ / ^/^/^I^I^I^\^\^\^,^N^--,^-- -__ , ,^„. -/^/^/^/^1^\^I^\^\^\^N^.,^..., -- — — — — -- ....._^N^\^/^/- /^/^/^/^I^I^1^I^\^\^\^\^N   N^\^\^I^7_^I^/^/^/^I^1^\^I^1^1^I^I^\^,.....^--^7^...-^__^,..,^\^I^I^,^_.00000/ / 1 \ Vo1001D0000000400\000000 -- — 10000100^000c7^/^I^.1 _0400.•^950• J00C2I^260.200150.10060O-60-100- 140- 900- R60- 300-960- 400x—axis [cmJFigure 7.19: Contours of the electric field (top) and a vector plot of the electric fieldfor a rectangular version of the last WC3 prototype. Electric field units are in V/cm.In these calculation, Vanode = 2300 V, Vcathode = —600 V, Vstrips = —300 V.Chapter 7. Description of the Chambers^ 57Table 7.2: Cell parameters of the last prototype chamber.7.5 mm pitch 5.0 mm pitchanode wire 0 ,um 50 25anode wire tension gm 100 80cathode wire q5 itm 100 100cathode wire tension gm 150 150L/R strip width mm 4.0 2.5HV strip width mm 3.0/2 2/2half-gap mm 3.75 3.75front wall too small. Consequently, the misalignments were rather large and affectedthe induced pulse heights (see section 8.3.4).In CHAOS, the inner and outer walls will consist of Rohacell with thin, nickeldeposited Kapton foils glued onto them. Rohacell, a foam type of material, creates lessmultiple scattering than other construction materials such as G10. In the prototype,G10 was used instead because no time was available to study the techniques neededto glue foils onto Rohacell. A simple mandril of the correct curvature (r=35 cm) wasrolled to facilitate gluing the foils on the G10 without stressing the glue joint. An evenpressure was applied while drying by covering the G10 with a plastic sheet, insertinglarge 0-rings between the G10 and the plastic and removing the air with a rotarypump. Results were satisfactory but only after trying several thicknesses of glue. Athin, very evenly spread layer was most successful.The back and side walls were glued onto the Noryl frame before stringing to pro-vide additional support against the wire tension. Mechanical dimensions are given intable 7.2 above.The cathode wire diameter was chosen such that the maximum surface field didnot exceed the nominal limit of 30 kV/cm. Two different anode diameters were chosenChapter 7. Description of the Chambers^ 58to investigate whether the diameter has any effect on the left-right resolution close tothe wire. An increased wire diameter requires a higher potential to achieve the sameelectron avalanche size or gas gain. This produces an larger, more radial electric fieldin the 7.5 mm section.The stringing of the wires using crimp pins is a relatively simple process, especiallywhen the wires are still accessible. The procedure is as follows: insert the top pins inthe Noryl bar and feed the wire through the pin, through the hole in the bottom barand then through the bottom crimp pin. The bottom pin is inserted and a weight issuspended on the wire from the bottom to obtain the correct wire tension. A specialinsertion tool is available to force the crimp pins in the Noryl holes. Finally, the pinsare crimped and the wire ends trimmed.The electronics boards are identical to those designed for the Dcal chambers (sec-tion 7.3). A distribution board sits on top of the crimp pins using the female `burgun-D'pins and decouples the high voltage from the anodes. A similar board at the bottom ofthe chamber distributes the high voltages to six different lines, three for each chamberhalf. Separating the signal board from the high voltage lines allows a larger distancebetween circuit lines helping to avoid discharges.The largest production problem proved to be the soldering of contacts to the nickelcoated Kapton. The nickel film is only several hundred angstroms thick and a drop ofsolder will easily evaporate the layer. A low temperature solder was used to attach athin copper braid from the nickel circuit lines to a distribution connector glued on theouter walls. Sometimes the nickel circuit line broke at a glue joint and loss of signalfrom some of the strips during the beam test was attributed to bad or failing contacts.The glued joints of the front and back walls were not as gas tight as hoped and thechamber was operated with a 20% gas loss (vol.) between the input and output lines.Drops of glue were used to seal the crimp pins at the wire exit and around the crimphigh voltageanode wirenorylcrimp pinBurgun-D pinsignalH.V.Weigle/ZiaVff77277/17,171777A/11,1177Asignal H.V^signal° cathode^Anode °signal° AnodeChapter 7. Description of the Chambers^ 59Figure 7.20: Top and side view of the WC3 prototype showing the cathode foils, cham-ber frame and cell configuration.Chapter 7. Description of the Chambers^ 60pin holes in the Noryl. It should be possible to use drops of solder instead as excessglue reduced the electrical contact to the `burgun-D' pins.7.2.3 Choice of drift gasA wide variety of drift gasses are available, with the choice of mixture depending onthe specific detector requirements. A high drift velocity gas such as CF 4 will be usedin the PC1 and PC2 proportional chambers to minimize the drift time thus increasingthe rate at which the cell can handle charged particles. High gas gain (electron multi-plication) can be achieved with photon quencher components added, generally organiccompounds.Stability of the drift velocity is an important criterion for drift chambers. Ideallythe velocity saturates at some electric field value less than that used in the chamber sothat small variations due to mechanical tolerances or high voltage instabilities do notsignificantly affect the arrival time. Constant drift velocities make track reconstructionmuch easier. Measurements [42] show that the electric field required to reach saturationincreases in a magnetic field.An argon-ethane 50:50 (vol.) mixture has been used for most of the WC3 tests. Thedrift velocity of this mixture saturates at 1 kV/cm in the absence of a magnetic field(vd 5.3 cm/pm) and is not very sensitive to variations in the gas proportions. Somerough estimates using Garfield indicate that a 3-5% variation in the ethane content donot significantly affect the arrival time.There are other gasses with properties that might be considered more advantageous.An argon-isobutane mixture has similar properties to argon-ethane but leads to a higherchamber deterioration rate unless a small, carefully controlled fraction of methylal isadded [41]. Small amounts of such third components usually have strong effects on thedrift properties [42] because the large number of possible molecular excitations changesChapter 7. Description of the Chambers^ 61the scattering cross sections. An argon-methane mixture has velocity saturation atmuch lower electric fields but still shows much more variation of the drift velocityover the electric field range relevant to the WC3 (1-2 kV/cm). It also has a higherlongitudinal diffusion coefficient and a larger Lorentz angle at any field.The Lorentz angle can be considerably reduced by using heavier gas componentssuch as xenon mixtures. For example, 01 = 51° for argon:ethane but 0, = 33° forxenon:ethane at 1.5 T for the same mixtures (50:50 vol.) and electric fields (1.3 kV/cm) [41].However, the high cost of xenon necessitates a gas recycling system, rendering this op-tion unattractive. A further reason for using standard mixtures such as argon-ethaneis that their properties such as diffusion rate and cluster formation have been exten-sively studied [43,44]. Argon-ethane is also one of the few drift gas types built intothe Garfield program, thus simplifying comparison of the model with the experimentalresults.Chapter 7. Description of the Chambers^ 627.3 Chamber Electronics7.3.1 IntroductionThe anode wires and cathode strip signals must be amplified, preferably as close tothe chamber as possible to reduce noise pick-up. The narrow pole gap of the Saganemagnet requires high density, compact boards. The circuits must be able to handlepulses of up to 10 MV/s slew rate of both polarities. The quality of the anode signalis not critical except that the noise level must be below the discriminator trigger level.For the cathode signal the noise level is crucial because one can not hope for morethan a 5% amplitude difference between the signals from the left and right strips. Itwas found that the noise must be reduced to less than about 5 mV peak-to-peak (pp)on the output of the pre-amplifiers. A second, inverting boosting stage is used for thecathode signals to compensate for the attenuation in the 40 m delay cables.Designing circuit boards for the wide band amplifiers needed for the short, fast ris-ing pulses proved to be difficult unless exceptional care was taken with the grounding.Most of the circuits oscillated to some extent and this was only eliminated after ad-ditional grounding (especially between the circuit board and the drift chambers) andshielding was provided. At these video frequencies all circuit board lines have a ca-pacitance, allowing cross-talk. In addition, ground loops through power supplies leadto feedback. Frequently it was necessary to place all modules in a single NIM bin toreduce oscillations.7.3.2 Wire chamber pre-amplifiersThe first prototype chamber preamp boards were designed for the DF1001 single chan-nel charge sensitive amplifier of Brookhaven design. It was intended to be used for allof the cathode, anode and cathode strip readouts. The gain of this surface mountedChapter 7. Description of the Chambers^ 63device is approx 30 db at 1 MHz. During the first months of testing most of the effortwent into reducing oscillations that swamped the signal. Finally, it was decided todesign a new double sided board with an extended ground surface and well separatedsignal and power supply lines. The board, designed using the AutoCad package, wasproduced on-site using a positive photochemical technique. When processing doublesided boards, positioning the positive films requires considerable care or the resultingcircuit traces would be misaligned. Higher density boards have to be produced off-site.To obtain full efficiency of the chamber the discriminators must be set at theirlowest level (30 mV for the Le Croy 821 quad discriminator). Initial tests showed thatfor large anode pulses (> 300 mV pp) the second overshoot could pass this thresholdand double trigger the data acquisition system. Pole zero filters were built and addedon the output to reduce the width and tail of the pulse.Space requirements inside the Sagane magnet force the use of more compact multi-channel preamplifiers, especially for the proportional chambers. A relatively new chip,the Fujitsu MB43458 was extensively tested for use with all of the CHAOS chambers.The gain, measured at 4.4 x 10 - 5 V/C is approximately the same as the DF1001 butthe four channels per dual-in-line package give a significantly higher channel density.No significant cross-talk (< 2 mV) was observed between the channels for real chamberpulses. Most importantly, the chip handles positive pulse amplitudes of nearly thesame magnitude as the negative pulse swings. Unlike the DF1001, only a single powersupply voltage of 10 V is needed. These pre-amplifiers were successfully installed on thecathode strips of the first prototype chamber and later used to amplify all the signalson the calibration chambers and final prototype. No pole zero filters were necessary forthese circuits. Compact double-sided plug-in boards accommodating up to 16 channelswere designed by D. Maas of the UBC Physics Department.Chapter 7. Description of the Chambers^ 647.3.3 Cathode invertersThe image cathode signal is a short rise time positive pulse. Since the commerciallyavailable analogue-to-digital converters integrate negative pulses, a method was neededto invert the signals with minimum distortion. During bench tests with the first pro-totype it became clear that a clean inversion is essential for good left-right separation.Figure 7.21 top and bottom show the normalized left-right signal (see Chapter 8 fora full definition) against drift (TDC) time. Both were taken under similar conditions— same chamber voltage, gas and 0-source — but with different inverters. The bottomdiagram shows data taken using the Le Croy 428F linear fan-in fan-outs. This mod-ule greatly increased the noise level and the quoted bandwidth is insufficient. Passivecircuits (inductor coils) were also tried but the available transformers produced a largeover-shoot. Compensation would require some impedance matching or a carefully setADC gate width to avoid integrating this tail.Good results were obtained with the Plessey SL560 [47], a single channel dual-in-linevideo amplifier with a maximum bandwidth of 350 MHz. The simple circuitry designedaround this chip (figure 7.22) will drive a 50 52 coaxial line and provide enough gain tocompensate for the losses in the 120 ns delay cables that synchronize the pulses withthe ADC gate. Driven at Vcc =10 V, the output swing is limited to 900 mV. ResistorR3 sets the gain, presently at a maximum of vot,t /vin, ti 1.5. Amplification can befurther increased by disconnecting pin 5 from the voltage supply V,. This increasesthe collector resistance and thus the gain in the first of the chip's three transistorstages. Blocking capacitor C3 ensures that the first stage remains correctly biasedwhile allowing amplification for high frequency signals. The internal output-currentresistor is bypassed because the 50 52 output loading would overheat the last stage.The external resistor R4 is used instead. A single sided, 12 channel prototype boardChapter 7. Description of the Chambers^ 65603612Z-.^• •II –12 — z • ,14.1:7, \ ;■;S.^ . .–36–60603612– 12– 36– 600 240^480^720x.z12000^240^480^720^960^1200TDC value (250 ps/count)TDC value (250 ps/count)Figure 7.21: Normalized cathode signals inverted using the SL560 (top) and the LeCroy 428F fan-in fan-out (bottom).R 1 = 51 0R2 = 7.5 KOR3 = 27 0R4 = 300 0C,,C, = 0.01 /IFC 3 = 2.2Chapter 7. Description of the Chambers^ 66Figure 7.22: Inverter amplifier circuitry.was designed, produced and tested during the December test run. Again, the highbandwidth implies that care must be taken to provide good grounding and preferablythe inverters and pre-amplifiers should be powered from the same voltage supply. Morecompact, 16 channel boards based on this circuit were designed [40] and will be usedon all the CHAOS cathode signals including those from the PC1 and PC2 chambers.Chapter 8Results8.1 Bench testing the first prototypeAll bench tests were performed using the SUSIQ [46] data acquisition system runningon a 286 PC. It histograms and tests the data collected by the CAMAC system. Stan-dard Le Croy 2249A 10 bit ADCs and Le Croy 2228 TDCs were used. The first step inthe operation of any new chamber is to investigate its efficiency as a function of anodevoltage, thus establishing the plateau curve. The efficiency is defined by the countingrate of the chamber in coincidence with two scintillators divided by the coincidence rateof the scintillators alone. The plateau curve of the prototype is shown in figure 8.23.The slower rise of the cathode efficiency is due to the smaller pulse height not passingthe 30 mV threshold of the discriminator. Because the left-right separation generallyimproved at higher voltages, towards the upper end of the plateau curve, all the cham-bers were operated at high gain. Table 8.3 summarizes the potentials applied to thewires and strips for all chambers and results presented in this chapter.Table 8.3: High voltages applied to the prototype and Dcal chambers.anode (v) cathode (V) strips (V)prototype I 2100 0 0Dcal chamber 2050 0 0Prototype II 7.5 mm 2450 -600 -300Prototype II 5.0 mm 2050 -300 -30067anodecathode wireChapter 8. Results^ 68110100090800 70604-10.) 5040301700^1800^1900^2000^2100^2200^2300^2400anode voltageFigure 8.23: The prototype plateau curve showing the anode and cathode efficiencyversus chamber voltage. No cathode voltage was applied.The new DF1001 and MB43458 electronics boards reduced the noise on the cathodesignals sufficiently to begin investigation of the signal properties. A typical ADC spec-trum is shown on figure 8.24. The first peak in the ADC spectrum is due to inducedsignals from hits in neighbouring cells and can be removed by including only thoseevents that have an associated TDC value for the wire in the cell under investigation.The resultant peak has the shape of the usual Landau energy loss distribution.There is no relation between cathode signal amplitude and distance of the trackfrom the wire (figure 8.25) as is to be expected from the statistical nature of theavalanche. The induced charge difference between left and right increases with signalamplitude, but the normalized difference defined by AN1r — Q: +1 is independent ofthe pulse height, as shown in figure 8.26. Further analysis shows that the first peak inthe ADC spectrum also contains useful information. In agreement with the results ofChapter 8. Results^ 691791peak due toneighbouring hits1343896S0446'^I^500 750^ 1000AC23131, / PASSALLFigure 8.24: Typical ADC spectrum showing induced signals on cathode strips.Breskin [35], even strips far away from the hit wire' can be used to resolve the positionambiguity of the track.8.2 November test8.2.1 Description of the experimental setupThe aim of the first test with the first prototype was to investigate the drift timerelationship and the left-right information as a function of drift distance, high voltageand angle of incidence in the absence of a magnetic field. A real particle beam allows amore realistic testing of the amplifier electronics. The cathode and anode pulse heightsare different from those obtained from the ruthenium ( 1°6Ru) 0 sources used for allbench tests because these sources emit electrons below minimum ionizing energies.•comparing LNG, — Q Q;+ , +c2 ,_, , where i is the wire numberi0250Chapter 8. Results^ 70600^438^875^1750tdc time (250 ps/count)Figure 8.25: Dot plot of the cathode signal amplitude versus drift time.Chamber efficiency as a function of incident beam rate was also measured.In the absence of collimation chambers, three thin, crossed scintillating fibers wereused to define the beam. The overlap cross section was approximately 2 mm 2 . Thechamber was mounted on a computer controlled x/y-table capable of 100 pm adjust-ments. The simple hardware trigger consisted of a quadruple coincidence between anin beam scintillator and the three fibers. The ADC gate could be generated by any ofthree anode wires under study. An argon-isobutane (75:25) gas mixture flowing at 100cc/min was used.8.2.2 ResultsThe time distance relation obtained by moving the chamber in steps of 1 mm perpendic-ular to the beam is shown in figure 8.27 for the two angles, 0° (chamber perpendicularChapter 8. Results50± 3010Iit—10.11 —30—50715030a.) 10Ua.)t4-I—10 44-I -30C210^200^400^600^800^1000.ADC value200^400^600^800^1000ADC valueFigure 8.26: Dot plot of the left-right difference signal versus cathode signal amplitude(bottom) and normalized signal difference ANh. versus signal amplitude (top).20^50^100^150Time in ns—50 200Chapter 8. Results14E'12 -E10 -a.>o 8-Q0c 2-0(r)Es 0-720^I^I^I1^2^3^4^4^6^ I^ I^6^10 11Distance from anode [mm]Figure 8.27: Measured x(t) relation at 0° and 48° and the left-right separation AN1,against drift distance for the first prototype.to the beam) and 48°. The first results on the left-right separation were satisfactorybut not as clean as those obtained during the bench tests. As expected, the cath-ode signals were smaller and so the inverter gain was set to the maximum. Figure 8.27shows the AN1,. for the cathode strips obtained by combining the data from some of thedifferent chamber positions. There are relatively few incorrect left-right assignments.There is no correlation between wrong assignment and pulse height, indicating thatnoise is not the cause. The cathode strips provided better left-right information thanthe cathode wires at all chamber voltages. For the 48° data the avalanche arrived atan angle with respect to the midplane. Thus it was expected to see large ANI,. on thediagonally opposed strips and reduced separation on the side-by-side strips. Althoughthis pulse difference was indeed larger for the diagonal strips, even the adjacent strippulses showed separation and the difference between the two techniques was not aslarge as expected.Chapter 8. Results^ 73The gain of the amplifiers, inverters and ADC's varies between channels. Thereforea gain and offset correction must be made for each combination of strips. All the datashown in this chapter have been adjusted by fitting a straight line to a dot plot of theADC values of the right and left strips. If m is the slope and b the y-intercept of thisfit then the calibration factors for the right strip aregain = 1— and offset = —blmmIt is only necessary to correct the ADC value of one of the two strips. This also savesa substantial amount of computing time.Rate efficiency resultsDuring the final part of this test the beam rate was increased to investigate the efficiencyof the chamber at high intensities. The ultimate rate limitation of a chamber (or multi-track resolution) is determined by the total drift time but the operating efficiency isreduced at much lower rates by the space charge effect (see section 2.2). As the anodepulse height is reduced due to the smaller avalanche, the discriminators trigger onfewer hits. If the space charge effect is limiting the electron gain, the same incidentparticle rate (no./sec.) spread over a longer anode wire will reduce the saturationeffect. The achievable rates can thus be expressed in particles per second per wire-length for a given drift cell width. Thus results quoted here should be treated as orderof magnitude estimates since the maximum rate will also depend on the preamplifiergain and discriminator levels.Particle detection efficiency of the first prototype are shown in the table 8.4 below.The second column indicates the expected rate for one cell of the WC3 having anactive area with a height of 9 cm, illuminated with uniform intensity. These results areunder-estimated because the 2 cm wide scintillator trigger in the November test didChapter 8. Results^ 74Table 8.4: Measured and expected chamber efficiencies at high incidence rates.Prototype I WC3 chamberrate (kHz) per cm rate (kHz) over 9 cm96%t 14 12690% 23 20780% 41 36950% 70 630not fully cover the width of the cell under study and the actual incidence rates mayhave been substantially higher than those quoted. The Le Croy 2735DC discriminatorcards which will be used in CHAOS have a much lower threshold than was used in thistest and so detect smaller pulse heights. The smaller wire pitch of the WC3 chamber(7.5 mm versus 10 mm in the prototype) will also allow a higher total beam intensity.8.3 March and August tests with magnetic field.8.3.1 Description of the experimental setupThe March and August tests shared a similar setup, shown on figure 8.28. The threecalibration chambers constructed for the tests were used to collimate the beam. Theprototype chamber under investigation was mounted on a remotely controlled x/y table(positioning accuracy 20 pm) at the centre of the magnet. Removal of the SAGANEpole tips increased the gap to 47 cm allowing all chambers to be positioned betweenthe poles, each separated by about 15 cm. This close positioning is essential to reducethe momentum spread (see section 8.3.2). The maximum field is however limited to1 T in this configuration. No accurate measurement of the magnetic field strengthor homogeneity was performed and therefore the magnetic coil current settings werebased on a Hall probe survey [48]. For the purpose of this test accurate field valuesChapter 8. Results^ 75M13 channel0-95cmTr beamFigure 8.28: Schematic diagram of the March and August setup. Distances are not toscale and scintillator S3 is not shown.were not essential. During the August test of the final prototype the magnet was in itsnormal configuration with the pole tips and shims bolted on thus permitting magneticfields of up to 1.6 T with the 20 cm gap. Space requirements then forced the Dcalchambers to be moved outside the pole tip area and into the fringe field. Picture 8.29shows the chambers and mounting hardware used in the March test and in subsequentcosmic ray runs. The delay on the trigger was reduced by locating most of the hardwarein and around the M13 beam line area. Signals from the anodes were discriminatedusing Le Croy 2735 amplifier/discriminator cards and digitized with the Le Croy 4290Chapter 8. Results^ 76Figure 8.29: Photograph showing the chambers mounted inside the magnet. The pro-totype chamber is the second from the left.Chapter 8. Results^ 77TDC system operating in a common stop mode. The TDC stop was provided by acoincidence of three scintillators. The cathode signals were inverted and boosted closeto the spectrometer and delayed through RG174 coax cables to the FERA 4300B ADCsystem located nearby. This system allowed automatic pedestal subtraction and datacompression. Only valid data words were transferred to the CAMAC system, thusreducing the number of words written to tape.The triggers used for the March and August beam tests were identical and are shownin figure 8.30. Although the trigger is formed as fast as possible to gate the FERA ADCsystem, the analogue signals still have to be delayed by 120 ns to arrive synchronously.The gate, generated by a triple coincidence and a busy from the computer outputregister, is 300-400 ns wide to allow for a 100 ns pulse width plus the maximum drifttime of all the chambers. An initial concern was that the long gate time would degradethe difference signal because additional noise on the tail of the signal is also integrated.The approach of the previous test (November) where the ADC gate was provided bythe hit anode wire signal cannot be used because it would require ADCs with separategating for each channel hit. No degradation was observed.8.3.2 Momentum dispersion in the Sagane magnetSpatial resolution measurement in a magnetic field was one of the main objectives ofthe second beam test. To measure the intrinsic chamber resolution, all other con-tributions such as multiple scattering and beam momentum spread must either beinsignificantly small or well defined so that they may be subtracted. The multiple scat-tering component is small, approximately 50 pm for 15 cm of air between chambers 2and a comparable amount from the chamber foils. Beam momentum spread can be2 The out of plane deviation is Ay = O m , • Ax // where Ax is the distance between the chambersand Om , the scattering angle.Chapter 8. Results^ 78Figure 8.30: Schematic of the hardware trigger used in the March and August beamtests. Actual delays and reshaping discriminators are not shown.Chapter 8. Results^ 79estimated as follows. The beam for the chamber whose resolution is being measured isdefined by two of the three other chambers. Two possible tracks for different momentaare shown in figure 8.28. The distances h 1 and h 2 at the prototype location are1,^h 1 , 2 = P1,2 - -2 ^-4/4,2 12 (8.20)where the chord l is the distance between the chambers and p the radius of curvature.This equation is only valid if h is measured at 1/2, the worst case. The measured spreadof the beam at the prototype chamber is thus bx = h i — h 2 . We require bx << 100 pmto measure a chamber a on the order of 100 to 200 pm. In a uniform magnetic field,momentum p and p are related by the formula,p = 0.2998 qBpwhere p is the momentum in MeV/c, B the field in T, q the particle charge in units ofe and p is in mm. Therefore,Sp bpP^Pwhere p is the beam momentum. Choosing a magnetic field of 1 T and a pion beammomentum of 250 MeV/c (near the maximum of the TRIUMF M11 beam line in-tensity), the maximum allowable beam particle radius difference Sp is 15 mm andmomentum spread Sp is 2%. By closing the jaws on the pion channel one can easilyobtain Sp/p 1%. Thus, using equation 8.20, the intrinsic beam width bx is reducedto about 40 pm. Momentum spread was therefore not considered in the resolutioncalculations.1400^1200: (b )woo:wBOO:LS 600:401)::200:/I^ ,^ 0 rrry125 250^375^500^0^125tdc [ns] on test HTP2250^375^500tdc [ns] on test GTC23Chapter 8. Results^ 80Figure 8.31: Typical drift time (ns) spectra of the prototype (a) and Dcal chambers(b).8.3.3 March beam test resultsResolution measurementsThis chamber test aimed to investigate the behaviour of the first (1 cm) prototype inmagnetic fields of 0.7 and 1.0 T. The calibration chambers were only used as collimators.As the histogram in figure 8.31 (a) shows, the drift times in the prototype chamberare very long. Using the information from the beam scan (displacement method) orby integrating and differentiating the above spectrum, the drift velocity towards theanode wire can be calculated (see figure 8.35). It is approximately 2 cm/ps over mostof the cell, much lower than the zero magnetic field saturated velocity of 5 cm/ps. Thisimplies that the electrons are being carried through the very low field sections of thedrift space.A commonly used data test in the analysis was defined such that for any given eventChapter 8. Results^ 81the data value was only histogrammed if the associated TDC value represented a drifttime that was shorter than that of a hit in a neighbouring cell. In fact, such doublehits accounted for almost 50% of the data. The prototype spectrum on figure 8.31 (a)was tested on such a software gate. The TDC spectrum of the calibration chambersshown on figure 8.31 (b) (on which no special cuts have been made) is much narrower,even when the different pitches are allowed for. The two large peaks (1,2) are producedin the regions of high electric field — near the anode and cathode respectively. Thethird peak outside the drift range of the cell is only observed with the magnetic fieldon. If the shortest-arrival-time test is applied this peak disappears, which is easilyexplained by using figure 3.6. Even for straight tracks passing within the physicalboundaries of one cell, electrons are carried into the neighbouring cell due to the E x /3'velocity component. The firing of the wire in the neighbouring cell is information thatcan be used to determine the left-right ambiguity but probably not for track positionreconstruction.The chamber resolutions were calculated as described in chapter 6.4. For the Dcalchamber, no x(t) calibration was done, thus the TDC spectrum was integrated anddifferentiated with respect to time. The end points of the TDC spectrum were deter-mined by extrapolating the fast rise and fall to the time axes after all the hits hadbeen eliminated that actually belonged to the neighbouring cells. The resulting veloc-ity distribution varied less than 10% between cells. It is estimated that the error inthe velocity distribution is of the order of this 10% variation and is the dominatingcontribution to the error in the resolution. The strong variation of between 5 cm/,usand 3 cm/its over the drift space gave a large fluctuation in the observed time resolutionat as can be observed in figure 8.32. None of the results have been corrected for thesoftware time-window width, which is set at 3 ns corresponding to a position widthof 40 to 65 pm. The results for the prototype chamber were calculated assuming theChapter 8. Results^ 82160140 —120^-=cell edgeV anode00^125^ 250^375^500TDC value [ns]Figure 8.32: Time distance spectra for four separate collimation windows showing thepeaks that were fitted to obtain the time resolution at for the first prototype in the 1 Tfield.calibration chambers have an accuracy independent of the drift distance. Note thateven though the drift velocity is lower over a larger fraction of the cell than in theDcal chambers and leads to very curved paths, the resolution of ti 140 pm is not worsethan that of these chambers. The apparent increase of the accuracy with drift distancemay be statistical. It does not contradict a Vi behaviour of the diffusion since thiscontribution is still small for such short distances. Errors due to primary statistics andelectronics (the TDC's alone have a 1 ns or equivalent 50 pm resolution) dominate theuncertainty.Chapter 8. Results^ 83240^1^I^I^I^I^I^1^1^1^240220-220-11111111A♦ •ai 140-^- ^viX^ Xrem datacorrected data• •4 ••120 -20 -100 i^i^i^i^i^i^i^i^i 0 1111111110.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0^0^1 2 3 4 5 6 7 8 9 10(a)^Distance from wire [mm] (b) Distance from wire [mm]Figure 8.33: Resolution measurements of the Dcal (a) and first prototype (b). Graph(a) also shows the raw crx 's, before subtracting the contribution of the other chambers(see equation 6.15).Left-right ambiguity200-E^^ E 180-200-160-Z Z.. .,-,b 140-Z^ 120-0 o..-'^100-a)^60-40 -The first prototype yielded no useful left-right information even at the lower field settingof 0.7 T. The long ADC integration time ensured that the measured induced pulseswere a consequence of several electron avalanches. Some clusters originating close tothe edges of the cell may drift around to the other side of the anode wire while thoseionized in high electric field regions could arrive on the same side as that of the particletrack. The Dcal chamber cells, of only half the size of those of the prototype chamber,have a higher electric field and thus performed far better. The Dcal chamber data aresummarized in figure 8.34. Shown is ANir calculated using adjacent strips and one ofthe two diagonal combinations at B z =0, 0.7 and 1.0 T. The adjacent strips resolved theambiguity well at 0 T but the separation decreased at 0.7 T and very little informationwas obtained at the highest B value. As predicted, the Lorentz force resulted in anavalanche behind and in front of the anode wire giving improved separation at highFigure 8.34: Left-right signal (AN/r ) as a function of drift time from the adjacent (left)and diagonal (right) strips at B z =0 (top) Bz =0.7 (middle) and B z =1.0 T (bottom).Chapter 8. Results 84250 11^1^1^1^1^1^1^1^1^1^1^1^1'^1^1^1^1300 350^400^450^500tdc1250- 125 =,.• . •^• ;"-5.5,1..t.r.(.7.•• •.•^•^•350 400tdcdiagonal strips125o• •• •^.•^•• ••••:•%.S.i....;• •-125 -7--250  --300• .^•• ••• •• .350^400^450^500tdc250^_^1^1^11 ^1 ^1^1^1^1^1^1^1^1^1^1•-250 -^• :I450350^400tdcadjacent strips2501250-125-250300 500B=14502501250- 125- 250300 500B=01^1^1^(^1^1^1^1^1^1^1^1^1^1^I^1^12501250-125 -=.••^•••• ••■i feiNit.?",.**4161/4..K24....040:Pit.1.**01 .0. 1!Z450^500• .^•••^•. . •-250 -^^300^350^400tdczB=0.7250 ^• ••••^••••••••....•1250=-125• ••::•14;:^g,4 axg:elz.."31s;.^0•434;100r-250 ^,^,300^350^400 500450tdcChapter 8. Results^ 8504)4)0^100^200^300^400^500^0^25^50^75^100^TDC [ns] ADC top left stripFigure 8.35: Time to distance relation for the prototype chamber and a dot plot of theADCs in the Dcal chambers. Shown are the software cuts.fields on the diagonal strips. Note that in all chamber tests at zero magnetic field, thediagonal combination results were never as clean as the adjacent strips. One possiblereason is that if the angle of incidence on the chamber is not zero, then there wouldno longer be a complete symmetry between the two cases. Signal noise could also haveplayed a role. The pulses from the adjacent strips were amplified through the sameMB43458 chip. Any pickup or oscillation on the board or chip may have partiallycancelled when the integrated charges were subtracted. For strips across the cell, twosignals amplified by different circuit boards were subtracted. No other explanationshave been found.The left-right separation was further investigated using tests on dot plots such asfigure 8.35 (b) which shows the typical relation between the ADC spectra for twodiagonal strips. Large signal difference is observed in the areas labelled box 1 and box3. A software cut shows that these pulses are from the third peak in the TDC spectrumChapter 8. Results^ 86and thus caused by electrons that drift in from a neighbouring cell. The data from box2 are from electrons evenly distributed through out the drift cell.8.3.4 August test resultsThe August set up was similar to that shown in figure 8.28 except that the Dcalchambers were placed outside the pole tips. The momentum spread was therefore muchlarger and no effort was made to measure the resolution of the final WC3 prototypechamber. In addition, the low beam rate for at 250 MeV/c would have requiredvery long runs.The majority of the tests concentrated on using the 7.5 mm pitch section of thenew prototype to determine whether the left-right ambiguity can be resolved in a 1.6 Tfield for all angles of incidence. An anode voltage scan was performed without magneticfield to determine the operating voltage at which good chamber efficiency was obtainedwhile the cathode pulses were well within the range of the ADC. Due to the largeranode wire diameter (50 pm versus 20 tim for the first prototype), the plateau regionbegan at a higher voltage. As a result, this section of the chamber was operated at2450 V. Strip voltages are shown in table 8.3. The anode voltage in the 5 mm pitchsection was set to 2050 V, the same operating voltage as the Dcal chambers which haveidentical wire diameters and drift space.Two typical ADC spectra in the 1.6 T field are shown on figure 8.36. The gain isslightly too large since some of the pulses in the long tail are outside the ADC range.The first spectrum shows the raw data while the second is gated on the condition thatthe arrival time in the cell under study is shorter than that of the neighbouring cells.There is a noticeable difference between this histogram and those obtained using theearlier prototypes outside a magnetic field (figure 8.24). More detailed analysis usingsoftware tests on the data showed that the deviation from the Landau distribution isChapter 8. Results^ 87112 io^-56 -0U 28adc value — raw data^ adc value — tested on fastest drift timeFigure 8.36: Typical ADC spectrum of a cathode strip in the last prototype for twodifferent cuts (B=1.6 T).caused by electrons that are ionized in the neighbouring cell but are swept into thecell under study by the Lorentz force, as shown in figure 3.6. One expects there to berelatively few electrons from such tracks compared to the number normally arriving atthe anode wire and thus a small signal height is produced. A histogram of the ADC incell i conditioned on a hit in cell i and a hit in cell i — 1 or i 1 for which the trackactually passes through cell i — 1 or i 1 shows the expected peak with the correctnumber of events to produce the shoulder in figure 8.36. For tracks close to the cellboundary (cathode) of cell i +1 or i —1 one would expect a large number of the clustersto be swept into the cell (i) under study and thus a higher ADC pulse. Tracks that passwell into the neighbouring cell on the other hand would have the vast majority of theelectrons drift towards the closer anode wire. A dot plot (figure 8.37) of pulse height incell i versus distance away from the boundary of cell i indeed shows a decreasing pulsesize for tracks closer to the neighbouring anode wires i — 1 or i 1.This result is an additional confirmation that the integrated pulse induced on the0400,-,tk0)-1^300-I-)00S-14-1....(1)0Zo^100(21d200Chapter 8. Results^ 88Figure 8.37: ADC pulse on a strip against drift (TDC) value for tracks that pass outsidethe physical boundary of the cell.cathode is the sum of the pulses induced by all avalanching clusters and not just theone arriving first. Although the size of the avalanche per cluster fluctuates, a reducednumber of initial electrons decreases the signal height.Unlike those from the Dcal chambers, the ADC spectra of the strips in a cell of thenew WC3 prototype do not show the pulse induced by an avalanche in the neighbouringcell. The rectangular geometry of the WC3 cell results in a smaller solid angle subtendedby the strips with respect to the anode wire of an adjacent cell. Thus the induced pulseis reduced and below the pedestal subtraction level of the ADCs.The left-right ambiguity for straight tracks in the absence of a magnetic field isresolved extremely well as shown in figure 8.38. The separation is better than thatobserved with either the Dcal or the first prototype. No data were taken with thesmaller pitch section so no direct comparison can be made between the different wireChapter 8. Results^ 89Lza175^225^275^325^375^175^225^275^325^375TP6 / HDP6F TP6 / HDD1P6Figure 8.38: Left-right separation without magnetic field for adjacent strips (left) anda diagonal combination (right).diameters. The improved ANir relative to the other chambers may be explained by thelarger pitch to half-gap ratio. The electron clusters drift at smaller angles to the wiremid plane (angle )3, see figure 3.6 (a)). One might therefore expect a smaller spread inthe azimuthal direction for all the avalanches that contribute to the signal.Figure 8.39 shows A/V ir for all combinations of the four cathode strips against theTDC time in the 1.6 T magnetic field. The combination that is expected to give the bestseparation is labelled D1 and is also indicated in figure 8.40. The information displayedon figure 8.39 permits determination of the azimuthal coordinate of the avalanche forany drift distance. The difference signal is optimal for tracks near the centre of the cellindicating that there the avalanche arrives directly behind and in front of the anode.This is confirmed by the cross-over of the signals from the side-by-side strips. However,the normalized difference signal does not vanish at the same distance from the anodewire for the front and back strips. This is attributed to the misalignment of the foilsChapter 8. Results^ 90250125Z—125—250^ —250100^175^250^325^400^100tdc [ns] B=1.6 T pitch 7.5 mm175^250^325^400tdc [ns]250 25015^ 1250^—125^ z.~-125—250 —250100^175^250^325^400^100^175^250^325^400tdc [ns] tdc [ns]Figure 8.39: ANir against TDC time in ns for all four combination of the strips.Straight tracks in a 1.6 T field.during construction of the chamber. If the front strips are not properly centred onthe anode wire than the charges induced on the front-left and front-right strips willbe equal only if the electron avalanches arrive slightly off-centre. The back strips, ifaligned properly, will still see an unequal pulse.For track in the high field region of the anode, these strips give the correct left-rightassignment. For longer drift paths the electrons curve around the anode and the stripspick up an equal amount of charge. At this point the other diagonal combination (D2)(lower right corner on figure 8.39) gives incorrect left-right assignment because the leftstrip actually sees the avalanche from a track to the right of the anode.During the second part of the test the chamber was rotated +45°. The difficultiesencountered in positioning a curved chamber at a precise angle with respect to a curvedB D2^B Dl00000000000^000000000000000000000 0000000000000 0000 0..•(.11/•---"N 06000000000 0(- cathode anode0000000000^000000000000000000000^00000000000000000000^0000000000(F DI^F D2Chapter 8. Results^ 91—0.5—0.4—0.2—0.30.60.20.40.9O  S-O^O^O^to^ !FsFigure 8.40: Drift lines from a straight track in high magnetic field in a cell of the WC3chamber.track resulted in a ±5° uncertainty in the track angle of incidence. The normalizedsignals for the diagonal combination D1 are shown on figure 8.41. For the —45° anglethe results are better than expected. Figure 8.42 (b) indicates that these tracks willionize clusters some of which, in the absence of a magnetic field, would drift to the frontof the anode. The strong Lorentz force carries all clusters to the right side of the anode,inducing pickup on the correct strip. The adjacent strips provide good separation fortracks close to the anode but again AN/7. tends to zero for tracks further away.The separation for +45° incident tracks is not as clear close to the anode wire asin the previous cases. The reduced AN1,. is explained with the aid of figure 8.42 (a).For the tracks close to the wire the clusters generated at the back of the wire may driftdown the left side of the cell, contributing to the pulse on the left strips of the D.1combination. In this case the adjacent strips produced no information while diagonalChapter 8. Results^ 92225^263^300^338^375^1 50^206^263^319^375tdc [ns] tdc [ns]Figure 8.41: AN/7. obtained from the combination D1 at +45° (left) and —45° (right)in the 1.6 T field.combination D2 indicated the wrong track side for all tracks.Drift times are shorter by almost a factor of 2 for tracks at +45°. The isochronesfor the WC3 are expected to look similar to those of figure 5.8. The strong deformationfrom a circular pattern is caused because in the —45° case electrons are forced to driftthrough regions of lower electric field, increasing the lorentz angle and producing longdrift paths. Incidence at opposite angles results in Lorentz angles that lead clusters tothe strong field close to the wire as shown on figure 8.42.0 0 0 0 0 0 0^; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0^0 0 0 0 0 0 0 0 0 0B D1B=+45F D0 0 0 0 0 0 0 00 0 00 0 0 00 0 0 0 ^0 000 0 0 0 0 00 0 0 0 0 0 0 0 0^000G000000Chapter 8. Results^ 93-sea-400se(a)^ [cm]0 0 0 0 0 ; 0 0 0 0 0 0 0 0 0 0 0 0 0 0^'^; 0 0 0 0 0 0 • 0 0 0 0 0 0 0; 0^0 0 000;000 0B D2t9=-45F D2Z Z(b)^ [cm]00 • DO 00 • 50^0 • • ^0 0 00 0 00 0 5 0 • 00 • 0 0 00^ 070 0 0 0 00Figure 8.42: Drift lines from tracks at 45° (a) and —45° (b) in the WC3 cell.Chapter 9Trackfitting9.1 IntroductionA simple trackfitting program was written which allows actual (reconstruction) reso-lution of a chamber to be measured. In addition, the program was used to investigatethe correction of chamber and wire positions using the residuals between reconstructedand predicted track coordinates. The latter will be of major concern to CHAOS. Withfour mechanically independent chambers it will be very difficult to align them withaccuracy comparable to the resolution of the chambers. Some technique will have tobe implemented to determine chamber rotations, displacements and, as a second ordercorrection, individual wire offset due to bad crimping. Finally, the program also pro-vides some insight into the accuracy of the left-right assignment. Given enough layers(four in our case), x 2 minimization should converge on the correct track. The left-rightassignments given by the strips can then be compared to those of the fitted track.9.2 AlgorithmNo attempt is made here to describe the program in detail but a flow chart of the mainalgorithm is given in figure 9.43. The program takes as its input TDC values and wirenumbers. Two external files provide the physical coordinates of the wires and someinitial estimate of the coefficients of the x(t) relation. The TDC values are convertedto a distance using a fourth order polynomial.94yesall done ?add residual tox value in look—up tablecall fit—routine, gettrack slope,interceptx 2 too large ?noper cell, per tdc bincollect x„ t —x driftdone alliterations ?nodetermine left/rightof track and getwire offset residualaverage the positionoffset residualssort out if cell belongsto a groupnonocorrect wholegroup wire coord.correctindividual cellaverage tdc residualfit new polynomialto look—up tablenoyesread wire coordinatescreate x—t lookup tableclear histogramsread in tdc valuesconvert tdc to xdriftcreate table of hitwire coordinates, XdrIftcalculate first guessof track parameterslower )(2 limitChapter 9. Trackfitting^ 95endFigure 9.43: Flowchart showing the order of the main tasks performed by the programTRACKFIT.Chapter 9. Trackfitting^ 96The fitting algorithm does not fit a straight line to a set of points. Rather it seeksto minimize the distance between a track and the isochrone that is described by theparticular TDC value for each hit wires [50]. The function that is minimized isx2 = E( Di - D, it)2whereD fit ^I (rn x Yi^— x i+ 771 2(9.21)Here D i is the drift distance obtained from the x(t) relations, m the slope and bthe intercept of the track in the coordinate system defined by the wire coordinates.Variables x i and y, contain the wire position and Dr' is thus the shortest distancebetween the wire and the track. The assumption is made that the isochrone is circular.This is probably a good estimate for the square cell design of the Dcal chamber atzero magnetic field but is not true at high field for reasons discussed previously (seesection 5.1). More sophisticated approximations can easily be implemented.The actual chi-squared minimization routine is due to Bevington [51] and was chosenmainly for its speed of convergence. Briefly, it searches for a global minimum in the x 2space by finding the derivative with respect to the unknown parameters (slope,interceptin this case) and varies the parameters in the direction of maximum slope. Experiencehas shown that the algorithm can easily be trapped into local minima, therefore greatcare must be taken to provide good initial estimates of the fitting parameters. Firstguesses of the track coordinates are made using the hit wire positions corrected by theleft-right assignments. It was found that just providing the wire coordinates frequentlydoes not produce the correct convergence. Alternatively all 2n possible combinations ofleft and right for all n wires could be fitted and the one with the smallest x2 selected.The minimization routine is very general. For the trackfit the program receives onlyChapter 9. Trackfitting^ 97an index pointing to the wire position (independent variable) and the drift length(dependent variable). The same algorithm is also used to fit new polynomials to thex(t) relations and to fit Gaussians to the residual histograms by providing it differentfunctions to minimize.Once the correct slope and intercept have been found, the residuals Ax are col-lected. The difference between the drift distances from the time-distance relations andcalculated drift distances (returned by the fitting routine) is summed for each TDCbin to correct the x(t) relation. After one iteration (one complete set of tracks) theresidual is averaged over the number of hits in that TDC bin and added to the existingdrift distance value at that bin. The procedure for the positioning offset correction issimilar. Here a sign is added to the residual depending on whether the track passed tothe left or right of the wire and a correction is made for the track angle of incidence,0. In other words, the wire position offset isAx = +(dri ft — calculated_dri ft) x cos(0)A wire with a correct x(t) relation but a positive x-offset (wire misalignment) willtherefore always give a negative Ax regardless of which side the track passed. Anequivalent relation holds for offsets in the y-direction. In CHAOS a similar method canbe applied except that corrections will be made in the r and directions.Convergence is very slow if both corrections are made at once. If one has a goodestimate of relative wire positions then it can be advantageous to fix those parametersand iterate to improve only the TDC relation. A first attempt with real data showedthat, due in part to the small number of tracks used the wires were moved inconsistentlyin all directions. The second implementation of the program allowed the wires to begrouped together, for example, all those belonging to one plane. Crimping or solderingerrors are likely to be substantially smaller than positioning errors of whole chambers.Chapter 9.^Trackfittingcell A300 1^1^1 11 50025D 4004-) 200 4-) 30015D2000 10050 100I^I^r-r" • 1-1 0- 1.0^-0,5^0.0^0.5 1.0Y—Yfit^[mm]cell AIteration 1600 800500w^600.}J 400 4-)300 400200 0U^200I DO111111 ' 111111198cell B11^1^Y,^1 11f- 1.0^-0.5cell B0,0^0,5^1. 0Y-Yrit [mm]- 1.0^- 0.5^0.0^0.5^1.0^- I . 0^-0.5^0.0^0.5^1,0Y —Yht [mm] Iteration 10^Y —Yrit [mm]Figure 9.44: Monte Carlo results for wire offsets and TDC relations before and afteriteration.Indeed, convergence improved when this technique was used. The residuals for thewires in one group are averaged and all wire positions in the group corrected by thesame amount. A similar grouping procedure might also be implemented for the x(t)relations for identical cells. In the Monte Carlo results presented in figure 9.44 trackspassed 4 planar layers separated by 20 cm with wires 4 cm apart. The tracks (104 )were generated randomly at all angles. A Gaussian distributed error of a = 100 ,amwas added to the drift distances to give a more realistic chamber simulation. Cell Awas offset in the x and y direction resulting in a residual spread around the origin (seeChapter 9. Trackfitting^ 99top and bottom left histograms on figure 9.44). If the offset is small (less than 1.0 mm)the two peaks will not be resolved and a broad Gaussian is observed. Cell B's residualsresulted from a run with an incorrect TDC-to-distance relation, producing a shift toone side. After 10 iterations the residual widths were reduced to their intrinsic minima.Corrected by the coefficients calculated from equation 6.19, the width of the lower twohistograms correspond to the 100 pm error with which the tracks were generated.9.3 Application to real dataDuring the cosmic ray test without magnetic field following the March run, not enoughdata were collected to properly test the algorithm. Problems with the 4290 TDCsystem as well as with the ADCs resulted in a lot of short runs. Only around 2500good hits passed the strict test that all chambers had single hits only and all stripsfired. No chamber position information was available except some approximate sizes ofthe mounting hardware. As no measurement of the x(t) relation at zero magnetic fieldhad previously been performed, the first estimate used in the trackfitting routines wasa straight line determined by the end points of the TDC spectrum. The first fits werevisually inspected (the program optionally plots the chamber layout, isochrones, fittedtracks and histograms) to make large chamber alignment corrections and to verify thecabling of all the channels. Results are shown in figure 9.45 which shows the residuals forthe three Dcal planes and the prototype plane. Dot plot figure 6.15 (b) which is based onthese results shows clearly that there are no more systematic deviations. Approximatingto first order that the resolutions of all the chambers are comparable and using equation6.19 one obtains a apecd = 190 pm and aPcham = 230 ,um. This resolution is worse thanwhat can be expected for chambers of this type (< 150 pm) but is largely due to thesmall number of hits ( 300/wire) and the fact that no individual wire offsets were250 ^350300 -250 -200m 150 -C -100 -50 -200 -o 150 -U100 -50 -a0 1.0-1- 1.0^-0.5^0.0^0.5^residual, Fit. group^11.0 0.5^0.0^0.5residual, fit, group^2^Chapter 9. Trackfitting^ 100^o- =100 ,um^ o-=171 ,umDcal front plane Dcal mid planea=104 ,u,m^ o-= 1 9 5 ,u, m300250 -200 -m350 ^300 -250 -L4f, 2007o 150 -100 -50 -o -- 1 0^0.0^0.5^1.0^residual, fit. group^310050 -1^0^1residual, fit. group^42Dcal rear plane Prototype IFigure 9.45: Residuals summed per chamber obtained from cosmic ray tracks at B=0 T.Chapter 9. Trackfitting^ 101considered in the correction of the time-to-distance relationship. More importantly,these results indicates that given little information on the chamber position and nox(t) calibration one can obtain a true resolution close to that expected.Far more data were available for the pion beam magnetic field runs. Since allchambers were inside the homogeneous field region, in principle one could fit circulartracks. It is relatively simple to show that the function to minimize is:x2 = { 2DP — 1.\/(x — xc)2 + (Y — Yc)2 — 7-11Here x and y are the wire coordinates. The right hand side of the equation is just theshortest distance between a circle (the track) and a point (the wire coordinate). Thethree fitting parameters (x c , yc , r) are the two coordinates of the circle centre and theradius of curvature. This algorithm has been implemented and tested using Monte-carlo data in a similar fashion as the straight tracks. However, during the March runthe position of the chambers had not been recorded. The second problem seems tobe that the fitting routine is very sensitive to the starting values. Since the trajectorypoints form only a small arc of the circle, the starting parameters given by the valuesof the hit wire positions can be very far off. An alternative method is to approximatethe track by a straight line over the cell region and use the minimization functionequation 9.21.9.4 Obtaining the track coordinates in CHAOS.Obtaining track information for CHAOS from the WC3 chamber is complicated becausethe time-distance relationship is a function of the track angle of incidence 9 as well asthe magnetic field. This section is merely intended to provide some suggestion asto possible approaches, none of which have been fully investigated. If Garfield couldaccurately predict x(t) relations in a strong field then a table could be calculated forChapter 9. Trackfitting^ 102Figure 9.46: Definition of the angle 9 and distances r, x.each angle of incidence and field setting. The two proportional chambers and the eightwire planes of WC4 could be used to obtain an approximate angle of incidence onWC3 and the track coordinate read from the look-up table. During a second iterationthe track slope is recalculated and an improved coordinate obtained from the WC3chamber. The x(t) relation can be defined such that the returned coordinate is thedistance from the anode along the wire plane or the distance to the isochrone closestto the track. For rectangular cells in a weak magnetic field, the coordinates are relatedsimply through x = r/ sin(9) because (see figure 9.46) the drift angle 0 is equal to thetrack angle 9. Garfield returns the coordinate of the track in the plane connecting thewires. The look-up table would therefore return the (R, 0) position of the track whereR is the chamber wire plane radius and 0 calculated from the wire number and thedrift distance.It should be possible to improve Garfield's prediction by entering experimentallyChapter 9. Trackfitting^ 103measured drift velocities and Lorentz angles [44] as a function of the magnetic field.The three parameters, electric field, drift angle and velocity completely determine thedrift behaviour of the electron clusters. This option should be further investigated.The look-up table x = f(t,O,B) could be corrected as discussed above, by collectingresiduals between predicted drift distances and calculated drift distance.A better reconstruction method could be implemented if it is possible to parameter-ize the track, involving for example, the unknown particle momentum. A minimizationfit could then be applied over all the chambers. This would give the best momentumresolution because the redundant number of planes in the CHAOS spectrometer wouldcompensate for the chamber inaccuracies. A fitting procedure would proceed as fol-lows. The distorted isochrones in the WC3 cell under the influence of a magnetic fieldcan be approximated to a circle over some range of incident angles. A look-up tablewould return the radius of that circular isochrone given the drift-time and a roughestimate of the track angle. A fitting routine would minimize the distance between thetrack, possibly linearized over the cell distance, and the isochrone, by varying the trackparameters. These include adjustments to the track vector in the WC4 chamber andadjusting the track position in PC1 and PC2 within limits allowed by the wire spacingin these chambers. The time-to-distance relation can then be iteratively corrected asin the trackfitting routine described above except that the corrections are performedper angular section per TDC bin. The advantages are two fold. The momentum of thetrack is found immediately. No complicated TDC calibrations have to be performed.Given enough data, the isochrones can be calculated from the residuals. Furthermore,the size of the look-up is reduced since the time-distance relationship is stored only fora relatively small number of angular sections.Chapter 10Summary and conclusionsThe CHAOS detector requires a very low mass drift chamber that operates in weak andstrong magnetic fields and which resolves the notorious left-right ambiguity for a largerange of track incidence angles. It should have a small pitch yet a relatively uniformfield and obtain an accuracy of 150 pm or better. The final WC3 prototype meets allof these requirements using a novel approach the solve the left-right assignments.The first prototype chamber showed that the left-right ambiguity can be resolvedfor straight tracks passing to within 0.5 mm of the wire by reading either cathodestrips or wires. A test in a 1 T magnetic field showed that the resolution is better than150 pm over the whole drift space but the cathode strips and wires no longer provideinformation on the azimuthal position of the avalanche. The calibration chambers havea comparable resolution but provided useful left-right information from the diagonallyopposed strips even at 1 T. The ratios of the induced charges on all surrounding stripsindicated that the low field in the chambers allows the Lorentz force to carry theelectrons to the far side of the sense wire.The final prototype, designed to obtain a higher electric field, also provided expe-rience with building a curved chamber and the use of crimp pins to string wires. Thesplit cathode strips and larger anode wire diameter produce an electric field exceeding1 kV/cm throughout the cell. The successful results from the August beam test clearlyshow that it is possible to resolve the left-right ambiguity in a drift cell of this geometryunder the influence of a 1.6 T magnetic field by digitizing the induced pulse on only104Chapter 10. Summary and conclusions^ 105two strips. As expected, this unique method achieves separation over a wide rangeof angles of incidence. Although no measurements were performed at lower magneticfield settings, simulations with the Garfield program indicate that AlVb., the normal-ized signal difference, will be reduced for the —45° tracks at lower field values. Theseparation for tracks from 0° to +45° is less dependent on the Lorentz angle and istherefore expected to remain the same.Both the MB43458 preamplifiers and the SL560 booster-inverter circuits successfullyhandle the high frequency wire pulses. The amplification does not significantly increasethe signal noise but good grounding must be provided to reduce oscillations and pick-up. The combined system has sufficient gain to compensate for signal attenuation inthe long (40 m) co-axial delay cables. The wide dynamic range of the 12 bit FASTBUSADCs will handle the large range of signal height better than the 10 bit FERA ADCsused in the March and August beam tests.The intrinsic resolution, o-,, of the actual CHAOS WC3 chamber is expected tobe below 150 pm but the calibration techniques must be further investigated. Theeffort should emphasize achieving accurate time-to-distance relations using Garfield.According to the results of De Boer et al. [29] (see section 5.1), the equations of motionfor drift electrons can be corrected using two gas dependent parameters. The advantageof using Garfield is that the program could then calibrate the chambers for differentmagnetic field settings.As a result of the experience with the final prototype the design for the CHAOSWC3 is now complete. The recommended drift cell has a 7.5 mm pitch, a half-gapof 3.75 mm, 50 ,um anode wires, 100 pm cathode wires and 3 mm wide high voltagestrips shared between adjacent cells. Several production questions do remain. The useof a low temperature solder paste is being investigated for soldering contacts on thevery thin nickel-Kapton foils. Preliminary test show that the solder paste contacts areChapter 10. Summary and conclusions^ 106strong and the heating process does not evaporate the nickel. Once mandrils becomeavailable the rolling and glueing properties of Rohacell can be studied. High voltagedistribution boards have to designed. More recent Garfield calculations suggest thatthe field shaping strips and the cathode wire can be operated at the same voltage (-600V), reducing the number of separate high voltage cables.Once the detectors are built and installed some beam time will be necessary todetermine the absolute positions of the chambers. It is proposed that the beam is aimedthrough the spectrometer with the magnet off. If the chambers are built in separateangular segments then data should be taken for various rotations of the spectrometerto allow all the different sections to be covered by the beam. The trackfitting algorithmdiscussed in Chapter 9 can be modified to fit straight tracks through all the chambersand find chamber rotation and position offsets.Bibliography[1] G.H Sanders, S. Sherman, K.T. Macdonald, Nucl Instr. and Meth. 156 (1978) 159[2] R.S. Henderson et al., IEEE Transactions on Nuclear Science vol 37, No 3 (1990)[3] P. Reeve, Private communication. (1990)[4] G. Smith, CHAOS Design Note (1990), unpublished[5] R. Veenhof, Garfield: a drift-chamber simulation program v.3.00, CERN programlibrary entry W5050 (1991)[6] All AutoCad diagrams were made by P. Amaudruz[7] L.E. Holloway, Nucl. Instr. and Meth. 225 (1984) 1[8] D.H. Wilkinson, Ionization Chambers and Counters, Cambridge University Press(1950)[9] J. Townsend, Electrons in Gases, Hutchinson's Scientific Publications (1947)[10] F. Sauli, Principles of Operation of Multiwire Proportional and Drift ChambersCERN 77-09 (1977)[11] J. Groh, E. Schenuit, H Spitzer, Nucl. Instr. and Meth. A293 (1990) 537[12] G. Charpak et al., Nucl. Instr. and Meth. 62 (1968) 537[13] J. Fischer, H. Okuno, A.H. Walenta, Nucl. Instr. and Meth. 151 (1978) 451[14] E. Roderburg et al., Nucl. Instr. and Meth. A252 (1986) 285[15] J. Heinze, Nucl. Instr. and Meth. 156 (1978) 227[16] C.M. Mea et al., MIT Technical Reports 129,130 (1982)[17] R. Djilkibaev et al., A Fast Chamber, to be submitted to Nucl. Instr. and Meth.[18] A.H. Walenta, J.Heintze, B.Schuerlein, Nucl. Instr. and Meth. 92 (1972) 373[19] G. Dellacasa, Nucl. Instr. and Meth. 176 (1980) 373107Bibliography^ 108[20] V. Palladino, B. Sadoulet, Application of the Classical Theory of Electrons inGases to Mulitwire Proportional and Drift Chambers, Berkeley Report xx (1974)[21] F. Sauli, Nucl. Instr. and Meth. 156 (1978) 147[22] E. Roderburg, Private Communication. (1990)[23] E. Chiavassa, et al., Nucl. Instr. and Meth. 156 (1978) 187[24] A. Breskin et al., Nucl. Instr. and Meth. 176 (1980) 373[25] G. Charpak, F. Sauli, W. Duinker, Nucl. Instr. and Meth. 108 (1973) 373[26] E. Chiavassa et al., Nucl. Instr. and Meth. 156 (1978) 373[27] G.H. Sanders, S.Herman, K.T. MacDonald, A. Smith, Nucl. Instr. and Meth. 156(1978) 159[28] B. Sadoulet, A. Litke, Nucl. Instr. and Meth. 124 (1975) 349[29] W. de Boer et al., Nucl. Instr. and Meth. 156 (1978) 249[30] W. de Boer et al., Nucl. Instr. and Meth. 176 (1980) 167[31] A. Breskin G. Charpak, F. Sauli, M.Atkinson, G.Schultz, Nucl. Instr. and Meth.124 (1975) 89[32] U. Becker et al., Nucl. Instr. and Meth. 205 (1983) 137[33] Chamber designed and constructed by P.Amaudruz[34] A. Breskin, G. Charpak, F. Sauli, Nucl. Instr. and Meth. 119 (1974) 9[35] A. Breskin, Nucl. Instr. and Meth. 151 (1978) 473[36] A.H. Walenta, Nucl. Instr. and Meth. 151 (1978) 461[37] Norman Wade Co., Vancouver, Canada.[38] Sicom Industries, Surrey, Canada.[39] P. Vincent, TRIUMF Detector Facility Darkroom Manual, TRIUMF, unpublished[40] Layout designed by P. Amaudruz[41] H. Daum et al., Nucl. Instr. and Meth. 152 (1978) 541Bibliography^ 109[42] A. Peisert, F.Sauli, Drift and Diffusion of Electrons in gases: a CompilationCERN EP84-08 (1984)[43] U. Binder et al., Nucl. Instr. and Meth. 217 (1983) 285[44] M. Atac et al., Nucl. Instr. and Meth. A249 (1986) 265[45] All Fujitsu MB43458 boards were designed by D. Maas, UBC Physics[46] Data acquisition software by P. Amaudruz and R. Tacik[47] Plessey Broad Band Amplifier Handbook Plessey Electronics (1985)[48] Field map measured by summer student C. MacGowen[49] R. Djilkibaev, Private Communication. (1990)[50] W.J. Taylor, The Spatial Resolution of the E787 Ultra- Thin Drift CHamber,BSc. Thesis, University of British Columbia.[51] P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences,McGraw Hill (1969)

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