Gas gain: 2-5x10^4 Preamplifier peaking time: 10-15ns Gas pressure: 3bars. Discriminator 1. Charge. Discriminator 2. Control Logic (JTAG Interface)

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1 EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH Bipolar versus Unipolar Shaping of MDT Signals Werner Riegler, Martin Aleksa Harvard University, CERN Abstract The MDT frontend electronics scheme, as presented in the TDR, was optimized for fast linear gases like Ar=N 2 =CH 4 9=4= [], but since these gases contain hydrocarbons which seem to be responsible for aging problems, the current baseline gas is Ar=CO 2 93=7 which shows nice aging properties but is slower and signicantly nonlinear. The nonlinearity and reduced speed have a signicant impact on the pulse shapes: the trailing edge resolution is reduced and we get multiple threshold crossings per signal with the current shaping scheme. The dierent pulse shapes as well the fact that trailing edge information and double track separation information were not found to be very useful made a complete review of the front end electronics specication necessary.

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3 Introduction At the time of the TDR [2] the baseline gas for the MDTs was Ar=N 2 =CH 4 9=4= (ns maximum drift time) and after detailed test beam studies of this mixture the following front end electronics specication was worked out (g. ): 38 Ω M Ω HV Wire diameter: um Tube diameter: 3cm Gas gain: 2-x^4 Preamplifier peaking time: -ns Gas pressure: 3bars Threshold 2 Threshold Discriminator M D T Preamp Diff Amp Shaping Amp ADC Leading Edge Trailing Edge 2 Logic LVDS Charge Discriminator 2 3 Phase Calibration System Control Logic (JTAG Interface) Figure : MDT frontend schematic and operating parameters as presented in the TDR. Preamp peaking time of ns to ns. Although the resolution is better for short peaking times a 'slower' preamp is preferred for reasons of stability and multiple hits. The dierence in resolution between a ns and ns peaking time preamp is about m and can even be reduced by performing a time slewing correction. Short gate ADC encoding the charge information in a pulse width. Measuring the signal charge with an ADC for -2ns after the threshold crossing time allows to correct for time slewing. It also provides very useful for monitoring purposes. Unipolar Pulse shaping. Although unipolar pulse shaping requires an active baseline restoration circuit to avoid baseline uctuations due to high rates (up to 4kHz/wire) it is preferred to bipolar shaping since. We get one threshold crossing per signal. 3

4 2. The trailing edge of the signal which is correlated to the bunch crossing can be measured to t 2ns and can be used to eliminate out of time events to increase pattern recognition eciency and reduce fake track rate. 3. The information of a second discriminator with high threshold can be encoded in the same channel. Programmable lter time constants. In order to adjust the tail cancellation circuit for dierent gases the lter time constants have to be programmable. Discriminator hysteresis is important to avoid multiple threshold crossings. A second discriminator with high threshold allows to identify muon signals that are piled up to background signals. The separation eciency was shown to be about 6% for a leading edge separation of > ns. Encoding the high threshold discriminator information in one channel with all the other hits gives on average.7 hits/signal. There are three modes of operation:. Time over threshold mode giving leading and trailing edge, one hit per signal. 2. ADC mode giving leading edge and charge, one hit per signal. 3. ADC+high threshold mode giving leading edge, charge and double track information. Four 24-channel TDCs are daisy chained into one front-end link. In the meantime, many things were studied in more detail or have been changed: Aging problems with gases containing hydrocarbons resulted in switching to the gas Ar=CO 2 93=7 which has a maximum drift time of 7ns and is very nonlinear. Adjusting the tail cancellation time constants such that we arrive at one hit per signal, the trailing edge resolution is strongly degraded ( t 8ns) which makes this information not very useful. The double track separation information was shown not to be useful for pattern recognition which is mainly due to the fact that, using the high threshold discriminator, we get multiple hits even for single tracks. Also the decreased resolution of the recuperated hit ( 6m) is a major drawback. The trailing edge information (even with a resolution of 2ns) was never used or found useful in simulation [3]. 4

5 In some high rate regions in the muon system it is not possible to daisy chain four TDCs into one front end link, but in order to keep the number of cables to the MDTs low it was important to daisy chain as many TDCs as possible into one link, which resulted in a non uniform scheme. Since the ReadOutDrivers (NIMRODs) have now been moved from the cavern to the USA and the front end links can not be m long, a dierent scheme was adopted. A data concentrator card will gather the TDC signals from one chamber and transmit them to the NIMRODs through an optical ber, so there is no need for daisy chaining TDCs. Each TDC is connected directly to the concentrator card. In the previous scheme, the maximum allowed data rate was 4kHz per tube with an average of.7 hits per signal. Using bipolar shaping for the new baseline gas results in an average of 3 hits per signal, so this solution would not be acceptable with the old readout scheme. However, the new scheme might impose dierent requirements on the maximum number of hits per signal, so for each front end scheme we have to study the implications on the readout. All that made a complete review of the frontend electronics scheme necessary. Especially the question of unipolar versus bipolar signal shaping has to be reconsidered since bipolar shaping would not require an active baseline restorer as well as programmable time constants, which would simplify the whole frontend scheme drastically.

6 2 MDT performance for dierent shaping schemes Most of the signals in the muon system result from background photons. These photons create high energy scattering electrons, some of them able to penetrate several tubes. The photon spectrum and other background characteristics are given in [4]. The average charge deposit per tube from a photon interaction is about 32keV which is two times more than the charge that muons leave in an MDT. This is mainly due to the fact that muon tracks are perpendicular to the wire while electrons created by the background photons are isotropic. All the simulations were done using GARFIELD to calculate the induced current signal and a stand alone program for electronics simulation. 2. Frontend electronics parameters The transfer function for preamp+lter for bipolar shaping was assumed to be g(s) = n!s ( + s) n+2! f(t) =( t= n + )(t=)n e t= t p = (n + p n+) () Since the delta response integrates to zero Z f(x) = e x x n+ n + j = (2) every signal convoluted with this transfer function integrates to zero. For unipolar signal shaping a preamp delta response g(s) = n! ( + s) n+! f(t) =(t=) n e t= t p = n (3) together with two pole zero lters g(s) = s+= s += 2! f(t) =( 2 )e t 2+(t) (4) was assumed. Sending a signal s(t) = exp( t= ) through a pole/zero lter with time constants and 2 results in a signal s(t) = exp( t= 2 ). Since wire chamber signals don't have an exponential form but are / (t+t ) one usually ts a sum of several exponentials to the signal and uses several pole/zero lters to cancel each of these exponentials []. Usually two lters are sucient. The transfer functions for both shaping schemes together with the response to a single ionization electron can be seen in g. 2. A photon signal together with the output of a time over threshold discriminator for both shaping schemes is shown in g. 3. From these gures we can infer that the standard 6

7 Frontend Deltaresponse.8.6 Response to a single Ionization Electron Unipolar Shaping.2 Unipolar Shaping Bipolar Shaping Bipolar Shaping Time [ns] Time [ns] Figure 2 : Frontend delta response for unipolar and bipolar shaping and response to a single ionization electron. The dotted lines show the signal at the dierent lter stages of the unipolar scheme. The 'high' dotted line shows the preamp output, the 'lower' dotted line shows the signal after the rst pole/zero lter, the 'upper' solid line shows the output of the whole chain. The unipolar signal is slightly bipolar since the time constants are adjusted assuming only the ion-tail of the signal. The slight undershoot is caused by the electron part of the signal. unipolar shaping scheme neither gives appropriate trailing edge resolution nor creates a single threshold crossing per signal for this specic gas. Introducing a large discriminator hysteresis helps to reduce the number of hits for the unipolar scheme (g. 4). We can also cancel the signal tail 'less strongly' in order to reduce the hit number, but as shown in g. 4, the dead time increases. However, since for bipolar shaping it takes additional time for the signal to return to the baseline from the undershoot, the dead time for both schemes turns out to be the same as shown later (g. 8). Figure shows that the signal shape also strongly depends on the position of the muon track along the tube. Now that we have a feeling for the problem we can start to look into the statistics of the problem i.e. we want to nd the number of hits per signal for dierent electronics schemes and operating conditions. The hit multiplicity for both schemes was calculated by creating signals at random distances for both gases Ar=N 2 =CH 4 9=4= and Ar=CO 2 93=7 with GARFIELD for photons and muons. 2.2 Bipolar Shaping The hit multiplicityversus threshold for dierent particles, gases, tube lengths and hysteresis settings is shown in gure 6. The Ar=CO 2 93=7 gas shows more hits due to the longer drift time and nonlinear space-drift time relation. Photons show a higher hit multiplicity compared to muons which is due to the increased charge deposit. Looking at the bipolar 7

8 Pulseheight (electrons) Photon Signal (Garfield) Unipolar Shaping Pulseheight (electrons) Photon Signal (Garfield) Bipolar Shaping Time [ns] Time [ns] Figure 3 : Photon signal for Ar=CO 2 93=7. The standard unipolar shaping scheme shows a hit multiplicity very similar the bipolar scheme. pulse in g. 3 one can infer that for a larger charge deposit more signal spikes 'will reach up the threshold'. The fact that every spike of the signal is bipolar also explains why dierent hysteresis settings and tube lengths have almost no eect on the hit multiplicity. To conclude we can say that for a threshold of 2e- we nd (on average) 2.6 hits for photons for Ar=CO 2 93=7. Since the signal rate is dominated by photons we have to adjust the readout for these numbers. However the hit multiplicity increases strongly when we increase the gas gain (and keep the threshold xed), so if we want our system to work also for a higher gas gain we even have to consider 3-4 hits on average. 2.3 Unipolar Shaping Although it is obvious from g. 3 that for the standard unipolar shaping scheme, i.e. using two pole/zero lters that cancel two exponentials of the signal tail according to [], will give more than one hit per signal, it will always be possible to arrive at one hit per signal if we cancel the signal tail less strongly. Fig. 7 shows that introducing large discriminator hysteresis also helps to reduce the hit number which also can be seen in g. 4. It is therefore possible to have one hit per signal even for a unipolar shaping scheme, however this is only possible if all the lter constants and the hysteresis are very carefully adjusted. In a standard tail cancellation scheme with two pole/zero lters [] one adjusts the time constants for dierent gases by changing the capacitors and therefore leaving the pole/zero ratios constant (this is the baseline scheme as presented in the TDR). Adjusting the lters in order to minimize the number of hits per signal requires programmable pole/zero ratios (ratio = to 2.). 8

9 Pulseheight (electrons) Photon Signal (Garfield) Unipolar Shaping Hysteresis = e-, Time over Threshold Pulseheight (electrons) Photon Signal (Garfield) Different Filter Time constants Time [ns] Figure 4 : Introducing Discriminator Hysteresis and using dierent tail cancellation time constants one can reduce the hit number but one introduces dead time (the increase is however small). Pulseheight (electrons) Photon Signal (Garfield) Unipolar Shaping Different Tubes and Positions Time [ns] Figure : The same muon signal for dierent tubes and tube lengths. The MDT transfer function aects the signal shape signicantly. 9

10 Average Number of Hits Shaping: Bipolar Mode: Time Over Threshold Hysteresis: Tube Length: 2m Average Number of Hits Shaping: Bipolar Mode: Time Over Threshold Hysteresis: Tube Length: m 2 2 Photons Ar/CO2 93/7 Photons Ar/N2/CH4 9/4/ Muons Ar/CO2 93/7 Muons Ar/N2/CH4 9/4/ Threshold (e-) Photons Ar/CO2 93/7 Photons Ar/N2/CH4 9/4/ Muons Ar/CO2 93/7 Muons Ar/N2/CH4 9/4/ Threshold (e-) Average Number of Hits Shaping: Bipolar Mode: Time Over Threshold Hysteresis:. x Threshold Tube Length: 2m Average Number of Hits Shaping: Bipolar Mode: Time Over Threshold Hysteresis = Threshold Tube Length: 2m 2 2 Photons Ar/CO2 93/7 Photons Ar/N2/CH4 9/4/ Muons Ar/CO2 93/7 Muons Ar/N2/CH4 9/4/ Threshold (e-) Photons Ar/CO2 93/7 Photons Ar/N2/CH4 9/4/ Muons Ar/CO2 93/7 Muons Ar/N2/CH4 9/4/ Threshold (e-) Figure 6 : Hit multiplicity for dierent gases, particles, tube lengths,thresholds and hysteresis settings for bipolar shaping. One can see that the hit multiplicity is not aected by hysteresis settings or tube lengths. The number of hits is higher for the Ar=CO 2 93=7 gas due to the longer drift time and nonlinear rt-relation. Photons cause more hits due to the increased charge deposit.

11 Average Number of Hits Shaping: Unipolar standard Mode: Time Over Threshold Hysteresis: Tube Length: m Average Number of Hits Shaping: Unipolar standard Mode: Time Over Threshold Hysteresis:.7 x Threshold Tube Length: m 2 2 Photons Ar/CO2 93/7 Photons Ar/N2/CH4 9/4/ Muons Ar/CO2 93/7 Muons Ar/N2/CH4 9/4/ Threshold (e-) Photons Ar/CO2 93/7 Photons Ar/N2/CH4 9/4/ Muons Ar/CO2 93/7 Muons Ar/N2/CH4 9/4/ Threshold (e-) Average Number of Hits Shaping: Unipolar Mode: Time Over Threshold Hysteresis: Tube Length: m Average Number of Hits Shaping: Unipolar Mode: Time Over Threshold Hysteresis:.7 x Threshold Tube Length: m 2 2 Photons Ar/CO2 93/7 Photons Ar/N2/CH4 9/4/ Muons Ar/CO2 93/7 Muons Ar/N2/CH4 9/4/ Threshold (e-) Photons Ar/CO2 93/7 Photons Ar/N2/CH4 9/4/ Muons Ar/CO2 93/7 Muons Ar/N2/CH4 9/4/ Threshold (e-) Figure 7 : Hit multiplicity for unipolar shaping. The rst gure shows the standard unipolar shaping scheme with a time over threshold discriminator and no hysteresis. The second gure shows that we can reduce the hit number by introducing hysteresis but we still get more that two hits for the Ar=CO 2 93=7 gas. The third and fourth gure show numbers for 'soft' tail cancellation. We can see that soft tail cancellation and large hysteresis helps to arrive at a single hit per signal.

12 3 Bipolar versus Unipolar Shaping It is instructive to compare our situation to the ATLAS Transition Radiation Tracker (TRT) which foresees a unipolar shaping scheme with active baseline restoration. Since the drift distances in the TRT are very short and the drift velocity is high (pressure bar) the signals are very short. Using a bipolar scheme would double the dead time since the signal undershoot has the same duration as the signal itself. Since in the MDT case the duration of the undershoot is short compared to the whole signal length and since we have to use 'soft' tail cancellation in a unipolar scheme to avoid multiple hits the dead time is essentially equal (g. 8) ns Figure 8 : Deadtime spectrum for Ar=CO 2 93=7 for unipolar and bipolar shaping. The dierence is insignicant. At this point it would seem natural that unipolar shaping would be the preferred solution, however we have to keep in mind that this requires active baseline restoration, large discriminator hysteresis and programmable time constants for dierent gases. Even if we have all these options they must be very carefully adjusted and we must work exactly at the dened operating point. This is a signicant complication compared to a bipolar scheme where we use only one lter with a xed time constant, no baseline restorer and no large hysteresis and where we don't have to adjust anything. The biggest concern for the bipolar scheme are multiple hits. An average of up to 3 hits per signal increases the data volume signicantly. Simulations of the TDC behavior showed that for a rate of 4kHz with.7 hits per signal on average there is no loss of leading edge hits. If we have 3 hits on average, the Level Buer on the TDC has to be extended. Whether the front end link can handle this rate has to be studied. 2

13 However even if we are able to read out all the hits there is a dierence between the unipolar and bipolar scheme: In case of a level one trigger all hits within the maximum drift time window (plus some propagation time) are read out. In case of unipolar shaping this window would contain background hits and muon hits, in case of bipolar shaping we would have after pulses in addition. Since we don't know whether a hit corresponds to a real leading edge or just an after pulse, the pattern recognition program has to treat all the hits with equal priority. However it was shown that this can even reduce the eciency, sowehave to nd some other algorithm. At a rate of 3kHz, the average time between two hits is 3s, the average time between two after pulses is much smaller ( 2ns). From this we can conclude that the rst hit in the drift time window is most probably a real leading edge. So the pattern recognition program would use only the rst hit in the time window. However, this way we eliminate also a small number of real hits and we reduce the single tube eciency. The impact of this is shown in the next chapter. Photon Muon us Figure 9 : Using only the rst hit in the drift time windowintroduces articial deadtime. However using all the hits in the time window can create problems in case of bipolar shaping due to multiple hits. In case of unipolar shaping we know that every hit corresponds to one particle, but in the bipolar scheme we don't know any more whether the hits correspond to the leading edge of a particle or whether it is just an after pulse. The point is that we lose information with the bipolar scheme. However, as shown in the next section, this eect is small. 3

14 4 How to decide on the shaping scheme It is of course desired to have a scheme that guarantees the same pattern recognition performance that is advertised in the TDR and also doesn't introduce major changes to the TDC or the readout scheme. We will estimate the impact of the dierent options on the pattern recognition eciency by looking at the single tube ineciency for several schemes. The results are shown in Fig. 2 and discussed below. It is however important to perform dedicated pattern recognition studies for the dierent schemes. The single tube ineciencies were calculated by randomly overlaying photon signals to the muon signal (according the given rate) and looking if the muon leading edge was lost (single events are shown in g. ). To get a feeling for the dierence between Ar=CO 2 93=7 and Ar=N 2 =CH 4 9=4= g. shows the rt-relations and the deadtime spectra for both gases. Although the average drift time is almost equal for both gases (248ns for Ar=N 2 =CH 4 9=4= and 2ns for Ar=CO 2 93=7), the 'photon induced deadtime spectrum' diers by almost 2ns (33ns for Ar=N 2 =CH 4 9=4= and 2ns for Ar=CO 2 93=7). The reason for that is the fact that photon interactions create high energy scatter electrons that either originate from the tube walls or end in the tube walls. Therefore the deadtime is dominated by the drift velocity close to the wall which is very low for the Ar=CO 2 mixture Rt-Relations Ar/N 2 /CH 4 9/4/ Ar/CO 2 93/ ns Figure : Rt-relation and dead time spectrum for both gases. The average deadtime is 33ns for Ar=N 2 =CH 4 9=4= and 2ns for Ar=CO 2 93=7. In the following we will present three dierent options. 4. Unipolar shaping We use a unipolar shaping scheme, widely programmable lter time constants, active baseline restoration, large discriminator hysteresis and carefully adjust all these parameters in 4

15 order to get on hit per signal. The single tube ineciency for a rate of 3kHz (Safety Factor ) is 2% for the Ar=CO 2 gas and 6% for the Ar=N 2 =CH 4 9=4= gas (g. 2). 4.2 Bipolar shaping, hit reduction in the TDC We use a bipolar shaping scheme which makes the front end electronics very simple. There are no parameters that have to be adjusted even if we change the gas. We haveup to 3 hits (on average) per single signal. The TDC LVL buer must be extended. The capacity of the readout scheme must be increased by a factor 3. Assuming that the pattern recognition program can only use the rst hit in the time window the single tube ineciency for a rate of 3kHz (Safety Factor ) is 23% for the Ar=CO 2 gas and 2% for the Ar=N 2 =CH 4 9=4= gas (g. 2). If the TDC would have the option to only give the rst hit in the time window the readout capacity would not have to be increased. 4.3 Bipolar shaping, articial deadtime We use a bipolar scheme and introduce articial deadtime in the discriminator to reduce the number of hits. The ADC information will be appended to the deadtime pulse. It is important to notice that the deadtime has to be equal or very close to the maximum drift time. If e.g. for Ar=CO 2 93=7 (7ns maximum drift time) we use a xed deadtime of ns it can happen that a late cluster, arriving at 6ns, triggers another ns pulse which would in that case increase the deadtime to :s. The single tube ineciency for a rate of 3kHz (Safety Factor ) is 2% for the Ar=CO 2 gas and 2% for the Ar=N 2 =CH 4 9=4= gas (g. 2).

16 Signal (e-) 2 2 Muon+Background Signal (e-) 2 2 Muon+Background Time (ns) Time (ns) Signal (e-) 2 2 Muon+Background Signal (e-) 2 2 Muon+Background Time (ns) Time (ns) Signal (e-) 2 2 Muon+Background Signal (e-) 2 2 Muon+Background Time (ns) Time (ns) Figure : Single events for a background rate of khz. The solid line indicates the muon signal, the dashed lines shows the photon background. The left gures show the unipolar scheme, the right gures the same event for the bipolar scheme. In case of a trigger, the TDC would send out all the hits in the time window from -ns to 8ns. 6

17 4 3 3 Ar/CO 2 93/7 Unipolar shaping Bipolar shaping, all Hits Bipolar shaping, first Hit Bipolar shaping, 7ns fixed deadtime Ar/N 2 /CH 4 9/4/ Unipolar shaping Bipolar shaping, all Hits Bipolar shaping, first Hit Bipolar shaping, ns fixed deadtime Figure 2 : Single tube ineciencies for Ar=CO 2 93=7 and Ar=N 2 =CH 4 9=4=. The % ineciency at Hz is the ineciency due to delta electrons created by the muon in the tube wall [4]. The 'Bipolar Shaping, all Hits' curve has to be interpreted carefully: the ineciency is lower since some of the piled up hits that are lost in the unipolar scheme are recuperated (see 'double track separation with strong tail cancellation' [4]). However, the multiple hits and the fact that the resolution of the recuperated hits is lower leaves the pattern recognition eciency almost unchanged. 7

18 Summary Because of high background rates we have to use either unipolar shaping with active baseline restoration or bipolar shaping in order to avoid baseline uctuations. The usual argument in favor of unipolar shaping - deadtime - does not apply in our situation. Because of our operating parameters -3bars and low gas gain - we have the peculiar problem of multiple hits. At the time of the TDR we decided on unipolar shaping because we get { one hit per signal { double track separation (eciency of 6% -8% for t >ns) [4] { trailing edge resolution of 2ns. Double track separation was never found to be useful [3], the trailing edge was never used and in addition the trailing edge resolution for Ar=CO 2 is only 8 ns compared to 2 ns for Ar=N 2 =CH 4 9=4=. In addition the drift properties of Ar=CO 2 are such that it is very hard to achieve one hit per signal. The background photons create high energy scattering electrons that 'look like tracks'. They deposit on average twice the energy of muons (muon tracks are perpendicular to the wire). The 'average' deadtime is 33ns for Ar=N 2 =CH 4 9=4= and 2 ns for Ar=CO 2 93=7. Bipolar shaping is very 'simple' (no programmable time constants, no baseline restoration circuit, no ne tuning). We get up to 3 hits on average per signal. The current TDC and readout can handle only two hits on average at a rate of 4kHz. Using bipolar shaping we lose information compared to unipolar shaping since we don't know whether a hit corresponds to a real leading edge or an after pulse (tube ineciency goes from 2% to 23% for Ar=CO 2 93=7). Essentially we can only use the rst hit in the time window. If we chose unipolar shaping we have to use 'non standard' tail cancellation with programmable pole/zero ratios (not the baseline). 8

19 There are 4 possible frontend schemes: { Unipolar shaping ('complex'): We need large discriminator hysteresis, programmable pole/zero ratios and an active baseline restoration circuit. We get one hit per signal and a single tube ineciency of 2% at 3kHz. { Bipolar Shaping ('simple'): We get up to 3 hits per signal (on average) and a single tube ineciency of 23% at 3kHz. The TDC Level buer and the readout capacity have to be extended. { Bipolar Shaping, rst hit TDC: The TDC buers have to be extended, the additional function of a rst hit readout has to be implemented. The single tube ineciency is 23% at 3kHz. { Bipolar Shaping, xed deadtime ('simple'): We have to introduce programmable deadtime (-8 ns). We get one hit per signal, the single tube ineciency is 2% at 3kHz. In order to decide on the shaping scheme we still have to study pattern recognition eciency, TDC occupancy and readout occupancy for the dierent schemes. 9

20 References [] M. Deile, J. Dubbert, N.P. Hessey et al., Testbeam Studies of the gas mixtures Ar : N 2 : CH 4 =9:4:... ATLAS internal note MUON-NO-22 (996), CERN. [2] ATLAS Muon Spectrometer Technical Design Report, CERN/LHCC/97-22, ATLAS TDR, (997) [3] Marc Virchaux, private communication [4] W. Riegler: MDT Eciency, Double Track Separation, ATLAS Muon Note 73, CERN 997 [] R.A. Boie, A.T Hrisoho and P. Rehak, signal shaping and tail cancellation for gas proportional detectors at high counting rates, NIM 92 (982). [6] On the NumberofLayers per Multilayer in MDT chambers Part I. Laporte J.F, Chavalier L, Guyot C, Virchaux M ATLAS Muon Note 26, CERN 996 [7] Pattern Recognition with MDT Chambers, Shank J, SliwaK,Taylor F, Zhou B, ATLAS Muon Note, CERN 997 2