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Further studies of cylindrical proportional counters for microdosimetric work
NUCLEAR INSTRUMENTS AND METHODS 157 (1978) 279-285 ; (~) NORTH-HOLLAND PUBLISHING CO.
F U R T H E R S T U D I E S OF C Y L I N D R I C A L P R O P O R T I O N A L C O U N T E R S FOR M I C R O D O S I M E T R I C WORK S. A. SAQ'AN and A. K. M. M. HAQUE
Department q]' Physics, Polytechnic of the South Bank, London SE10AA, England Received 12 July 1978 Walled and wall-less tissue-equivalent cylindrical proportional counters of unit elongation have been constructed and their performance extensively studied and compared with that expected from the theory of conventional proportional counter. The difference in behaviour between the walled and wall-less counters as regards energy resolution, gas gain, sensitive volume etc., is attributed to the wide grid structure of the latter. The transit time of single electrons released from the cathode walls by UV light has been measured in tissue-equivalent gas as a function of E/p for working pressures of 81, 57, 30 and 20 torr. 1. Introduction The characteristics of the wall-less proportional counter unit designed by Wilson 13) have been studied 5,~°) in our experimental set-up. To enable us to obtain microdosimetric distributions of energy deposition both in the wall-less and walled modes of such a design a modified counter unit has been constructed. The characteristics of this counter (wall-less) have been found to be identical as those of the original; the walled counter behaved sufficiently differently from the wall-less counter that it merits a detailed reporting as regards energy resolution, gas gain, and the magnitude of the field tube potentials, which have been discussed in detail later. In the earlier work, the sensitive v o l u m e of the wall-less counter has been delineated using the electrical conducting paper and the collimated alpha particle beam techniques" a further study of the variation of the sensitive v o l u m e (and the gas gain) with the potential applied to the aluminium tank has been made. It is worth noting that the behaviour of both counters have been studied over an extended range of anode potentials. The transit time of single electrons is an important parameter effectively determining the count rate the counter can handle; this has been measured for electrons released by UV light from the walls of the counter as a function of E / p for different working pressures.
circle of diameter 2 . 5 4 c m around a collecting anode of the same material and diameter. The vertical extent of the sensitive volume is defined by two stainless steel field correcting tubes of in-
2. A p p a r a t u s
The construction details of the cylindrical wallle:~s proportional counter have been described earlie?°). To recapitulate briefly, the sensitive v o l u m e is defined by eight stainless steel parallel wires of diameter 0.125 ram, m o u n t e d concentrically on a
Fig. 1. Walled proportional counter, tissue equivalent cylinder used as cathode.
280
s.
A,
SAQ'AN
AND
ternal diameter 0.34 cm. The field tubes are separated from the collecting wire by a PTFE insulator. The whole assembly is contained in an aluminium tank lined with tissu-equivalent plastic. In order to use the system as a walled counter, a cylinder of Shonka tissue equivalent plastic is used as the cathode: to facilitate placement and removal of the wall (cathode) it is constructed in two halves which are held together with nylon screws and touch the grid wires. Fig. 1 shows the walled counter in position with the rest of the assembly. An Ortec 109PC pre-amplifier together with an Ortec 410 main amplifier have been used for pulse shaping and amplification during the study of the characteristics. The output from the amplifier has been analysed by a 2400 N D multichannel analyser. For microdosimetric m e a s u r e m e n t s a special low-noise ( 1 5 0 - 2 0 0 r m s electrons) pre-amplifier has been used in conjunction with Harwell main amplifier (2196).
A.
K.
M.
M.
HAQUE
// Z,0
/
3O
z
2
:!
020 t/3 Ld
10
+ Theoretical{ min )
3. Energy resolution The total relative variance, due to energy E deposited by alpha particles in the sensitive v o l u m e of a proportional counter, can be expressed as follows, as discussed in our earlier work: a)
V = ~
4 Ire 4 Z 2 Z N x
(F+b) +
(AE) 2
,
0
01 E
-1/2
02 -i/2 ( KeY j
Fig. 2. Walled and wall-less c o u n t e r resolution vs E parison w i t h theoretical resolution.
03 I: C o m -
(1)
where o• - average energy per ion pair (31.1 eV)6), F - Fano f a c t o r - 1, b - a constant - 0.5-1, ze - Charge on alpha particles, N - n u m b e r of a t o m s / c m 3 of the absorber, Z - atomic n u m b e r of the absorber and x - path length. The first term covers the relative variance due to the fluctuation of the initial ionization and gas multiplication, while the second term is due to the straggling of energy loss of alpha particles in a thin absorber. Fluctuations due to electronics shift, pressure and t e m p e r a t u r e variation and alpha-particle beam collimation have been ignored. Energy resolution has been calculated from eq. (1) and compared with resolution experimentally obtained with walled and wall-less counters as shown in fig. 2. It can be seen that resolution of the wall-less counter is always poorer than the calculated m a x i m u m resolution while that of the walled counter is almost in coincidence with the calculated m i n i m u m value. It is thought that the
discrepancy between the values of resolution in the two modes has been caused by the diffusion of electrons into and out of the sensitive volume, which is defined by a widely spaced grid structure of the wall-less counter. It is difficult at present to give a figure attributable to the effect of diffusion on resolution, but it remains our aim to study the problem. Our earlier work on the delineation of the sensitive v o l u m e using electrically conducting paper and collimated alpha-particle beam methods show that the error in defining the diameter is not more than ~ 1.5%. Although one can draw two reasonable straight lines through the experimental resolutions obtained for the walled and wall-less counters, as shown in fig. 2, there remains, however, one data point (that at pressure of 5 torr) which deviates considerably. This is believed to be due to an error in the pressure calibration.
4. Gas gain Gas gain of the walled and wall-less proportional counters has been measured using the pulse
C Y L I N D R I C A L P R O P O R T I O N A L COUNTERS
281
5
.///,,,,u / /
//7 4/d//
2 10
/
_wo
,oo
,f//// Z
/ d
'
/
1'o
1;
' Anode Vottage xlO0
Fig. 3. Gas gain for walled and wall-less counters at different pressures. From right to left; pressures: 81, 57, 30 and 20 tort.
generator method. analyser has been to that due to the pha particles in the then be calculated G = CT Vg~/Ee,
A multichannel pulse height used to equate the pulse peak energy deposited by 24~Am alsensitive volume. Gas gain can using the formula (2)
where ('~ - test capacitance, lJi: - pulser output, E - e n e r g y deposited in the sensitive v o l u m e , and e - electronic charge. T h e practice of measuring gas gain by using the pulse generator m e t h o d ca,n lead to a considerable error due to the pulse shaping net workT"8). A correction formula ~) for gas gain w h e n used by Saq'an and Haque did not produce a good agreem e n t with the expression for gas gain due to Campion4), which is widely accepted for proportional counters used in microdosimetric measurements. Fig. 3 shows the measured gas gain for the walled and wall-less counters at pressures 81, 57, 3(1 and 20.5 torr without any correction due to the shaping net work. The discrepancy in gas gain be-
tween the walled and the wall-less counters is t h o u g h t to be due to the effect of the potential on the external container, which is 60% of that on the anode. The electric field at any point inside the sensitive v o l u m e is the net result of the fields due to the anode and the external container. T h e wide open grid (grid area 1.2% of that of the sensitive volume) is not sufficient to terminate on it the interna! or external fields in both direction. Srdoc ~2) has observed a similar effect due to which a higher voltage ( = 5 % ) had to be applied to the wall-less counter to obtain the s a m e gas gain as the walled counter. In the present work it has been found that to obtain the s a m e gas gain the anode potential of the wall-less counter has to be about 15% higher than that of the walled counter. A comparison of gas gain f'or both counters with the expression due to C a m p i o n has been presented in fig. 4, after normalizing the gain of both the counters. It appears to us that one or both of the followirig factors may have been contributory to the poor a g r e e m e n t between the present m e a s u r e d values of gas gain and those obtained from the expression due to C a m p i o n . Clearly, further work will be necessary to clear up this matter:
282
s.A.
SAQ'AN AND A. K. M. M. HAQUE
2
!
/
lg
<
1:
1:I/
Wolled Wail l e s s - -
i __
4
8
1
i
12 Anode
Camplon
l
I
I
Voltage
/
16
1/, x100
Fig. 4. Gas gain for walled and wall-less counters normalised to Campion's values: pressures 81, 57, 30 and 20 torr as in fig. 3, 1) T h e uncertainty of the correction due to the pulse shaping network for lack of adequate knowledge of the positive ion mobility in tissue-equivalent gas. 2) The assumption that the expression due to C a m p i o n is equally applicable for such high E/p values as is usually met in microdosimetry. Some gas gain m e a s u r e m e n t s at the two highest pressures have been checked by using 5.89 keV Xrays from a SSFe source. The agreement with the results obtained with alpha particles are better than ± 3 % . T h e discrepancy in gas gain between the walled and wall-less counters led the present workers to investigate the effect of the potential on the alum i n i m u m tank on gas gain and the sensitive volume. This has been carried out with a SSFe source as follows : The position of the m e a n pulse height distribution was obtained at different potentials on the tank ranging from f l = O . l - l , B - p o t e n t i a l on tank/potential on anode. Below B = O . 1 the shape of the pulses starts to change, the fall and rise times increasing appreciably. This is to be expected and is due to the collection of electrons pro-
duced outside the sensitive v o l u m e which reach the avalanche region later than those produced inside the sensitive volume. The transparent grid cannot stop these electrons and the field outside the sensitive v o l u m e is not sufficient to sweep t h e m away. Therefore distributions below B - 0 . 1 have not been considered. The relative gas gain, obtained from the pulse height distributions has been plotted against B as shown in fig. 5. 5. Sensitive volume of the counter The delineation of the sensitive v o l u m e of the wall-less counter (2.54cm d i a m . × 2 . 5 4 c m high) can be divided into two parts: (1) delineation of the circular boundary and (2) delineation of the vertical extent of the cylindrical volume. The former has been carried out using the electrically conducting paper and the alpha beam m e t h o d s ; the latter by measuring the relative gas gain at various field tube potentials when an alpha particle beam has been fired at the anode at various distances above and below the central plane. It has been found that a potential on the field tubes of 44.5% of that on the anode and a potential on the a l u m i n i u m tank of 60% of that on the anode are necessary to obtain a cylindrical v o l u m e of the a b o v e - m e n t i o n e d dimensions. A further study of the effect of variation of the potential on the a l u m i n i u m tank has been carried out which essentially confirms the results obtained ~L
c
o\
g2 o,
-_o a,
\
\ o\ \
50
Fig. 5. Relative gas gain vs /3.
100
%
CYLINDRICAL
PROPORTIONAL
with the electrically conducting paper and alpha beam methods. The principle of the m e t h o d is as follows' The m e a s u r e m e n t is based on the change in relative gas gain due to a change in /3 and in the track length of monoenergetic alpha particles. At a given value of /3 and gas gain G, the average pulse heights from 55Fe X-rays and collimated alpha particles from 241Am are given as follows: Px-
EeAG mC t ,
(3)
L(dE/dx) eAG Pet =
(DCt
(5)
If /3 is changed to fl', i.e. average track length changes to Lj, then eq. (5) changes to t"x P"
E E,, (dE/dx)"
(6)
Therefore ( P J P . ) _ L, (P'x/P'~) L,
,283
TABLE 1 Experimental results.
B,
Ln/L
0.1 0.2 0.4 0.5 0.6 0.7 0.8 1.0
1.193 1.097 1.045 1.028 1.000 0.995 0.973 0.938
Change in Ln(%) 19.3 9.7 4.5 2.8 - 0.5 - 2.7 - 6.2
+ + + +
(4) ,
where E - energy o f 55Fe X-rays, e - electronic charge, A - amplifier gain, G - gas gain, co - energy per ion pair, C t - input capacitance of the detector, L - average track length of collimated alpha particles fired centrally across a diameter, d E / d x stopping power of alpha particles. If the gas pressure, anode voltage, amplifier gain and /3 are kept constant, then eqs. (3) and (4) give G E ]3~ = L(dE/dx)"
COUNTERS
(7)
Since all the quantities on the left hand side of eq. (7) are measured experimentally, it will be possible to find the change in the track iength of the sensitive volume. If/3 = 60% is considered to give a circular cross section j°) with Z representing unit length, then { n / L (L n is the average track length corresponding to /3~) can be calculated from the experimental resuits which are shown in table 1. These results are in the same direction as obtained by Wilson 13) and Burlin et al?) using conducting paper technique for different values of/3. The circular boundary of the walled counter is limited by the cathode diameter; in order to define its vertical extent the effect of the potential on the field tubes on the gas gain has been studied by firing collimated alpha particles through two holes,
diam. 3 ram, one drilled centrally and the other 1.1 cm above it. A similar dependence of gas gain on the field tube potential as that found in the wall-less counter has been noticed, i.e. the gas gain increases as the collimated alpha particle beam moves towards the field tubes, when the potential on them is less than the optimum value and vice versa. The optimum value of the field tube potential for the walled counter was found to be 36% of that on the anode compared to the theoretical value of 37%, as calculated from equation V = Vo[1 - log(r/a)/log(b/a)],
(8)
where r - field tube radius, a - anode radius, b - cathode radius, 1% - potential applied to the anode, and V - potential applied to the field tubes (the cathode being earthed). If the field tube potential in the wall-less counter conforms to the theoretical value of 37%,, the relative gain will increase by = 2 5 % when the alpha beam is incident centrally. If the beam position is moved toward the field tubes, the gain is expected to rise sharply. 6. T r a n s i t t i m e
The transit time of electrons is one of t h e important parameters which determines the counting rate that can be handled to avoid pulse pile-up in the counter used for microdosimetric measurements exposed to a high flux radiation field. It is believed that very little experimental data exist on the transit time of electrons in a tissue-equivalent gas at low pressure and high E / p values. Rainbow et al. 9) used ultra-violet light, from a short duration spark, to release photoelectrons
284
s.A.
SAQ'AN AND A, K. M. M. HAQUE
from the cathode of a proportional counter for the purpose of measuring the transit time. The counter, having a cathode diameter of 2.3 cm and anode diameter of 0.0025cm, was filled with A r + C ~ H 8 mixture at atmospheric pressure. Campion ;) used the satellite pulses produced at a very high gas g a i n s 1 0 6 to measure the transit time in a proportional counter filled with CH 4 and C H 4 + A r at atmospheric pressure. The satellite pulses have been proved to be due to the photoelectrons released from the cathode. Bambynek l) has suggested that the electron transit time in a cylindrical counter can be calculated from the expression given below:
f dS Tr = aS(a ) I s`"' S2 ~ , J S(r)
Bell jar
Mirror
'll
(9)
~(S)
where S - E/p V/cm.torr, a - anode radius and /,~ - drift velocity of electrons. As the drift velocity of electrons bi~~ in a tissue-equivalent gas is not known, it is difficult to calculate the transit time as a function of E/p.
7. Apparatus The apparatus shown schematically in fig. 6, used in this project, consisted in the main of the walled counter and an arrangement to have UV
L ~ T E'C'P
~J*_
[~
~-~L}
Steel
measurements. light incident on the inner surface of the cathode. UV light was produced from a short duration discharge lamp and admitted into the bell jar enclosure through an air tight quartz window, then re-
orr
1.0 0.8 0.6 O.A 450
I
I
500
550
--1 1100
:1.
~ 0.8
7 t orr
oo
13'o
t
1.oo
t o r r
0.6
O.A 600
i
I
650
700
I
950 1000 (E/p) V/Cm,torr
Fig, 7. Electron transit time as a function of E/p.
"~
Fig. 6. Schematic diagram of apparatus used for transit time
1.z, 1.2
{
1050
1100
i
C Y L I N D R I C A L P R O P O R T I O N A L COUNTERS
flected by an a l u m i n i u m coated central mirror a n d finally focused by a c o n v e x quartz lens o n t o a central hole o f d i a m e t e r 3 m m on the c a t h o d e wall. P h o t o e l e c t r o n s were released f r o m a thin a l u m i n i tim film deposited on the inner surface o f the cathode. T h e set o f pulses p r o d u c e d at the a n o d e was fed to the input o f a wide b a n d T e k t r o n i x 7 A 1 5 A amplifier used in a T e k t r o n i x (type 7403N) oscilloscope. T h e o t h e r set o f pulses p r o d u c e d by the discharge lamp from across the 5 E2 resistor (fig. 6) was fed to a similar amplifier used on the s a m e oscilloscope. W h e n the oscilloscope operated in the alternate m o d e , the time delay (i.e. the transit time) b e t w e e n the two sets o f pulses could be measured. T h e time delay b e t w e e n the pulses from the discharge lamp and the start o f the rise time o f the fastest proportional c o u n t e r pulses has been measured as a function o f E/p. T h e results are s h o w n i~3 fig. 7. T h e s e results are corrected for the delay d u e to the s h a p i n g and amplification s y s t e m o f the proportional c o u n t e r pulses. It can be seen that for all the pressures used, the transit time decreases as E/p increases in an exponential fashion to an a p p r o x i m a t e l y c o n s t a n t value o f 4 0 0 - 5 0 0 ns. T h e E/p values for this m i n i m u m t::ansit time are inversely proportional to the pressure. Direct c o m p a r i s o n o f o u r results with the data o f C a m p i o n 3) is difficult because o f the difference in gas m i x t u r e , c o u n t e r design and operating conditions.
285
W e w o u l d like to t h a n k Mr. A. J. L. Collinson, H e a d o f the D e p a r t m e n t o f Physics and Dr. P. J. C a m p i o n o f the National Physical Laboratory for m a n y helpful d i s c u s s i o n s : Messrs. R. S. Pocock, C r u t t e n d e n and D. Joy and o t h e r technical staff o f the Physics D e p a r t m e n t for m u c h help during the prosecution o f this work.
References L) w, Bambynek, Nucl, Instr. and Meth. ll2 (1973) 103. 2) T. E. Burlin, D. M. Benstock and L. M. Haddow, Proc. 3rd Syrup. on Microdosimetry, EUR 4810 (1972) p. 656. 3) p. j. Campion, Int. J. Appl. Rad. Isotopes 19 (1968) 219. 4) p. j. Campion, Proc. 3rd Syrup. on Microdosimetry, EUR 4810 (1972) p. 601. s) A. K. M. M Haque and S. A. Saq'an, Proc. 6th Syrup. on Microdosimetry, Brussels (1978). 6) M. Kemmochi, Health Phys. 30 (1976) 439. 7) C. D. Kemshel, K. G. Beauchamp and P. W. Benjamin, Nucl. Instr. and Meth. 68 (1969) 153. 8) E. Mathieson and M. W. Charles, Nucl. Instr. and Meth. 72 (1969) 155. 9) M. T. Rainbow, A. G. Fenton and K. B. Fenton, Aust. J. Phys. 19 (1966) 583. 10) S. A. Sao'an and A. K. M M. Haque, Nucl. Instr. and Meth. 137 (1976) 545. ll) S. A. Saq'an, Ph. D. Thesis (CNAA, Polytechnic of the South Bank, 1978). 12) D. Srdoc, Proc. 2nd Syrup. on Microdosime#y, EUR - 4452 (1970) p. 153. 13) K. S. J. Wilson, Proc. 2nd Syrup. on Microdosimetry, EUR4452 (1970) p. 235.
F U R T H E R S T U D I E S OF C Y L I N D R I C A L P R O P O R T I O N A L C O U N T E R S FOR M I C R O D O S I M E T R I C WORK S. A. SAQ'AN and A. K. M. M. HAQUE
Department q]' Physics, Polytechnic of the South Bank, London SE10AA, England Received 12 July 1978 Walled and wall-less tissue-equivalent cylindrical proportional counters of unit elongation have been constructed and their performance extensively studied and compared with that expected from the theory of conventional proportional counter. The difference in behaviour between the walled and wall-less counters as regards energy resolution, gas gain, sensitive volume etc., is attributed to the wide grid structure of the latter. The transit time of single electrons released from the cathode walls by UV light has been measured in tissue-equivalent gas as a function of E/p for working pressures of 81, 57, 30 and 20 torr. 1. Introduction The characteristics of the wall-less proportional counter unit designed by Wilson 13) have been studied 5,~°) in our experimental set-up. To enable us to obtain microdosimetric distributions of energy deposition both in the wall-less and walled modes of such a design a modified counter unit has been constructed. The characteristics of this counter (wall-less) have been found to be identical as those of the original; the walled counter behaved sufficiently differently from the wall-less counter that it merits a detailed reporting as regards energy resolution, gas gain, and the magnitude of the field tube potentials, which have been discussed in detail later. In the earlier work, the sensitive v o l u m e of the wall-less counter has been delineated using the electrical conducting paper and the collimated alpha particle beam techniques" a further study of the variation of the sensitive v o l u m e (and the gas gain) with the potential applied to the aluminium tank has been made. It is worth noting that the behaviour of both counters have been studied over an extended range of anode potentials. The transit time of single electrons is an important parameter effectively determining the count rate the counter can handle; this has been measured for electrons released by UV light from the walls of the counter as a function of E / p for different working pressures.
circle of diameter 2 . 5 4 c m around a collecting anode of the same material and diameter. The vertical extent of the sensitive volume is defined by two stainless steel field correcting tubes of in-
2. A p p a r a t u s
The construction details of the cylindrical wallle:~s proportional counter have been described earlie?°). To recapitulate briefly, the sensitive v o l u m e is defined by eight stainless steel parallel wires of diameter 0.125 ram, m o u n t e d concentrically on a
Fig. 1. Walled proportional counter, tissue equivalent cylinder used as cathode.
280
s.
A,
SAQ'AN
AND
ternal diameter 0.34 cm. The field tubes are separated from the collecting wire by a PTFE insulator. The whole assembly is contained in an aluminium tank lined with tissu-equivalent plastic. In order to use the system as a walled counter, a cylinder of Shonka tissue equivalent plastic is used as the cathode: to facilitate placement and removal of the wall (cathode) it is constructed in two halves which are held together with nylon screws and touch the grid wires. Fig. 1 shows the walled counter in position with the rest of the assembly. An Ortec 109PC pre-amplifier together with an Ortec 410 main amplifier have been used for pulse shaping and amplification during the study of the characteristics. The output from the amplifier has been analysed by a 2400 N D multichannel analyser. For microdosimetric m e a s u r e m e n t s a special low-noise ( 1 5 0 - 2 0 0 r m s electrons) pre-amplifier has been used in conjunction with Harwell main amplifier (2196).
A.
K.
M.
M.
HAQUE
// Z,0
/
3O
z
2
:!
020 t/3 Ld
10
+ Theoretical{ min )
3. Energy resolution The total relative variance, due to energy E deposited by alpha particles in the sensitive v o l u m e of a proportional counter, can be expressed as follows, as discussed in our earlier work: a)
V = ~
4 Ire 4 Z 2 Z N x
(F+b) +
(AE) 2
,
0
01 E
-1/2
02 -i/2 ( KeY j
Fig. 2. Walled and wall-less c o u n t e r resolution vs E parison w i t h theoretical resolution.
03 I: C o m -
(1)
where o• - average energy per ion pair (31.1 eV)6), F - Fano f a c t o r - 1, b - a constant - 0.5-1, ze - Charge on alpha particles, N - n u m b e r of a t o m s / c m 3 of the absorber, Z - atomic n u m b e r of the absorber and x - path length. The first term covers the relative variance due to the fluctuation of the initial ionization and gas multiplication, while the second term is due to the straggling of energy loss of alpha particles in a thin absorber. Fluctuations due to electronics shift, pressure and t e m p e r a t u r e variation and alpha-particle beam collimation have been ignored. Energy resolution has been calculated from eq. (1) and compared with resolution experimentally obtained with walled and wall-less counters as shown in fig. 2. It can be seen that resolution of the wall-less counter is always poorer than the calculated m a x i m u m resolution while that of the walled counter is almost in coincidence with the calculated m i n i m u m value. It is thought that the
discrepancy between the values of resolution in the two modes has been caused by the diffusion of electrons into and out of the sensitive volume, which is defined by a widely spaced grid structure of the wall-less counter. It is difficult at present to give a figure attributable to the effect of diffusion on resolution, but it remains our aim to study the problem. Our earlier work on the delineation of the sensitive v o l u m e using electrically conducting paper and collimated alpha-particle beam methods show that the error in defining the diameter is not more than ~ 1.5%. Although one can draw two reasonable straight lines through the experimental resolutions obtained for the walled and wall-less counters, as shown in fig. 2, there remains, however, one data point (that at pressure of 5 torr) which deviates considerably. This is believed to be due to an error in the pressure calibration.
4. Gas gain Gas gain of the walled and wall-less proportional counters has been measured using the pulse
C Y L I N D R I C A L P R O P O R T I O N A L COUNTERS
281
5
.///,,,,u / /
//7 4/d//
2 10
/
_wo
,oo
,f//// Z
/ d
'
/
1'o
1;
' Anode Vottage xlO0
Fig. 3. Gas gain for walled and wall-less counters at different pressures. From right to left; pressures: 81, 57, 30 and 20 tort.
generator method. analyser has been to that due to the pha particles in the then be calculated G = CT Vg~/Ee,
A multichannel pulse height used to equate the pulse peak energy deposited by 24~Am alsensitive volume. Gas gain can using the formula (2)
where ('~ - test capacitance, lJi: - pulser output, E - e n e r g y deposited in the sensitive v o l u m e , and e - electronic charge. T h e practice of measuring gas gain by using the pulse generator m e t h o d ca,n lead to a considerable error due to the pulse shaping net workT"8). A correction formula ~) for gas gain w h e n used by Saq'an and Haque did not produce a good agreem e n t with the expression for gas gain due to Campion4), which is widely accepted for proportional counters used in microdosimetric measurements. Fig. 3 shows the measured gas gain for the walled and wall-less counters at pressures 81, 57, 3(1 and 20.5 torr without any correction due to the shaping net work. The discrepancy in gas gain be-
tween the walled and the wall-less counters is t h o u g h t to be due to the effect of the potential on the external container, which is 60% of that on the anode. The electric field at any point inside the sensitive v o l u m e is the net result of the fields due to the anode and the external container. T h e wide open grid (grid area 1.2% of that of the sensitive volume) is not sufficient to terminate on it the interna! or external fields in both direction. Srdoc ~2) has observed a similar effect due to which a higher voltage ( = 5 % ) had to be applied to the wall-less counter to obtain the s a m e gas gain as the walled counter. In the present work it has been found that to obtain the s a m e gas gain the anode potential of the wall-less counter has to be about 15% higher than that of the walled counter. A comparison of gas gain f'or both counters with the expression due to C a m p i o n has been presented in fig. 4, after normalizing the gain of both the counters. It appears to us that one or both of the followirig factors may have been contributory to the poor a g r e e m e n t between the present m e a s u r e d values of gas gain and those obtained from the expression due to C a m p i o n . Clearly, further work will be necessary to clear up this matter:
282
s.A.
SAQ'AN AND A. K. M. M. HAQUE
2
!
/
lg
<
1:
1:I/
Wolled Wail l e s s - -
i __
4
8
1
i
12 Anode
Camplon
l
I
I
Voltage
/
16
1/, x100
Fig. 4. Gas gain for walled and wall-less counters normalised to Campion's values: pressures 81, 57, 30 and 20 torr as in fig. 3, 1) T h e uncertainty of the correction due to the pulse shaping network for lack of adequate knowledge of the positive ion mobility in tissue-equivalent gas. 2) The assumption that the expression due to C a m p i o n is equally applicable for such high E/p values as is usually met in microdosimetry. Some gas gain m e a s u r e m e n t s at the two highest pressures have been checked by using 5.89 keV Xrays from a SSFe source. The agreement with the results obtained with alpha particles are better than ± 3 % . T h e discrepancy in gas gain between the walled and wall-less counters led the present workers to investigate the effect of the potential on the alum i n i m u m tank on gas gain and the sensitive volume. This has been carried out with a SSFe source as follows : The position of the m e a n pulse height distribution was obtained at different potentials on the tank ranging from f l = O . l - l , B - p o t e n t i a l on tank/potential on anode. Below B = O . 1 the shape of the pulses starts to change, the fall and rise times increasing appreciably. This is to be expected and is due to the collection of electrons pro-
duced outside the sensitive v o l u m e which reach the avalanche region later than those produced inside the sensitive volume. The transparent grid cannot stop these electrons and the field outside the sensitive v o l u m e is not sufficient to sweep t h e m away. Therefore distributions below B - 0 . 1 have not been considered. The relative gas gain, obtained from the pulse height distributions has been plotted against B as shown in fig. 5. 5. Sensitive volume of the counter The delineation of the sensitive v o l u m e of the wall-less counter (2.54cm d i a m . × 2 . 5 4 c m high) can be divided into two parts: (1) delineation of the circular boundary and (2) delineation of the vertical extent of the cylindrical volume. The former has been carried out using the electrically conducting paper and the alpha beam m e t h o d s ; the latter by measuring the relative gas gain at various field tube potentials when an alpha particle beam has been fired at the anode at various distances above and below the central plane. It has been found that a potential on the field tubes of 44.5% of that on the anode and a potential on the a l u m i n i u m tank of 60% of that on the anode are necessary to obtain a cylindrical v o l u m e of the a b o v e - m e n t i o n e d dimensions. A further study of the effect of variation of the potential on the a l u m i n i u m tank has been carried out which essentially confirms the results obtained ~L
c
o\
g2 o,
-_o a,
\
\ o\ \
50
Fig. 5. Relative gas gain vs /3.
100
%
CYLINDRICAL
PROPORTIONAL
with the electrically conducting paper and alpha beam methods. The principle of the m e t h o d is as follows' The m e a s u r e m e n t is based on the change in relative gas gain due to a change in /3 and in the track length of monoenergetic alpha particles. At a given value of /3 and gas gain G, the average pulse heights from 55Fe X-rays and collimated alpha particles from 241Am are given as follows: Px-
EeAG mC t ,
(3)
L(dE/dx) eAG Pet =
(DCt
(5)
If /3 is changed to fl', i.e. average track length changes to Lj, then eq. (5) changes to t"x P"
E E,, (dE/dx)"
(6)
Therefore ( P J P . ) _ L, (P'x/P'~) L,
,283
TABLE 1 Experimental results.
B,
Ln/L
0.1 0.2 0.4 0.5 0.6 0.7 0.8 1.0
1.193 1.097 1.045 1.028 1.000 0.995 0.973 0.938
Change in Ln(%) 19.3 9.7 4.5 2.8 - 0.5 - 2.7 - 6.2
+ + + +
(4) ,
where E - energy o f 55Fe X-rays, e - electronic charge, A - amplifier gain, G - gas gain, co - energy per ion pair, C t - input capacitance of the detector, L - average track length of collimated alpha particles fired centrally across a diameter, d E / d x stopping power of alpha particles. If the gas pressure, anode voltage, amplifier gain and /3 are kept constant, then eqs. (3) and (4) give G E ]3~ = L(dE/dx)"
COUNTERS
(7)
Since all the quantities on the left hand side of eq. (7) are measured experimentally, it will be possible to find the change in the track iength of the sensitive volume. If/3 = 60% is considered to give a circular cross section j°) with Z representing unit length, then { n / L (L n is the average track length corresponding to /3~) can be calculated from the experimental resuits which are shown in table 1. These results are in the same direction as obtained by Wilson 13) and Burlin et al?) using conducting paper technique for different values of/3. The circular boundary of the walled counter is limited by the cathode diameter; in order to define its vertical extent the effect of the potential on the field tubes on the gas gain has been studied by firing collimated alpha particles through two holes,
diam. 3 ram, one drilled centrally and the other 1.1 cm above it. A similar dependence of gas gain on the field tube potential as that found in the wall-less counter has been noticed, i.e. the gas gain increases as the collimated alpha particle beam moves towards the field tubes, when the potential on them is less than the optimum value and vice versa. The optimum value of the field tube potential for the walled counter was found to be 36% of that on the anode compared to the theoretical value of 37%, as calculated from equation V = Vo[1 - log(r/a)/log(b/a)],
(8)
where r - field tube radius, a - anode radius, b - cathode radius, 1% - potential applied to the anode, and V - potential applied to the field tubes (the cathode being earthed). If the field tube potential in the wall-less counter conforms to the theoretical value of 37%,, the relative gain will increase by = 2 5 % when the alpha beam is incident centrally. If the beam position is moved toward the field tubes, the gain is expected to rise sharply. 6. T r a n s i t t i m e
The transit time of electrons is one of t h e important parameters which determines the counting rate that can be handled to avoid pulse pile-up in the counter used for microdosimetric measurements exposed to a high flux radiation field. It is believed that very little experimental data exist on the transit time of electrons in a tissue-equivalent gas at low pressure and high E / p values. Rainbow et al. 9) used ultra-violet light, from a short duration spark, to release photoelectrons
284
s.A.
SAQ'AN AND A, K. M. M. HAQUE
from the cathode of a proportional counter for the purpose of measuring the transit time. The counter, having a cathode diameter of 2.3 cm and anode diameter of 0.0025cm, was filled with A r + C ~ H 8 mixture at atmospheric pressure. Campion ;) used the satellite pulses produced at a very high gas g a i n s 1 0 6 to measure the transit time in a proportional counter filled with CH 4 and C H 4 + A r at atmospheric pressure. The satellite pulses have been proved to be due to the photoelectrons released from the cathode. Bambynek l) has suggested that the electron transit time in a cylindrical counter can be calculated from the expression given below:
f dS Tr = aS(a ) I s`"' S2 ~ , J S(r)
Bell jar
Mirror
'll
(9)
~(S)
where S - E/p V/cm.torr, a - anode radius and /,~ - drift velocity of electrons. As the drift velocity of electrons bi~~ in a tissue-equivalent gas is not known, it is difficult to calculate the transit time as a function of E/p.
7. Apparatus The apparatus shown schematically in fig. 6, used in this project, consisted in the main of the walled counter and an arrangement to have UV
L ~ T E'C'P
~J*_
[~
~-~L}
Steel
measurements. light incident on the inner surface of the cathode. UV light was produced from a short duration discharge lamp and admitted into the bell jar enclosure through an air tight quartz window, then re-
orr
1.0 0.8 0.6 O.A 450
I
I
500
550
--1 1100
:1.
~ 0.8
7 t orr
oo
13'o
t
1.oo
t o r r
0.6
O.A 600
i
I
650
700
I
950 1000 (E/p) V/Cm,torr
Fig, 7. Electron transit time as a function of E/p.
"~
Fig. 6. Schematic diagram of apparatus used for transit time
1.z, 1.2
{
1050
1100
i
C Y L I N D R I C A L P R O P O R T I O N A L COUNTERS
flected by an a l u m i n i u m coated central mirror a n d finally focused by a c o n v e x quartz lens o n t o a central hole o f d i a m e t e r 3 m m on the c a t h o d e wall. P h o t o e l e c t r o n s were released f r o m a thin a l u m i n i tim film deposited on the inner surface o f the cathode. T h e set o f pulses p r o d u c e d at the a n o d e was fed to the input o f a wide b a n d T e k t r o n i x 7 A 1 5 A amplifier used in a T e k t r o n i x (type 7403N) oscilloscope. T h e o t h e r set o f pulses p r o d u c e d by the discharge lamp from across the 5 E2 resistor (fig. 6) was fed to a similar amplifier used on the s a m e oscilloscope. W h e n the oscilloscope operated in the alternate m o d e , the time delay (i.e. the transit time) b e t w e e n the two sets o f pulses could be measured. T h e time delay b e t w e e n the pulses from the discharge lamp and the start o f the rise time o f the fastest proportional c o u n t e r pulses has been measured as a function o f E/p. T h e results are s h o w n i~3 fig. 7. T h e s e results are corrected for the delay d u e to the s h a p i n g and amplification s y s t e m o f the proportional c o u n t e r pulses. It can be seen that for all the pressures used, the transit time decreases as E/p increases in an exponential fashion to an a p p r o x i m a t e l y c o n s t a n t value o f 4 0 0 - 5 0 0 ns. T h e E/p values for this m i n i m u m t::ansit time are inversely proportional to the pressure. Direct c o m p a r i s o n o f o u r results with the data o f C a m p i o n 3) is difficult because o f the difference in gas m i x t u r e , c o u n t e r design and operating conditions.
285
W e w o u l d like to t h a n k Mr. A. J. L. Collinson, H e a d o f the D e p a r t m e n t o f Physics and Dr. P. J. C a m p i o n o f the National Physical Laboratory for m a n y helpful d i s c u s s i o n s : Messrs. R. S. Pocock, C r u t t e n d e n and D. Joy and o t h e r technical staff o f the Physics D e p a r t m e n t for m u c h help during the prosecution o f this work.
References L) w, Bambynek, Nucl, Instr. and Meth. ll2 (1973) 103. 2) T. E. Burlin, D. M. Benstock and L. M. Haddow, Proc. 3rd Syrup. on Microdosimetry, EUR 4810 (1972) p. 656. 3) p. j. Campion, Int. J. Appl. Rad. Isotopes 19 (1968) 219. 4) p. j. Campion, Proc. 3rd Syrup. on Microdosimetry, EUR 4810 (1972) p. 601. s) A. K. M. M Haque and S. A. Saq'an, Proc. 6th Syrup. on Microdosimetry, Brussels (1978). 6) M. Kemmochi, Health Phys. 30 (1976) 439. 7) C. D. Kemshel, K. G. Beauchamp and P. W. Benjamin, Nucl. Instr. and Meth. 68 (1969) 153. 8) E. Mathieson and M. W. Charles, Nucl. Instr. and Meth. 72 (1969) 155. 9) M. T. Rainbow, A. G. Fenton and K. B. Fenton, Aust. J. Phys. 19 (1966) 583. 10) S. A. Sao'an and A. K. M M. Haque, Nucl. Instr. and Meth. 137 (1976) 545. ll) S. A. Saq'an, Ph. D. Thesis (CNAA, Polytechnic of the South Bank, 1978). 12) D. Srdoc, Proc. 2nd Syrup. on Microdosime#y, EUR - 4452 (1970) p. 153. 13) K. S. J. Wilson, Proc. 2nd Syrup. on Microdosimetry, EUR4452 (1970) p. 235.