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A theoretical investigation into the efficiency characteristics of low pressure spark chambers
NUCLEAR INSTRUMENTS
AND METHODS
148 ( 1 9 7 8 ) 4 9 7 - 5 0 1
; ©
NORTH-HOLLAND
P U B L I S H I N G CO.
A THEORETICAL INVESTIGATION INTO THE EFFICIENCY CHARACTERISTICS OF LOW PRESSURE SPARK CHAMBERS D. MAJUMDAR
Cosmic Ray Laboratory, Department of Physics, Presidedcy College, Calcutta-700012, India Received 20 June 1977 Efficiency characteristics of parallel plate spark chambers were previously studied experimentally as a function of pulse voltage and argon pressure in the range 5-760 torr. Theoretical explanations of the efficiency curves obtained therefrom are considered in the present work in the frame-work of the avalanche-streamer model of gas discharge suitably modified in the region of low pressure. We obtain separate expressions for efficiencies of defined sparks and glow type discharges in the spark chambers which fairly agree with the experimental curves. We conclude that glow discharges are initiated only when the effective number of seed electrons in the chamber gap does not exceed 2 per cm. It also appears that the clustering effect plays a significant role only in the case of defined sparks in argon and not in helium.
1. Introduction A study of spark chamber characteristics at low gas pressures has recently been made by us 4) and also by other investigatorsl-5). Our aim in these investigations was finally to utilize low pressure spark chambers as an ionization discriminator of charged particles from which it might be possible to obtain information on charges of individual particles. In this respect it is important that one should find a reasonably accurate relation between the spark chamber efficiency and the specific ionization. In a recent experiment studying the efficiency characteristics of low pressure spark chambers, Ohashi s) has pointed out that in the low pressure working region, the most frequently used relation 1'/ = 1 - e x p ( - n d )
(1)
does not hold. In our experiment 4) a comparatively detailed measurement on the efficiencies of parallel plate spark chambers in the pressure range 5-760 torr using argon and argon plus alcohol was carried out. It was observed that up to a critical pressure region only defined sparks were possible. But below this region we noticed defined sparks as well as glows appearing in the chamber gaps. The efficiency characteristics of both these types of discharges were studied in this experiment. In the present paper, a theoretical investigation into these efficiency characteristics has been made particularly to clarify the relation between the number of original electrons produced by the incident charged particle and the spark chamber efficiency at low gas pressure.
2. Discharge mechanism at low working pressures and the expressions for efficiencies At higher pressures, sparks in a spark chamber are defined. But as the pressure is lowered below the critical pressure (about 30 torr for commercially pure argon), both defined and undefined discharges appear in the chamber. The undefined discharges are glow-like in character and as the pressure is gradulally decreased their efficiency is observed to increase, pass through a maximum and then drop again. The origin of glow discharges has been explained by Bunaciu and Kulander and others as due to increased photon radiation at lower pressures3). TO explain the efficiency characteristics of glow discharges we shall, however, assume that these discharges are the result of primary and secondary avalanches forming at sufficiently large distances so that the space charge fields between any two of them do not appreciably interact with one another. It is obvious that this condition will be fulfilled onlY when, the pressure is low and the number of seed electrons per cm is very small. When the above condition is satisfied, the possibility of merging of a primary or a secondary avalanche with a primary avalanche is minimised and consequently the discharge instead of being confined into a single streamer along the electric field vector, spreads in a larger volume in the form of a diffused glow. Assuming the validity of the above mechanism, let us first derive an expression for the efficiency of glow discharges as follows. Let nd be the average number of seed electrons in a gap width d cm
498
~g
T
D. M A J U M D A R
al?). We note that good agreement is obtained for M = 2. This implies that with the present experimental condition using an argon-filled chamber (gap width 1.3 cm), glow discharges occur when the number of seed electrons in the gap is 1 or 2 but not more. Next, we consider the efficiencies for defined sparks. If at most M seed electrons are responsible for a glow-type discharge in a low pressure spark chamber, then for a defined spark discharge the condition should be m>M. Hence the efficiency for defined sparks at high E/p is given by
"6
-4
.2
qs = e x p ( - n d ) 0
~ m=M+l
I
20 ¸
40 60 pd (cm. Torr]
80
= 1 - exp(-nd)
Fig. 1. Calculated and experimental dependence of the glow efficiency on pd. Curves correspond to eq. (2) for values of M = 1, 2 and 3, and n o = 110 ions/cm. Experimental points are taken from Mundra et al. Gas: argon, plate voltage: 9.9 kV, and gap width: d = 1.3cm.
of the parallel electrodes of the spark chamber. If
E/p is large, then supposing that at most M electrons are required to initiate a glow discharge, we obtain the efficiency of this type of discharge as M
q~ = e x p ( - n d )
~
(rid)m/m!,
(2)
m=l
assuming the Poisson distribution. In fig. 1 eq. (2) is plotted for different values of M and for no= l l 0 i o n s / c m , where no is the total specific ionization at S.T.P. in argon. The experimental points are taken from the results of Mundra et I'O .80 M= I
,60
~s
T .40 '20 0 20
=
l
40
60
t 80
pd (cm. Tort)
I
I
moo
120
I 14.0
),
Fig. 2. Dependence of the spark efficiency on pd. Curves correspond to eq. (3) for n o = 57 ions/cm, and M = 1, 2 and 3. Experimental points are taken from Mundra et al. Gas: argon, plate voltage: 9.9 kV, d = 1.3 cm.
(nd)m/m!
M Z m=O
(nd)m/ra!"
(3)
The solid lines in fig. 2 are the efficiency curves using the above equation for various values of M. The experimental plots for the initial rise of spark efficiency with pd shown in this figure have been taken from the work of Mundra et al. The best fit is obtained for M = 2 and no = 57 ions/cm. The acceptance of this reduced value of no may be explained by supposing that as the concentration of seed electrons increases, the clustering effect becomes pronounced. To fit the experimental curves of efficiencies of low pressure spark chambers using argon and helium as working gas, Ohashi suggests the empirical relation connecting gas pressure with efficiency: r/ = 1 - exp [-no
d(p/po)~].
(4)
In fig. 3 the reproduction of the best fit curves of Ohashi resembles the experimental points for helium and argon which corresponds rather to primary than to total ionization. For the purpose of comparison r/s vs pressure from eq. (3) for M = 2 has also been plotted in the same figure. We find a better agreement with the experimental points when the values of no are taken to be 40 and 10 for argon and helium respectively.
3. Efficiency characteristics in the higher pressure region Let us now consider the track efficiencies for fillings at higher pressures. According to the Raether-Meek condition, if xc denotes the critical length of an avalanche for the avalanche-tostreamer transition, then xc = 20/~, (5)
EFFICIENCY
CHARACTERISTICS
1.0
f l x
X Ar
+ .75
i
H.
cu.v~
/
n,
Im 1~)Author ,I
S .50
,
/
OF S P A R K C H A M B E R S
499
. . . . . " X ~ . , , ' ~-
/
-/7/
/,," ""
/ /// /
/,"
/+ /
.25
• 01
'1
I
Pressure ( otm )
•
Fig. 3. Dependence o f spark efficiency vs pressure. Solid curves correspond to eq. (3) for M = 2, and n o = 40, 10 and 7. Dotted
curves are reproduced from Ohashi for no = 30 and 5. Experimental points are also taken from Ohashi. where ~ is the first Townsend coefficient. The condition implies that those seed electrons in the chamber gap whose distance from the anode is less than xc would not be able to initiate the avalanche-streamer transition, and hence their number should be excluded from the effective number of seed electrons which can ultimately initiate the discharge. If d be the actual gap length, the effective gap length under this condition will be de = d - x c . Hence we write the general expression for the efficiency of sparks:
M
r/s = 1 - exp(-nd=) ~ (nd=)"/m!.
(6)
m=O
The threshold voltage is defined as the voltage for which r/s--,0. This condition is satisfied when we put dr = 0, i.e. d = x= = 20/~. (7) An exact expression for a~ is difficult to obtain. However, one can consider the following approximate expression in the present case: ot = Ap exp ( - Bp/E), (8)
14
o 12
t
>
io
Symbol Gopsi=e
//
',I
/
,Ig v
g e .u
i-
i
|
IOO
IOOO pd
(cm. Tort)
pd.
)
Fig. 4. Dependence of the threshold voltage on Experimental points are taken from Munclra et al., whereas the solid curve corresponds to eq. (10) for B ' = 6 3 V/cm.torr, and C ' = ]400V.
500
D. M A J U M D A R
theoretical curve showing a much faster decrease. A similar deviation between computed and experimental curves for the dependence of efficiency on pulse voltages is observed from fig. 5b. The above discrepancies could be accounted for by considering that as the pressure increases, the clustering effect and/or the value of M increases; however, a more definitive conclusion may be reached at from further accurate experiments.
where A and B are two constants whose values for argon are given as 1 4 c m - l . t o r r -~ and 180 V/cm. torr respectively f o r E / p ~ 100 V/cm. torr. If the threshold voltage is denoted by V0, then by using eqs. (7) and (8) we get Vo = B p d / l n ( A p d / 2 0 ) . (9) To compare eq. (9) with the threshold voltage curves obtained by Mundra et al., we note that the experimental threshold voltage depends both on the pulse length (i.e., RC-value) and the factor C / ( C + C s ) , where C and Cs are the capacities of the discharge condenser and the spark chamber respectively. Moreover, in the above experiment threshold curves were drawn in terms of the 5C22 hydrogen thyratron plate voltage which is slightly greater than the actual pulse voltage owing to a constant voltage drop in the tube. Considering these factors, we should write for the experimental threshold voltage
4. Remarks 1) We note that a glow-type discharge may be initiated by a single seed electron inside the effective gap length of the spark chamber. For further clarification let us consider the streamer formation mechanism in a streamer chamber. In this case also the individual avalanche-streamer transition occurs chiefly from single seed electrons; but the primary avalanche transforms into a well defined streamer along the direction of the electric field. As the streamer chambers operate in a pressure region considerably higher than that of glow discharges, the free path of the photons responsible for the generation of secondary avalanches must be considerably small. Hence in a streamer chamber, secondary avalanches are produced close to the primary one, and are, therefore, directed towards it from regions where the space charge field is sufficiently strong. 2) We infer from the above analysis that although clustering of primary electrons is effective above
(10)
Vo = B ' p d / l n ( A p d / 2 0 ) + C ' ,
where B' and C' are two new constants. Fig. 4 shows that very good agreement between theory and experiment is obtained when one puts B ' = 63 V/cm.torr and C ' = 1400 V. T h e fall of efficiency with pressure when the pulse voltage is kept fixed was also investigated by Mundra et al. and has been reproduced in fig. 5a. The computed values of r/s vs pressure of argon from eq. (6) are also plotted in the same figure. It appears that the agreement is only qualitative, the °.,.3°° I'0
E)- 50 Torr
? ""
- 4 0 0 Tar r
Y
.6
'4
.2
0
l
600 > pd(cm.
I 800 Torr)
I000
I 2
I 6
4 Plate
8
voltoge(kV)
I0
12
14
)
Fig. 5. Dependence of the spark efficiency on (a) pd (higher values) and (b) voltage. Curves correspond to eq. (6) for M= 2, no =57 ions/cm:and~d= 1.3 cmr~:,Experimental points are taken from Mundra et at. for (a) V=9:9 kV and for (b)p= 50 and 400 torr.
E F F I C I E N C Y C H A R A C T E R I S T I C S OF SPARK CHAMBERS
the low pressure region where defined sparks are possible, it does not appear to be as prominent as guessed by Ohashi; further, in the case of glow discharges the clustering effect seems to be totally negligible. This could be accounted for by considering that glows occur only when the number of seed electrons does not exceed 2 per cm. For helium used in the spark chambers, the clustering effect is negligible even for defined sparks and this is what should be expected as the specific number of ion pairs produced in helium is small. For argon we find values of no to be 57 and 40 per cm from the experimental results of ourselves and Ohashi respectively. These values are considerably less than the standard value of total specific ionization, but greater than the primary specific ionization indicating that clustering partially effects the spark efficiency in argon. The observed differ-
501
ences in the values of no obtained from the above two experiments can be accounted for by considering the larger delay (1/is) used in the latter. I wish to thank my colleague Dr. J.P. Mundra for important discussions.
References 1) R. J. Sutter, G. Nennett, J. Fischer, J. L. Friedes, H. Pal-
evsky and R. Persson, Nucl. Instr. and Meth. 54 (1967) 71. 2) S. Dahlgren, S. Kullanderand R. Lorensi,Nucl. Instr. and Meth. 89 (1970) 29. 3) T. Bunaciu and S. Kullander, Nucl. Instr. and Meth. 54 (1968) 173. 4) j. p. Mundra, D. Majumdar, K. Mazumdar, J. Mukherjee and P. K. Sen Chaudhury,Nucl. Instr. and Meth. 98 (1972) 589. 5) y. Ohashi, Nucl. Instr. and Meth. 113 (1973) 217.
AND METHODS
148 ( 1 9 7 8 ) 4 9 7 - 5 0 1
; ©
NORTH-HOLLAND
P U B L I S H I N G CO.
A THEORETICAL INVESTIGATION INTO THE EFFICIENCY CHARACTERISTICS OF LOW PRESSURE SPARK CHAMBERS D. MAJUMDAR
Cosmic Ray Laboratory, Department of Physics, Presidedcy College, Calcutta-700012, India Received 20 June 1977 Efficiency characteristics of parallel plate spark chambers were previously studied experimentally as a function of pulse voltage and argon pressure in the range 5-760 torr. Theoretical explanations of the efficiency curves obtained therefrom are considered in the present work in the frame-work of the avalanche-streamer model of gas discharge suitably modified in the region of low pressure. We obtain separate expressions for efficiencies of defined sparks and glow type discharges in the spark chambers which fairly agree with the experimental curves. We conclude that glow discharges are initiated only when the effective number of seed electrons in the chamber gap does not exceed 2 per cm. It also appears that the clustering effect plays a significant role only in the case of defined sparks in argon and not in helium.
1. Introduction A study of spark chamber characteristics at low gas pressures has recently been made by us 4) and also by other investigatorsl-5). Our aim in these investigations was finally to utilize low pressure spark chambers as an ionization discriminator of charged particles from which it might be possible to obtain information on charges of individual particles. In this respect it is important that one should find a reasonably accurate relation between the spark chamber efficiency and the specific ionization. In a recent experiment studying the efficiency characteristics of low pressure spark chambers, Ohashi s) has pointed out that in the low pressure working region, the most frequently used relation 1'/ = 1 - e x p ( - n d )
(1)
does not hold. In our experiment 4) a comparatively detailed measurement on the efficiencies of parallel plate spark chambers in the pressure range 5-760 torr using argon and argon plus alcohol was carried out. It was observed that up to a critical pressure region only defined sparks were possible. But below this region we noticed defined sparks as well as glows appearing in the chamber gaps. The efficiency characteristics of both these types of discharges were studied in this experiment. In the present paper, a theoretical investigation into these efficiency characteristics has been made particularly to clarify the relation between the number of original electrons produced by the incident charged particle and the spark chamber efficiency at low gas pressure.
2. Discharge mechanism at low working pressures and the expressions for efficiencies At higher pressures, sparks in a spark chamber are defined. But as the pressure is lowered below the critical pressure (about 30 torr for commercially pure argon), both defined and undefined discharges appear in the chamber. The undefined discharges are glow-like in character and as the pressure is gradulally decreased their efficiency is observed to increase, pass through a maximum and then drop again. The origin of glow discharges has been explained by Bunaciu and Kulander and others as due to increased photon radiation at lower pressures3). TO explain the efficiency characteristics of glow discharges we shall, however, assume that these discharges are the result of primary and secondary avalanches forming at sufficiently large distances so that the space charge fields between any two of them do not appreciably interact with one another. It is obvious that this condition will be fulfilled onlY when, the pressure is low and the number of seed electrons per cm is very small. When the above condition is satisfied, the possibility of merging of a primary or a secondary avalanche with a primary avalanche is minimised and consequently the discharge instead of being confined into a single streamer along the electric field vector, spreads in a larger volume in the form of a diffused glow. Assuming the validity of the above mechanism, let us first derive an expression for the efficiency of glow discharges as follows. Let nd be the average number of seed electrons in a gap width d cm
498
~g
T
D. M A J U M D A R
al?). We note that good agreement is obtained for M = 2. This implies that with the present experimental condition using an argon-filled chamber (gap width 1.3 cm), glow discharges occur when the number of seed electrons in the gap is 1 or 2 but not more. Next, we consider the efficiencies for defined sparks. If at most M seed electrons are responsible for a glow-type discharge in a low pressure spark chamber, then for a defined spark discharge the condition should be m>M. Hence the efficiency for defined sparks at high E/p is given by
"6
-4
.2
qs = e x p ( - n d ) 0
~ m=M+l
I
20 ¸
40 60 pd (cm. Torr]
80
= 1 - exp(-nd)
Fig. 1. Calculated and experimental dependence of the glow efficiency on pd. Curves correspond to eq. (2) for values of M = 1, 2 and 3, and n o = 110 ions/cm. Experimental points are taken from Mundra et al. Gas: argon, plate voltage: 9.9 kV, and gap width: d = 1.3cm.
of the parallel electrodes of the spark chamber. If
E/p is large, then supposing that at most M electrons are required to initiate a glow discharge, we obtain the efficiency of this type of discharge as M
q~ = e x p ( - n d )
~
(rid)m/m!,
(2)
m=l
assuming the Poisson distribution. In fig. 1 eq. (2) is plotted for different values of M and for no= l l 0 i o n s / c m , where no is the total specific ionization at S.T.P. in argon. The experimental points are taken from the results of Mundra et I'O .80 M= I
,60
~s
T .40 '20 0 20
=
l
40
60
t 80
pd (cm. Tort)
I
I
moo
120
I 14.0
),
Fig. 2. Dependence of the spark efficiency on pd. Curves correspond to eq. (3) for n o = 57 ions/cm, and M = 1, 2 and 3. Experimental points are taken from Mundra et al. Gas: argon, plate voltage: 9.9 kV, d = 1.3 cm.
(nd)m/m!
M Z m=O
(nd)m/ra!"
(3)
The solid lines in fig. 2 are the efficiency curves using the above equation for various values of M. The experimental plots for the initial rise of spark efficiency with pd shown in this figure have been taken from the work of Mundra et al. The best fit is obtained for M = 2 and no = 57 ions/cm. The acceptance of this reduced value of no may be explained by supposing that as the concentration of seed electrons increases, the clustering effect becomes pronounced. To fit the experimental curves of efficiencies of low pressure spark chambers using argon and helium as working gas, Ohashi suggests the empirical relation connecting gas pressure with efficiency: r/ = 1 - exp [-no
d(p/po)~].
(4)
In fig. 3 the reproduction of the best fit curves of Ohashi resembles the experimental points for helium and argon which corresponds rather to primary than to total ionization. For the purpose of comparison r/s vs pressure from eq. (3) for M = 2 has also been plotted in the same figure. We find a better agreement with the experimental points when the values of no are taken to be 40 and 10 for argon and helium respectively.
3. Efficiency characteristics in the higher pressure region Let us now consider the track efficiencies for fillings at higher pressures. According to the Raether-Meek condition, if xc denotes the critical length of an avalanche for the avalanche-tostreamer transition, then xc = 20/~, (5)
EFFICIENCY
CHARACTERISTICS
1.0
f l x
X Ar
+ .75
i
H.
cu.v~
/
n,
Im 1~)Author ,I
S .50
,
/
OF S P A R K C H A M B E R S
499
. . . . . " X ~ . , , ' ~-
/
-/7/
/,," ""
/ /// /
/,"
/+ /
.25
• 01
'1
I
Pressure ( otm )
•
Fig. 3. Dependence o f spark efficiency vs pressure. Solid curves correspond to eq. (3) for M = 2, and n o = 40, 10 and 7. Dotted
curves are reproduced from Ohashi for no = 30 and 5. Experimental points are also taken from Ohashi. where ~ is the first Townsend coefficient. The condition implies that those seed electrons in the chamber gap whose distance from the anode is less than xc would not be able to initiate the avalanche-streamer transition, and hence their number should be excluded from the effective number of seed electrons which can ultimately initiate the discharge. If d be the actual gap length, the effective gap length under this condition will be de = d - x c . Hence we write the general expression for the efficiency of sparks:
M
r/s = 1 - exp(-nd=) ~ (nd=)"/m!.
(6)
m=O
The threshold voltage is defined as the voltage for which r/s--,0. This condition is satisfied when we put dr = 0, i.e. d = x= = 20/~. (7) An exact expression for a~ is difficult to obtain. However, one can consider the following approximate expression in the present case: ot = Ap exp ( - Bp/E), (8)
14
o 12
t
>
io
Symbol Gopsi=e
//
',I
/
,Ig v
g e .u
i-
i
|
IOO
IOOO pd
(cm. Tort)
pd.
)
Fig. 4. Dependence of the threshold voltage on Experimental points are taken from Munclra et al., whereas the solid curve corresponds to eq. (10) for B ' = 6 3 V/cm.torr, and C ' = ]400V.
500
D. M A J U M D A R
theoretical curve showing a much faster decrease. A similar deviation between computed and experimental curves for the dependence of efficiency on pulse voltages is observed from fig. 5b. The above discrepancies could be accounted for by considering that as the pressure increases, the clustering effect and/or the value of M increases; however, a more definitive conclusion may be reached at from further accurate experiments.
where A and B are two constants whose values for argon are given as 1 4 c m - l . t o r r -~ and 180 V/cm. torr respectively f o r E / p ~ 100 V/cm. torr. If the threshold voltage is denoted by V0, then by using eqs. (7) and (8) we get Vo = B p d / l n ( A p d / 2 0 ) . (9) To compare eq. (9) with the threshold voltage curves obtained by Mundra et al., we note that the experimental threshold voltage depends both on the pulse length (i.e., RC-value) and the factor C / ( C + C s ) , where C and Cs are the capacities of the discharge condenser and the spark chamber respectively. Moreover, in the above experiment threshold curves were drawn in terms of the 5C22 hydrogen thyratron plate voltage which is slightly greater than the actual pulse voltage owing to a constant voltage drop in the tube. Considering these factors, we should write for the experimental threshold voltage
4. Remarks 1) We note that a glow-type discharge may be initiated by a single seed electron inside the effective gap length of the spark chamber. For further clarification let us consider the streamer formation mechanism in a streamer chamber. In this case also the individual avalanche-streamer transition occurs chiefly from single seed electrons; but the primary avalanche transforms into a well defined streamer along the direction of the electric field. As the streamer chambers operate in a pressure region considerably higher than that of glow discharges, the free path of the photons responsible for the generation of secondary avalanches must be considerably small. Hence in a streamer chamber, secondary avalanches are produced close to the primary one, and are, therefore, directed towards it from regions where the space charge field is sufficiently strong. 2) We infer from the above analysis that although clustering of primary electrons is effective above
(10)
Vo = B ' p d / l n ( A p d / 2 0 ) + C ' ,
where B' and C' are two new constants. Fig. 4 shows that very good agreement between theory and experiment is obtained when one puts B ' = 63 V/cm.torr and C ' = 1400 V. T h e fall of efficiency with pressure when the pulse voltage is kept fixed was also investigated by Mundra et al. and has been reproduced in fig. 5a. The computed values of r/s vs pressure of argon from eq. (6) are also plotted in the same figure. It appears that the agreement is only qualitative, the °.,.3°° I'0
E)- 50 Torr
? ""
- 4 0 0 Tar r
Y
.6
'4
.2
0
l
600 > pd(cm.
I 800 Torr)
I000
I 2
I 6
4 Plate
8
voltoge(kV)
I0
12
14
)
Fig. 5. Dependence of the spark efficiency on (a) pd (higher values) and (b) voltage. Curves correspond to eq. (6) for M= 2, no =57 ions/cm:and~d= 1.3 cmr~:,Experimental points are taken from Mundra et at. for (a) V=9:9 kV and for (b)p= 50 and 400 torr.
E F F I C I E N C Y C H A R A C T E R I S T I C S OF SPARK CHAMBERS
the low pressure region where defined sparks are possible, it does not appear to be as prominent as guessed by Ohashi; further, in the case of glow discharges the clustering effect seems to be totally negligible. This could be accounted for by considering that glows occur only when the number of seed electrons does not exceed 2 per cm. For helium used in the spark chambers, the clustering effect is negligible even for defined sparks and this is what should be expected as the specific number of ion pairs produced in helium is small. For argon we find values of no to be 57 and 40 per cm from the experimental results of ourselves and Ohashi respectively. These values are considerably less than the standard value of total specific ionization, but greater than the primary specific ionization indicating that clustering partially effects the spark efficiency in argon. The observed differ-
501
ences in the values of no obtained from the above two experiments can be accounted for by considering the larger delay (1/is) used in the latter. I wish to thank my colleague Dr. J.P. Mundra for important discussions.
References 1) R. J. Sutter, G. Nennett, J. Fischer, J. L. Friedes, H. Pal-
evsky and R. Persson, Nucl. Instr. and Meth. 54 (1967) 71. 2) S. Dahlgren, S. Kullanderand R. Lorensi,Nucl. Instr. and Meth. 89 (1970) 29. 3) T. Bunaciu and S. Kullander, Nucl. Instr. and Meth. 54 (1968) 173. 4) j. p. Mundra, D. Majumdar, K. Mazumdar, J. Mukherjee and P. K. Sen Chaudhury,Nucl. Instr. and Meth. 98 (1972) 589. 5) y. Ohashi, Nucl. Instr. and Meth. 113 (1973) 217.