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Recombination: An important effect in multigap resistive plate chambers
ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 610 (2009) 649–653
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Recombination: An important effect in multigap resistive plate chambers K. Doroud a,b,, H. Afarideh b, D. Hatzifotiadou c, J. Rahighi b, M.C.S. Williams c, A. Zichichi c,d a
World Laboratory, Geneva, Switzerland Amirkabir University of Technology, Tehran, Iran Sezione INFN, Bologna, Italy d PH Department, CERN, Geneva, Switzerland b c
a r t i c l e in fo
abstract
Article history: Received 20 July 2009 Received in revised form 4 September 2009 Accepted 20 September 2009 Available online 26 September 2009
We have simulated the gas avalanche in a multigap resistive plate chamber (MRPC). The results were then compared with our data from the MRPC [1]. Up to now, the total amount of charge produced in a gas gap is considered to be given by the total number of positive ions generated by the gas avalanches. However, the total charge generated by the simulation program is much too large and is in conflict with our data. Our data indicate that nearly 100% of the negative ions recombine with the positive ions. The recombination effect dramatically reduces the amount of charge in the gas gap: a very important feature for MRPC technology especially for the rate capability. & 2009 Elsevier B.V. All rights reserved.
Keywords: Resistive plate chambers Multigap Simulation Recombination MRPC
1. Introduction The Multigap Resistive Plate Chamber (MRPC) is the timing detector used for the Time-of-flight (TOF) of the ALICE experiment [2]. This detector has excellent time resolution with a s less than 50 ps, a long streamer-free efficiency plateau and good rate capability up to 1 kHz cm2 [3]. From the measurement of the total amount of charge produced in the gas gap [1], it is clear that space charge effects are important. We have simulated the performance of the MRPC using the detector design implemented for the ALICE TOF. We find it interesting that the only way that we could make the simulation agree with the measurements for the fast and total charge is to allow the negative ions created in the avalanche to recombine with the positive ions. For the avalanche simulation, we have followed the Lippmann and Riegler 1.5D model [4]. Our conclusion is that a recombination close to 100% is needed for the total charge to agree with the data.
2. The multigap resistive plate chamber The MRPC used for the ALICE TOF consists of two stacks of five gas gaps making 10 gaps in total. Each gap is 250 mm in width. A cross-section is shown in Fig. 1. Corresponding author.
E-mail address: [email protected] (K. Doroud). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.09.055
The operation of a MRPC has been discussed previously [2]. Essentially the induced signal is produced by the movement of charge in any of the gas gaps. To calculate this induced charge, we have used the Ramo’s theorem [5] and the concept of weighting field. This has been discussed for the case of resistive plate chamber by Riegler [6]. To calculate the weighting field one applies 1 V to the readout electrode (the anode readout pad in the case described in this paper) and 0 V on all other electrodes (the cathode readout pad). In this calculation, the following dimensions and constants have been used: relative dielectric constant of 8 for the glass plates (400 and 550 mm thick); relative dielectric constant 5.5 for the PCB (0.8 mm thick) and relative dielectric constant of 1 for the gas gaps (250 mm thick). The weighting field, EW , has a value of 0:53 mm1 . The induced current is v , where Q is the charge and ~ v the velocity vector. iðtÞ ¼ Q ~ EW ~ For the fast charge signal, Qfast , we sum the signal due to the movement of the electrons in each time step from time zero until the time when the avalanche stops developing (when all electrons have reached the anode). In the results that follow, we will consider the total induced P charge; this is defined by Qp EW d, where the summation is made over all gas gaps (10 in this case), Qp is the total positive charge that arrives onto the cathode surface, EW is the weighting field and d is the width of the gas gap. We use this variable since this was experimentally measured by Akindinov et al. [1]. To calculate the rate capabilities, the current that flows through the resistive plates is important and thus the total charge, Qp , has to be considered rather than the induced total charge.
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3. Simulation
Cross section of double-stack MRPC 130 mm active area 70 mm
C
I
A
H G J
E F
D B
C
Fig. 1. The 10 gap MRPC. It is divided into two stacks. A: connector for signal; B: pins for signal from cathode pads to be brought to central pcb; C: honeycomb panel; D: PCB (0.8 mm thick); E: gas gaps (250 mm thick); F: central PCB (1.6 mm thick); G: internal glass plates (400 mm thick); H: external glass plates (550 mm thick); I: cathode pickup pads; and J: anode pickup pads.
The total induced charge would be equal to the total charge generated in the gas gap if one included the passage of the charge through the dielectric layers to the pick-up electrodes; however, the movement of charge through the resistive plates occurs over too long a time scale ð 1 sÞ to be measurable; in addition, with this design of MRPC, the pick-up electrodes are separated from the coating used to apply the high voltage by a 0.8 mm thickness of pcb. The charge goes to the external circuit through this coating and does not pass through the pcb. Thus the total induced charge (even if we waited for the charge to traverse the resistive plate) will always be less than the total charge generated inside the gas gap. However, the concept of the weighting field easily allows us to calculate the difference between our definition of the total induced charge (the charge induced on the readout pads when all the charges generated in the gas gap have reached the anode or cathode surfaces) and the actual charge that has accumulated on the surface of the anode or cathode. If one assumes that all dielectric layers (except for the gas gaps) have zero thickness, then the induced total charge will be equal to the actual charge on the surface of the anode or cathode. In the case of the 10 gap MRPC, setting the thickness of the glass plates and the pcb to zero gives a weighting field of 0:8 mm1 , compared to the weighting field of 0:53 mm1 calculated using the actual thickness of the dielectric material. This means that we would have to multiply the total induced charge by 0:8=0:53 ¼ 1:5 to get the actual amount of charge seen by the external circuit supplying the voltage.
We first simulate avalanches in individual 250 mm gap and then add together 10 gaps to simulate the signal from MRPC described above. One or more of these gaps may have no avalanche. The Townsend coefficient, a, attachment coefficient, Z, drift velocity, v, and diffusion coefficients (both transverse and longitudinal) are needed in the simulation. We use MAGBOLTZ [7] to calculate the above coefficients for the particular gas that we are using (93% C2 F4 H2 and 7% SF6 ). The values of these parameters for an electric field of 100 kV/cm are a ¼ 126:8 mm1 , Z ¼ 8:2 mm1 and v ¼ 21:62 cm ms1 . The 250 mm gas gap is divided into 500 slices. Through-going 500 MeV/c muons will create electron and positive ion pairs; this is simulated using the HEED [8] program; the number of electrons and their position are then put into the corresponding slice of gas in the gap. The avalanche then evolves by moving and multiplying the electrons for a given time interval. The time interval used in our simulation is the time needed for an electron to move 0:5 mm at a velocity v0, the drift speed at the applied electric field E0 . The electric field experienced by an electron is given by the applied electric field modified by the charges located in other position slices (space charge). This space charge, created by electrons, positive and negative ions, affects the growth of the avalanche and is very important especially when the density of charge is high. We consider that the charges are spread on disks, each with a Gaussian radial distribution. We calculate the strans of this distribution by assuming that pffiffiffi the avalanche spreads transversely according to strans ¼ DT : L, where DT is the transverse diffusion coefficient and L the distance of the disk from the initial cluster position. Thus to calculate the electric field at a given slice we have to calculate the electric field experienced by this disk of electrons caused by all other disks of charge and the applied electric field. This procedure is known as the 1.5D model (see Lippmann and Riegler [4]). The space charge has the effect of limiting the growth of the avalanche; the electrons located at the head of the avalanche experience the field from the positive ions. Thus the size of this disk is important for the calculation of space charge; the bigger the disk, the weaker is the space charge. In Fig. 2 we show the electric field and the distribution of the electrons, positive and negative ions for a developing avalanche. The 0 ps plot shows the initial situation. Three clusters of ionisation are created by a through-going particle. The electric field is initially constant across the width of the gas gap and has a value due to the applied voltage of 100 kV/cm. In the second plot, for a time of 440 ps, clusters 1 and 2 have merged together; the electrons follow a Gaussian distribution due to the longitudinal diffusion; small perturbations of the electric field can be observed due to the charges in the gas gap. In the third plot, at 630 ps, half of the electrons from cluster 3 have already reached the anode. The space charge distortion of the applied electric field is becoming large. The distribution of the electrons is no longer Gaussian due to the large variation of the electric field. The 710 ps plot shows that almost all the electrons from cluster 3 have now reached the anode. In the final plot at 1.46 ns all the electrons have now reached the anode; there is a residual charge in the gas gap produced by the positive and negative charges in the gas gap and the electrons that are deposited on the surface of the anode. When the electrons arrive at the anode, they are accumulated on the surface of the resistive plate and they are included in the calculation of the electric field; we believe that this is reasonable since the avalanche development is fast ð 1 nsÞ and the characteristic time constant of the resistive plate is long. It is
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K. Doroud et al. / Nuclear Instruments and Methods in Physics Research A 610 (2009) 649–653
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Fig. 2. The electric field and number of charges (electrons, positive ions and negative ions) in a gas gap of width 250 mm displayed for six times. The applied electric field is 100 kV cm1 . The 0 ps plot shows the initial situation with three clusters of ionisation; at 440 ps, the first two clusters have merged together, the electrons have a Gaussian spread due to longitudinal diffusion; the 610 ps plot shows the electric field is strongly affected by space charge; note that in the final two plots (880 and 1.46 ns) the distribution of negative ions follows the positive ions.
important to note that the distribution of negative ions follows closely the distribution of positive ions.
4. Results All resistive plate chambers have some rate dependant effects caused by the charge produced in the gas gaps; this charge has to pass through the resistive plate and this current will generate a voltage drop that will decrease the electric field in the gas gap. In general one wants to ensure that the fast charge (produced by the fast moving electrons) is sufficiently large while at the same time minimising the total charge generated inside the gas gap. Thus the ratio of fast charge to total charge is of crucial importance to users of MRPC technology. For an electric field of 100 kV cm 1, the Townsend coefficient, a, is 1269 cm1 and the attachment coefficient, Z, is 82 cm1 for
our particular gas mixture. Thus, without any space charge effects, one would expect a gas gain of eðaZÞd ¼ 7:7 1012 , where d is the width of the gas gap (250 mm). This is an enormous gas gain; a single electron avalanching across the gap would produce 1:2 mC of charge inside the gas gap. However space charge does exist and its effect is to reduce the growth of the avalanche by some orders of magnitude. We have used five values of the electric field in the simulation (95, 100, 110, 120 and 130 kV cm1 ). For each of these electric fields, we generate 500 ‘‘single-gap’’ events. For each ‘‘multigap’’ event we make a random selection of 10 single gap events. The value of the weighting field allows us to compute the fast charge (due to the movement of electrons in the gas) correctly. In Fig. 3 we show the result of the simulation and the published measurement [1] of the ratio fast/total induced charge. For the simulation we first made a scatter plot for all the multigap events for the five different electric field values. Obviously the low
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K. Doroud et al. / Nuclear Instruments and Methods in Physics Research A 610 (2009) 649–653
electric field ð95 kV cm1 Þ populated the left hand side of the plot (low values of the fast charge) while the higher electric field produced events with larger fast charge. A profile histogram was then made and the points plotted. The measured values were produced in a similar fashion combining data with various applied high voltages. For the simulation we show two variants to calculate the total charge. The first method (curve labelled ‘‘No recombination’’) takes into account the number of positive ions in the gas gap due to the avalanche. The second method (curve labelled ‘‘100% recombination’’) considers the positive and negative ions at each position step (there is a step every 0:5 mm); the number of negative ions is recombined with a corresponding number of positive ions and this results in a reduction of the number of positive ions. The remaining positive ions are then summed up over the width of the gas gap and used
as the total charge. It is clear from Fig. 3 that the measurement strongly favours the ‘‘100% recombination’’ variant of total charge. However, the simulation using the values of avalanche parameters obtained from running MAGBOLTZ [7] gives a fast charge that is too small; this is the data labelled ‘‘Normal DT ’’ ; we thus need some modification to the simulation to reduce the overestimation of the space charge. One way to do this would be to enlarge the disks of charge. In the simulation we have only considered the axial electric field along the direction of avalanche growth; however there is also the radial electric field. There is a repulsive force acting to explode the electron cloud. Lippmann and Riegler have considered this radial field. To simulate this correctly each disk has to be divided into a series of rings; this model is known as the 2D model. Even using fast algorithms the increase of computation time is considerable ( 1 day per
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Fig. 3. Ratio of fast charge/total induced charge as a function of fast charge. The total induced charge is calculated either by considering just the positive ions in the gas gaps due to the avalanche (no recombination) or by first recombining the negative and positive ions and then considering the remaining positive ions (labelled as 100% pffiffiffi recombination). The transverse diffusion coefficient DT is multiplied by various factors, 2, 3 and 4 for this simulation.
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ARTICLE IN PRESS K. Doroud et al. / Nuclear Instruments and Methods in Physics Research A 610 (2009) 649–653
avalanche according to Lippmann [9]); thus using the 2D model is not practical for this study. Instead we choose to modify the InffiffiffiFig. 3 we show the result coefficient of transverse diffusion, DT . p of the simulation multiplying DT by 2, 3 and 4. One sees that increasing DT moves the curve along the abscissa, but does not change the slope. We choose a factor 3 and show the result of this simulation in Fig. 4. We alter the percentage of recombination from 100% to 97% and 94%. Varying the percentage does vary the slope and some value between 95% and 100% fits the data. Clearly the value of total induced charge obtained from ‘‘No recombination’’ does not describe the data.
5. Discussion Is such a high fraction of recombination plausible? The value of transverse diffusion is 100 mm cm1 for this gas mixture so that a typical radius of the cloud of electrons after moving half the gap would be 10 mm. We see from Fig. 2 that 106 charges in a 0:5 mm step is a typical value. The number of molecules in such a volume ð160 mm3 Þ is 4 109 . Thus the percentage of ions in this volume is 0.025%. Gas molecules of oxygen and nitrogen at room temperature have 1010 collisions per second [10]; thus in a nanosecond a given negative ion has a 0.25% probability of colliding (and thus recombining) with a positive ion resulting in a characteristic recombination time of 400 ns. Oscilloscope pictures shown in Ref. [1] indicate that the total drift time is 1000 ns; thus the 400 ns recombination time appears to be too long since the clouds of ions will separate before the ions can recombine. However inspecting Fig. 2 we see that in the location of most of the positive and negative ions (between 150 and 250 mm) the field is very low or even negative, thus these ions will not be transported to the cathode or anode but will stay in this location and are likely to recombine. Given this, such a high fraction of recombination can be understood. We cannot exclude that some fraction of the electrons may directly recombine with the positive ions without going through the intermediary of attachment and formation of a negative ion. For the small gas gaps typically used in MRPCs [1,2], the intense space charge stops the avalanche growing; however in the
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low field region generated by the space charge the attachment coefficient becomes large and many electrons become attached. This effect additionally stops the avalanche growing. The negative ions then recombine with the positive ions and thus dramatically reduce the amount of charge in the gas gap. This reduction is very important for the rate capability of the MRPCs.
6. Conclusion The high fraction of recombination of positive and negative ions substantially reduces the total amount of charge in the small gas gaps of the multigap resistive plate chambers. This allows MRPCs to operate at relatively high rates using glass with high resistivity (1012 21013 O cm).
Acknowledgments We have been particularly helped in this work by the stimulating discussions and help from Werner Riegler, Christian Lippmann and Rob Veenhof. We are indebted to them for being so generous with their time and knowledge. References [1] A.N. Akindinov, et al., Nucl. Instr. and Meth. A 531 (2004) 515 10.1016/ j.nima.2004.04.246. [2] A. Akindinov, et al., Nucl. Instr. and Meth. A 456 (2000) 16 10.1016/S01689002(00)00954-2. [3] A. Alici, et al., Nucl. Instr. and Meth. A 579 (2007) 979 10.1016/ j.nima.2007.06.027. [4] C. Lippmann, W. Riegler, Nucl. Instr. and Meth. A 517 (2004) 54 10.1016/ j.nima.2003.08.174. [5] S. Ramo, Proc. IRE 27 (1939) 584. [6] W. Riegler, Nucl. Instr. and Meth. A 491 (2002) 258. [7] S. Biagi, MAGBOLTZ: transport of electrons in gas mixtures, /http://consult. cern.ch/writeup/magboltz/S. [8] I. Smirnov, HEED: details of this program available at /http://consult.cern.ch/ writeup/heed/S. [9] Detector Physics of Resistive Plate Chambers, Dissertation of Christian Lippmann, 2003, available at /http://www-linux.gsi.de/lippmann/files/Dis sertation.pdfS. [10] M. Ohring, The Materials Science of Thin Films, second ed., Elsevier Science & Technology Books, 2001, ISBN-13: 9780125249751.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Recombination: An important effect in multigap resistive plate chambers K. Doroud a,b,, H. Afarideh b, D. Hatzifotiadou c, J. Rahighi b, M.C.S. Williams c, A. Zichichi c,d a
World Laboratory, Geneva, Switzerland Amirkabir University of Technology, Tehran, Iran Sezione INFN, Bologna, Italy d PH Department, CERN, Geneva, Switzerland b c
a r t i c l e in fo
abstract
Article history: Received 20 July 2009 Received in revised form 4 September 2009 Accepted 20 September 2009 Available online 26 September 2009
We have simulated the gas avalanche in a multigap resistive plate chamber (MRPC). The results were then compared with our data from the MRPC [1]. Up to now, the total amount of charge produced in a gas gap is considered to be given by the total number of positive ions generated by the gas avalanches. However, the total charge generated by the simulation program is much too large and is in conflict with our data. Our data indicate that nearly 100% of the negative ions recombine with the positive ions. The recombination effect dramatically reduces the amount of charge in the gas gap: a very important feature for MRPC technology especially for the rate capability. & 2009 Elsevier B.V. All rights reserved.
Keywords: Resistive plate chambers Multigap Simulation Recombination MRPC
1. Introduction The Multigap Resistive Plate Chamber (MRPC) is the timing detector used for the Time-of-flight (TOF) of the ALICE experiment [2]. This detector has excellent time resolution with a s less than 50 ps, a long streamer-free efficiency plateau and good rate capability up to 1 kHz cm2 [3]. From the measurement of the total amount of charge produced in the gas gap [1], it is clear that space charge effects are important. We have simulated the performance of the MRPC using the detector design implemented for the ALICE TOF. We find it interesting that the only way that we could make the simulation agree with the measurements for the fast and total charge is to allow the negative ions created in the avalanche to recombine with the positive ions. For the avalanche simulation, we have followed the Lippmann and Riegler 1.5D model [4]. Our conclusion is that a recombination close to 100% is needed for the total charge to agree with the data.
2. The multigap resistive plate chamber The MRPC used for the ALICE TOF consists of two stacks of five gas gaps making 10 gaps in total. Each gap is 250 mm in width. A cross-section is shown in Fig. 1. Corresponding author.
E-mail address: [email protected] (K. Doroud). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.09.055
The operation of a MRPC has been discussed previously [2]. Essentially the induced signal is produced by the movement of charge in any of the gas gaps. To calculate this induced charge, we have used the Ramo’s theorem [5] and the concept of weighting field. This has been discussed for the case of resistive plate chamber by Riegler [6]. To calculate the weighting field one applies 1 V to the readout electrode (the anode readout pad in the case described in this paper) and 0 V on all other electrodes (the cathode readout pad). In this calculation, the following dimensions and constants have been used: relative dielectric constant of 8 for the glass plates (400 and 550 mm thick); relative dielectric constant 5.5 for the PCB (0.8 mm thick) and relative dielectric constant of 1 for the gas gaps (250 mm thick). The weighting field, EW , has a value of 0:53 mm1 . The induced current is v , where Q is the charge and ~ v the velocity vector. iðtÞ ¼ Q ~ EW ~ For the fast charge signal, Qfast , we sum the signal due to the movement of the electrons in each time step from time zero until the time when the avalanche stops developing (when all electrons have reached the anode). In the results that follow, we will consider the total induced P charge; this is defined by Qp EW d, where the summation is made over all gas gaps (10 in this case), Qp is the total positive charge that arrives onto the cathode surface, EW is the weighting field and d is the width of the gas gap. We use this variable since this was experimentally measured by Akindinov et al. [1]. To calculate the rate capabilities, the current that flows through the resistive plates is important and thus the total charge, Qp , has to be considered rather than the induced total charge.
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3. Simulation
Cross section of double-stack MRPC 130 mm active area 70 mm
C
I
A
H G J
E F
D B
C
Fig. 1. The 10 gap MRPC. It is divided into two stacks. A: connector for signal; B: pins for signal from cathode pads to be brought to central pcb; C: honeycomb panel; D: PCB (0.8 mm thick); E: gas gaps (250 mm thick); F: central PCB (1.6 mm thick); G: internal glass plates (400 mm thick); H: external glass plates (550 mm thick); I: cathode pickup pads; and J: anode pickup pads.
The total induced charge would be equal to the total charge generated in the gas gap if one included the passage of the charge through the dielectric layers to the pick-up electrodes; however, the movement of charge through the resistive plates occurs over too long a time scale ð 1 sÞ to be measurable; in addition, with this design of MRPC, the pick-up electrodes are separated from the coating used to apply the high voltage by a 0.8 mm thickness of pcb. The charge goes to the external circuit through this coating and does not pass through the pcb. Thus the total induced charge (even if we waited for the charge to traverse the resistive plate) will always be less than the total charge generated inside the gas gap. However, the concept of the weighting field easily allows us to calculate the difference between our definition of the total induced charge (the charge induced on the readout pads when all the charges generated in the gas gap have reached the anode or cathode surfaces) and the actual charge that has accumulated on the surface of the anode or cathode. If one assumes that all dielectric layers (except for the gas gaps) have zero thickness, then the induced total charge will be equal to the actual charge on the surface of the anode or cathode. In the case of the 10 gap MRPC, setting the thickness of the glass plates and the pcb to zero gives a weighting field of 0:8 mm1 , compared to the weighting field of 0:53 mm1 calculated using the actual thickness of the dielectric material. This means that we would have to multiply the total induced charge by 0:8=0:53 ¼ 1:5 to get the actual amount of charge seen by the external circuit supplying the voltage.
We first simulate avalanches in individual 250 mm gap and then add together 10 gaps to simulate the signal from MRPC described above. One or more of these gaps may have no avalanche. The Townsend coefficient, a, attachment coefficient, Z, drift velocity, v, and diffusion coefficients (both transverse and longitudinal) are needed in the simulation. We use MAGBOLTZ [7] to calculate the above coefficients for the particular gas that we are using (93% C2 F4 H2 and 7% SF6 ). The values of these parameters for an electric field of 100 kV/cm are a ¼ 126:8 mm1 , Z ¼ 8:2 mm1 and v ¼ 21:62 cm ms1 . The 250 mm gas gap is divided into 500 slices. Through-going 500 MeV/c muons will create electron and positive ion pairs; this is simulated using the HEED [8] program; the number of electrons and their position are then put into the corresponding slice of gas in the gap. The avalanche then evolves by moving and multiplying the electrons for a given time interval. The time interval used in our simulation is the time needed for an electron to move 0:5 mm at a velocity v0, the drift speed at the applied electric field E0 . The electric field experienced by an electron is given by the applied electric field modified by the charges located in other position slices (space charge). This space charge, created by electrons, positive and negative ions, affects the growth of the avalanche and is very important especially when the density of charge is high. We consider that the charges are spread on disks, each with a Gaussian radial distribution. We calculate the strans of this distribution by assuming that pffiffiffi the avalanche spreads transversely according to strans ¼ DT : L, where DT is the transverse diffusion coefficient and L the distance of the disk from the initial cluster position. Thus to calculate the electric field at a given slice we have to calculate the electric field experienced by this disk of electrons caused by all other disks of charge and the applied electric field. This procedure is known as the 1.5D model (see Lippmann and Riegler [4]). The space charge has the effect of limiting the growth of the avalanche; the electrons located at the head of the avalanche experience the field from the positive ions. Thus the size of this disk is important for the calculation of space charge; the bigger the disk, the weaker is the space charge. In Fig. 2 we show the electric field and the distribution of the electrons, positive and negative ions for a developing avalanche. The 0 ps plot shows the initial situation. Three clusters of ionisation are created by a through-going particle. The electric field is initially constant across the width of the gas gap and has a value due to the applied voltage of 100 kV/cm. In the second plot, for a time of 440 ps, clusters 1 and 2 have merged together; the electrons follow a Gaussian distribution due to the longitudinal diffusion; small perturbations of the electric field can be observed due to the charges in the gas gap. In the third plot, at 630 ps, half of the electrons from cluster 3 have already reached the anode. The space charge distortion of the applied electric field is becoming large. The distribution of the electrons is no longer Gaussian due to the large variation of the electric field. The 710 ps plot shows that almost all the electrons from cluster 3 have now reached the anode. In the final plot at 1.46 ns all the electrons have now reached the anode; there is a residual charge in the gas gap produced by the positive and negative charges in the gas gap and the electrons that are deposited on the surface of the anode. When the electrons arrive at the anode, they are accumulated on the surface of the resistive plate and they are included in the calculation of the electric field; we believe that this is reasonable since the avalanche development is fast ð 1 nsÞ and the characteristic time constant of the resistive plate is long. It is
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K. Doroud et al. / Nuclear Instruments and Methods in Physics Research A 610 (2009) 649–653
0 -50 250
Fig. 2. The electric field and number of charges (electrons, positive ions and negative ions) in a gas gap of width 250 mm displayed for six times. The applied electric field is 100 kV cm1 . The 0 ps plot shows the initial situation with three clusters of ionisation; at 440 ps, the first two clusters have merged together, the electrons have a Gaussian spread due to longitudinal diffusion; the 610 ps plot shows the electric field is strongly affected by space charge; note that in the final two plots (880 and 1.46 ns) the distribution of negative ions follows the positive ions.
important to note that the distribution of negative ions follows closely the distribution of positive ions.
4. Results All resistive plate chambers have some rate dependant effects caused by the charge produced in the gas gaps; this charge has to pass through the resistive plate and this current will generate a voltage drop that will decrease the electric field in the gas gap. In general one wants to ensure that the fast charge (produced by the fast moving electrons) is sufficiently large while at the same time minimising the total charge generated inside the gas gap. Thus the ratio of fast charge to total charge is of crucial importance to users of MRPC technology. For an electric field of 100 kV cm 1, the Townsend coefficient, a, is 1269 cm1 and the attachment coefficient, Z, is 82 cm1 for
our particular gas mixture. Thus, without any space charge effects, one would expect a gas gain of eðaZÞd ¼ 7:7 1012 , where d is the width of the gas gap (250 mm). This is an enormous gas gain; a single electron avalanching across the gap would produce 1:2 mC of charge inside the gas gap. However space charge does exist and its effect is to reduce the growth of the avalanche by some orders of magnitude. We have used five values of the electric field in the simulation (95, 100, 110, 120 and 130 kV cm1 ). For each of these electric fields, we generate 500 ‘‘single-gap’’ events. For each ‘‘multigap’’ event we make a random selection of 10 single gap events. The value of the weighting field allows us to compute the fast charge (due to the movement of electrons in the gas) correctly. In Fig. 3 we show the result of the simulation and the published measurement [1] of the ratio fast/total induced charge. For the simulation we first made a scatter plot for all the multigap events for the five different electric field values. Obviously the low
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K. Doroud et al. / Nuclear Instruments and Methods in Physics Research A 610 (2009) 649–653
electric field ð95 kV cm1 Þ populated the left hand side of the plot (low values of the fast charge) while the higher electric field produced events with larger fast charge. A profile histogram was then made and the points plotted. The measured values were produced in a similar fashion combining data with various applied high voltages. For the simulation we show two variants to calculate the total charge. The first method (curve labelled ‘‘No recombination’’) takes into account the number of positive ions in the gas gap due to the avalanche. The second method (curve labelled ‘‘100% recombination’’) considers the positive and negative ions at each position step (there is a step every 0:5 mm); the number of negative ions is recombined with a corresponding number of positive ions and this results in a reduction of the number of positive ions. The remaining positive ions are then summed up over the width of the gas gap and used
as the total charge. It is clear from Fig. 3 that the measurement strongly favours the ‘‘100% recombination’’ variant of total charge. However, the simulation using the values of avalanche parameters obtained from running MAGBOLTZ [7] gives a fast charge that is too small; this is the data labelled ‘‘Normal DT ’’ ; we thus need some modification to the simulation to reduce the overestimation of the space charge. One way to do this would be to enlarge the disks of charge. In the simulation we have only considered the axial electric field along the direction of avalanche growth; however there is also the radial electric field. There is a repulsive force acting to explode the electron cloud. Lippmann and Riegler have considered this radial field. To simulate this correctly each disk has to be divided into a series of rings; this model is known as the 2D model. Even using fast algorithms the increase of computation time is considerable ( 1 day per
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Fast Charge [fC] Fig. 4. Ratio of fast charge/total induced charge as a function of fast charge. The total induced charge is calculated either by considering just the positive ions that remain in the gas gaps due to the avalanche (no recombination) or by first recombining the negative and positive ions and then considering the remaining positive ions. The transverse diffusion coefficient DT is multiplied by a factor 3 for this simulation.
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avalanche according to Lippmann [9]); thus using the 2D model is not practical for this study. Instead we choose to modify the InffiffiffiFig. 3 we show the result coefficient of transverse diffusion, DT . p of the simulation multiplying DT by 2, 3 and 4. One sees that increasing DT moves the curve along the abscissa, but does not change the slope. We choose a factor 3 and show the result of this simulation in Fig. 4. We alter the percentage of recombination from 100% to 97% and 94%. Varying the percentage does vary the slope and some value between 95% and 100% fits the data. Clearly the value of total induced charge obtained from ‘‘No recombination’’ does not describe the data.
5. Discussion Is such a high fraction of recombination plausible? The value of transverse diffusion is 100 mm cm1 for this gas mixture so that a typical radius of the cloud of electrons after moving half the gap would be 10 mm. We see from Fig. 2 that 106 charges in a 0:5 mm step is a typical value. The number of molecules in such a volume ð160 mm3 Þ is 4 109 . Thus the percentage of ions in this volume is 0.025%. Gas molecules of oxygen and nitrogen at room temperature have 1010 collisions per second [10]; thus in a nanosecond a given negative ion has a 0.25% probability of colliding (and thus recombining) with a positive ion resulting in a characteristic recombination time of 400 ns. Oscilloscope pictures shown in Ref. [1] indicate that the total drift time is 1000 ns; thus the 400 ns recombination time appears to be too long since the clouds of ions will separate before the ions can recombine. However inspecting Fig. 2 we see that in the location of most of the positive and negative ions (between 150 and 250 mm) the field is very low or even negative, thus these ions will not be transported to the cathode or anode but will stay in this location and are likely to recombine. Given this, such a high fraction of recombination can be understood. We cannot exclude that some fraction of the electrons may directly recombine with the positive ions without going through the intermediary of attachment and formation of a negative ion. For the small gas gaps typically used in MRPCs [1,2], the intense space charge stops the avalanche growing; however in the
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low field region generated by the space charge the attachment coefficient becomes large and many electrons become attached. This effect additionally stops the avalanche growing. The negative ions then recombine with the positive ions and thus dramatically reduce the amount of charge in the gas gap. This reduction is very important for the rate capability of the MRPCs.
6. Conclusion The high fraction of recombination of positive and negative ions substantially reduces the total amount of charge in the small gas gaps of the multigap resistive plate chambers. This allows MRPCs to operate at relatively high rates using glass with high resistivity (1012 21013 O cm).
Acknowledgments We have been particularly helped in this work by the stimulating discussions and help from Werner Riegler, Christian Lippmann and Rob Veenhof. We are indebted to them for being so generous with their time and knowledge. References [1] A.N. Akindinov, et al., Nucl. Instr. and Meth. A 531 (2004) 515 10.1016/ j.nima.2004.04.246. [2] A. Akindinov, et al., Nucl. Instr. and Meth. A 456 (2000) 16 10.1016/S01689002(00)00954-2. [3] A. Alici, et al., Nucl. Instr. and Meth. A 579 (2007) 979 10.1016/ j.nima.2007.06.027. [4] C. Lippmann, W. Riegler, Nucl. Instr. and Meth. A 517 (2004) 54 10.1016/ j.nima.2003.08.174. [5] S. Ramo, Proc. IRE 27 (1939) 584. [6] W. Riegler, Nucl. Instr. and Meth. A 491 (2002) 258. [7] S. Biagi, MAGBOLTZ: transport of electrons in gas mixtures, /http://consult. cern.ch/writeup/magboltz/S. [8] I. Smirnov, HEED: details of this program available at /http://consult.cern.ch/ writeup/heed/S. [9] Detector Physics of Resistive Plate Chambers, Dissertation of Christian Lippmann, 2003, available at /http://www-linux.gsi.de/lippmann/files/Dis sertation.pdfS. [10] M. Ohring, The Materials Science of Thin Films, second ed., Elsevier Science & Technology Books, 2001, ISBN-13: 9780125249751.