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Results of the calibration of multicell drift chamber prototypes for the L3-LEP muon spectrometer
Nuclear Instruments and Methods in Physics Research A263 (1988) 343-350 North-Holland, Amsterdam
343
RESULTS OF THE CALIBRATION OF MULTICELL DRIFT CHAMBER PROTOTYPES FOR THE L3-LEP MUON SPECTROMETER M. CERRADA, I. DURAN, E. GONZALEZ, L. MARTINEZ, P. OLMOS, J. SALICIO and C. WILLMOTT
Division of Particle Physics, CIEMAT-JEN, Madrid, Spain
Received 20 January 1987 and in revised form 1 June 1987 Prototypes of large drift chambers, designed to measure the coordinate of the muons along the electron-positron beam direction in the L3-LEP muon spectrometer, have been built in the CIEMAT-JEN . We report measurements of the drift velocity and space resolution obtained with these modules .
1. Introduction The Division of Particles Physics at the CIEMATJEN is building 96 large multicell drift chambers to measure the coordinate along the beam axis (Z axis) of the trajectories of the muons produced in e +e- interactions or coming from the cosmic ray background . These chambers will be coupled to other chambers measuring the coordinates of the muons in the bending plane of a magnetic field generated by a long solenoid . The design accuracies are 500 and 250 pm per wire in the Z and orthogonal directions, respectively. A considerable effort has been devoted to define technical specifications for the so-called Z chambers . The first modules built following the final design have been extensively tested in order to establish their mechanical and electrostatic properties . The resolution of the chambers has been studied, in a cosmic ray installation, using a self calibrated approach based on successive approximations . In section 2 we review the main features of the detectors. Section 3 describes the experimental setup of the cosmic ray test station and in section 4 the data samples used in this study are summarized . The self calibrated method of analysis is presented in section 5 and the results obtained with this approach are discussed in section 6. Section 7 is left for conclusions. 2. Overall description of the drift chambers (Z-chambers) The multicell drift chambers discussed in this paper are built following the idea developed by Becker and collaborators [1]. The Z-chambers are specifically desig0168-9002/88/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
ned to cover large detection surfaces, have good mechanical rigidity and can be constructed in a relatively simple way. The electric field configuration and the drift velocity were studied theoretically and with the help of a prototype [2]. The results lead to the definition of the cell size (45.9 mm of maximum drift length), working with a 91%-9% argon-methane gas mixture called P9 . The maximum expected drift time is 1.5 ps . The detectors consist of two superposed layers of drift cells. Each of these cells is made by two parallel aluminium I-beams connected to a negative high voltage, acting in this way as the cathodes of the cell, giving both mechanical rigidity to the structure and shaping the electrical drift field. The anode is a gold-plated molybdenum 50 pm diameter wire placed in the middle of the cell . The cell's dimensions are 27 mm high, 91 .8 mm width and 1880 mm long, with a maximum drift path of 45 .9 mm. The cell is closed by two aluminum sheets 1 mm thick, isolated from the profiles by means of 1 mm fiber-glass strips, 43 mm width. The cells of the upper plane are shifted by half the cell size with respect to the lower one (see fig . 1) . This configuration solves the left-right ambiguity in the definition of the side crossed by the particle, provided that the angle between its track and the normal to the chamber is less than 1.36 rad. The precisions achieved in the location of the anode wires and cathode profiles, critical for the chamber resolution, are 130 and 250 pm respectively. A detailed description of these detectors has been given elsewhere [3]. The efficiency curve of one cell versus wire potential is shown in fig. 2. The profile potential was -2500 V with an argon-methane mixture (90-10%) . The geometry of the drift paths is shown in fig. 3, where the sense wire potential was 2150 and -2500 V for the I beam .
M. Cerrada et al. / Calibration of multicell drift chamber prototypes
344
FIBER GLASS INSULATOR
Fig. 1 . Schematic view of the structure of the multicell drift chamber .
T V
12
0.8 0.6 0.4 0.2 0.
1.8
1.9
2.
2.1 2 .2 23 0103 Sense Wire Potential (V.)
Fig . 2 . Efficiency versus wire potential (cathode at -2500 V).
Fig. 3 . Electric field configuration in a drift cell (the wire and the I beam potentials are 2150 and -2500 V, respectively) .
M. Cerrada et al. / Calibration of multicell drift chamber prototypes
345
3 . The experimental setup used in the determination of the drift parameters for the Z-chambers
3.1 . The trigger A hodoscope made by two scintillator plastics (NE102) of 80 X 20 cm2 surface, with a 2 m gap, is used to produce the trigger signal when a particle crosses the cosmic station . The chambers are placed in the gap. This configuration selects cosmic ray particles with a maximum incidence angle of 15 ° with respect to the normal direction to the wire plane . The light produced in each plastic is collected by XP2020 Philips photomultipliers at both ends . The trigger signal is formed by the coincidence of the four discriminated pulses coming from the photomultipliers . Meantimers (LeCroy model 624) have been used as the coincidence circuits . This method avoids the uncertainty in the trigger time due to the light propagation in the scintillator (5 ns/m) and
Fig . 4 . Diagram of the cosmic ray trigger .
Scintillator
E E
J E E 0 N 1
Lead
z
E7::-
ScintiIlator
Fig. 5 . Sketch of the experimental setup of the cosmic ray station .
346
M. Cerrada et al. / Calibration ofmulticell drift chamberprototypes
muon time of flight (3 ns/m) between them. Using and-gates as coincidence units we would define the start signal with a total uncertainty of the order of 10 ns, which would be added to the errors in the drift time measurements; this implies, in our experimental conditions, uncertainties of 300 pm in drift coordinates (the same order than the expected resolution) . With the mean time coincidence system (fig. 4), we are able to reduce this figure to 60 um (2 ns) (a factor 5) compensating both the light propagation time (meantimer 1, 2) and muon time of flight (meantimer 3). A shielding, made with 5 cm thick lead blocks, has been disposed above the lower scintillator in order to eliminate all the muons with energies lower than 160 MeV . This reduces the number of particles with of multiple scattering of angles greater than 5 x 10-4 rad producing tracks apart from a straight line in 250 ,um . The cosmic ray particle rate detected by our trigger system was 4 s -' . 3.2. Setup of the chambers Three drift chambers (Dl, D2, 133) were located between the two plastic scintillation counters. With this configuration, 6 planes of wires can be used for fitting the trajectory of the muon to a straight line . Each chamber has 4 reference points . The wire positions with respect to them are known with a precision of 130 Am. The average distances between the chambers Dl-D2 and D2-D3 were measured at the reference points with a 100 jAm precision (see fig. 5). Since drift chambers measure the projection of the
cosmic ray trajectories in planes perpendicular to the wires, it is necessary to know the wire parallelism between different chambers with a precision better than the expected space resolution. In the final setup, the wires of the three chambers were aligned within 200 I.Lm. Only 8 of the 120 drift cells of the chambers Dl and D2 and 10 drift cells of D3 were electronically active during the data acquisition period. 3.3. The data acquisition electronics An amplifier and a discriminator are attached to each wire, shaping the input pulses and producing fast (30 ns) ECL output signals which are transmitted to the data acquisition system through twisted pair cables [4]. The common discrimination threshold is fixed to 40 mV, the lowest possible value compatible with large insensitivity to rf noise and small dispersion in the trigger time (stop signal of the TDC). The drift times are measured with TDCs of the type LeCroy LRS2228A in standard CAMAC crate; the start command for all the modules is provided by the trigger signal, the ECL pulses from each wire produce the stop command for each channel. The Bus, with 4 TDC modules (32 channels), is controlled by an interface module GPIB [5] which establishes the communication with a PDP 11/24 Master Computer. A Driver in the operating system of the PDP allows to handle the GPIB module with a Fortran computer program which controls the CAMAC system. The measured times are transfered through a DECNET link to a PDP 11/34
DECNET Fig.
6. Block diagram of the drift time readout system.
347
M. Cerrada et al. / Calibration of multicell drift chamber prototypes
computer, supporting a high speed asynchronous communication with the UNIVAC 1108 of the Computer Center, where the processes of reconstruction and analysis are carried out. Fig. 6 shows the block diagram of the data acquisition and data transfer systems used in this experiment.
Xh = Xk
(-1)PW(T)(To+ T)'
(2) This average velocity can be parametrized in terms of a (M -1) order polynomial in the measured time T +
M
W(t) _ Y_ bn Tn-1 , n=1
4. Data samples During February-March 1985 data were taken with three different potentials for the cathode profiles ( - 2000 V, - 2500 V, - 3000 V) and a single potential for the wires (+2150 V). The statistics accumulated with the -2000 V, - 2500 V, - 3000 V setups were 9418, 33 843 and 12 466 events, respectively. The selection criteria of more than 1 hit in each chamber were imposed and events with more than 17 hits were rejected . 5. Analysis procedure A special procedure for the computation of the relation between the drift space and the drift time has been implemented, taking into account the unknown position of the incoming particle . Since more than three planes are available, a self calibration technique based on the reconstruction of cosmic ray trajectories crossing the detectors is used . Similar methods have been previously considered [61, although the present situation has the additional complication of the inhomogeneity of the drift field . The space-time relation can be written as a function of the instantaneous drift velocity, V(t), in the form Xh=Xk+(-1)p
drift velocity, W(T), as
f.
"d
V(t) dt,
where Xh is the input position of the particle in the chamber, Xk is the wire position in the kth cell crossed by the particle, P is set equal to 1 (0) if the impact occurs at the left (right) side of the wire and td is the drift time. This time can be expressed as: =T+ To, td where T is the time measured by the TDC and To is the difference between the time required for the trigger signal to reach the TDC module and the propagation time of the wire signals to the Stop input of the TDC . The wire position in the cell is obtained with the equation: Xk =X~+Lk, X. being the position of wire number 0, considered as the reference for the chamber position, and L is the cell half width. We can write eq. (1) in terms of an average mean
and eq. (2) becomes
M
Xh =Xc +Lk+(-1)p(To+T) Y, bn Tn -1 . n=1
The method is based on assigning to the parameters X, To and b in eq. (3) initial values obtained by alternative procedures (theoretical calculations, measurements, - - - ). This first parametric estimation leads to an approximate reconstruction of the trajectories and permits to define a residue, d X(t) = (Xh - X,), as the difference between the estimated position Xh and the intersection X between the fitted trajectory and the cell reference plane. For a large number of tracks with drift times in the interval (t - e, t + c), where e defines the accuracy that can be achieved, and with a well defined parity P (0 = Right, 1 = Left), residue distributions characterized by the mean dXR,L (t) are obtained, these mean values depend on the systematic errors appearing in the estimation of the parameters describing the space-time relation. Using eq. (3), the expression M
YXI,L(T)=AX,~ +(-1)p Y,
n=1
Tn -1
[bn 4TD
+(T+TD )dbn +4TDdbn 1,
(4)
is derived. Eq. (4) allows to estimate the errors AX, 4Tp and
28
E E
24
U 0
w 20
0
16
12
0.
0.2
0.4
0.6
0.8
1.
1 .2
DRIFT TIME fps)
1 .4
1 .6
Fig . 7. Dependence of the drift velocity with drift time (cathode at -2500 V).
348
M. Cerrada et al. / Calibration of multicell drift chamber prototypes chamber with respect to an overall reference is derived from eq. (4) : 4X.=1/2[~ITR(T)+ZXL(T)], where the right hand side has been averaged over the full T range. To evaluate the corrections of the parameters To and b at each iteration, the following equation has to be solved : A(T) ='£[2[_XL(T) - :I_ XR(T )]
6.
=Tobi-To b 1 +T m (b'-b m ) M
4 .5
+ Y, T"-'[TO'b,,' -Tob +b;,_1-bn(5)
FWHM= 1200rm
n-=2
where To and b are the corrected values of the parameters To and bn . This evaluation implies to perform a least square fit of the measured values of 4(T,.), at values of T covering the full range of T, to the expression (5), being To and b;, the free parameters .
3.
6 . Results 0
L
.- 10
-7.5
-5 .
-25
0.
2 .5
5.
7~5
10 .
RESIDUES (mm)
Fig . 8. Distribution of the residues of the fitted track from the straight line (cathode at -2500 V) . 4 bn in the parameters and to correct their values using XR (T) and YXL (T ) . With the measured magnitudes 2[this new parametric estimation, the procedure can be repeated until the desired accuracy is achieved or convergence is obtained . In this case, M = 4 was used and the imposed accuracy was of the order of 100 g m in AX, 3 ns in 4To and 0 .1% in Ab . The expression for the error in the position of the
The method described in section 5 allows to compute, from the experimental data, the drift velocity and resolution of the detectors. During the first step, computation of the drift velocity is carried out rejecting all the events with residues larger than 600 pm. This selection discards events having low energy, noise or misidentified hits, biasing the calibration, and reduces the total sample by 35% . When the drift velocity is parametrized with a third order polynomial, the procedure requires 5 to 12 iterations to converge . Fig . 7 shows the drift velocity as a function of the drift time. Average mean drift velocities of 29 .0 ± 0 .7, 30 .40 ± 0 .6 and 31 .6 ± 0 .5 cm/16s were obtained with cathode potentials of - 3000, - 2500 and - 2000 V respectively .
Fig. 9 . Sketch of the wire configuration in two adjacent cells. x, is the measured distance between the particle position and the ith wire.
349
M. Cerrada et al. / Calibration of multicell drift chamber prototypes
E E
X X E
Fig . 10. Distribution of the sum x 1 + x z versus x 1 (cathode at -2500 V) .
Once the parameters of the space-time relation have been found, the chamber resolution can be calculated taking into account all the events in the sample . Two different methods are used. The first approach estimates the resolution as the standard deviation of the distribution of the residues from all the impacts for every track crossing the chamber under consideration . The residue is computed as the difference between the measured points and the fitted u x 10 ,
s 4
3
1'
2
1
X,
Imm)
trajectory . A resolution of about 600 ,um (hwhm) is achieved, as shown in fig. 8. Effects due to multiple scattering of low energy particles in the Z chamber are included in this figure . The second approach is based on the wire configuration of the two planes of a chamber. The fixed wire gap implies that the sum of drift distances measured at both wires is a constant for each incoming angle. For normal incidence its value is equal to 45 .9 mm, half of the cell width (fig . 9) . For tilted tracks, the sums can be corrected according to their angles . Fig. 10 shows the sum of distances from the incident track to the wire, after the angle correction, measured in both planes, as a function of the distance in the lower plane. A deviation of the mean value of this distribution from 45 .9 mm, would indicate the presence of systematic errors in the parametrization. The bandwidth gives a measurement of the space resolution that amounts to approximately 600 pm (hwhm), as can be seen in fig. 11 where the accumulated distribution of the sum of distances of two adjacent cells are plotted. 7. Conclusions
0
1 n ,. IS .. .n 48
~
I 46
.
0.
k 44
r" X1-X2 (mm)
Fig . 11 . Distribution of the sum of the distances measured by
the wires of two adjacent cells (cathode at -2500 V) .
Three multicell drift chambers have been constructed, operated and calibrated in a cosmic ray station at CIEMAT-JEN . A trigger and data acquisition system have been implemented and an analysis procedure has
350
M. Cerrada et al. / Calibration of multicell drift chamber prototypes
been developed. The relation drift velocity versus drift time has been measured and two methods leading to the determination of the space resolution, corrected for systematic errors, have been used . Both methods give compatible estimations of the space resolution, around 600 pm, in good agreement with the value required in the technical specifications .
We are grateful to our colleagues Prof. U. Becker, D. Osborne and Dr . M. White, from the Massachusetts Institute of Technology, for the essential training and advice in the early phases of the project. Finally, the strong support of Dr . M. Aguilar-Benitez, Prof. J.A . Rubio and R. Gavela is gratefully acknowledged.
Acknowledgements
References
We are pleased to thank the effort of all the people at the CIEMAT-JEN who have made the construction of the chambers possible. The outstanding work of the team of technicians at the CIEMAT-JEN Workshops lead by D.J. Alvarez Taviel and F. Saes is greatly acknowledged .
[1] [2] [3] [4] [5] [6]
U. Becker et al., Nucl . Instr. and Meth. 128 (1975) 593. I. Duran et al ., Anales de Fisica B81 (1985) 168. B. Adeva et al ., submitted to Anales de Fisica B. H. Cuniz et al ., Nucl . Instr. and Meth. 91 (1971) 211 . GPIB, General Purpose Interface Bus IEEE STD 488-1982. C. Dellacasa et al ., Nucl . Instr. and Meth . 176 (1980) 363.
343
RESULTS OF THE CALIBRATION OF MULTICELL DRIFT CHAMBER PROTOTYPES FOR THE L3-LEP MUON SPECTROMETER M. CERRADA, I. DURAN, E. GONZALEZ, L. MARTINEZ, P. OLMOS, J. SALICIO and C. WILLMOTT
Division of Particle Physics, CIEMAT-JEN, Madrid, Spain
Received 20 January 1987 and in revised form 1 June 1987 Prototypes of large drift chambers, designed to measure the coordinate of the muons along the electron-positron beam direction in the L3-LEP muon spectrometer, have been built in the CIEMAT-JEN . We report measurements of the drift velocity and space resolution obtained with these modules .
1. Introduction The Division of Particles Physics at the CIEMATJEN is building 96 large multicell drift chambers to measure the coordinate along the beam axis (Z axis) of the trajectories of the muons produced in e +e- interactions or coming from the cosmic ray background . These chambers will be coupled to other chambers measuring the coordinates of the muons in the bending plane of a magnetic field generated by a long solenoid . The design accuracies are 500 and 250 pm per wire in the Z and orthogonal directions, respectively. A considerable effort has been devoted to define technical specifications for the so-called Z chambers . The first modules built following the final design have been extensively tested in order to establish their mechanical and electrostatic properties . The resolution of the chambers has been studied, in a cosmic ray installation, using a self calibrated approach based on successive approximations . In section 2 we review the main features of the detectors. Section 3 describes the experimental setup of the cosmic ray test station and in section 4 the data samples used in this study are summarized . The self calibrated method of analysis is presented in section 5 and the results obtained with this approach are discussed in section 6. Section 7 is left for conclusions. 2. Overall description of the drift chambers (Z-chambers) The multicell drift chambers discussed in this paper are built following the idea developed by Becker and collaborators [1]. The Z-chambers are specifically desig0168-9002/88/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
ned to cover large detection surfaces, have good mechanical rigidity and can be constructed in a relatively simple way. The electric field configuration and the drift velocity were studied theoretically and with the help of a prototype [2]. The results lead to the definition of the cell size (45.9 mm of maximum drift length), working with a 91%-9% argon-methane gas mixture called P9 . The maximum expected drift time is 1.5 ps . The detectors consist of two superposed layers of drift cells. Each of these cells is made by two parallel aluminium I-beams connected to a negative high voltage, acting in this way as the cathodes of the cell, giving both mechanical rigidity to the structure and shaping the electrical drift field. The anode is a gold-plated molybdenum 50 pm diameter wire placed in the middle of the cell . The cell's dimensions are 27 mm high, 91 .8 mm width and 1880 mm long, with a maximum drift path of 45 .9 mm. The cell is closed by two aluminum sheets 1 mm thick, isolated from the profiles by means of 1 mm fiber-glass strips, 43 mm width. The cells of the upper plane are shifted by half the cell size with respect to the lower one (see fig . 1) . This configuration solves the left-right ambiguity in the definition of the side crossed by the particle, provided that the angle between its track and the normal to the chamber is less than 1.36 rad. The precisions achieved in the location of the anode wires and cathode profiles, critical for the chamber resolution, are 130 and 250 pm respectively. A detailed description of these detectors has been given elsewhere [3]. The efficiency curve of one cell versus wire potential is shown in fig. 2. The profile potential was -2500 V with an argon-methane mixture (90-10%) . The geometry of the drift paths is shown in fig. 3, where the sense wire potential was 2150 and -2500 V for the I beam .
M. Cerrada et al. / Calibration of multicell drift chamber prototypes
344
FIBER GLASS INSULATOR
Fig. 1 . Schematic view of the structure of the multicell drift chamber .
T V
12
0.8 0.6 0.4 0.2 0.
1.8
1.9
2.
2.1 2 .2 23 0103 Sense Wire Potential (V.)
Fig . 2 . Efficiency versus wire potential (cathode at -2500 V).
Fig. 3 . Electric field configuration in a drift cell (the wire and the I beam potentials are 2150 and -2500 V, respectively) .
M. Cerrada et al. / Calibration of multicell drift chamber prototypes
345
3 . The experimental setup used in the determination of the drift parameters for the Z-chambers
3.1 . The trigger A hodoscope made by two scintillator plastics (NE102) of 80 X 20 cm2 surface, with a 2 m gap, is used to produce the trigger signal when a particle crosses the cosmic station . The chambers are placed in the gap. This configuration selects cosmic ray particles with a maximum incidence angle of 15 ° with respect to the normal direction to the wire plane . The light produced in each plastic is collected by XP2020 Philips photomultipliers at both ends . The trigger signal is formed by the coincidence of the four discriminated pulses coming from the photomultipliers . Meantimers (LeCroy model 624) have been used as the coincidence circuits . This method avoids the uncertainty in the trigger time due to the light propagation in the scintillator (5 ns/m) and
Fig . 4 . Diagram of the cosmic ray trigger .
Scintillator
E E
J E E 0 N 1
Lead
z
E7::-
ScintiIlator
Fig. 5 . Sketch of the experimental setup of the cosmic ray station .
346
M. Cerrada et al. / Calibration ofmulticell drift chamberprototypes
muon time of flight (3 ns/m) between them. Using and-gates as coincidence units we would define the start signal with a total uncertainty of the order of 10 ns, which would be added to the errors in the drift time measurements; this implies, in our experimental conditions, uncertainties of 300 pm in drift coordinates (the same order than the expected resolution) . With the mean time coincidence system (fig. 4), we are able to reduce this figure to 60 um (2 ns) (a factor 5) compensating both the light propagation time (meantimer 1, 2) and muon time of flight (meantimer 3). A shielding, made with 5 cm thick lead blocks, has been disposed above the lower scintillator in order to eliminate all the muons with energies lower than 160 MeV . This reduces the number of particles with of multiple scattering of angles greater than 5 x 10-4 rad producing tracks apart from a straight line in 250 ,um . The cosmic ray particle rate detected by our trigger system was 4 s -' . 3.2. Setup of the chambers Three drift chambers (Dl, D2, 133) were located between the two plastic scintillation counters. With this configuration, 6 planes of wires can be used for fitting the trajectory of the muon to a straight line . Each chamber has 4 reference points . The wire positions with respect to them are known with a precision of 130 Am. The average distances between the chambers Dl-D2 and D2-D3 were measured at the reference points with a 100 jAm precision (see fig. 5). Since drift chambers measure the projection of the
cosmic ray trajectories in planes perpendicular to the wires, it is necessary to know the wire parallelism between different chambers with a precision better than the expected space resolution. In the final setup, the wires of the three chambers were aligned within 200 I.Lm. Only 8 of the 120 drift cells of the chambers Dl and D2 and 10 drift cells of D3 were electronically active during the data acquisition period. 3.3. The data acquisition electronics An amplifier and a discriminator are attached to each wire, shaping the input pulses and producing fast (30 ns) ECL output signals which are transmitted to the data acquisition system through twisted pair cables [4]. The common discrimination threshold is fixed to 40 mV, the lowest possible value compatible with large insensitivity to rf noise and small dispersion in the trigger time (stop signal of the TDC). The drift times are measured with TDCs of the type LeCroy LRS2228A in standard CAMAC crate; the start command for all the modules is provided by the trigger signal, the ECL pulses from each wire produce the stop command for each channel. The Bus, with 4 TDC modules (32 channels), is controlled by an interface module GPIB [5] which establishes the communication with a PDP 11/24 Master Computer. A Driver in the operating system of the PDP allows to handle the GPIB module with a Fortran computer program which controls the CAMAC system. The measured times are transfered through a DECNET link to a PDP 11/34
DECNET Fig.
6. Block diagram of the drift time readout system.
347
M. Cerrada et al. / Calibration of multicell drift chamber prototypes
computer, supporting a high speed asynchronous communication with the UNIVAC 1108 of the Computer Center, where the processes of reconstruction and analysis are carried out. Fig. 6 shows the block diagram of the data acquisition and data transfer systems used in this experiment.
Xh = Xk
(-1)PW(T)(To+ T)'
(2) This average velocity can be parametrized in terms of a (M -1) order polynomial in the measured time T +
M
W(t) _ Y_ bn Tn-1 , n=1
4. Data samples During February-March 1985 data were taken with three different potentials for the cathode profiles ( - 2000 V, - 2500 V, - 3000 V) and a single potential for the wires (+2150 V). The statistics accumulated with the -2000 V, - 2500 V, - 3000 V setups were 9418, 33 843 and 12 466 events, respectively. The selection criteria of more than 1 hit in each chamber were imposed and events with more than 17 hits were rejected . 5. Analysis procedure A special procedure for the computation of the relation between the drift space and the drift time has been implemented, taking into account the unknown position of the incoming particle . Since more than three planes are available, a self calibration technique based on the reconstruction of cosmic ray trajectories crossing the detectors is used . Similar methods have been previously considered [61, although the present situation has the additional complication of the inhomogeneity of the drift field . The space-time relation can be written as a function of the instantaneous drift velocity, V(t), in the form Xh=Xk+(-1)p
drift velocity, W(T), as
f.
"d
V(t) dt,
where Xh is the input position of the particle in the chamber, Xk is the wire position in the kth cell crossed by the particle, P is set equal to 1 (0) if the impact occurs at the left (right) side of the wire and td is the drift time. This time can be expressed as: =T+ To, td where T is the time measured by the TDC and To is the difference between the time required for the trigger signal to reach the TDC module and the propagation time of the wire signals to the Stop input of the TDC . The wire position in the cell is obtained with the equation: Xk =X~+Lk, X. being the position of wire number 0, considered as the reference for the chamber position, and L is the cell half width. We can write eq. (1) in terms of an average mean
and eq. (2) becomes
M
Xh =Xc +Lk+(-1)p(To+T) Y, bn Tn -1 . n=1
The method is based on assigning to the parameters X, To and b in eq. (3) initial values obtained by alternative procedures (theoretical calculations, measurements, - - - ). This first parametric estimation leads to an approximate reconstruction of the trajectories and permits to define a residue, d X(t) = (Xh - X,), as the difference between the estimated position Xh and the intersection X between the fitted trajectory and the cell reference plane. For a large number of tracks with drift times in the interval (t - e, t + c), where e defines the accuracy that can be achieved, and with a well defined parity P (0 = Right, 1 = Left), residue distributions characterized by the mean dXR,L (t) are obtained, these mean values depend on the systematic errors appearing in the estimation of the parameters describing the space-time relation. Using eq. (3), the expression M
YXI,L(T)=AX,~ +(-1)p Y,
n=1
Tn -1
[bn 4TD
+(T+TD )dbn +4TDdbn 1,
(4)
is derived. Eq. (4) allows to estimate the errors AX, 4Tp and
28
E E
24
U 0
w 20
0
16
12
0.
0.2
0.4
0.6
0.8
1.
1 .2
DRIFT TIME fps)
1 .4
1 .6
Fig . 7. Dependence of the drift velocity with drift time (cathode at -2500 V).
348
M. Cerrada et al. / Calibration of multicell drift chamber prototypes chamber with respect to an overall reference is derived from eq. (4) : 4X.=1/2[~ITR(T)+ZXL(T)], where the right hand side has been averaged over the full T range. To evaluate the corrections of the parameters To and b at each iteration, the following equation has to be solved : A(T) ='£[2[_XL(T) - :I_ XR(T )]
6.
=Tobi-To b 1 +T m (b'-b m ) M
4 .5
+ Y, T"-'[TO'b,,' -Tob +b;,_1-bn(5)
FWHM= 1200rm
n-=2
where To and b are the corrected values of the parameters To and bn . This evaluation implies to perform a least square fit of the measured values of 4(T,.), at values of T covering the full range of T, to the expression (5), being To and b;, the free parameters .
3.
6 . Results 0
L
.- 10
-7.5
-5 .
-25
0.
2 .5
5.
7~5
10 .
RESIDUES (mm)
Fig . 8. Distribution of the residues of the fitted track from the straight line (cathode at -2500 V) . 4 bn in the parameters and to correct their values using XR (T) and YXL (T ) . With the measured magnitudes 2[this new parametric estimation, the procedure can be repeated until the desired accuracy is achieved or convergence is obtained . In this case, M = 4 was used and the imposed accuracy was of the order of 100 g m in AX, 3 ns in 4To and 0 .1% in Ab . The expression for the error in the position of the
The method described in section 5 allows to compute, from the experimental data, the drift velocity and resolution of the detectors. During the first step, computation of the drift velocity is carried out rejecting all the events with residues larger than 600 pm. This selection discards events having low energy, noise or misidentified hits, biasing the calibration, and reduces the total sample by 35% . When the drift velocity is parametrized with a third order polynomial, the procedure requires 5 to 12 iterations to converge . Fig . 7 shows the drift velocity as a function of the drift time. Average mean drift velocities of 29 .0 ± 0 .7, 30 .40 ± 0 .6 and 31 .6 ± 0 .5 cm/16s were obtained with cathode potentials of - 3000, - 2500 and - 2000 V respectively .
Fig. 9 . Sketch of the wire configuration in two adjacent cells. x, is the measured distance between the particle position and the ith wire.
349
M. Cerrada et al. / Calibration of multicell drift chamber prototypes
E E
X X E
Fig . 10. Distribution of the sum x 1 + x z versus x 1 (cathode at -2500 V) .
Once the parameters of the space-time relation have been found, the chamber resolution can be calculated taking into account all the events in the sample . Two different methods are used. The first approach estimates the resolution as the standard deviation of the distribution of the residues from all the impacts for every track crossing the chamber under consideration . The residue is computed as the difference between the measured points and the fitted u x 10 ,
s 4
3
1'
2
1
X,
Imm)
trajectory . A resolution of about 600 ,um (hwhm) is achieved, as shown in fig. 8. Effects due to multiple scattering of low energy particles in the Z chamber are included in this figure . The second approach is based on the wire configuration of the two planes of a chamber. The fixed wire gap implies that the sum of drift distances measured at both wires is a constant for each incoming angle. For normal incidence its value is equal to 45 .9 mm, half of the cell width (fig . 9) . For tilted tracks, the sums can be corrected according to their angles . Fig. 10 shows the sum of distances from the incident track to the wire, after the angle correction, measured in both planes, as a function of the distance in the lower plane. A deviation of the mean value of this distribution from 45 .9 mm, would indicate the presence of systematic errors in the parametrization. The bandwidth gives a measurement of the space resolution that amounts to approximately 600 pm (hwhm), as can be seen in fig. 11 where the accumulated distribution of the sum of distances of two adjacent cells are plotted. 7. Conclusions
0
1 n ,. IS .. .n 48
~
I 46
.
0.
k 44
r" X1-X2 (mm)
Fig . 11 . Distribution of the sum of the distances measured by
the wires of two adjacent cells (cathode at -2500 V) .
Three multicell drift chambers have been constructed, operated and calibrated in a cosmic ray station at CIEMAT-JEN . A trigger and data acquisition system have been implemented and an analysis procedure has
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M. Cerrada et al. / Calibration of multicell drift chamber prototypes
been developed. The relation drift velocity versus drift time has been measured and two methods leading to the determination of the space resolution, corrected for systematic errors, have been used . Both methods give compatible estimations of the space resolution, around 600 pm, in good agreement with the value required in the technical specifications .
We are grateful to our colleagues Prof. U. Becker, D. Osborne and Dr . M. White, from the Massachusetts Institute of Technology, for the essential training and advice in the early phases of the project. Finally, the strong support of Dr . M. Aguilar-Benitez, Prof. J.A . Rubio and R. Gavela is gratefully acknowledged.
Acknowledgements
References
We are pleased to thank the effort of all the people at the CIEMAT-JEN who have made the construction of the chambers possible. The outstanding work of the team of technicians at the CIEMAT-JEN Workshops lead by D.J. Alvarez Taviel and F. Saes is greatly acknowledged .
[1] [2] [3] [4] [5] [6]
U. Becker et al., Nucl . Instr. and Meth. 128 (1975) 593. I. Duran et al ., Anales de Fisica B81 (1985) 168. B. Adeva et al ., submitted to Anales de Fisica B. H. Cuniz et al ., Nucl . Instr. and Meth. 91 (1971) 211 . GPIB, General Purpose Interface Bus IEEE STD 488-1982. C. Dellacasa et al ., Nucl . Instr. and Meth . 176 (1980) 363.