Nulear Instruments and Methods in Physis Researh A 342 (1994) 538-543 North-Holland NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Setion A Count-loss mehanism of self-quenhing streamer (SQS) tubes A. NohtoMi a,* 1, T. Sakae a, M. Matoba a, N. Koori b 'Department of Nulear Engineering, Kyushu University, Fukuoka 812, Japan b Faulty of Integrated Arts and Sienes, The University of Tokushima, Tokushima 77, Japan (Reeived 17 May 1993 ; revised form reeived 25 Otober 1993) The ounting response of SQS tubes is superior to that of onventional GM tubes. The ount-loss mehanism of SQS tubes is governed by two different sorts of the spae-harge effet, namely a loal spae-harge effet and a global spae-harge effet. The existene of a dead zone leads to the loal spae-harge effet around eah streamer ; this effet is dominant at lower exposure rate onditions than 2 mr/h. On the other hand, the global spae-harge effet omes from aumulation of slowly-drifting positive ions inside the whole tube, and is dominant at higher exposure-rate onditions than 5 mr/h. 1. Introdution Self-quenhing streamer (SQS) tubes are attrative devies for radiation monitoring in high exposure-rate onditions beause the ounting response of SQS tubes is muh superior to that of onventional GM tubes [1,21. The ounting response of GM tubes is usually desribed by using the term "dead time" ; GM tubes almost ompletely lose their sensitivity during a ertain period (i.e. the dead time) after a Geiger disharge. On the other hand, as far as SQS tubes onerned, the details of ount-loss behaviour have not yet been well understood. SQS tubes operate without severe ount losses under high exposure-rate onditions where GM tubes are ompletely paralyzed. In suh onditions, the ount-loss mehanism of SQS tubes must be different from that of GM tubes. The most dominant fator for ount losses of SQS tubes may be the ontinuous eletri-field distortion aused by aumulation of slowly-drifting positive ions aumulated inside the whole tube. So far, the ounting response of SQS tubes has not been quantitatively studied yet. In this artile we disuss the ount-loss mehanism of SQS tubes omparing it with that of GM tubes. Some alulations are performed to explain the measured ounting response of an SQS tube on the basis of two ount-loss mehanisms. 2. Measurement of ounting response The ounting response of the SQS mode was measured as the way desribed in our previous papers [1,21 and ompared with that of the GM mode. The ylindrial gas ounter used was made of a stainless steel pipe whose inner diameter was 14 mm ; a gold-plated tungsten anode wire of 5 wm in diameter was strethed along the axis to have an effetive ounter length of 15 mm. The ounter was filled with Ar(75) + isoc,h,o(25). For seleting the ounter-operation mode, the gas pressure was hosen to be 76 Torr for the SQS mode and 15 Torr for the GM mode. The ounter was irradiated by 6 Co -y-rays from the outside of the ounter. Exposure rate of -y-rays at the ounter position was hanged by adjusting the distane between the soure and the ounter. The ounting effiieny of this ounter is.1 for 6 Co -y-rays in both the SQS and GM modes. The disrimination level of a saler was set to be 1/1 of SQS- or GM-signal amplitude obtained at a low exposure rate of less than 5 mr/h. As shown in Fig. 1, the ount rate is proportional to the exposure rate up to about 1 mr/h. Above this exposure rate, the ount rate shows a drasti differene from the expeted rate for the GM mode (HV = 1.5 kv). For the SQS mode (HV = 2.5 kv), the measured ount rate follows exposure rate with some ount losses and indiates saturation above 7 mr/h. * Corresponding author. Elsevier Siene B.V. SSDI 168-92(93)E1222-J
A. Nohtomt et al. /Nul. Instr. and Meth. in Phys. Res. A 342 (1994) 538-543 539 3. Count-loss mehanisms 3.1. Count losses due to the dead zone (loal spae-harge effet) The ount rate of the GM tube in Fig. 1 shows a paralysable response. The paralysable model of deadtime behaviour for random events ourring at an average rate n (Eq. 4-27 of ref. [3]) explains the measured result well as indiated in Fig. 1, that is m = n e - "T, where m is the reorded ount rate, and T the dead time of the GM tube. In this estimation we assumed T = 2 ws. In the paralysable model, the events that our during a dead time are onsidered to be lost ompletely. This assumption is not adequate for SQS tubes beause streamer-like disharges are limited along the anode wire and more than two streamers an grow simultaneously at different positions inside the tube. Hene the model is extended in order to evaluate the ounting response of SQS tubes. A funtion w(t) is newly introdued to express the sensitivity of tubes as a funtion of time as (t) =1-S Lt) (2) where t is the time after a pulse generation, S(t) the dead length on the anode wire, L the whole anode wire length. The value of S(t) is obtained from the measurement of dead-zone harateristis (Fig. 2) [4,5]. Dead-zone harateristis are related not only to the dead time but also to the dead length of the tube. Thus 1o' 1 a 1 ' 1' " SOS tube (measured) O GM tube (measured) ----- GM tube (alulated) expeted ount rate,o - '. o 1' 1e 1o' 1o' 1' 1' Exposure Rate (mrth) Fig. 1. Counting response of an SQS tube and a GM tube. A dot line indiates an estimated one for the GM tube aord ing to the paralysable model, Eq. (1), with the dead time r = 2 N.s. Q 8 Co o r -rays Ar(75)+IsoC 4Hto(25) E u w L m L ç 2 4 6 8 1 Time from Pulse Formation (Ns) Fig. 2. Dead zone harateristis of an SQS tube and a GM tube. the expressions of the paralysable model (Eqs. 4-25 and 4-27 of ref. [3]) beome P(t) dt=n e -n' dt, (3) m =n J.w(t)P(t) dt, (4) where P(t) dt is a distribution funtion of time-interval between random events ourring at an average rate n. This formulation is generally available for gas ounters with various dead-zone harateristis and is also valid for GM tubes under a simple assumption suh as 5(t) =L, <t<t, =, T < t. (5) Hene w(t) is expressed as w(t)=, <t<t, = 1, T < t. (6) Substituting Eqs. (3) and (6) into Eq. (4), we find that Eq. (4) agrees with Eq. (1). The dead-zone harateristis of the SQS mode in Fig. 2 indiate that the spae-harge effet due to a dead zone is valid only in the narrow part (about 2 m just after the pulse formation) around the position where eah streamer ours (referred as "loal spaeharge effet"). In the present ase, for simpliity of analysis, we expressed 8(t) of the SOS tube (in Fig. 2) as a triangle-shaped region ; 2.5 S(t) =-4 t+ 2.5, <t<4, =, 4 < t, [S(t) in m, t in ws]. (7) Substituting these equations into Eq. (2) we get w(t)=.6t+.76, <t<4, = 1, 4 < t, [t in its]. (8)
54 A. Nohtomt et al. INut. Instr. and Meth. in Phys. Res. A 342 (1994) 538-543 Consequently the ount loss of the SOS tube due to the dead zone is desribed by Eq. (4) with Eqs. (3) and (8) at low exposure rates. 3.2. Count losses due to the aumulation of slowly-drifting positive ions (global spae-harge effet) Under higher exposure-rate onditions, more positive ions are generated by inident radiations oming into the tube with short time-intervals. They are aumulated in the whole tube volume beause of their slow drift veloity. Those ions keep the eletri field distorted by a spae-harge effet during -y-ray irradiation (referred as "global spae-harge effet"). As a result, the output pulse amplitude dereases ; if the amplitude beomes smaller than the threshold of the disriminator, the event will not be deteted. Hendriks [6] presented an analytial formulation to allow the estimation of the eletri-field distortion aused by the aumulation of positive ions in proportional ounters, although the formulas desribed in the original paper ontained a mistake, whih has been pointed out and orreted by some authors [7,8]. Aording to the orreted formulation, if uniform irradiation is ahieved throughout the volume of the o-axial proportional ounter of a length L, the time-averaged ion density p in the ounter is given as MPR ln(b/a) where M is the number of ions generated from a disharge, whih orresponds to avalanhe size, P the pressure of the ounting gas, R the mean inident rate on the tube, a the anode wire radius, b the athode radius, A the mobility of ions and Vo the applied voltage to the anode. As found in Eq. (9), p is independent to the radial position in the tube. By using Eq. (9), Poisson equation is solved under a proper boundary ondition to obtain the eletri field in the ounter. Then the eletri field around the anode wire is approximated as Vo peb 2 E(r) = r ln(b/a) 4e or ln(b/a) ' (1) where r is the radius of polar oordinate, e the harge of an eletron, eo the permittivity in vauum. If now we put peb 2 dv= 4E,, (11) then we obtain from Eq. (1) Vo - dv E(r) - r ln(b/a) (12) Eq. (12) shows that spae harges redue the applied stati eletri field due to the applied potential by an amount of dv. e refer to Vo - dv as "effetive applied voltage". Here it should be noted that an atual p value annot be obtained from Eq. (9) in a simple way beause the alulated eletri-field (Eq. (12)) again affets the value of M in Eq. (9). Repeating suh a feedbak proess, the ion density will reah an equilibrium value. It is neessary, therefore, to evaluate the equilibrium ion density peq for the disussion of SOS tubes, in whih muh more ions are generated by eah disharge than those in proportional tubes. The equilibrium ion density pequ allows us to evaluate the redution of pulse amplitude and the aompanied ount losses by taking aount of the avalanhe-size urve and the transition-probability urve. 4. Calulated results and disussion e alulated the ount losses of the SQS tube by onsidering the two sorts of ount-loss mehanisms mentioned above, namely the ount losses due to the dead zone and those due to the aumulation of positive ions. Firstly, we estimated the ount losses due to the dead zone as the way desribed in setion 3.1. Fig. 3 shows the normalized ounting-response with alulated results. The result for the GM tube, the same one as in Fig. 1, is indiated again in a different way. As shown in the figure, the measured result is well explained by the alulation for the GM tube. On the other hand, the alulated result for the SOS tube does not agree with the measured values at high exposure rate [9]. Espeially more than 2 mr/h, the ount té too (normalized at 1 mr/h ) Exposure Rate (mr/h) - " - SOS tube (alulated) ----- GM tube (alulated) " SOS tube (measured) top Fig. 3. Normalized ounting-response of an SQS tube and a GM tube. The alulation was arried out by onsidering the ount losses due to the dead zone only. O - - m tç ".5 u " GM tube (measured) - _._._-_._._. t
A. Nohtomi et al. /Nul Instr. and Meth. in Phys. Res. A 342 (1994) 538-543 541 losses beome almost onstant sine the interval distribution of pulses onentrates in short time intervals. It is neessary, therefore, to take another ount-loss mehanism into aount in suh high exposure-rate onditions. Note that obvious superiority of the SOS tube over the GM tube observed around a few mr/h depends on the differene of their dead-zone harateristis. Seondly, the ount losses due to the aumulation of slowly-drifting ions were evaluated as the way desribed in setion 3.2. The equilibrium ion density pequ. was obtained by a reterative alulation using a personal omputer. In the alulation, the value of M was dedued from an approximated avalanhe-size urve (solid line in Fig. 4a), whih is expressed as SOSmode : NsQs = 9.6 X 1 (.54V+7 ) proportional mode : NPro = 5.49 X 1(3.9V- 2) V 5 2.1, =6.7X1( 243V+1 ), 2.1<V<2.3, = 2.21 X 1(.9V+5), 2.3 < V, [avalanhe size in no. of eletrons, V in kv]. (13) Here the avalanhe size of the SOS mode, NsQs, is represented by that of double SQSs beause double 9 > Ylé 6 Y â Û Y Fig. 5. Calulated effetive applied voltage Vo -dv and equilibrium ion density Pequ. SQSs are dominant around the atual applied voltage of 2.5 kv. Fig. 4b shows the measured transition probability from the proportional mode to the SOS mode as a funtion of high voltage. This urve was simplified as follows; PI =, <V<2.28, =6.18V-14.1, 2.28<V-<2.45, = 1, 2.45 < V, [V in kv], (14) where P, is the transition probability. Finally, for a given high voltage, the value of M was alulated as a a O at 1- w C Ov " " N Ûl " L VCa< Q.5 1 6 1 6 1 6 1.5 2. 2.5 3. (b) " measured SOS mode proportional mode Ar(75)+IsoC 4H is (25) 76 Torr 55 Fe X-rays proportional mode 1 6 1.5 2. 2.5 3. High Voltage (kv) bib -4- (a), SOS mode measured -9- approximated line Fig. 4. Avalanhe-size urve (a) and transition-probability urve from the proportional mode to the SQS mode (b). The fitting urves used for the alulation are also indiated. M=NsosXPt+Nr,,OX(I - P,). (15) By using the obtained pegn, the effetive applied voltage Vo - dv was determined at eah exposure rate. The values of V(1 - dv and pequ are indiated in Fig. 5. Ê û U 1' 16 16 14 alulated " measured SOS tube w Ar(75)+IsoCH 16 (25) Â i" 76 Torr 1-1 to ' 11 1, to' Exposure Rate (mr/h) Fig. 6. Counting response of an SQS tube omparing with the alulated results. The alulation was arried out by onsid ering the ount losses due to both the dead zone and the aumulated ions.
542 A. Nohtomi et al. /Nul. Instr. and Meth. in Phys. Res A 342 (1994) 538-543 w a. a d Ä U.5 1 ( normalized at 1 mr1h ) SOS tube " measured 1' 1' 1' Exposure Rate (mr/h) Fig. 7. Normalized ounting-response of an SQS tube. The ontribution of two different ounting-loss fators to the estimated ount losses are indiated separately. The effetive applied voltage deviates down from 2.5 kv at exposure rates more than 1 mr/h. As shown in Fig. 4b, less than 2.45 kv, some pulses do not grow up to streamers and result in proportional mode pulses. Those pulses in the proportional mode are not deteted beause of their small pulse amplitude less than the disrimination level of saler. If ions are aumulated so muh at high exposure rates, the effetive applied voltage beomes lower than 2.45 kv and ount losses will start. Fig. 6 shows the alulated result of the ounting response of SQS tube by onsidering both influenes due to the dead zone and the positive-ion aumulation. The alulation well explains the measured ounting response through a wide range from 1 to 3 mr/h. Contribution of two different spae-harge effets to the ount losses is indiated separately in Fig. 7 for the purpose of disussing details of ount-loss mehanisms of the SOS tube. The ount losses due to the dead zone explain the measured results less than 2 mr/h. In other words, the ounting response annot be understood at all in suh low exposure-rate region without taking aount of the influene of dead zone. On the other hand, more than 5 mr/h, the experimental result is well explained by the ount losses due to the aumulation of slowly-drifting positive ions. The disagreement from 2 to 5 mr/h in Fig. 7 is hiefly aused by the hange in the dead-zone harateristis. The dead-zone value may inrease as inrease in exposure rate [4] #i. That is mainly beause the dead length beomes longer ; plural streamers our simultaneously at different positions inside the tube. #i Though we have not onfirmed it experimentally, this inrease in dead-zone value may saturate and begin to derease at muh higher exposure-rate. 1 4 e tentatively used the dead-zone harateristis obtained at 2 mr/h (Fig. 2) where uniform irradiation along the whole tube length was ahieved. If the inrease in the dead length is taken aount exatly, Eq. (4) may be valid up to around a few hundred mr/h. From Fig. 7, it is lear that the origin of ount losses hanges from the loal spae-harge effet to the global spae-harge effet with inrease in the exposure rate. At low exposure-rate onditions, suh as 1 mr/h, the loal spae-harge effet around eah streamer is important. This means that eah inident radiation merely has some possibility to interat with the single disharge generated just before (within the dead time) and to be lost ; the probability of suh event depends both on the time interval between two suessive inident radiations and on the inident position along the tube. Namely this kind of interation is both time- and position-dependent. Therefore that is observed as the dead-zone harateristis whih are derived from the deviation of output-frequeny distribution from the expeted one in no ount-loss ase [1,2,4,5]. On the other hand, in high exposure-rate onditions, suh as 1 mr/h, inident radiations feel ontinuous field distortion spreading whole the tube. In this ase, the dominant fator for ount losses is the global spaeharge effet, whih brings the redution of the mean pulse amplitude. The global spae-harge effet is an averaged effet on time and position. 5. Conlusion The ount-loss mehanism of SOS tubes is suessfully explained by taking aount of the spae-harge effets due to the dead zone and the aumulation of slowly-drifting positive ions. The alulated results larify that the hief influene of the spae harges hanges, as the inrease of exposure rate, from the loal effet around eah streamer, whih is time- and position-dependent effet, to the global effet over the whole tube, whih is an averaged effet on time and position. The redution of pulse amplitude due to umulative ions finally beomes signifiant for the ount losses of SOS tubes under high exposure-rate onditions ; while the ounting-rate apability of GM tubes is mainly limited by the dead-zone harateristis at the far lower exposure-rate onditions. Referenes [1] N. Koori, A. Nohtomt, M. Hashimoto, K. Yoshioka, I. Kumabe, S. Mstsubara, M. Yoshizumi and T. Oshima, IEEE Trans. Nul. Si. NS-37 (199) 17. [2] N. Koori, A. Nohtomi, K. Yoshioka, T. Sskae, M. Mstoba, Y. Uozumi and S. idodo, Nul. Instr. and Meth. A 299 (199) 8.
A. Nohtomi et al. / Nul. Instr. and Meth. in Phys. Res. A 342 (1994) 538-543 543 [3] G.F. Knoll, Radiation Detetion and Measurement, 2nd [7] Z. Pawlowski and. Cudny, Nul. Instr. and Meth. 157 ed. (iley, 1989). (1978) 287. [4] A. Nohtomi and N. Koori, J. Nul. Si. and Tehnol. 29 [8] H. Sipila, V. Vanha-Honko and J. Bergqvist, Nul. Instr. (1992) 284 and Meth. 176 (1978) 381. [5] A. Nohtomi, T. Sakae, M. Matoba and N. Koori, IEEE [9] N. Koori, A. Nohtomi and M. Hirota, J. Nul. Si. and Trans. Nul. Si. NS-39 (1992) 719. Tehnol. 3 (1993) 974. [6] R.. Hendriks, Rev. Si. Instr. 4(9) (1969) 1216.