Spurious pulses in methane filled proportional counters

International Journal of Applied Radiation and Isotopes, 1969, Vol..20~ PP. 479-492. Pergamon Press. Printed in Northern Ireland

Spurious Pulses in Methane Filled Proportional Counters P. J . C A M P I O N and M. W. J. KINGHAM Division of Radiation Science, National Physical Laboratory, Teddington, England

(Received 1 January 1969) T h e time distribution of spurious pulses in methane filled proportional counters under various conditions is presented. I n all cases the spectra were found to be continuous up to the positive ion transit time at which point a weak ion-cathode effect was observed. T h e average mobility of the positive ions in methane was found to be 2.4 4-0.1 c m / s e c p e r v o h / c m . Possible mechanisms for the production of spurious pulses prior to this transit time are discussed; an ion-molecule reaction is believed to be responsible for spurious pulses in the middle time range while those produced within the first few tens of microseconds m a y result either from electrons becoming trapped in the dense positive ion cloud or from a two stage process involving hydrogen radicals. An upper limit for the probability of a spurious pulse occurring when a counter was operated at the centre of the plateau (for Fe-55 X-rays) was estimated as 2 x 10-~ per genuine pulse. F A U S S E S I M P U L S I O N S D A N S LES C O M P T E U R S REMPLIS DE MI~THANE

PROPORTIONNELS

O n pr6sente la distribution en temps des fausses impulsions d a m les compteurs proportionnels remplis de m~thane. En tous les cas les spectres se montr~rent continuels jusqu'~ la p~riode de transit des ions positifs ~k quel point un effet faible de cathode ionique se fit voir. Pour la mobilit6 moyerme des ions positifs dans le m6thane on trouva la valeur 2,4 ~ 0,1 cm/sec par volt/cm. O n discute des m6canismes possibles pour la production de fausses impulsions avant cette p~riode de transit; on suppose uric r6action ion-molecule ~tre responsable pour les fausses impulsions d a m la r~gion centrale de temps tandis que celles produites d a m les premieres quelques dizaines de microsecondes pourraient suivre ou d'~lectrons retenus d a m le nuage ~pais d'ions positifs ou bien d ' u n proc6d6 k deux 6tapes impliquant des radicaux d'hydrog~ne. O n a esfim6 un chiffre de 2 × 10 -5 comme la limite sup6rieure pour la propabilit~ q u ' u n e fausse impulsion survienne q u a n d un compteur foncfionne au centre du plateau (pour les rayons X du Fe-55). /IIOH~HbIE I/IMHVJIbCbI B H A H O 3 I H E H H t ~ I X M E T A H O M HPOHOP~HOHAglI~HbIX CqETqHHAX 3Aec~ AaeTc~ pac~peneJIeH,e no BpeMeHH JIOE~HI,IX HMIIyJIbCOB B HaIIOJIHeHHKIX MeTaHOM np0II0p~0Ha~IbHHX CqeTqHHax B pasHo05pasHLIX yCJX0BHAX. ]30 Bcex c a y q a u x cneRTp~ o~a3~Ba~iHcb HenpepblBHblMH ~(0 MOMeHTa IIp0XOH~eHHH IIOJI0hgnTeJIbH0r0 Hona, Korea Ha6~mAaJic~ cJla6~i~ HOHH0-HaTORH~i~ o ~ e ~ T . Cpe~nna HO~BHH~HOCTb HOJIOKqHTeJIbHbIX a0~OS B MeTaHe o~asaaacL 2,4 ± 0,1 eM/ceH. Ha B0~bT/CM. 05cym~amTcn paanHe MexaHH3MKI 06pa30BaHH~ JIOmH~X ~Mny~I~COB A0 3T0r0 BpeMeHH npoxomAeH~n; BO3MOH~HO~ tITO pea~a Hon-Mo~e~y~a BM3MBaeT JI0~r~nI~Ie HMny~II,C~I B cepeAnHe A~ana3oHa BpeMeHH, B TO BpeMH, I~aK HMnyJn, cI,I B TeqeHHe nepBl,iX geeaTHOB M~IHpoceHyHA M0ry~ np0~lCX0~lTl, B pe3y~l~TaTe 8axBaTa 9~IeHTp0HOB HJIOTHbIMHOHHMM 05JIaHOM HJIH BcJIeAeTBHe AByx~a3n0ro npo~ecca, B HOTOp0M HpHHHMalOT y~acTHe p a ~ m a a ~ l BoA0p0Aa. BepxHHH rpaHn~a Bep0HTHOCTH B03HHHHOBeHHH ~Iomnoro HMnyJII, Ca 6M~Ia onpeAeJ~eHa Hall 2 × 10 -~ Ha I HaCTOH~H~ HMnyJIbe. 479

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FALSCHE Z/~HLIMPULSE IN M I T METHAN GEFI~LLTEN PROPORTIONALEN Z.~HLERN Die zeitliche Verteilung von falsehen Z~hllmpulsen in mit Methan geftiUten proportionalen Z~ihlern wird unter verschiedenen Bedingungen angegeben. In allen F~tllen land man die Spektren kontinuierlieh bis zur Laufzeit positiver Ionen, wo eine schwache Ionen-KathodenWirkung beobachtet wurde. Die durehschnittliche Beweglichkeit positiver Ionen in Methan wurde als 2,4 ± 0,I em/sje V/era festgesteUt. M6gliehe Mechanismen fiir die Erzeugung falscher Z~xlimpulse vor dieser Laufzeit werden er6rtert; man glaubt, dass eine Ion-MolekiilReaktion fiir falsehe Z~ihlimpulse im mittleren Zeitbereich verantwortlich ist, w~arend die innerhalb der ersten zehn Mikrosekunden erzeugten Impulse entweder yon in der diehten positiven Ionenwolke eingefangenen Elektronen herrtihren oder yon einem zweitsufigen Vorgang, bei dem Wasserstoff-Radlkale eine Rolle spielen. Eine obere Grenze ftir die Wahrseheinliehkeit des Auftretens eines falsehen Z~ihlimpulses beim Betrieb eines Z/ihlers in der Mitte des Plateaus (ftir Fe-55 R6ntgenstrahlen) wurde zu 2 × 10-5 je wahren Z~b_limpuls geseh~ttzt. INTRODUCTION IN ABSOLUTE disintegration rate measurements gas filled proportional counters are often used because they can operate at m u c h greater counting rates than Geiger counters. For such purposes it is usual to operate the proportional counter on a plateau, that is on the relatively flat portion of either the counting rate vs. the high voltage ( E H T ) curve for a fixed bias, or the counting rate vs. pulse height curve for a fixed E H T , the former m o d e of operation being the more usual. I f examined in detail such plateaux are rarely flat and the question arises as to whether the slope represents a genuine increase in efficiency or is due to spurious pulses; this has obvious implications for absolute counting. I n addition curiosity motivates the investigation of the end of the plateau region. This p a p e r attempts to answer these questions for methane filled proportional counters. While the occurrence of spurious pulses in Geiger counters is well known and has been investigated by m a n y authors the same cannot be said for proportional counters. T h e topic has been studied recently by GENZ et al. ¢1~ and has also been investigated in this Laboratory. A previous communication ~*) reported investigations relating to the mechanism of the pulse discharge in proportional counters filled with methane and also with a mixture of 90 per cent argon and I0 per cent methane. I t was observed that a cathode photoelectric effect was present under certain conditions and that such an effect could give rise to a train of pulses ("satellite pulses") following a genuine pulse. However

the electron transit time (which determines the time scale of satellite pulses) is sufficiently short in most counters compared with the imposed dead time that double pulsing is avoided. T h e present p a p e r is concerned with rather longer time intervals, that is from about 2/zsec u p to the ion transit time (several hundred /zsec) and beyond. This is roughly the time region investigated by Genz et al. who found, for a counter filled with a mixture of argon and 13 per cent propane at one atmosphere pressure, a marked effect due to the interaction of the positive ions with the cathode. A similar effect is reported here but, in addition, spurious pulses are observed which must be attributed to other causes; in fact it will be shown that under m a n y circumstances most spurious pulses in m e t h a n e filled counters occur within the first 20/,sec after a genuine pulse. APPARATUS T h e gas purification and handling systems, and proportional counters have been described previously ~'). I n most experiments sources of Fe-55 were used to provide a suitable counting rate, although in some experiments the counter was triggered with single electrons produced by a cathode photo-electric effect. For this purpose a weak continuous source of light illuminated the cathodO 3~. A multichannel analyser was used in the time m o d e in order to examine the distribution of pulse intervals in the time range extending from about 50/~sec to several msec. I n this mode the analyser is normally quiescent at channel zero. T h e

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J P.H.A. -l(multiscal¢r) Fio. 1. Block diagram of the electronics. The delay in the "start" circuit of the time to amplitude converter (TAC) is just sufficient to prevent the TAC starting and stopping on the same pulse. arrival of a " s t a r t " pulse advances the address at a constant rate until all channels have been transversed when the analyser returns to its quiescent state. Pulses subsequent to the " s t a r t " pulse are stored in the channel corresponding to the elapsed time from the arrival of the start pulse. T h e m i n i m u m effective channel width for this particular analyser was 25/~sec, and, in order to study the shorter time range in detail, a time-to-amplitude converter (TAC) with a time base of 80/~sec was used in conjunction with a second multichannel analyser. A block d i a g r a m is shown in Fig. 1. Both time analysis systems were calibrated at intervals throughout the course of these experiments by means of a double pulse generator and an oscilloscope. I t should be noted that these two systems are different in principle: in the first a completely r a n d o m distribution of time intervals will yield a statistically uniform distribution of counts in the multichannel analyser, while the second system will yield an exponential distribution. This is a direct result of the fact that, once the T A G is started, the very next pulse will stop it. I f however the r a n d o m pulse rate is m a d e sufficiently small the exponential will approximate to a horizontal distribution and this condition was achieved in the present

experiments by a suitable choice of source strength. (In this p a p e r a distinction is drawn between r a n d o m (i.e. genuine) pulses and spurious pulses.) I n order to eliminate any residual distortion of the time spectra due to the inherent nature of the T A C system the observations were corrected on a digital computer using the method described by CoA'rEs(4). This correction amounted to less than 5 per cent in the worst case. A further reason for working with low counting rates is that the ratio of spurious to r a n d o m counting rates increases as the overall counting rate decreases. T h e counting rates used in the experiments described below varied between 30 and 200 cps; this necessitated long counting times, usually overnight, in order to achieve a reasonable statistical accuracy. O v e r such periods small pressure variations in the gas flow system and changes in the ambient temperature caused a relative m o v e m e n t of the plateau with respect to the E H T of a few tens of volts. Since the plateaux were more than a hundred volts long such drifts were not serious for measurements made at the nominal centre of the plateau. However in order to make measurements on the steeply rising part of the curve beyond the plateau it was necessary to introduce a feed back system. T h e basis of

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Fio. 2. The lower curve is the time spectrum obtained at the centre of a plateau using a Fe-55 source. The counter dimensions were 2.86 cm diameter cathode, 10 × 10-a cm dia. anode, and the pressure of CFI4 was 740 torr. The calculated gas gain was 7 x lift. The upper curve is the result of a linearity check of system using two pulse generators. this feed back was a commercially available digital pulse height stabilizer, Model G-100 manufactured by Special Electronics Systems, Brussels, to control the E H T so that measurements could be m a d e at a fixed point on the curve. T h e stabilizer adjusted the E H T to a value at which the counting rates at its two inputs were equal. One of these inputs* was derived, as shown in Fig. 1, from the direct counting rate after passing through a scaler, the scaling factor of which was variable from 1 to 99. T h e second input was obtained from a gate which allowed all pulses, occurring in an interval of time after a triggering pulse, to pass; however a small internal delay prevented the pulse which opened the gate from passing through the gate. T h e gate width was variable in steps up to 75 #see. So long as the probability of recording a genuine pulse within the gate width was small the second input recorded mainly spurious pulses. I f therefore the variable scaler was set to divide by 50, for example, the system stabilized at a point which was approximately 2 per cent above the counting rate on the plateau. Since the object of the stabilizer was * Neither input was obtained from any "pulseheight" analysis. The commercial description of this instrument is therefore somewhat misleading in this case.

to remove long term drifts a time constant of several minutes was incorporated into the system. Some preliminary experiments were performed with a linear amplifier and single channel pulse height analysers in both the "start" and "stop" circuits. I t was found that the ratio of spurious to r a n d o m pulses could be significantly increased by setting a window to accept only very small pulses in the " s t o p " circuit. Despite this advantage such discrimination was not used since it was difficult to set the window in the same relative position in the pulse height spectrum as the conditions (pressure E H T , counter dimensions, etc.) were changed. An alternative way of reducing r a n d o m pulses was also investigated. T h e radioactive source was replaced by a deuterium flash l a m p which illuminated part of the cathode, the l a m p being triggered at uniform rates up to several kilocycles per second. T h e system was discarded since the l a m p itself generated after-pulses which could not be readily distinguished from those due to the counter.

RESULTS Several time spectra were taken at the centre of the plateau using counters of various cathode and anode radii and different gas pressures. It will be shown below (see for example Figs. 3, 4

Spurious pulses in methanefilled proportional counters and 5) that, just beyond the end of the plateau, spurious pulses were observed with a m a x i m u m probability at the end of the imposed dead time, the probability decreasing quite rapidly with increasing time at least for pressures near atmospheric. It is reasonable to suppose that, if spurious pulses occur on the plateau, their time distribution will be similar to those at the end of the plateau. O n this basis no evidence was found for any spurious pulses, an upper limit of 1 to 2 x 10-4 spurious pulses per genuine pulse being found from the n u m e r of "start" pulses and the estimated m i n i m u m n u m b e r of pulses required to produce a significant deviation from the r a n d o m distribution. T h e n u m b e r o f " s t a r t " pulses was found from the counts recorded in the scaler with a small correction ( < 1 per cent) applied for the dead time of the TAC. In order to reduce this limit still further a very long run was m a d e using a low counting rate ( < 4 0 cps) and the time distribution obtained is shown in Fig. 2, where only the results of the T A C system are presented. T h e results for the other system showed that the time spectrum was flat within statistics out to the limit of the time range, in this case 5 msec. Also shown in Fig. 2 is the result of a typical linearity test obtained by applying the pulses from two independent pulse generators running at slightly different frequencies to the input of the amplifier, the E H T to the counter being switched off. Such tests revealed the presence of a slight departure from linearity in the TAC-multichannel analyser system of a few per cent at small time intervals. A Zz test taken over the first 20 points showed that there was no significant difference between the two distributions shown in Fig. 2. O n the other hand if 200 counts, distributed approximately as found at the end of the plateau, were deliberately added to the observations a Z 2 test indicated that there was a difference at the 99.9 per cent confidence level. Taking this as the m i n i m u m n u m b e r of spurious pulses that could have been detected in this experiment gives an u p p e r limit of 2 X 10-5 spurious pulses per genuine pulse. I f however spurious pulses occur at the centre of the plateau with a less marked distribution a correspondingly less stringent limit would be obtained. However any significant difference in the time spectra would imply a different mechanism for the

483

production of spurious pulses which, although not impossible, seems rather unlikely. As the E H T was increased to a point just beyond the plateau region time spectra were obtained which had shapes such as those shown in Figs. 3-5, viz a monotonic decrease in the distribution from the dead time to a time corresponding to the positive ion transit time at which point a peak m a y or m a y not be present. T h e background counting rate at large time intervals agreed with that calculated from the channel width and the detector counting rate; the level of this calculated background is indicated by a broken line. In these and subsequent figures the ordinates are plotted as the probability (of obtaining a pulse) per/~sec, obtained by dividing the observed channel counts by the total n u m b e r of start pulses and the channel width. I n order to ascertain the probability of obtaining a spurious pulse per microsecond due account must be taken of the background. Figure 3 shows that as the pressure is reduced the probability of a positive ion effect at the cathode increases, while the mechanism which is responsible for spurious pulses immediately after the dead time becomes less probable. From the counter dimensions, the E H T and the time corresponding to the peak of the positive ion cathode effect the average mobility, /~+, of the positive ions was calculated for a variety of conditions such that the product of gas pressure and the transit time ranged from 3 x 104 to 1.2 X 106 torr/~sec. No significant variation of/~+ was found over this range and the average value was 2"4 4-0.1 cm/sec per V / c m at 760 torr. Some experiments were carried out with a wire grid placed a few m m in front of the cathode, the grid being earthed while a variable bias was applied to the cathode. With the cathode positively biased such a system has been shown to suppress any cathode photoelectric effect, while with a suitable negative bias the detector behaved as an ordinary counter c~). Typical time spectra taken with positive and negative cathode biases are shown in Fig. 4. For most of the ion transit time the probabilities in the two cases are identical although there is some divergence as the ions approach the cathode. It should be noted that, with the cathode positively biased the effective

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FIO. 5. Time spectra taken in a counter triggered by a Fe-55 source (circles) or a single electron source (triangles). The counter dimensions were 3.8 cm dia. cathode, 2.5 × 10--s cm dia. anode. c a t h o d e is the grid a n d the calculated i o n transit time for this case is i n d i c a t e d b y a a r r o w i n Fig. 4. A c o m p a r i s o n of t i m e spectra t a k e n w i t h a Fe-55 source a n d a single electron source is shown i n Fig. 5. T h e o n l y difference i n the

e x p e r i m e n t a l c o n d i t i o n b e t w e e n the two cases is the E H T w h i c h was 3450 V for the Fe-55 source a n d 3725V for the single electron source. T h i s corresponded to a n increase i n gas g a i n of" approximately 4 ×. I n the a t t e m p t to investigate the role t h a t

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FIG. 6. Time spectra taken in a counter using pure methane (circles) and a mixture of methane and 5% ethylene (triangles). The counter dimensions were 3.8 em dia. cathode, 5.1 × 10-a cm dia. anode. The gas gain was approximately 106 in both eases. h y d r o g e n radicals m a y play in the production of spurious pulses some experiments were performed in which a few per cent of ethylene (a k n o w n scavenger o f h y d r o g e n radicals (5'6)) was a d d e d to the methane. A comparison of time spectra taken with pure m e t h a n e and with a mixture o f m e t h a n e a n d 5 ~o ethylene is shown in Fig. 6. These spectra were taken some 200 V b e y o n d the end of the plateau, and the conditions were adjusted so t h a t the gas gain was the same in b o t h cases. I n a separate experiment it was established that, for the counter used to obtain these results, the admixture of 5 ~o ethylene required an increase in the counter potential o f 50 V to obtain the same gas multiplication as for p u r e m e t h a n e . * A similar comparison taken at just a few volts b e y o n d the end of the plateau * The ionization potential of C2H 4 is 10.51 eV, compared with 12.99 eV for CH4(7). At first sight one might expect that this would reduce the counter potential required to achieve the same gain in the mixture. However the electrons in a Townsend avalanche have a distribution of energies which is determined in part by the electric field and in part by the energy level structure of the molecules with which they collide. Ethylene is known to have lower lying levels than methane (s) and hence the mean electron energy is undoubtedly less in the mixture than in pure methane.

showed a r a t h e r smaller decrease in the n u m b e r of spurious pulses with the methane-ethylene mixture. CALCULATIONS Before embarking on a discussion of these results it will be useful to summarize some of the available d a t a relevant to discharges in m e t h a n e a n d to make some order of m a g n i t u d e calculations. (a) Avalanche dimensions Using as a basis equation 1 of Kef. (2) with the parameters A = 7-2 c m -1 tort"-x, B = 188 V c m -1 tort -1 it is possible to m a k e an estimate of the physical size of the individual avalanche. T a k i n g the radius at which the ionization reached 0.1 per cent of the total as an a r b i t r a r y starting point a n d allowing for simple diffusion of the electron cloud the avalanche envelopes obtained u n d e r various conditions are shown in Fig. 7 where the dimensions are plotted in units of the anode radius, a. I n view of several uncertainties a n d approximations in these calculations the envelopes are depicted b y triangles r a t h e r t h a n b y a n y m o r e complex figures; m o r e o v e r space charge effects have been ignored. H o w e v e r they serve to indicate the relative differences between various counter

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Fio. 7. Calculated dimensions of Townsend avalanches. The avalanche is assumed to "start" at a radius beyond which only 0.1 per cent of the total ionization occurs. The avalanche spreads in lateral directions (along and around the anode) by diffusion of the electrons. Dimensions are given in units of the anode radius, a. The numbers within the triangles represent the calculated ion densities (in units of 10x~ ions per cm a) in sections of thickness 0.1a. The calculations ignore space charges and the effect of the radial field on the lateral spread of the avalanches. Avalanches A~ B and C correspond to the experimental conditions under which the 745-, 400- and 200- torr results of Fig. 3 were obtained respectively, while D and E correspond to the conditions with which the circle and triangle data of Fig. 5 were obtained.

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P. d. Campion and M. IV. J. Kingham

operating conditions. A further calculation gave the density of ionization as a function of radial distance and the results are also indicated in Fig. 7 where the densities are shown at intervals of one tenth of the anode radius. Thus in case (A) (which corresponds to the experimental conditions existing in Fig. 3, 745 tort) the ion densities reach 5 × 1014 ions/cm 8 but as the pressure is reduced, and diffusion enlarges the avalanche, this reduces to 3 x 1012 ions/cm 3 at 200 torr.* Using these dimensions the time required for a positive ion created at the surface of the wire to move out to the radius at which the avalanche starts (i.e. the 0.1 per cent point mentioned above) has been calculated. For the conditions represented in Fig. 7 these times vary from 5nsec, case (D) to 24nsec, case (C). These times are very roughly twice the time it would take for the positive and negative ions (if present in the avalanche) to separate, i.e. they separate in times of the order of 10nsec or less, and hence any direct mechanism for spurious pulse production which involves the interaction of positive and negative ions can be excluded. Further, if ion-radical reactions are important they must occur within similar time intervals. (b) Ion species M a n y measurements of the mass spectrum of the ions produced by electron collisions in methane have been made. At sufficiently low pressures so that the ions do not interact with one another or with neutral gas molecules, the more a b u n d a n t ions are: CH4+(100), CH3+(80), CH2+(15), CH+(7) and C+(2), where the numbers in brackets indicate the approximate relative abundances. I n addition negative ions, notably H - , have been observed in small abundances, cg'x0) I t seems likely that the same ions are produced, in perhaps similar proportions, in the p r i m a r y interactions in a Townsend avalanche although subsequent ion-molecule reactions will considerably modify the p r i m a r y spectrum. At 0.2 tort, for example, W~XLER and JEsse. ~12) found that the CH5 + and C~Hs+ * In passing it is interesting to note that, assuming it requires 30 eV per electron created, the absorbed dose to the gas within the avalanche is of the order of a megarad--and is delivered in less than a nanosecond.

ions accounted for 70 per cent of all the observed fragments. More recent studies have suggested that free hydrogen radicals are formed in the primary processes in the radiolysis of methane tS), the abundance of H being somewhat greater than that of the CH4 + ion. Further, the yield of hydrogen in the radiolysis of methane was found to increase markedly in the presence of an electric field m ). LOEB/la) gives the following expression, originally due to Langevin, for the mobility, K, of an ion of mass m moving in a gas of molecular weight M, as : - 0.235 K =

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V m oloov/(D - 1 ) M

(1)

where p, Po are the densities of the gas at the temperature and pressure considered and at 0°C, 760 torr, respectively, and D is the dielectric constant of the gas at STP. According to this equation the mobilities of the CH~ + and C,H5 + ions are 2.53 and 2.27 cm/sec per V / c m at 760 torr respectively in reasonable agreement with the observed value. T h e difference between the mobilities of these two ions @~10 per cent) is considerably less than the width (fwhm) of the peaks attributed to the positive ion cathode effect. DISCUSSION From a simple comparison of a normal proportionM counter plateau and the response function of the same detector to single electrons it is clear that the plateau ends at about the point at which single electrons can be detected. Thus, in agreement with GENz et al.m, it is concluded that spurious pulses are due to single electrons, or, at most, to a few electrons. I t is probable that spurious pulses m a y be produced in most if not all proportional discharges but that they only become apparent when the overall gain is sufficient to detect a single electron. Thus while all the plateau experiments using a Fe-55 source showed no evidence for spurious pulses down to a limit of 2 × 10 .5 spurious pulses per genuine pulse, a "single electron plateau" experiment did reveal the presence of some spurious pulses. I t m a y be, with sufficiently low noise amplifiers that single electrons can be detected with a negligible

Spurious pulses in methanefilled proportional counters probability for spurious pulse production. However, with the amplifier used here this was not possible although an imposed dead time of 20/tsec would have been sufficient to reduce the probability of a spurious pulse to negligible proportions. It is concluded that under the conditions reported here any plateau slope for Fe-55 represents a genuine increase in the efficiency of detection. T h e distinct peak observed at the end of some time spectra may clearly be attributed to the interaction of the positive ions with the cathode. Since the observed mobility was constant over a range of pressures and transit times it would appear that beyond at least 3 × 104 torr #sec the ionic species does not change appreciably although small mass changes cannot be excluded as demonstrated by equation 1. O n the other hand it is difficult to pinpoint a mechanism to account for the remaining spurious pulses generated at less than the positive ion transit time, but it is possible to make three qualitative observations. First, since no spurious pulses are observed after the positive ion transit time it is almost certain that those pulses occurring in the medium time range (i.e. from a few tens of gsec onwards) are due to a mechanism involving ions. T h e alternative is a mechanism involving uncharged radicals and there is no a priori reason that such a mechanism should cease when the ions are collected at the cathode. T h e results of Fig. 6 also suggest that free radical reactions are not significant in this time range since the presence of a radical scavenger does not alter the distribution appreciably. Second, the majority of spurious pulses are produced by a mechanism which does not involve a cathode photoelectric effect (Fig. 4), although such a mechanism may occur to some slight extent as the ions approach the cathode. T h e third observation is that there appears to be a marked correlation between the calculated ionization density within the avalanche and the probability of observing spurious pulses at short time intervals; compare Figs. 3 and 5 with Fig. 7. T h e results shown in Fig. 6 indicate that the probability of obtaining a spurious pulse in this time range is remarkably sensitive to the admixture of ethylene, at least for points well beyond the end of the plateau.

489

T h e following are possible mechanisms for the production of spurious pulses: 1. Prompt radiation from the Townsend avalanche giving rise to a photoelectric effect either at the cathode {s) or in the gas ~14). However, in both cases the time scale is such that neither effect could be responsible for the spurious pulses reported in this paper. ~ 2. Trapped radiation. This phenomenon has been observed in gas discharge studies {15} and could lead to the production of delayed photoelectrons at the cathode. T h e evidence typified by Fig. 4 however rules out this mechanism. 3. Negative ions formed in t h e primary ionization process or as the primary electrons drift towards the anode. While these processes may occur (although so far as the second is concerned the CH4- ion has not been observed in mass spectroscopy) it is not possible to attribute any spurious pulses to these processes in a counter triggered by single electrons. T h e fact that spurious pulses are observed with single electrons and that the time spectra are, in general terms, similar to those obtained With a Fe-55 source suggests that these mechanisms are not very significant. 4. Negative ions formed in the Townsend avalanche. As mentioned earlier it is possible that such ions may be produced to a small extent and it is conceivable that these ions may become trapped in the positive ion cloud until the latter has drifted some way towards the cathode. As the density of the cloud decreases so the probability that the negative ions escape increases. T h e y would then drift back to the anode, release an electron in the high field region, and thus cause a spurious avalanche. Using the ion densities and avalanche dimensions given in Fig. 7 it can be shown that the Debye shielding length* is very much less than the dimensions of the avalanche for all cases which show sharp rises in the time spectra near zero * The Debye shielding length is an estimate of the minimum dimensions of a plasma in order that an ion be influenced by the surrounding cloud rather than the externally imposed fieldcle). For an ion to become trapped the ratio of this shielding length to the dimension of the avalanche head should be much less than unity.

P. J. Campionand M. W. J. Kingham

490

time and hence trapping of negative ions in these cases would indeed be possible. However ion-ion recombination during the dead time of the system must be considered. I f the n u m b e r of positive ions is large compared with that of negative ions and assuming that the ion cloud expands in a radial plane only, then it can be shown that:

N(t)

=

N(o) exp (--~ran+ ~2t ln~ (b/a)~]

(2)

where N(o), N(t) are the total numbers of negative ions at times zero and t seconds respectively, n+ is the density of positive ions at time zero, 0cr the recombination coefficient, a, b the anode and cathode radii, K the mobility and V the counter potential. Diffusion has been neglected since it is small comparedwith themotion of the ions due to the electric field. Assuming a conservative value of 10 -n cmS/sec for 0c~ then the exponent in this equation becomes typically - - 2 0 to --50 for t = 2 #see and hence there is a completely negligible chance that a negative ion will exist within the positive-ion cloud beyond this time. T h u s trapped negative ions can be ruled out as a possible mechanism. 5. Electrons trapped within the positive-ion cloud. Calculations similar to those for negative ions apply but in this case it is considerably more difficult to obtain values for some of the p a r a m eters. For example the electron temperature enters into the calculation for the Debye shielding length. Although SCHLUMBOHM~17) gives kT as a function of the reduced field strength E[p for methane it is clear that those electrons which are most likely to become trapped are going to be considerably cooler than the average electron temperature. I f taking one extreme, thermal temperatures are assumed then the Debye shielding lengths obtained are identical to the negative ion case and trapping is possible. O n the other hand if the electron temperature ct~ appropriate to the field strength is used the Debye shielding length becomes comparable with the avalanche dimensions and trapping is unlikely. T h e actual situation probably lies somewhere between these limits and hence it must be assumed that at least some trapping m a y take place. However another difficulty arises in estimating a value

for the electron-ion dissociative recombination coefficient.* Most of the measurements of this coefficient have been m a d e on simple molecular ions ~zs-~°) and the results show that the coefficient tends to increase with the complexity of the ion and decrease with increasing electron temperature. Although no measurements have been m a d e for methane it would seem that its value probably lies between 10 -e and 10-~ cmS/sec. For the higher value the result is again identical with the negative ion case and electron trapping although possible cannot lead to spurious pulses owing to rapid recombination of the electrons. But for the lower value of 0cr a few electrons would remain at t-----2/~sec although by t = 10 #sec the exponential term is essentially zero. Thus it is unlikely that electron trapping is responsible for spurious pulses but the mechanism cannot be completely ruled out. T h e effect of the addition of a small percentage of ethylene could be explained in a qualitative way by the lowering of the electron temperature to such an extent that electron-ion recombination effectively removes most of the electrons with 2/~sec. 6. Free radical reactions. I n view of the scavenging properties of ethylene the results of Fig. 6 m a y be construed as evidence for a free radical mechanism operating at short time intervals. T h e fact that these pulses appear to be correlated with ionization density is not incompatible with this hypothesis since the free radical density is presumably closely related to the ionization density, Making the reasonable assumption that the total n u m b e r of free radicals formed per genuine pulse is roughly independent of pressure then the correlation between the spurious pulse rate and pressure would suggest that it is not a radical-molecule reaction unless a three-body collision is involved. This leaves ion-radical or radical-radical reactions as possibilities. Now the distance m o v e d by the ions under the influence of the electric field is an order of magnitude greater than that moved by the radicals due to diffusion; further the ion movement during the electronic dead time of the system is also some ten times the length of the original avalanche. Thus, unless the radicals * Radiative recombination coefficients are of the order 10-x* cmS/sec and can be neglected.

Spurious pulses in methanefilled proportional counters are generated in processes which occur well before the start of the ionization avalanche, it would seem that the radicals and ions are not in the same physical location at the time the spurious pulses occur. This leaves radicalradical reactions. The radiative recombination of two hydrogen radicals is presumably a rare process for the same reason that radiative ion recombination is improbable; see for example McDANIEL (ls). I n any case the dissociation energy, D [ H H I , is only 4"5 eV which is insufficient to ionize methane although is probably greater than the work function of the cathode. However no photoelectric effect is operative in this time range. Further, rectastable hydrogen radicals cannot be involved since the 2s½ metastable state in the hydrogen atom has a very short life in the presence of strong electric fields owing to mixing with the 2P½ statO ~1). Thus if hydrogen radicals are responsible then the mechanism must involve a two stage process in which a radical reacts with an ion (in a time of the order of tens of nanoseconds) to form a very reactive ion. This intermediate ion then subsequently undergoes a reaction with a methane molecule in which an electron is released and which produces a spurious pulse. 7. Ion-molecule reactions. Such reactions are well known, although a literature search has revealed no evidence that any positive ionmolecule reaction in methane releases an electron. Nevertheless this mechanism seems the most likely cause of spurious pulses particularly in the middle time range, but is also likely to contribute to a greater or lesser extent in the short time range. It should be emphasized that if such a mechanism is responsible for spurious pulses it is a rather rare process. U n d e r the conditions used in these experiments one spurious electron is produced in roughly 5 × 1014 ion-molecule collisions; this corresponds to a reaction cross section of about a microbarn. However not all the ions are identical and it m a y well be that the reaction cross section is more typical with either the ion being a rare species or the molecule an impurity. CONCLUSION From the general shape of the time spectra it is evident that there are several mechanisms

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operating which produce spurious pulses in methane filled proportional counters. O f these the ion-cathode effect is the only one that can be identified with any degree of certainty; it is not however a particularly prolific source of spurious pulses (at least in methane) when compared with other mechanisms. I n order to discuss the latter it is convenient to consider two time ranges, viz the short term, extending from the dead time to a few tens of microseconds, and the medium term extending from this point to the positive ion transit time. I n the short term it appears that the responsible mechanism is either free electrons becoming trapped within the positive-ion cloud and subsequently being released or a two-stage mechanism in which free radicals interact with other products in the discharge to form an intermediate ion which subsequently undergoes an ion-molecule reaction in which a free electron is produced. As the techniques of radiation chemistry improve it will no doubt be possible to identify these reactions more specifically. Indeed the general techniques described here could be developed into a useful analytical tool.

Acknowledgements--Discussions with Mr. A. WILLIAMS and Dr. S. C. ELLISon various aspects of this work were most helpful and are gratefully acknowledged. REFERENCES l. GENZ I-L, HARMERD. S. and Fn~K R. W. Nucl. Instrum. Meth. 60, 195 (1968). 2. CAm,ION P. J. Int. J. appl. Radiat. Isotopes 19~ 219 (1968). 3. CAMPIONP. J. and MURRAYD. K. Int. J. appl. Radiat. Isotopes 18, 203 (1967). 4. COATESP. B. J. Phys. (E) 1, 878 (1968). 5. SIECKL. W. and JOHNSONR. H. J. phys. Chem. 67, 2281 (1963). 6. BONEL. I. and FIRESTONER. F. J. phys. Chem. 69~ 3652 (1965). 7. BOWMANC. R. and MILLERW. D. J. Chem. Phys. 42, 681 (1965). 8. HF.RZBERO G. Electronic Spectra of Polyatomic Molecules, D. Van Nostrand, New York (1966). 9. SMrTHL. G. Phys. Rev. 51, 263 (1937). 10. BAILEYT. L., McGumm J. M. and MUSCHLITZ E. E. J. Chem. Phys. 22, 2088 (1954). 11. TALROSEV. L. Actions Chimique et Biologiques des Radiations VI, 87 (1967). 12. WEXLER S. and JEssE N. J. Am. Chem. Soc. 84, 3425 (1962).

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$3. LOEB L. B. Basic Processes of Gaseous Electronics, University of California Press, Berkeley and Los : Angeles (1961). 14. RAETm~R H. Electron Avalanches and Breakdown in Gases, Butterworths, London (1964). I5. PHEta, S A. V. Phys. Rev. 114, 1011 (1959). 16. McDANIEL E. W. Collision Phenomena in Ionized Gases, John Wiley, New York (1964).

17. SCHLUMBOHMH. Z. Phys. 182, 317 (1965). 18. BARDSLEYJ. N. J. Phys. B. 1, 365 (1968). 19. WELLER C. S. and B I o ~ I M. A. Phys. Rev. Lett. 19, 59 (1967). 20. COURTG. R. and SAYERSJ. Br. J. appl. Phys. 15, 923 (1964). 21. JAECKS D., VAN ZYL B. and GEBALrm R. Phys. Rev. 137A, 340 (1965).