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Cosmic ray tests of a liquid argon calorimeter Bougerolle, Stephen Edward 1989

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COSMIC R A Y TESTS OF A LIQUID A R G O N C A L O R I M E T E R Stephen Edward Bougerolle B. Sc. (Physics) University of Lethbridge, 1987  A THESIS S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F T H E REQUIREMENTS F O R T H E D E G R E E O F M A S T E R OF SCIENCE  in T H E F A C U L T Y O F G R A D U A T E STUDIES DEPARTMENT OF PHYSICS  We accept this thesis as conforming to the required standard  T H E UNIVERSITY O F BRITISH C O L U M B I A  April 1989  (?) Stephen Edward Bougerolle  In  presenting  degree at the  this  thesis  in  University of  partial  fulfilment  of  of  department  this thesis for or  by  his  or  scholarly purposes may be her  representatives.  permission.  of  r Ay $ / c S  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  rApr.'<  H j  If3<f  for  an advanced  Library shall make it  agree that permission for extensive  It  publication of this thesis for financial gain shall not  Department  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  is  granted  by the  understood  that  head of copying  my or  be allowed without my written  Abstract  A series of tests have been performed on a liquid argon calorimeter module at the Test Beam Facility at the Stanford Linear Accelerator Centre. We find that the calorimeter performs according to design. Several performance parameters have been measured. The charge-collection efficiency in a tower of the calorimeter was observed to be 87%. This loss is due mainly to recombination; absorption by oxygen impurity seems insignificant. No detectable energy loss has been observed when a particle moves through the crack between adjacent towers. The cross-talk between two adjacent towers was measured and found to be in agreement with a simple model.  n  Table of Contents  Abstract  ii  List of Tables  v  List of Figures  vii  Acknowledgement  viii  1  Introduction  1  2  Apparatus  6  2.1 Physical setup  6  2.2 Tracking  8  2.3 Trigger  8  2.4 Data Acquisition 3  10  Theory of Ionization Chambers  13  3.1 Energy Loss Due to Ionization  13  3.2 Ionization Chambers  14  3.3 Absorption 4  .  16 18  Data Reduction  4.1 Tracking  18  4.2 Chamber Alignment  19  4.3 LAC calibration  20 in  5  6  4.4 Module Location  21  4.5 Data Sets  22  4.6  22  Summary  High Voltage Response  28  5.1  Data Sets .  28  5.2  Analysis  28  5.3  Results  • • 29 3 3  Cross-Talk'  6.1 Theory  33  6.2  35  Analysis  6.3 Error Analysis 6.4 7  •  Results  38 3  Position Response  7.1  37  Data Set  9  39  7.2 Results  40  A  Charge Sharing in the L A C  42  B  Position Cuts  45  Bibliography  49  iv  List of Tables  4.1  Peak Energy Losses  23  5.1  High-Voltage Test Data Sets . . .  29  6.1  EMI Cross-talk . :  36  6.2  HAD2 Cross-talk  37  v  List of Figures  1.1 Side view of SLD  . 4  1.2 A typical barrel LAC module  5  2.1 Physical setup  7  2.2 LAC test trigger electronics  9  2.3 LAC signal processing  11  2.4 Block diagram of LAC tower + front-end electronics  12  3.1 Charge collected including germinate recombination  15  3.2 Charge collection efficiency for different levels of impurity  17  4.1 Raw spectra showing pedestal and signal shape .  24  4.2 Calibrated, isolated EMI spectrum  25  4.3 Calibrated, isolated EM2 spectrum  26  4.4 Calibrated, isolated HAD2 spectrum  27  5.1 Typical Spectrum and Landau+Noise distribution  30  5.2 Response of the calorimeter as a function of applied voltage  31  6.1 Cross-Section of a LAC tower junction  34  6.2 Tower grouping for cross-talk measurement  36  7.1 Mean signal as a function of entry and exit position  40  7.2 Mean signal as a function of entry position andfixedangle  41  A.l LAC tower and blocking capacitor  43  vi  B.l Map of towers in an endcap module B.2 Relevant vectors in position requirements .• . . B.3 Position requirements  46 47 . 48  vii  Acknowledgement  This project could not have been completed without the help of numerous people. In particular, I would like to thank my supervisor, Randy Sobie, for his endless patience, help, and whip-cracking. Marc Turcotte provided endless helpful hints and stood in for me on many occasions when I was not present to do some necessary job. Iris Abt, Alan Honma, Erik Vella, provided and maintained the software and electronics used. Peter Rowson, Mike Shaevitz, and everyone else from Nevis have been an invaluable source of information and help with the endcap module itself. And of course none of this would go on without approval and support from SLD and SLAC. While working on this, I have been supported by a scholarship from the Natural Sciences and Engineering Research Council of Canada.  viii  Chapter 1  Introduction  +  The SLAC Linear Collider (SLC) will produce e e~ collisions at an energy y/s = 100 GeV near the mass of the Z°-boson. This will result in a high production rate of the Z°, one of the mediators of the weak interaction, whose decays will be observed in the SLD detector. The SLD detector is a large, general purpose 4ir detector (seefigure1.1) containing a number of subsystems for tracking, particle identifiction, energy measurement and muon tracking. First is the vertex detector, an array of Charge-Coupled Devices (CCDs) which will provide very accurate position measurements (resolution « 5^m) at a distance of approximately 15 mm from the interaction point. This allows very precise reconstruction of vertices in the decay of the Z° itself as well as heavy fermions produced from the Z°.  Outside the vertex detector is the Central Drift Chamber (CDC), which provides longer-range tracking data to a resolution of 100/i.m. The CDC consists of a barrel and two endcap sections, which together cover 97% of the full Att solid angle. The CDC is contained inside a Cerenkov Ring Imaging Detector (CRID). As a particle passes through the CRID, it produces a ring of Cerenkov radiation which is focused onto a photon detector. The radius of the ring is dependent on the velocity of the particle and can be used to separate ir, K, e and p over a momentum range of 0.2 to 30 GeV/c. 1  Chapter 1.  Introduction  2  Outside the CRID is the detector of interest here, the Liquid Argon Calorimeter (LAC). The LAC will be described in more detail later, but in short is a conventional sampling calorimeter of lead and liquid argon (LAr). Outside the LAC is the detector's magnet, which generates a 0.6 Tesla "solenoid" +  field, oriented along the axis of motion of the incoming e and e~. The magnet has a largefluxreturn yoke made of iron segmented into 14 layers 5 cm thick, separated by 3.2 cm gaps. This arrangement has been used to advantage to build a Warm Iron Calorimeter (WIC), which uses the iron as the passive medium. The gaps contain plastic drift tubes similar to those used in the Mont Blanc Proton Decay experiment[2], where the deposited energy is read out. Two layers of tubes are oriented perpendicular to each other, and can be read out to give position measurements for outgoing muons. The LAC is divided into four sections, each containing alternating layers of Pb and LAr. Going outwards from the interaction point, the first section is the EMI, which contains 8 layers of alternating 2 mm Pb tiles and 2.75 mm  LAr gaps. The next section  is EM2, which has the same structure as the EMI but extends to 20 layers rather than 8. Beyond this are two sections HAD1 alternating 6 mm  Pb tiles and 2.75 mm  The EM and HAD  and HAD2, each of which contain 13 layers of LAr gaps.  sections are so named because their lengths are chosen so that  most of an electromagnetic shower is contained in the EM segment, while most of a hadronic shower is contained in the HAD section. The EM section is divided into towers which subtend an angle of 36 mrad in the actual detector, while the HAD  towers cover  an angle of 72 mrad. These angles are again chosen to correspond to typical expected shower sizes in each section. The LAC is further divided into a barrel and two endcap pieces, which are of fundamentally different construction. In the barrel, the EM and HAD  sections are  Chapter 1. Introduction  3  composed of separate modules (288 of each - see figure 1.2), while each endcap consists of 16 pie-shaped modules, each containing an EM and HAD section. During the summer of 1988, an endcap module was set up in a LAr bath box in the SLAC Test Beam Facility, where its characteristics were studied using cosmic ray muons. Among the features studied are the spectrum of energy deposited in the detector, the induced false signal in one tower due to an event in another tower (cross-talk), and the variation in response of the detector with the position at which a particle enters it. The cosmic ray analysis detailed hereafter provides thefirstdata on how this detector will perform when the SLD experimental run begins.  4  Chapter 1. Introduction  B  PI «5Z0  1TT1T1-1 ,C£L  oooooo  3900  f UJ-J  CflTL  2946  III///  M  f,  III/  i  j)  LPL  / ' ' / / / / /  U0U1D ARGON ' 1J J I t « - u n i ^ I L  /  • • • xfe  in n I'j^tpyf . / , ////////sss * K  CERENKOV RIN3 IMAGIN3 DETECTOR  Figure 1.1: Side view of SLD Detailed vertical section in the plane including the e beams of one quadrant of the detector. Dimensions are in millimeters[l]. ±  Chapter 1.  Introduction  5  Figure 1.2: A typical barrel LAC moddle Isometric view of an electromagnetic- and hadronic stack aaacodule of the barrel calorimeter [1].  Chapter 2  Apparatus  The cosmic ray tests were conducted in the Test Beam Facility at SLAC. The physical setup consisted of a large dewar containing the module in a liquid argon bath box, with cosmic ray detector arrays placed outside the dewar. Data collection was handled by a chain of electronics running from the LAC daughterboard through CAMAC to a VAX 11/780 where the data was stored on disk. 2.1  Physical setup  The dewar itself is approximately 4 meters long and 1.5 meters high. It contains a bath box (which is inserted on rollers) just large enough to hold one endcap module (seefigure2.1). The bath box isfilledwith LAr and recirculated using a system which is expected to be comparable to that of the final SLD detector. The level of impurities in the argon is expected to be less than 1 part per million. The electric field in the endcap module was maintained by a standard industrial high-voltage supply capable of producing 0-5000 V at very low current draw. For normal use, afieldof « 11000 V/cm was maintained between planes, although several runs were completed with other field strengths for test purposes (to be described later).  6  Chapter 2.  Apparatus  Cosmic  Deuiar  Figure 2.1: Physical setup  Chapter 2.  2.2  Apparatus  8  Tracking  Tracking and triggering were done using two detector arrays made at TRIUMF. Each array contained two Multi-Wire Proportional Chambers (MWPCs), 30 x 30 cm in size with a delay-line readout, capable of resolving position t© better than a millimeter of accuracy, and two "paddle" scintillators which overlapped the area of the MWPCs. The gas used to operate the MWPCs was a mixture of 70% Argon, 30% Ethane, and a trace of freon. The chambers were run at their "plateau" voltage of 3100V (supplied by standard industrial HV supplies, as with the endcap module). One array was installed above the dewar and one below, at a projection angle near that of the towers of interest in the endcap module. Due to multiple scattering of a cosmic-ray particle, the angle of motion of the particle in each array can be substantially different. So, the two sets of MWPCs were used independently to track the particle to the top and bottom of the module. By this method, the theoretical accuracy of the tracking system is about 1 mm. 2.3  Trigger  The basic cosmic-ray trigger consists of a coincidence between all four scintillators. This signal is then relayed back to CAMAC, where it is compared with a "ready" signal from the VAX and timing signals from the LAC electronics. If all is ready, data is read in from the LAC and the MWPCs (see figure 2.2). Including a "dead time" of approximately 30% due to time sharing on the VAX, the observed trigger rate averaged about 330 events per hour, which agrees with the expected rate of « 450 per hour.  Chapter 2.  Apparatus  DflQ Ready  Scintillators  ,TDC  ^—•Trigger 1 Cosmic Ray Trigger  . — , Daughterboard Trigger  Timing Control Cosmic Ray Veto  Figure 2.2: LAC test trigger electronics  Chapter 2.  2.4  Apparatus  10  Data Acquisition  The MWPC data consists of 16 TDC signals, two for each plane in each chamber. The TDC counts time from the trigger until a pulse is received at each end of the delay line in an MWPC plane. The difference in the two times for a plane then gives the position of the track. The LAC data consists of 192 values, representing the charge collected in 48 towers in the endcap module. The raw signal from each is fed into a LAC daughterboard, which amplifies and shapes the pulse, integrating the current from the tower to give the charge collected. The pulse height is then measured at two different times, with a separation of 3 ^xs, giving the peak ("signal") and background ("baseline"), as shown infigure2.3. These values are digitized in an ADC and sent to the VAX with a gain of one and a gain of eight, giving four numbers per tower (seefigure2.4). In normal operation mode the baseline is sampled at 180 Hz, just before an event can be expected from the SLC. This corrects for any long-term drifting of the baseline. For the cosmic ray tests, the SLC signal is replaced by the cosmic ray trigger. It is possible to run the LAC daughterboard in a calibration mode as well as datataking mode. During this operation, LAC signals are imitated by injecting a precisely known amount of charge from a 7.6 pF calibration capacitor into the normal datataking route. Several sets of data were taken in calibration mode; no significant change with time was observed in the channels studied. Data from the LAC and MWPCs is combined into a single event record (with time information) and written to disk on the VAX, where it is processed later.  Chapter 2.  11  Apparatus  There is a 3 fis lapse between the signal and baseline pulses. Figure 2.3: LAC signal processing  Chapter 2.  Apparatus  Daughterboard  Shaper  qCt> Blocking I Cap.  C  cal  < Preamp  ^v=fCq) -r'o-  LAC  Tower  Postamp  *>2  A  CRL Ref. Level  Tff  CRL P a t t e r n In, O u t , Strobe Preamp/Shaper  Analog Storage Unit  Hybrid  Figure 2.4: Block diagram of LAC tower + front-end electronics  Chapter 3  Theory of Ionization Chambers  3.1  Energy Loss Due to Ionization  As a particle passes through a medium, its energy E decreases according to the BetheBloch formula[4] dE  47rN z e  dx  mv  2  Z  4  0  (3.1)  A  2  e  where m is the mass of an electron, z and v are the charge (in units of e) and velocity e  of the ionizing particle, [3 = v/c, N is Avogadro's number, Z, A, and I are the atomic 0  number, mass number, and mean ionization potential of the atoms in the medium, and x is the path length of the particle. A muon must have energy E > 750MeV to traverse the endcap module. In this energy region, the energy loss varies logarithmically with  7  = (1 — ft ) / . As a result, 2  -1  2  we can assume that dE/dx is approximately constant for the events we study. Such particles are referred to as minimum ionizing. The number of ion pairs produced N is related to the energy lost by the ionization potential I from above: ^ N = 1  dE , r»dE —dx ~ II— Jo dx dx  (3.2)  where the particle travels a length I through the medium. For LAr, J = 23.6 eV[5].  13  14  Chapter 3. Theory of Ionization Chambers  3.2  Ionization Chambers  In an ionization chamber such as the LAC, the LAr is kept in a high-strength electric field. When free electrons are produced, they drift towards the anode producing the electricfield(a lead tile in this case). If the charge is produced in a line between two plates, the current seen at the tile is[6]  d K  id)  (3.3)  i(t) = { 0  t>t  d  and the charge observed  Qdt) = {  Mi-Hi)') ^  (3.4) t > t  d  where N is the number of electrons produced, e the charge of an electron, t the time since passage of the ionizing particle, td the total time for all electrons to be collected, v the drift velocity of the electron in the LAr, and d the maximum drift length. In practice, v and td are replaced by the mean path length of the particle. As t —> td, the charge collected'approaches |iVe and we see only half the deposited charge as signal. In addition to the above, we must account for the recombination of the drifting electrons with Ar ions. Two types of recombination are expected; columnar, where the electrons drift into ions on their "way to the plate, and germinate where the electrons are recaptured by the Ar ion immediately after separation [7]. For a LAr system it has been shown that the germinate theory bestfitsthe observed results[9]. This predicts a response with voltage as given infigure4.1.  15  Chapter 3. Theory of Ionization Chambers  Recombination  Losses  in L A r  1.0 H  0.6 -I  0.4  H 0  1  1000  1  1—:  2000 3000 High V o l t a g e ( V )  1  4000  5000  Figure 3.1: Charge collected including germinate recombination  16  Chapter 3. Theory of Ionization Chambers  3.3  Absorption  In addition to the loss due to recombination, impurities in the LAr can cause the drifting electrons to be absorbed. In particular, it is expected that small levels of oxygen can have noticeable effects (for example, see refs. [8],[10]). The absorption loss rate is given by a standard exponential-decrease model dN(t)  (3.5)  -k,N,N(t)  dt  N(t) = N e  -k N t s  (3.6)  s  0  where N(t) is the number of electrons at time t, N the number of electrons initially 0  produced, k the rate of absorption (determined from the absorption cross-section) and s  N the impurity concentration. s  Substituting 3.6 into equation 3.3 gives  = N e-  Qc  v /e = Ne d \t (k N y  0  /  -k.N.tdt  Qc  e  _±  f  td  JO  te  -k.Nst  dt  (3.7)  and after integrating -k,N,t  0  d  s  s  d  + kN s  s  u(k N yj s  (3.8)  s  We can replace the drift velocity v and the drift time td = d/v with the mean path length A = ^ r - This gives  Qc  = N e^ 0  1-^(1-e-<»)  (3.9)  where Q is the total charge observed, as in the ideal case. Figure 3.2 shows the charge c  collection efficiency for different levels of impurity.  Chapter 3. Theory of Ionization Chambers  High V o l t a g e ( V )  Figure 3.2: Charge collection efficiency for different levels of impurity  17  Chapter 4  Data Reduction  The data obtained requires processing before it can be used for analysis. TDC data from the MWPCs must be converted to give track parameters and these must be corrected for errors in the tracking system. Pulse heights from the LAC must be calibrated to give the energy deposited in each tower by a cosmic ray particle. The exact position of the endcap module in the dewar had to be determined. 4.1  Tracking  In any given MWPC, there are two planes of wires, each giving a measure of the position of a track along one axis. In each plane, the wires are laid across a delay-line strip. The induced signals in the delay-line propagate to both ends of the wire. If the propagation time to one end is T\ and the time to the other end is r 2 , then the position of the point measured is given by  x = a(T -T \+P 2  X  (4.1)  where a and 0 are constants which vary for each plane. The sum of the two signals, t = T\ + r 2 should be approximately constant for any s  given plane, given that only one particle causes a pulse in the chamber. This is used to advantage to cut out events with bad tracking data. If r, is outside the "normal" range of values for that plane, the position measurement from that MWPC is not used. This largely eliminates events where the cosmic ray particle creates a shower in the 18  19  Chapter 4. Data Reduction  endcap module - producing multiple tracks in the bottom MWPCs, which show up as bad position measurements. Further cuts are placed on each TDC signal - which can reasonably be expected to be greater than zero seconds and less than full scale. If any signal from an MWPC failed this cut, the position measurement from that MWPC is discarded. Any event which failed the "shower" cut above, or which did not have at least two usable MWPC measurements, was discarded. 4.2  Chamber Alignment  The location of the MWPCs with respect to the dewar was measured to an accuracy of approximately a centimetre. We improved on this measurement by taking a special data set with the module removed so that the effect of multiple scattering on the cosmic ray particles is minimal and their tracks are almost linear (with the module in place, the mean multiple scattering angle for a 2 GeV muon is 4.2°; with the module removed it drops to 0.3°). The four positions (for this process, only events with four good measurements were 2  r  used) were then fit to a line, and the total \ f° the data set was used as a statistic to determine how accurate the position parameters are. Using this statistic, the problem then becomes one of simple multi-dimensional function minimization. There are six parameters determining the location of each chamber; three position offsets and three rotation angles. The position of the bottommost chamber was taken to befixedand the other three chambers were adjusted relative to it.  Chapter.4. Data Reduction  4.3  20  L A C calibration  Out of the four numbers from each LAC channel (signal, baseline, signal x 8, baseline x 8) only the x8 data was used as the muon signal is too small to be observed in the low gain. First, the baseline is subtracted from the signal (each x8) to obtain the pulse height in the electronics. The pulse height must then be calibrated. This is done using a set of curves obtained by running the daughterboard in calibration mode (see Chapter 2) at various values of injected charge. The signal from these runs is thenfitto a polynomial to give a relation between the signal seen at the ADC and the actual signal output from the module. This relation is approximately linear, but thefitwas done to higher order for more accuracy, becoming in fact cubic. The resulting curve is used to calibrate the signal-baseline pulse height and obtain a spectrum in volts. The charge is obtained by multiplying this spectrum with the value of the calibration capacitor (seefigure2.4). Several sets of data were taken with no cosmic ray trigger, giving a "pedestal" measurement of the pulse height. This pedestal value must then be subtracted from the pulse height above (after undergoing the same calibration process) to obtain the physical pulse height - the pulse out that is actually due to charge read out from the module. Each tower in a module is connected to a blocking capacitor (seefigure2.4) which shares the collected charge. Thus, when we read out the charge from the module a further correction must be made to obtain the charge actually deposited in the tower. The fraction / of charge collected in the tower is given by (see Appendix A)  (4.2)  21  Chapter 4. Data Reduction  where  Cuock  is the blocking capacitance and  C tai to  is a function of the tower capacitance  and Cblock-  From  this signal we can then determine the total energy deposited. The charge  collected differs from that deposited by a charge collection efficiency factor (which was derived in chapter 3), and the charge deposited is related to the energy deposited by the ionization potential of LAr. Putting all these factors together, wefinallyhave the energy deposited in the LAC tower; a spectrum calibrated in MeV. 4.4  Module Location  Given pulse heights and position information, we must know where the towers of the endcap module are located. As with the chamber geometry, this was done first by measurement and improved using afitto the cosmic ray data. A single EMI tower (with complete coverage in the cosmic ray telescope) was selected, and an "isolated" data set was taken, consisting of events which deposited energy in this tower but none of the towers around it. This was accomplished by requiring the minimum signal in the central tower to be at least 3 standard deviations above zero, and the signal in each surrounding tower to be at most 0.5. The size and shape of the tower is known and can be adjusted in position to compare to the projected entry position of a track. Thefitstatistic was taken to be the mean distance from the tower of all tracks which were not projected to be inside it. The best location is taken to be that which minimizes this value. Since the position data is taken relative to the bottom-most chamber, which lies flat on thefloorof TBF and is approximately level with the module, we need only worry about adjusting the position of the module in two dimensions. Thefitthus had  Chapter 4. Data Reduction  22  3 parameters; two offsets and one rotation angle. 4.5  D a t a Sets  For most studies, we need a set of events where the cosmic rays are known to all go through one tower. We first require the "entry" and "exit" positions (meaning the projected position of a track using the two wire chambers closest to the tower in question) to be greater than 1 cm inside the edge of the tower being studied. This has the effect of largely reducing "bad" events (ie, those where the particle goes through a different tower). Due to multiple scattering, linear tracking is not entirely accurate, and we must correct for errors due to this. So, we further require that the difference in the track angles in the top and bottom chamber (ie, the multiple scattering angle) be less than 0.15 radians in both planes. This largely eliminates bad events due to scattering of that particle out of the tower. Since the multiple scattering angle is inversely proportional to to the momentum of the particle this cut biases the resulting spectrum by eliminating low-energy events. Even after all this, we are still left with some bad events, so a final requirement is made that the signal in the central tower must be three standard deviations above zero. 4.6  Summary  Typical spectra of the raw, uncorrected data (in ADC counts) are given infigure4.1. Note the pedestal and muon peaks in each spectrum. The final calibrated and isolated spectra are shown infigures4.2, 4.3, and 4.4. Assuming constant dE/dx, the energy losses for a typical cosmic ray event (E = 3  Chapter 4. Data Reduction  Section EMI EM2 HAD2  23  Table 4.1: Peak Energy Losses Theoretical Experimental Error 10 MeV 11 MeV 0.3 MeV 24 2.0 25 2.0 16 14"  GeV in the EM sections, E = 2.6 GeV in HAD2) have been estimated and compared with the observed peak values (see table 4.1).  24  Chapter 4. Data Reduction  Raw 300  EM1, E M 2 , H A D 2  i  i  i  I  0  I 25  I 50  I  Spectra i  i  j  200  HAD'2 ji  EM2 100  EM1 0 -50  l -25  T 75  I  100  I  125  150  The spectra above have been translated in ADC counts and re-scaled in height for easier comparison. Figure 4.1: Raw spectra showing pedestal and signal shape  Chapter 4. Data Reduction  25  Isolated a n d C a l i b r a t e d EM1 S p e c t r u m I  120  ,  I  I  I  L.  100H 80 60 40 20 H  4 •20  ^4 20  40  Energy (MeV)  Figure 4.2: Calibrated, isolated EMI spectrum  60  Chapter 4.  26  Data Reduction  Isolated and C a l i b r a t e d EM2 S p e c t r u m I I , I  14 12 I 10  Ld  £ 6Z3 4H 2H *1 »ttr^a=tx»»-***:*aat:--.  •20  20 Energy  40  (MeV)  Figure 4.3: Calibrated, isolated EM2 spectrum  60  Chapter 4.  Data Reduction  27  Isolated and C a l i b r a t e d HAD2  Spectrum  40  U30O" -Q 2 0  10H  •20  r 0.  ft  Hi  h-.t^.^yT.t.^i-t^^^%T-t'-^=t-*--t1-t-..T-.r-t.-t  20 E n e r g y (MeV)  40  Figure 4.4: Calibrated, isolated HAD2 spectrum  60  Chapter 5  High Voltage Response  5.1  Data Sets  A special set of data was taken from one of the HAD2 towers studying the dependence of its signal on the high voltage applied across it. The signal obtained from the tower at each of these voltages was then compared with theory and used to obtain the efficiency of the calorimeter as a function of sampling voltage. We find that the efficiency can be entirely explained by germinate recombination losses. Spectra were obtained at 10 voltage levels, from 200 to 5000 V (normal operating voltage is 3100 V). Approximately 5000 raw events were collected in each spectrum. After applying isolation requirements, about 750 events were left on average (see table 5.1).  5.2  Analysis  Theory predicts that the energy loss by a minimum-ionizing charged particle traversing a thin slab of material should follow a Landau distribution. In fact, the LAC consists of alternating layers of Pb and LAr, each of which introduces a Landau-distributed energy spread[ll], and the result should be the convolution of all of these. The signal out of the calorimeter is also subject to electronic noise, which induces a Gaussian noise distribution in addition. Varying the voltage in the calorimeter also changes the rise-time of the outgoing  28  Chapter 5.  High Voltage Response  29  Table 5.1: High-Voltage Test Data, Sets ;  Voltage Number of events Signal Peak (naaiV) Error (mV)  200 400 600 800 1000 1500 2000 3100 4000 5000  657 554 606 905 629 426 729 989 512 760  2.63 3.56  [ -.0.13 ; (0:25 | (0.:26 ; (0:25 ! 0.39 ess i ;0:23 ! (0.33  3.71  4.21 4.72 4.60 4.75 4.69 4.99 5.02  1.31  i  ; (0.33  pulse, but the integration time of the amplifier (3 /xsj)  Ikamg enough that the high  voltage test is not affected by this. For the purposes of this test, we assumed the spectrum «Bem to be a Landau distribution convolved with a Gaussian distribution. For each of tribe spectra, we thenfitthis to the data using MINUIT[12] and use the result to ohtaiaa tthe most probable energy loss of a charged particle passing through the calorimeter ((;sse figure 5.1). 5.3  Results  The most probable energy loss at each voltage has been (computed from the Landau+Noisefitand a typical spectrum is displayed in :fignme 5.2. Since the absolute efficiency is not known a priori wefitthe voltage distribution to theoretical efficiency curves, varying the oxygen impurity and normalizing fac*ar.. This gives an impurity level of 0.068lJ;o|8 PP  m  anQl :am  efficiency at 3100 V of  86.9 ±7.8%. The data infigure5.2 have been normalized to the best-fit value of the charge  Chapter 5. High Voltage Response  Figure 5.1: Typical Spectrum and Landau+Noise distribution  30  Chapter 5. High Voltage Response  31  Variation of efficiency with applied high voltage. Also plotted are theoretical efficiency curves for impurities of 1 ppm and 10 ppm oxygen. Figure 5.2: Response of the calorimeter as a function of applied voltage  Chapter 5. High Voltage Response  32  collection efficiency. Also plotted are the theoretical curves for various impurities. We conclude that at the 90% confidence level, the oxygen impurity is < 3.2 ppm.  Chapter 6  Cross-Talk  As charge is collected in a LAC tower, the potential on each tile changes and induces a potential between tiles in adjacent towers. As a result of this, an event in one tower induces a signal in neighbouring towers, dubbed "cross-talk". We have measured the cross-talk in a set of EMI and HAD2 towers. EM2 data was not analyzed as the number of events here was too small to give useful statistics. 6.1 Theory The capacitance of a tile in an EMI tower can be approximated by the parallel-plate formula C = 2KtoA/d, where A is the area of the tile, d is the gap between it and an adjoining plate, k is the dielectric constant of the medium (1.53 for LAr), and 12  e0 = 8.85 x 10~ Farads/m. Using this form we calculate (for example) a capacitance of 0.38 nF for a typical EMI tower whereas the actual value for this tower is 0.90 nF- The discrepancy can be explained by the simplicity of this model; it does not allow for such things as edge effects or the varying size of the tiles in the tower. Each tile is not a plane, but has some thickness to it. This causes a second parallelplate effect between tiles in adjacent towers (seefigure6.1). This second capacitance is " given by C = Ke £t/w x  0  where I is the length of the tile side, t is its thickness, and w is  the gap between adjacent towers. For our sample EMI tower, we calculate a cross-talk of 6.8 pF. 33  Chapter 6.  Cross-Talk  Figure 6.1: Cross-Section of a LAC tower junction  34  Chapter 6.  35  Cross-Talk  m  The cross-talk x  a  tower i from an event in tower j is defined by  * - |  (6.D  where S is the signal read out from tower x. x  Further cross-talk is caused in the daughterboard electronics, but measurements show that this has no significant effect for the towers of interest here. The energy deposited is proportional to the charge collected in the tower. Since each tower is maintained at the same voltage, the charge collected varies with the capacitance of the tower and we have  t U  2Aw  (6.2)  which, for our sample tower, is equal to 1.3%. 6.2  Analysis  A group of 9 towers was selected as shown infigure6.2. The data consisted of the isolated data set for the center tower. For every event, the cross-talk between the center tower and each of the 8 adjacent towers was calculated, as well as the total cross-talk in the 4 towers which share an edge with the central tower, and the 4 towers which do not. Finally, the mean value was calculated for each of these measurements over the entire data sample, and compared to our theoretical calculation (see Table 6.2). The same procedure was used to analyse a HAD2 data set (see table 6.3).  Chapter 6.  36  Cross-Talk  1  2  3  X  4  X  ©  x 6  X 7  8  9  1  1  Figure 6.2: Tower grouping for cross-talk measurement  Table 6.1: EMI Cross-talk Tower 1 2 3 4 6 7 9 2+4+6 1+3+7+9  Theoretical 0.0% 2.1 0.0 1.8 2.1 0.0 0.0 6.1 0.0  Observed 0.86% 2.7 1.7 4.0 1.8 1.2 1.1 8.5 4.9  Error 2.2% 2.2 2.2 2.2 2.2 2.2 2.2 3.8 4.4  Chapter 6.  37  Cross-Talk  Table 6.2: HAD2 Cross-talk Tower 1 2 3 4 6 7 8 9 2+4+6+8 1+3+7+9  6.3  Theoretical 0.00% 4.79 0.00 4.89 4.89 0.00 4.14 0.00 18.7 0.00  Observed 2.7 % 3.4 3.0 4.5 5.0 3.1 3.2 2.0 16.1 10.9  Error 1.5% 1.5 1.5 1.5 1.5 1.5 1.5 1.5 2.7 3.0  Error Analysis  As discussed in Chapter 3, the pulse height in the daughterboard is related to the x8 gain signal S and baseline B by  V  U  / data  \  U  / pedestal  where for the purposes of error analysis we have assumed the calibration curve to be linear with slope D. This is justifiable since the differences between the observed and a linear calibration are minor. The error SV is then given by  SV  =  V2  (6.4)  where 65 and SB are the errors in a signal and baseline measurement and 6D is the error in the calibration slope (obtained from its variation with time). We can derive an upper limit on this error by placing a reasonable upper limit on S — B (ie, the highest observed value). Doing so gives us an error SV = 0.115 mV. The  Chapter 6.  38  Cross-Talk  cross-talk we measure is given by  (6.5) and the error Sx is J  :1\ /2 6  X  =  (6.6)  where P, is the induced pulse height for the tower of interest and Si is the pulse in the center tower. 6.4  Results  One of the towers in EMI was found to be improperly calibrated due to previously unknown problems with the electronics. As a result, the total cross-talk measurement contains data from only 3 of the 4 bordering towers. From the tables, we can see that the observed results are close to those predicted by our simple model.  Chapter 7  Position Response  The towers in a LAC module are arranged with a projection angle such that any particles coming from the interaction point in an SLC run should go directly through one tower. However, some particles go through cracks as well as the towers themselves. Hence, we look at the response of the calorimeter as a function of position.  7.1  Data Set  An isolated data set was taken for an EMI tower, but for this measurement we relaxed the isolation bounds to 1.5 cm outside the tower in question (at the top and bottom) so the sample will include events where the particle does not go (entirely) through the tower of interest. The data in this set is further restricted by requiring that the entry and exit position of the particle be a certain distance inside the tile along one axis. In effect, a "band" running down the center of the tile is selected, and only particles which go through"this band are used (see Appendix B for details). The geometry of the detector arrays severely restricts the range of angles an incoming track can have. As a result, the entry position of a track is roughly a linear function of the exit position (see figure 7.1), and the position response has only one degree of freedom.  39  40  Chapter 7. Position Response  Correlation 1.0  i  i  i  ~I  1  H  I  i  of Entry  a n d Exit  i  u [—i i  1  r-  i  I—i—i  Positions i  I—i—i  i_  c o '  O Q_  x  .4  . 0  -|  .4  Entry  .6  1.0  Position  The strong correlation between entry and exit position implies a minimal angular spread and suggests a one-dimensional form of the position dependence. The tower extends from 0 to 1 units on this scale, and its actual width is 7 cm.. Figure 7.1: Mean signal as a function of entry and exit position 7.2  Results  Examining figure 7.2 we see that the signal drops noticeably at the edge of the tower; however, the signal in the adjacent tower picks up at this point, and their sum remains constant. This implies that there is no detectable energy loss when a particle moves through a crack between towers. But because of low statistics, the errors on this measurement are large enough that we can not rule out the-possibility of such a loss.  41  Chapter 7. Position Response  Signal v s . entry  position  20  ' >  0  ^  20  i * 1 ' •  j  [ I Center+Adjacent  D C  Adjacent  C7>  §  'to  f  i  *  c 0 o v 20  H  B  i J  0  -0.2  S  1  *  S  |  B  §  §.  B  i  !  B  1  1' ,  Center  s *  1 8  0.0 0.2 0.4 0.6 0.8 1.0 1.2 Entry position (normalized units)  1.4  The mean signal in the central EMI tower (bottom), adjoining tower (center) and their sum (top) as a function of the entry position of an incoming particle. Figure 7.2: Mean signal as a function of entry position and fixed angle  Appendix  A  Charge Sharing in the L A C  Every LAC tower is connected in series to a "blocking" capacitor, which protects the preamp electronics from any high-voltage surge (seefigureA.l). As a result, the charge seen in the preamp is not that deposited in the tower, but only a fraction of it. While the "cold" capacitance of a tower (its capacitance in LAr) cannot be measured directly, we can measure the cold capacitance of the blocking capacitor, and that of the tower+blocking combination. Using these two values, we can determine the total charge deposited given the amount of charge in the preamp. The cross-talk capacitance is ignored in this analysis. Its effect must be calculated separately. When a charge Q is deposited in a tower, the charge stored in the tower and blocking capacitors is related by  y  Qblk  Qtow  Cblk  Ctow  ^  where V is the voltage drop across each capacitor, Q is the charge stored in each, and x  we have  Q = Qbik + Q  i o w  = {C  m  + C )V tow  (A.2)  The charge collected by the preamp is Qbik, so that the fraction of charge observed is  42  Appendix A.  Charge Sharing in the LAC  43  q<tl>  •0Blocking J _ Cap.  Preamp  I  LAC Tow er  Figure A.l: LAC tower and blocking capacitor  Appendix A. Charge Sharing in the LAC  j _  Qbik _ Q  where C  i o i  —  £ ?c™ blk  Cbik  j _ Ctot  Cbik + C ow t  Cbik  is the total capacitance of the system.  Appendix B  Position Cuts  Since the endcap module is fan-shaped(seefigureB.l), the tower geometry does not lend itself to simple restrictions on position and angle. Instead, what has been done is to place requirements on the entry and exit positions (in the top and bottom faces of the tower) of a cosmic ray particle going through the tower. For every tower, the positions of the 8 corners are known. Since the tower tiles lie in planes of equal z (see chapter 3), the position restrictions become a simple twodimensional problem. For any two points (xi,yi), (x2,j/2) in a plane (ie, two tower corners) there is a position vector v between the two (seefigureB.2)  v = (x - a;i)t 2  + (t/2  (B.l)  - yi)i  and an orthogonal unit vector v±  v± —  , yj(x 2  xf x  ===== + (y -yi) 2  2  where i and j are the appropriate unit basis vectors. For any third point (2:3,2/3), we can obtain its distance D from the line (ie, tower side) connecting (xi,yi) and (£2,2/2) from  D  = p.-  ±  =  (z3 - ai)(y2 - yi) - (ya - yi)(*2 - *i) \A>2 - xi) + {V2 - y i ) 2  45  2  ^ ^ B3  Appendix B. Position Cuts  Figure B.l: Map of towers in an endcap module  46  Appendix B. Position Cuts  Figure B.2: Relevant vectors in position requirements where P = (x - Xy)i + (y - yi)j. 3  3  Using this formula, to ensure that a track goes through a tower, we require D to be negative for all 4 sides (in the proper orientation) on the top and bottom faces, which is equivalent to requiring that the particle enter and exit at least a length D inside the top and bottom tiles (see figure B.3). For the position response, the same method was used, but along one dimension (ie, from two opposing sides) D was required to be negative, forming a "band" inside the tile, while on the other dimension, D could take on any value up to some positive limit (used only to eliminate irrelevant data).  Appendix B. Position Cuts  48  Top view of a LAC tower, showing the position response (left) and isolation (right) limits on the entry position of a particle. Figure B.3: Position requirements  Bibliography  [1] SLD Design Report, Rev. 5 April 1988, SLAC-273 [2] E. Iarocci, Proceedings of the International Conference on Instrumentation for Colliding Beam Physics, G. Feldman, ed. (Stanford, 1982) [3] Press, Flannery, Teukolsky and Vetterling, Numerical Recipes, Cambridge University Press, 1986 [4] Donald H. Perkins, Introduction to High Energy Physics, 2nd Ed., Addison-Wesley, 1982 [5] M. Miyajima et al, Phys. Rev. A 9(1974) 1438 [6] W.J. Willis and V. Radeka, Nucl. Instrum. and Meth. 120(1974) 221 [7] L. Onsager, Phys. Rev. 54(1938) 554 [8] E. Buckley et al, CERN-EP/88-120 [9] J.P. Dodelet, P.G. Fuochi and G.R. Freeman, Canadian Journal of Chemistry 50(1972) 1617 [10] W. Hoffmann, U. Klein, M. Schulz, J. Spengler, and D. Wegener, Nucl. Instrum. . and Meth. 135(1976) 151 [11] L.D. Landau, J. Phys. (U.S.S.R.) 8(1944) 204 [12] F. James and M. Roos, Comp. Phys. Comm. 10(1975) 343  49  


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