Relativistic Rise Measurements with Very Fine Sampling Intervals
IEEE Transactions on Nuclear Science
Introduction The mocivacion of this work was to ^etenslne whether the technique of charged particle identification via the relativlstlc rise in the ionization loss can be significantly improved by virtue of very small sampling intervals. He used a fast-sampling ADC and a longitudinal drift geometry tc provide a large number of samples from a single drift chamber gap, achieving sampling intervals roughly 10 times smaller than any previous study. A single layer drift chamber was used, and crack*
... s used, and crack* of 1 meter length were simulated by combining together samples from many identified particles in this detector. Using these data we have studied the resolving power for particle identification as a function of sample size, averaging technique, and the number of discrimination levels (ADC bits) used for pulse height measurements. There Is a considerable amount of literature on the question of the choice of gas sample length to optimize the mass resolution for various experimental applications. Nonetheless, until recently 2 the application of sample sizes less than 1 cm NTP has not been examined critically, and the consensus has been that very small sample sizes would bring little improvement. As a practical matter, transverse drift detectors such as EPI, ISIS, CRISIS, etc. would have been intolerably costly if they had been designed with sub-cm gas sampling. The outstanding difficulty with this technique has been the long Landau tail of the energy loss distribution due to the small and thus statistically variable number of very energetic collisions. The standard approach to this problem is to take many independent samples and then retain only the 50Z or so with the lowest dE/dx ionization loss, thus reducing the effect of the o-ray component in the samples retained. Since the average energy loss in 1 cm of Argon is % 3 KeV one cannot eliminate (5-rays of that eaergy clearly in such samples. By taking much smaller samples we expected to be able to use truncation techniques to eliminate 6-rays much more efficiently. We also expected co demonstrate that one could use crude ADC resolution such as 1, 2 or 3 bits. A 1 cm sample of Argon contains many low energy primary collisions and the measured energy thus has less information about the shape of the underlying energy loss distribution than could be obtained from smaller samples. In this work we will show that improved knowledge of the shape derived from smaller samples can contribute substantially to the ability to identify particles. Description of the Apparatus The ionization detector is shown in Fig. 1 . The ionizing particle passes through the drift chamber in the direction of drift field. Thus by sampling the -DISCLAIMER > 'esoo^S'tntitv 'of The ( infringe vvaielv owned ;ighti. Pol&en service bv 1'ade name, traaemarii. msiufji: •oly I'S c^d o r s^fiTcnT, r ECO cn^pcndfl I rO^p, of current amplitude from the chamber in short time intervals, it is possible to obtain the ionization in very short track length samples. The chamber gas was 802 A, 20Z CO2 and was operated with a drift field of % 1.5 KV/cm which corresponded to i .25 nn oi gas length for each 10 ns time interval. One has to be cautious of a literal translation of time to track length because diffusion tends to mix adjoining samples (below .5 an). Furthermore the very nature of the current waveform which has a fast risetime (< 4 ns) but a long l/(t -1-t0) tail (tQ % 1 ns),3 which tends to correlate the avalanche size content of many time samples and thus reduce the resolution of independent samples. The electronics for the dE/dx measurements axe shown in Fig. 2 . Low noise amplifiers (equivalent noise charge 3,000 electrons) 4 were attached to each of four anode wires. The chamber was operated at a gas gain of % 3 x 10*. A small portion of the signal from each amplifier went to individual ADC's and TDC's. The remaining signals were mixed and passed through a relay controlled attenuator. The signal then was shaped by two pole-zero filters and an integration time constant (4 ns) was applied. This shaped signal went to two 5-bit 100 MHz flash encoders. The flash encoders have a time aperature uncertainty of less than 100 ps. Thus the time slices were very uniform. These measurements were done in the 3NL ACS B4 beam. Runs at t 3.5 GeV/c were tagged to select p 1 , IT-and e-using Cerenkov counters Cl and C2, shower counter S and time-of-flight counters Tl and T5, Fig. 3 . In addition, the trigger selection was gated to equalize the number of each particle type. Tlmc-of-flight and shower counter pulse heights were recorded so that subsequent analysis cuts could insure the purity of the p, ir and e samples. Between ACS spill cycles a few test events from both a current pulser at the amplifier inputs and a Fe 55 Y source were recorded. In particular, the Fe 33 events were used to control the overall long term gains to % IS. The current pulser verified that amplifier gains were stable to < 12. Time Adjusted Pulse Height Distributions Several hundred Fe events were recorded with each data run. Adding the pulse height vs. time of all events gives a composite pulse shape (Fig. 4) . To minimize the cross correlation of the time samples, the two pole-zero adjustments were made to minimize the tail of this distribution without producing undershoot. Fe-53 and pulser events were recorded before every beam spill and used to normalize the system gain. Because Fe-" produces a 5.9 Kev localized cluster of ionization the system gain was reduced 10 times during this portion of the bean cycle. Tracks that pass near the anode wire produce avalanches almost immediately relative co the particle DISTRIBUTION OF THIS DOCUMENT IS UHUMITEB ;v passage while tracks passing near the field wires begin producing avalanches 50-60 ns latar. In order to sae the average pulse height shape, all events of each type ware summed with the time referenced to the leading edge (Fig. 5) . The leading edge amplitude is % 3 times higher than that froa the long flat tall because ionization la collected from both sides of the anode plane for the first 3 ma. Also near the anode the drift velocity Is higher. The long flat plateau corresponds to % 1 cm of uniform drift field. The dE/dx Information used In this work was taken froa a limited part of each event, % 5 mm of gas, In ordar to minimize uncertainties due to varying drift velocity near tha anode and uncertain length of track near the field cathode. Samples were selected from time bins 17 to 36. One meter long cracks of 5 different time sample sizes were assembled by taking contiguous samples from each event. The 40 na sampling for example uses bins 17, 18, 19, 20 for its first sample, bins 21, 22, 23, 24 for tha second one, etc. until a full meter of track is assembled. The sample sizes were 10, 20, 40, 160 and 640 ns corresponding to approximately .25, .5, 1, 4 and 16 ma per track sample. The 16 ma track segments required the combining of samples from 3 events. Time Slice Pulse Height Distributions The data presented are from 3.5 GeV/c negative beam runs although the positive beam runs yielded indistinguishable results. Figure 6a, b and c through 8a, b and c show pulse height distributions P(E) of e, ir and p for time slices of 20, 160 and 640 ns T«Jponding to approximately .5, 4 and 16 ma of gas. Following standard practice we use the truncated mean as the measura of ionization loss. For one meter of gas the samples are ordered from minimum to maximum pulse height. 100Z sample recension means 100Z of the samples are retained and sunned to measure the ionization in one meter of gas. 90Z retention means the smallest 90Z of the samples are retained and suaawd, etc. Dash marks are Included on these figures Co show where SOX and 90S of ehe samples occur. 100Z retention is simply the integral of the P(E) distribution and does not depend on sample size. We define RA to be the ratio of sunned energy losses for tracks retained at AZ of tha total number of samples. Thus Rioo corresponds to the rise in the measured average energy loss. (This number is not usually quoted in the literature.) For electrons and protons at 3.5 GaV/c, we find R^OO " 1*36. A more frequently quoted number is the ratio of the most probable energy losses and we observe this ratio to be 1.52 in good agreement with previous measurements.2 The face that the two ratios are not tha same indicates the shape of P(E) is also changing as the rise occurs. The fractional energy g(A) contained in samples retained to AX of the total samples is plotted vs. percent retention A in Figs. 9a, b, c, and d. g(A) AZ of samples / E-P(E)dE E.P(E)dE Relativistlc Rise vs. Sample Size and Truncation RA(e,p) can be written RA(a,p) -g(A)./g(A)p *R10Q(e,p) where R1QO(e,p) -1.36 is the untruncated relativlstic rise. At 3.5 GeV/c protons are at the minimum of tha relativistic rise curve and tha electrons are fully saturated on the Fermi plateau. We find that In general g(A)s > g(A)p so the procedure of truncating the data enhances the observed relativistic rise RA(e,p). For the 640 ns samples and a retention of 402 of the samples we find g(A) /g(A) % 1.12 which yields a Jt*o(«»P) of 1<52 in i ood agreement with other data. For this case about 25Z of tha energy is retained. Tha actual energy cutoff point par sample is % 3 Kev for this % 16 ma of gas. We find g(A)./g(A)p for this sample length Is essentially the same from 10Z sample retention to 90Z sample retention, so the observed relativistic rise is not sensitive to the level of truncation once the largest few percent of' the samples are removed. For the 20 as samples, as expected, we do a much cleaner job of eliminating the enargetic collisions. Tha energy cutoff for 40Z sample retention is % 100 ev and the retained energy is only about 121 of the total. Host significantly g(40),/g(40p is now 1.37 which gives K4O< a >P) " 1-84. In fact g(A),/g(A)p Increases from about 1.12 at 90Z sample retention to 2.18 at 10Z sample retention resulting in corresponding increases in tha relativistic rise. This dramatic rise in g(A)e/ g(A)_ is the result of the fact that there is relatively more energy in the smaller samples for the electrons than for the protons. One has to be careful in translating this into a statement about the P(E) distributions because the same percent sample retention corresponds to different energy cutoffs for electrons and protons. However, by comparing Fig. 6a and 6c , we can observe that P(E) for protons (at the minimum of tha dE/dx curve) has a substantial number of zero energy samples while the corresponding P(E) for electrons has many fewer zero samples. Thus there is a sample retention level 0v< 15Z) for which the retained proton energy will be essentially zero, while the retained electron energy will be finite. The calculated relativistic rise for this level of truncation would be vary large, but this does sot appear to be a practical approach because the amount of retained energy is very small and the relative statistical fluctuations are large. As the fraction of retained samples is increased, the average energy in the retained samples increases, thus ehe effect of the distribution of zero and smal? energy samples on gA is diluted and RA will approach R.j.00-As shown below, we find that sample retentions of froa 30-60J seem Co be Che best compromise for particle selectivity. This effect has not been observed previously because as can be seen from Fig. 8a and 3c , when the data is taken using "large" (^ 16 nm) samples, there are no zeros for either protons or electrons and the average fractional retained energies per sample are not very different. The information abour, the distribution of the small energy losses has been lost by averaging over a sample which contains many individual energy loss events. In fact, in the limit of very large samples one would expect P(E) to become relatively narrow, thus gA would become a straight line and RA -*-Rioo for any Figure 10 is a plot of the observed R(e,p) and R(ir,p) as a function of sample size and truncation which summarizes these results. The increase in the observed relativistic rise for small samples is the result of our being able to use our more detailed information on the energy loss (particularly on very small losses) to emphasize differences in the underlying P(E) distributions for the electrons and protons. Since the observed relativiscic rise depends on the shape of the ?(E) distributions at lower energies it can be affected by shifts or uncertainties in the electronic baseline offsets for the amplifiers and the ADC. The three particle types were recorded simultaneously minimizing any such effects, and the baseline was stable during the data taking. We estimate that the baseline offset uncertainty is less than 1/4 of the lowest ADC level. With 40Z of the samples retained, this could produce a systematic error which varies smoothly froa 20S for the 20 n* samples to 2.5Z for the 640 ns sampIts. Particle Identification Selectivity The observation of enhanced relativlstic rise with small sample size and severe truncation is not sufficient to assure improved particle identification selectivity. The separation of the particles must be related to the width of tha sample distributions. Figure 11 shows how this varies with sample size for the electron data. This is the percent standard deviation <J of a 60!! retained sample of 30 one-meter tracks. To compare our results in particle selectivity with other results we define a figure of merit S. i E A" " 20 B A-B energy distributions applicable to detectors with thin layers of gases. He observe quite good agreement with our data for sample thicknesses £ 5 mm. For samples thinner than S mm the agreement is not quite as good. The predicted distributions tend to be narrower and peak at lower energy losses. This is probably caused by the fact that the model ignores diffusion of the drifting electrons which introduces correlations in adjacent samples because of our method of ionization sampling. This effect is, of course, more important for sample thicknesses of the order of a diffusion length (^ 0.5 mm). Further analysis of the model predictions with a truncated mean method similar to the one used for the analysis of our data reveals characteristics similar to the ones discussed in the previous sections although the effect of the relativistic rise as a function of sample size and truncation is noc aa pronounced as it appears in the data. where EA and Eg are the truncated mean particle A and B energies and aA and ctg their standard deviations. S is Che number of standard deviations particle A lies from particle B when a selection threshold is set to give 97.52 efficiency for detecting particle B. Figure 12 gives these S values vs. sample size for our data taken at 3.5 GeV/c with 40% and 602 truncations. One must take care in interpreting many standard deviations too literally. From our data we cannot show that these distributions are gausaian beyond 2a. Indeed the rare high energy knock on electrons will effect Che distributions. Possibly the spatial resolution of this kind of drift chamber will allow elimination of these cases. Fig. 12 is a point for ISIS 1 taken from the review paper of Ref. 2. This S value was calculated from the pulse height distributions for ir and e at 500 MeV/c which is equivalent to p and e at 3.5 GeV/c. He attribute the higher selectivity value of our 16 mm sample data to the fact chat our data were taken with a single layer of gas using one ADC. Thus Che usual variances that arise in a multi-layer device due to gain variations, offset corrections, cross talk, etc. were eliminated. A multi-layer detector utilizing fast ADC's and longitudinal drift would of course also be susceptable to these effects. Although the observed relativistic rise is sensitive to the baseline offset che sensitivity S is not. Included in ADC Resolution A retained sample cut of 405! for che 10 ns samples corresponds to an energy cutoff < 100 ev. This suggests that although the dynamic range of energy losses ranges from 0 to many Sev, the most useful information will be in the range of •£ 100 ev. Thus a simple four or eight level ADC (2 or 3 bits) with an upper threshold of ^ 100 ev. and resolutions of 25 to 13 ev. may be sufficient to provide excellent particle selectivity. He note that for our 403! retained samples all samples above the fourth level were removed and thus a 4 level ADC with the appropriate threshold would reproduce this result. Comparison With a Model He have compared our data with theoretical predictions of a recently published model by Allison and Cobb. 2 This model uses the experimentally measured photoabsorption cross sections for various noble gases and a convolution method to calculate ionization He have studied the ionization loss in small gas samples using a longitudinal drift ionization detector and fast analog to digital conversion techniques. We find this technique can substantially improve tha mass resolution capability of gas particle decectors. He have also shown that only a rather coarse ADC resolution is required to capture all the information needed with the truncated mean sampling method of determining the relative energy loss.