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A charged particle identification system with broad energy range
NUCLEAR
INSTRUMENTS
AND METHODS
31
(1964) 269-278; © N O R T H - H O L L A N D
PUBLISHING
CO.
A CHARGED PARTICLE IDENTIFICATION SYSTEM WITH BROAD ENERGY RANGE* L. W. SWENSON
Bartol Research Foundation of the Franklin Institute Swarthmore, Pennsylvania Received 2 May 1964 A charged particle identification system is described which utilizes the EdE/dx product as computed by an analog multiplying circuit. The multiplier circuit permits compensation for the normal energy dependence of the EdE/dx product. The
response of the system has been measured for protons, deuterons and alpha particles in the 2-18 MeV range using solid state E and dE/dx detectors.
1. Introduction
diodes, Giannelli and Stanchi9) have used the logarithmic response of the emitter-base junction of certain transistors to construct circuits with a logarithmic response. A resistive logarithmic attenuator with a wide dynamic range has been reported by Vincent and KainC°). These logarithmic response circuits together with summing circuits have been used to effect the EdE/dx product. The above circuits have the advantage of simplicity and sometimes lower cost, but this advantage is offset in the case of diodes by their limited dynamic range or accuracy. Aitken ~) has described a system of multiplying the E and dE/dx voltage pulses by exploiting the amplitudeto-time conversion in a multichannel analyzer. The time duration of the analyzer conversion pulse (proportional to E) is used to gate on and off a linear sweep circuit which has a slope proportional to dE/dx. The output of the multiplying (sweep) circuit is then synchronized to gate the multichannel analyzer. The principle of operation is similar to that of the earlier system described by Wolfe et al.4). These systems may require of the order of 10(O200 #see to effect a multiplication and hence an identification. Routing of different particle types to different memory quadrants would then be impossible with most analyzers without introducing still more delay. In all the above mentioned systems it was assumed the particle groups in the EdE/dx product spectrum would be identified by setting single channel analyzer windows to cover these different groups. The success of the identification then depends on the degree to which the product is independent of E. The energy independence requirement may be circumvented by the plotting oscilloscope technique ~2' ~3). In this technique the E and dE/dx voltage pulses are stretched and displayed on an x - y oscilloscope. The spots on the scope may then be recorded photographically, but such a method lacks count capacity and is slow. To avoid the photographic method a mask may be placed on the face of the x - y scope and the un-
A common particle identification technique is to use an electronic multiplying circuit to obtain the product of the specific energy loss dE/dx in a transmission counter and the total energy E of the particle. The specific energy loss dE/dx of a particle of mass M and charge z is given by the non-relativistic expression ~) dx - const. T
Jog
(1)
where m is the electron mass and I is the average ionization potential of the stopping material. The EdE/dx product to first order is energy independent and proportional to Mz 2. Several early schemes 2-4) for obtaining the EdE/dx product demonstrated the value of the method for obtaining particle identification information. These systems were limited in their speed, versatility and energy range. A circuit developed by Brisco 5) and by Stokes6) has been widely used. The Brisco-Stokes circuit utilizes a pair of Raytheon QK-329 squaring tubes. Their circuit is more accurate and has a larger dynamic range than previous designs. Multiplication is accomplished by use of the relation 4AB = (A + B) 2 - (A - B) 2 where, B ----AEand A = E' + E o + KAE. E'is the energy loss of the particle in the counter in which it is completely stopped and Kis a normalizing constant. Stokes, Northrop and Boyer7) have shown that improved separation of different particle types is obtained by adding a constant Eo to the energy E'. The inclusion of E o in A partially compensates for the logarithmic term in B. The result is that the product is less energy dependent. In the Brisco-Stokes circuit the constant E o is added to E' by the addition of a d.c. bias applied to the deflectors of the QK-329 tubes. Wahlin s) has exploited the logarithmic response of biased germanium * Supported by a grant from the National Science Foundation.
269
270
L.W. SWENSON
masked region of the oscilloscope face viewed with a photomultiplier which developes a gating pulse which in turn may be used to gate a multichannel analyzer when the energy spectrum is to be stored~4). For experiments when the number of events to be analyzed is not too large each pair of E and dE/dx events may be analyzed individually by hand after an experiment is completed 15) or stored in the memory of a 3 dimensional pulse height analyzer and sorted out either " o n " or "off" line by a computer. The later arrangement probably represents the ultimate in accuracy and elegance, but may be prohibitively time consuming of computer time for experiments requiring the analysis of a large number of data points. An additional possibility is the use of time of flight for charged particle identification. Time of flight has been used for identification of fission fragments and is extendable to other slow charged particles.
dE/dx signals are transmitted through a pair of wide band amplifiers to a tunnel diode fast coincidence circuit. The coincidence requirement rejects most neutron or gamma ray background pulses as well as charge particles not passing through both detectors. The coincidence output is used to gate the multiplier and the multiehannel analyzers. The E' and dE/dx signals are summed (after proper normalization) at the input of an adder amplifier. The adder amplifier output and the dE/dx signal are amplified and shaped by two delay line amplifiers and fed to the multiplier circuit. The multiplier spectrum is analyzed by single channel analyzers (two are shown in fig. 1). Each single channel position is set to cover a group of one particle type, viz. protons, deuterons or alpha particles. The output of each single channel analyzer passes through a shaping circuit and then as a routing pulse to the storage 400 channel analyzer. The E' and dE/dx sum
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2. System description A block diagram of the particle identification system to be described in the present communication is shown in fig. 1. The E' and dE/dx detectors are silicon surface barrier detectors, but could also be proportional or scintillation counters. The detector signals are l~assed through charge sensitive preamps with 50/~sec time constants to several cathode followers. The E' and
pulses identified with each particle type are thus routed to different memory quadrants of the storage analyzer. To facilitate the positioning of the single channel analyzer windows a second monitoring 400 channel analyzer is used. The multiplier spectrum is displayed by the monitor analyzer which is coincidence or anticoincidence gated by one of the single channel analyzer outputs suitably shaped. Coincidence gating of the
A CHARGED PARTICLE IDENTIFICATION SYSTEM WITH BROAD ENERGY RANGE
monitor analyzer permits display of a selected particle group. The discrimination levels between different particle groups can be continuously monitored in this manner while data is being accumulated in the storage analyzer. All circuitry is transistorized with the exception of the charge sensitive preamps and the Nuvistor cathode followers. The delay line amplifiers, single channel analyzers and 400 channel analyzers are commercial Radiation Instrument Development Laboratory models. Pulse shapes and relative timing of signals at different points in the system are illustrated in fig. 2.
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The Nuvistor cathode followers and the adder amplifier circuit are shown in fig. 3. Nuvistors were used since they provide the high input impedance characteristic of a vacuum triode and at the same time lend themselves to physically compatible inclusion with transistors in modular circuit construction. The same basic circuit is used for all other cathode followers shown in the system block diagram with fixed 4.7 kt2 cathode loads. The adder amplifier is a conventional operational amplifier heavily feed back to provide unit gain. The input o f the operational amplifier being a virtual ground provides a convenient sum point for adding the E' and dE/dx signals. The small difference in sensitivity o f the E' and dE/dx preamps is compensated by adjustment o f the 5 kt2 pots serving as cathode E'' ~'X dE
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loads for the two cathode followers. The adder amplifier output is a conventional p n p - npn complementary pair emitter follower. 3.2. PULSESHAPER The pulse shaping circuit shown in fig. 4a accepts pulses of either polarity and consists of a standard univibrator, inverter and output complementary pair emitter follower. The emitter follower is the same as that used in the adder amplifier output. A positive or negative 10 V pulse of width determined by the coupling capacitor C is provided at the output. When required a 1.0 or 1.5/~sec delay may be inserted between points A and A'. The delay circuit is shown in fig. 4b. The delay line is matched at the input end by the output
impedance of the driving emitter follower and a series 390 f2 resistance. The output end of the delay line is terminated by a 500 f2 resistance. The three remaining transistors serve to restore, without phase inversion, the pulse height lost in termination of the delay line and provide an emitter follower output. A square output pulse is assured by operating these transistors between cut off and saturation. 3.3. FAST COINCIDENCECIRCUIT The fast coincidence circuit shown in fig. 5 consists of a pair of tunnel diode fast discriminators and a coincidence unit. The circuit design follows that of Whetstone and Kounosu 16) and the principle of operation will not be described in detail. The input pulses are
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negative and supplied by 50 f2 lines in order to match the input impedance of the inverting transformers. The discriminator tunnel diode operating points are adjusted by the 10 turn 10 kf2 pot so as to trigger at a low level on the leading edge of the input pulse• The trigger level can be set to trigger reliably on 10-20 mV input pulses. When the input pulse spectrum includes pulses of different heights there will be a timing uncertainty or "jitter" associated with the triggering of the discriminator tunnel diode. To minimize the "jitter" or "'walk" it is desirable to make the input pulse height of the order of 10-100 times the threshold level. When junction detectors are used the detector signal must be passed through a wide band amplifier of gain 10-100 to meet the above requirement with as little deterioration of pulse rise time as possible. Under these conditions the time jitter contribution from the tunnel diode discriminator is well under 5nsec. Coincidence resolving times in the 5-10 nsec range are easily obtained with 100% coincidence efficiency. A resolving time of 100 nsec is usually sufficient for the present application. 3.4. MULTIPLIERCIRCUIT The multiplier circuit to be described here was first designed by R. ChaselT). The Chase circuit consisted of
twelve transistor switching stages, was capable of a linearity of 4% and was designed to operate with vacuum tube amplifiers in the 3-50 V range. The circuit to be described here follows the design principles of the Chase circuit extended to 36 switching stages. The present circuit is designed to be used with solid state amplifiers in the 0.3-10 V range and with a response linearity of 1%. The principle improvements in the circuit design are improved dynamic range and linearity. A coincidence gate has also been added. The two inputs to the multiplier circuit are AE, the E OUT
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274
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pulse from the d E / d x detector and E = E ' + KAE, the output pulse from the adder amplifier which is proportional to the total energy of the stopped particle. E ' is the signal from the detector in which the particle is completely stopped. Kis a gain normalizing constant. The circuit enables one to add a constant continuously adjustable d.c. voltage Eo to the E signal. The multiplier then takes the product of (E + go) and AE. The multiplier circuit operates on the principle of a voltage divider; and its operation is most easily visualized if we imagine E and Euut to appear at the terminals of a voltage divider as in fig. 6a. One may express the output voltage a s g o u t = DkE, where k
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the base emitter junction of the transistors as it increases from zero, driving them to cutoff (opens the switches) in succession. The operation of the k t h stage is illustrated in fig. 6b. The k t h switch will open and r k will be added to the divider chain when A E > (AE)k, where (AE)k is the A E input voltage which is just large enough to raise the base of the kth transistor near ground potential. It follows that (gE)k = BRR/R', (3) where B is the base bias supply voltage and R k the bias resistor at the k t h transistor. To m a k e D k proportional to ,dE we set Ok = A(AE)k (4) where A is a constant to be chosen as convenient. Once A E k is specified as a function of k, D k and Z k will follow
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Fig. 7. E dE/dx multiplying circuit.
A CHARGED PARTICLE IDENTIFICATION SYSTEM WITH BROAD ENERGY RANGE where P is a constant. I f 2 is s o m e c o n s t a n t , the c o n dition
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(9)
where a = 2/(2 - P ) a n d (dE)k = a k - I ( A E ) I .
(10)
Once the value o f a in eq. (9) a n d A in eq. (4) have been c h o s e n t h e r e m a i n i n g circuit p a r a m e t e r s follow f r o m eqs. (2), (3), (4) a n d (5). T h e c o n s t a n t a is c o m p l e t e l y d e t e r m i n e d b y t h e degree to w h i c h the m u l t i p l i e r response is r e q u i r e d t o r e s e m b l e a linear response. T h e d e v i a t i o n f r o m linea r i t y o f the m u l t i p l i e r response is due t o the step response o f Dk as a f u n c t i o n o f k. F r o m eqs. (4) a n d (10) it follows t h a t Dk = ak-lD1
(11)
a n d t h a t the average value o f D over the interval Dk to D k - 1 is a+l ½(Dk + D k - 1 ) -- 2a Dk. T h e highest f r a c t i o n a l d e v i a t i o n o f D k f r o m a linear response at t h e k t h stage m a y be w r i t t e n as flk = Dk -- ½(Dk + O k - 1 ) _ a -- 1 ½(Dk + D k - 1 ) a + 1" H e n c e once fl is specified the p a r a m e t e r a is d e t e r m i n e d by a = (fl + 1)/(1 -- fl).
(12)
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T h e foregoing design considerations were d e v e l o p e d in c o o p e r a t i o n with P. K w o k l S ) . T h e a c t u a l l i n e a r i t y o b t a i n a b l e in practice is m u c h better t h a n the design linearityfl. I n practice the switches are n o t ideal, further s o m e feed b a c k f r o m a n y given switch to n e i g h b o r i n g switches is p r o v i d e d t h r o u g h the chain o f 10 kf2 resistors. F o r the design o f the m u l t i p l i e r circuit s h o w n in fig. 7 a design l i n e a r i t y fl = 5 . 7 5 ~ was chosen, which corres p o n d s t o a = 1.122. A d y n a m i c r a n g e o f A E I = 0.337
(8)
f r o m which it follows t h a t R k = ak-lR1
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T h e t o t a l n u m b e r o f switches r e q u i r e d in the circuit design for a given ct a n d a ( d y n a m i c r a n g e a n d linearity) is t h e n n - 1 = log s / l o g a. (14)
TABL~ 1 Table of component values for 36-state multiplier circuit to be used with transistorized amplifiers. (AE)~, Rk, Zk and r~ calculated for multiplier circuit of AE pulse height range 0.3 to 10 V. Rk = R'AEk/4.5, R ' = 150 k.Q for k = 1-12 and R ' = 15 k.Q for k=12-36, Dk=AE/100, R=20k.Q. The brackets grouping resistor values for k > 25 indicate the number of switches were doubled in this range. Precision resistors are necessary only for the rk values. k
AEe (volt)
Rg (calc)
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1.08 1.22
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to AE~ = 10.0 V or ct ~, 30 was imposed upon the design. The number of transistors required to realize these conditions is n ~ 30. The values of all other parameters for the circuit of fig. 7 are given in table 1, for A = 0.01 (chosen for convenience), B = 4.5 V, R = 20 kO, R' = 150 kt2 for k = 1-12 and R' = 15 kg2 for k = 12-36. A larger value of R' was used for k = 1-12 to obtain a higher input impedance at the AE input to the multiplier circuit. In an effort to improve the absolute deviation of D k from linearity in the range k = 25 to k = 30 (or AE = 5.22 to 10.0 where the deviations are largest) six more switches were added in this range. The AE intervals between successive switches were then only half as large in this range. The addition although not essential to the circuit design results in a further decrease in the fractional deviation from a linear response in the k = 25-30 range.
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4. Multiplier response The product of E and dE/dx is energy dependent due to the logarithmic dependence of dE/dx on E in eq. (1). As first pointed out by Stokes, Northrop and Boyer7), the response of the multiplier may be improved by the addition of a constant term Eo to the energy E before multiplying by dE/dx. The resulting product is then
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the divider ratio D, is not to be disturbed. A transistorized amplifier (not shown) was used for this purpose the input stage of which was a Nuvistor cathode follower. Care must be taken in the circuit layout to provide shielding between the r k resistor chain and the AEinput signal. The AE signal is much larger than the signal developed along the rk resistor chain and if this chain is not properly shielded the output pulse will be distorted. Such distortion is characterized by the presence of a negative undershoot on the leading edge of the output pulse.
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and 10 V. E0 = 0 and K = 0. E and dE amplifiers were commercial RIDL 30-23 models. Input pulse was 1.4 psec in duration. A typical linearity of about 1 ~ for the actual circuit is illustrated by the plot of fig. 8 taken by inserting a pulse of constant pulse height into the E input and a pulse of variable height into the AE input. An additional transistor switch has been added to permit the multiplier to be coincidence gated. A positive 5 V pulse from the fast coincidence circuit is required to gate the input on when the gate switch is in the on position. The gating pulse should be at least as wide as the E and AE input pulses. The E and AE pulses were delay line shaped to 1.4 /~sec, however, the circuit will function satisfactorily with pulses 0.7 psec in duration. The output signal from the multiplier must be delivered to an amplifier with a high input impedance if
(15)
for particles of charge z, mass number # and energy E (in MeV) passing through a silicon dE/dx detector. If an argon proportional dE/dx counter is used the number in the argument becomes 10.7. C is a constant and # -- 1 - 4 for protons, deuterons, tritons and He a, and alpha-particles respectively. The effect the choice of the parameter E o has on the calculated product is shown in fig. 9. The fact that the product is still not completely independent of E results from the incomplete compensation of the log term by the (E + Eo)/E factor in eq. (15). If identification of different particle types is to be effected over a wide range of particle energies a choise of E 0 must be made which makes the product of fig. 9 most nearly resemble horizontal straight lines. If attention is momentarily restricted to the separation of protons and deuterons it appears that Eo = 1.74 is a reasonable choice. Optimum separation of other particle types may dictate another choice o f E o. Particular attention must be given to cases where the energy range extends to low energies (below 3-4 MeV). A 30-stage multiplier circuit has also been constructed is) for use with vacuum tube amplifiers in the 2-100 V range, with a response linear within 1 ~ . The 30-stage circuit has been successfully used to separate over a broad energy range the proton, deuteron and alpha-particle reaction products from 30 MeV alphaparticle induced reactions19'2°). The circuit parameters for the 30-stage circuit are given in table 2.
A CHARGED
PARTICLE
IDENTIFICATION
SYSTEM
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277
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278
L.W. SWENSON
TABLE 2 Table of component values for 30-stage multiplier circuit to be used with vacuum tube amplifiers. (AE)e, Re, Ze and re calculated for multiplier of dE pulse height range 2-100 V. Re = R'AEe[4.5, R" = 15 k-Q, De = L1E/935 and R = 20 k-Q. The brackets grouping resistor values for k > 25 indicate the number of switches were doubled in this range. Precision resistors are necessary only for the re values. In actual construction R' consisted of a 12 k-Q resistor in series with a 5 k.Q, 1 turn carbon pot.
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Ee
Re
(volt)
(calc)
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10 k-Q 11 13 15 17 20 23 27 31 35 41
Zk 47.7 -Q 54.6 63.1 72.7 83.8 96.7 111.3 128.3 147.6 171.0 197.0 230.5 264.5 306.5 352.5 410.0 475.0 550.0 640.5 736.0 851.5 988.0 1155 1346 1570 1835 2142
rk
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5. System performance The o u t p u t pulse height of the multiplier is shown i n fig. 10 as a f u n c t i o n of incident particle energy E. Monoenergetic protons, deuterons a n d alpha particles were incident u p o n the dE/dx - E telescope o b t a i n e d b y elastically scattering these particles from a A u leaf target. The proton, deuteron a n d alpha particle beams were produced b y the U n i v e r s i t y of P e n n s y l v a n i a t a n d e m V a n de Graaff. The E a n d dE/dx surface barrier detectors used for this m e a s u r e m e n t had depletion depths of 1.3 m m a n d 15/tm respectively. As m a y be seen the measured system response is i n reasonable agreement with the calculated response a n d n o t completely i n d e p e n d e n t of energy for the reason pointed out in the previous section. A choice o f Eo =
1.6 MeV is a reasonable one, a n d permits p r o t o n d e u t e r o n separation over the complete .energy range shown. Particles of higher energy (12-40 MeV) will also be easily identified as the multiplier response is nearly fiat at higher energies. The system resolution was typically 5 - 2 0 ~ , where the system resolution is defined as the full width at h a l f m a x i m u m o f the multiplier o u t p u t spectrum when monoenergetic particles of a single type are incident u p o n the E - dE/dx telescope. The system r e s o l u t i o n is determined primarily by the resolution of the dE/dx detector, which is influenced by the low energy threshold imposed u p o n the system. The low energy threshold determines the m a x i m u m allowable thickness of the dE/dx detector, which i n t u r n establishes the high energy limit if the dE/dx detector signal to noise ratio is to be kept within prescribed limits. The above ment i o n e d detectors set the lower energy threshold at 1.0 MeV for protons, 1.2 MeV for deuterons, 3.8 MeV for alpha particles, a n d m a i n t a i n a dE/dx resolution ( F W M H ) of 5 - 2 0 ~ over the 2-12 MeV p r o t o n a n d d e u t e r o n range or 6-18 MeV alpha-particle range. A p p r e c i a t i o n is extended to R. Chase for c o m m u n i cating his circuit design to the author. The assistance of P. K w o k in developing the formal circuit analysis is gratefully acknowledged. A p p r e c i a t i o n is also extended to the operators of the University of P e n n s y l v a n i a T a n d e m Accelerator for their helpful assistance.
References 1) M. S. Livingston and H. Bethe, Rev. Mod. Phys., 9 (1937) 245. 2) F. A. Aschenbrenner, Phys. Rev., 98 (1955) 657. 3) G. Igo and R. M. Eisberg, Rev. Sci. Instr., 25 (1954) 450. 4) B. Wolfe, A. Silverman and J. W. DeWire, Rev. Sci. Instr., 26 (1955) 504. 5) W. L. Brisco, Rev. Sci. Instr., 29 (1958) 401. 6) R. H. Stokes, Rev. Sci. Instr., 31 (1960) 768. 7) R. H. Stokes, J. A. Northrop and K. Boyer, Rev. Sci. Instr., 29 (1958) 61. 8) L. Wahlin, Nucl. Instr. and Meth., 14 (1963) 281. 9) G. Giannelliand L. Stanchi, Nucl. Instr. and Meth., g (1960)79. 10) C. H. Vincent and D. Kaine, Proc. Eighth Scintillation Counter Symposium 1962 IRE Transactions. 11) j. H. Aitken, Nucl. Instr. and Meth., 14 (1961) 343. 12) Carl E. Anderson, D. A. Bromly and M. Sachs, Nucl. Instr. and Meth., 13 (1961) 238. 13) L. G. Kuo, M. Petravi6 and B. Turko, Nucl. Instr. and Meth., 10 (1961) 53. 14) C. D. Goodman and J. Need, Phys. Rev., 110 (1958) 676. 15) D. Bodansky, R. K. Cole, W. G. Cross, C. R. Gruhn and I. Halpern. Phys. Rev., 126 (1962) 1082. 16) A. Whetstone and S. Kounosu, Rev. Sci. Instr., 33 (1962) 423. 17) R. Chase (private communication). 18) p. C. Kwok, B. S. Thesis, M. I. T. (1961) (unpublished). 19) L. W. Swenson and C. R. Gruhn, Bull. Am. Phys. Soc., 8 (1963) 356. 20) C. R. Gruhn and L. W. Swenson, Bull. Am. Phys. Soc., g (1963) 357.
INSTRUMENTS
AND METHODS
31
(1964) 269-278; © N O R T H - H O L L A N D
PUBLISHING
CO.
A CHARGED PARTICLE IDENTIFICATION SYSTEM WITH BROAD ENERGY RANGE* L. W. SWENSON
Bartol Research Foundation of the Franklin Institute Swarthmore, Pennsylvania Received 2 May 1964 A charged particle identification system is described which utilizes the EdE/dx product as computed by an analog multiplying circuit. The multiplier circuit permits compensation for the normal energy dependence of the EdE/dx product. The
response of the system has been measured for protons, deuterons and alpha particles in the 2-18 MeV range using solid state E and dE/dx detectors.
1. Introduction
diodes, Giannelli and Stanchi9) have used the logarithmic response of the emitter-base junction of certain transistors to construct circuits with a logarithmic response. A resistive logarithmic attenuator with a wide dynamic range has been reported by Vincent and KainC°). These logarithmic response circuits together with summing circuits have been used to effect the EdE/dx product. The above circuits have the advantage of simplicity and sometimes lower cost, but this advantage is offset in the case of diodes by their limited dynamic range or accuracy. Aitken ~) has described a system of multiplying the E and dE/dx voltage pulses by exploiting the amplitudeto-time conversion in a multichannel analyzer. The time duration of the analyzer conversion pulse (proportional to E) is used to gate on and off a linear sweep circuit which has a slope proportional to dE/dx. The output of the multiplying (sweep) circuit is then synchronized to gate the multichannel analyzer. The principle of operation is similar to that of the earlier system described by Wolfe et al.4). These systems may require of the order of 10(O200 #see to effect a multiplication and hence an identification. Routing of different particle types to different memory quadrants would then be impossible with most analyzers without introducing still more delay. In all the above mentioned systems it was assumed the particle groups in the EdE/dx product spectrum would be identified by setting single channel analyzer windows to cover these different groups. The success of the identification then depends on the degree to which the product is independent of E. The energy independence requirement may be circumvented by the plotting oscilloscope technique ~2' ~3). In this technique the E and dE/dx voltage pulses are stretched and displayed on an x - y oscilloscope. The spots on the scope may then be recorded photographically, but such a method lacks count capacity and is slow. To avoid the photographic method a mask may be placed on the face of the x - y scope and the un-
A common particle identification technique is to use an electronic multiplying circuit to obtain the product of the specific energy loss dE/dx in a transmission counter and the total energy E of the particle. The specific energy loss dE/dx of a particle of mass M and charge z is given by the non-relativistic expression ~) dx - const. T
Jog
(1)
where m is the electron mass and I is the average ionization potential of the stopping material. The EdE/dx product to first order is energy independent and proportional to Mz 2. Several early schemes 2-4) for obtaining the EdE/dx product demonstrated the value of the method for obtaining particle identification information. These systems were limited in their speed, versatility and energy range. A circuit developed by Brisco 5) and by Stokes6) has been widely used. The Brisco-Stokes circuit utilizes a pair of Raytheon QK-329 squaring tubes. Their circuit is more accurate and has a larger dynamic range than previous designs. Multiplication is accomplished by use of the relation 4AB = (A + B) 2 - (A - B) 2 where, B ----AEand A = E' + E o + KAE. E'is the energy loss of the particle in the counter in which it is completely stopped and Kis a normalizing constant. Stokes, Northrop and Boyer7) have shown that improved separation of different particle types is obtained by adding a constant Eo to the energy E'. The inclusion of E o in A partially compensates for the logarithmic term in B. The result is that the product is less energy dependent. In the Brisco-Stokes circuit the constant E o is added to E' by the addition of a d.c. bias applied to the deflectors of the QK-329 tubes. Wahlin s) has exploited the logarithmic response of biased germanium * Supported by a grant from the National Science Foundation.
269
270
L.W. SWENSON
masked region of the oscilloscope face viewed with a photomultiplier which developes a gating pulse which in turn may be used to gate a multichannel analyzer when the energy spectrum is to be stored~4). For experiments when the number of events to be analyzed is not too large each pair of E and dE/dx events may be analyzed individually by hand after an experiment is completed 15) or stored in the memory of a 3 dimensional pulse height analyzer and sorted out either " o n " or "off" line by a computer. The later arrangement probably represents the ultimate in accuracy and elegance, but may be prohibitively time consuming of computer time for experiments requiring the analysis of a large number of data points. An additional possibility is the use of time of flight for charged particle identification. Time of flight has been used for identification of fission fragments and is extendable to other slow charged particles.
dE/dx signals are transmitted through a pair of wide band amplifiers to a tunnel diode fast coincidence circuit. The coincidence requirement rejects most neutron or gamma ray background pulses as well as charge particles not passing through both detectors. The coincidence output is used to gate the multiplier and the multiehannel analyzers. The E' and dE/dx signals are summed (after proper normalization) at the input of an adder amplifier. The adder amplifier output and the dE/dx signal are amplified and shaped by two delay line amplifiers and fed to the multiplier circuit. The multiplier spectrum is analyzed by single channel analyzers (two are shown in fig. 1). Each single channel position is set to cover a group of one particle type, viz. protons, deuterons or alpha particles. The output of each single channel analyzer passes through a shaping circuit and then as a routing pulse to the storage 400 channel analyzer. The E' and dE/dx sum
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Fig. 1. Block diagram of particle indentificationsystem.
2. System description A block diagram of the particle identification system to be described in the present communication is shown in fig. 1. The E' and dE/dx detectors are silicon surface barrier detectors, but could also be proportional or scintillation counters. The detector signals are l~assed through charge sensitive preamps with 50/~sec time constants to several cathode followers. The E' and
pulses identified with each particle type are thus routed to different memory quadrants of the storage analyzer. To facilitate the positioning of the single channel analyzer windows a second monitoring 400 channel analyzer is used. The multiplier spectrum is displayed by the monitor analyzer which is coincidence or anticoincidence gated by one of the single channel analyzer outputs suitably shaped. Coincidence gating of the
A CHARGED PARTICLE IDENTIFICATION SYSTEM WITH BROAD ENERGY RANGE
monitor analyzer permits display of a selected particle group. The discrimination levels between different particle groups can be continuously monitored in this manner while data is being accumulated in the storage analyzer. All circuitry is transistorized with the exception of the charge sensitive preamps and the Nuvistor cathode followers. The delay line amplifiers, single channel analyzers and 400 channel analyzers are commercial Radiation Instrument Development Laboratory models. Pulse shapes and relative timing of signals at different points in the system are illustrated in fig. 2.
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The Nuvistor cathode followers and the adder amplifier circuit are shown in fig. 3. Nuvistors were used since they provide the high input impedance characteristic of a vacuum triode and at the same time lend themselves to physically compatible inclusion with transistors in modular circuit construction. The same basic circuit is used for all other cathode followers shown in the system block diagram with fixed 4.7 kt2 cathode loads. The adder amplifier is a conventional operational amplifier heavily feed back to provide unit gain. The input o f the operational amplifier being a virtual ground provides a convenient sum point for adding the E' and dE/dx signals. The small difference in sensitivity o f the E' and dE/dx preamps is compensated by adjustment o f the 5 kt2 pots serving as cathode E'' ~'X dE
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loads for the two cathode followers. The adder amplifier output is a conventional p n p - npn complementary pair emitter follower. 3.2. PULSESHAPER The pulse shaping circuit shown in fig. 4a accepts pulses of either polarity and consists of a standard univibrator, inverter and output complementary pair emitter follower. The emitter follower is the same as that used in the adder amplifier output. A positive or negative 10 V pulse of width determined by the coupling capacitor C is provided at the output. When required a 1.0 or 1.5/~sec delay may be inserted between points A and A'. The delay circuit is shown in fig. 4b. The delay line is matched at the input end by the output
impedance of the driving emitter follower and a series 390 f2 resistance. The output end of the delay line is terminated by a 500 f2 resistance. The three remaining transistors serve to restore, without phase inversion, the pulse height lost in termination of the delay line and provide an emitter follower output. A square output pulse is assured by operating these transistors between cut off and saturation. 3.3. FAST COINCIDENCECIRCUIT The fast coincidence circuit shown in fig. 5 consists of a pair of tunnel diode fast discriminators and a coincidence unit. The circuit design follows that of Whetstone and Kounosu 16) and the principle of operation will not be described in detail. The input pulses are
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negative and supplied by 50 f2 lines in order to match the input impedance of the inverting transformers. The discriminator tunnel diode operating points are adjusted by the 10 turn 10 kf2 pot so as to trigger at a low level on the leading edge of the input pulse• The trigger level can be set to trigger reliably on 10-20 mV input pulses. When the input pulse spectrum includes pulses of different heights there will be a timing uncertainty or "jitter" associated with the triggering of the discriminator tunnel diode. To minimize the "jitter" or "'walk" it is desirable to make the input pulse height of the order of 10-100 times the threshold level. When junction detectors are used the detector signal must be passed through a wide band amplifier of gain 10-100 to meet the above requirement with as little deterioration of pulse rise time as possible. Under these conditions the time jitter contribution from the tunnel diode discriminator is well under 5nsec. Coincidence resolving times in the 5-10 nsec range are easily obtained with 100% coincidence efficiency. A resolving time of 100 nsec is usually sufficient for the present application. 3.4. MULTIPLIERCIRCUIT The multiplier circuit to be described here was first designed by R. ChaselT). The Chase circuit consisted of
twelve transistor switching stages, was capable of a linearity of 4% and was designed to operate with vacuum tube amplifiers in the 3-50 V range. The circuit to be described here follows the design principles of the Chase circuit extended to 36 switching stages. The present circuit is designed to be used with solid state amplifiers in the 0.3-10 V range and with a response linearity of 1%. The principle improvements in the circuit design are improved dynamic range and linearity. A coincidence gate has also been added. The two inputs to the multiplier circuit are AE, the E OUT
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274
L.W. SWENSON
pulse from the d E / d x detector and E = E ' + KAE, the output pulse from the adder amplifier which is proportional to the total energy of the stopped particle. E ' is the signal from the detector in which the particle is completely stopped. Kis a gain normalizing constant. The circuit enables one to add a constant continuously adjustable d.c. voltage Eo to the E signal. The multiplier then takes the product of (E + go) and AE. The multiplier circuit operates on the principle of a voltage divider; and its operation is most easily visualized if we imagine E and Euut to appear at the terminals of a voltage divider as in fig. 6a. One may express the output voltage a s g o u t = DkE, where k
ri
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the base emitter junction of the transistors as it increases from zero, driving them to cutoff (opens the switches) in succession. The operation of the k t h stage is illustrated in fig. 6b. The k t h switch will open and r k will be added to the divider chain when A E > (AE)k, where (AE)k is the A E input voltage which is just large enough to raise the base of the kth transistor near ground potential. It follows that (gE)k = BRR/R', (3) where B is the base bias supply voltage and R k the bias resistor at the k t h transistor. To m a k e D k proportional to ,dE we set Ok = A(AE)k (4) where A is a constant to be chosen as convenient. Once A E k is specified as a function of k, D k and Z k will follow
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(5)
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(6)
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Fig. 7. E dE/dx multiplying circuit.
A CHARGED PARTICLE IDENTIFICATION SYSTEM WITH BROAD ENERGY RANGE where P is a constant. I f 2 is s o m e c o n s t a n t , the c o n dition
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(A e)k - (A )k-1
(7)
will require t h a t the r a t i o o f the u n c e r t a i n t y in trigger voltage for the k t h stage to the interval o f A E between the k a n d the k - 1 stages b e i n d e p e n d e n t o f k. F r o m e q u a t i o n s (3), (5) a n d (6) we find Rk/(Rk -- R k - 1 ) = 2/P
(9)
where a = 2/(2 - P ) a n d (dE)k = a k - I ( A E ) I .
(10)
Once the value o f a in eq. (9) a n d A in eq. (4) have been c h o s e n t h e r e m a i n i n g circuit p a r a m e t e r s follow f r o m eqs. (2), (3), (4) a n d (5). T h e c o n s t a n t a is c o m p l e t e l y d e t e r m i n e d b y t h e degree to w h i c h the m u l t i p l i e r response is r e q u i r e d t o r e s e m b l e a linear response. T h e d e v i a t i o n f r o m linea r i t y o f the m u l t i p l i e r response is due t o the step response o f Dk as a f u n c t i o n o f k. F r o m eqs. (4) a n d (10) it follows t h a t Dk = ak-lD1
(11)
a n d t h a t the average value o f D over the interval Dk to D k - 1 is a+l ½(Dk + D k - 1 ) -- 2a Dk. T h e highest f r a c t i o n a l d e v i a t i o n o f D k f r o m a linear response at t h e k t h stage m a y be w r i t t e n as flk = Dk -- ½(Dk + O k - 1 ) _ a -- 1 ½(Dk + D k - 1 ) a + 1" H e n c e once fl is specified the p a r a m e t e r a is d e t e r m i n e d by a = (fl + 1)/(1 -- fl).
(12)
I f t h e t o t a l n u m b e r o f switches t o be used in the circuit is n, t h e n the A E d y n a m i c r a n g e will be given b y (~
- -
(AE)n (AE) 1 _
_
- -
a n-1.
T h e foregoing design considerations were d e v e l o p e d in c o o p e r a t i o n with P. K w o k l S ) . T h e a c t u a l l i n e a r i t y o b t a i n a b l e in practice is m u c h better t h a n the design linearityfl. I n practice the switches are n o t ideal, further s o m e feed b a c k f r o m a n y given switch to n e i g h b o r i n g switches is p r o v i d e d t h r o u g h the chain o f 10 kf2 resistors. F o r the design o f the m u l t i p l i e r circuit s h o w n in fig. 7 a design l i n e a r i t y fl = 5 . 7 5 ~ was chosen, which corres p o n d s t o a = 1.122. A d y n a m i c r a n g e o f A E I = 0.337
(8)
f r o m which it follows t h a t R k = ak-lR1
275
(13)
T h e t o t a l n u m b e r o f switches r e q u i r e d in the circuit design for a given ct a n d a ( d y n a m i c r a n g e a n d linearity) is t h e n n - 1 = log s / l o g a. (14)
TABL~ 1 Table of component values for 36-state multiplier circuit to be used with transistorized amplifiers. (AE)~, Rk, Zk and r~ calculated for multiplier circuit of AE pulse height range 0.3 to 10 V. Rk = R'AEk/4.5, R ' = 150 k.Q for k = 1-12 and R ' = 15 k.Q for k=12-36, Dk=AE/100, R=20k.Q. The brackets grouping resistor values for k > 25 indicate the number of switches were doubled in this range. Precision resistors are necessary only for the rk values. k
AEe (volt)
Rg (calc)
0.337 0.378 0.425 0.478 0.535 0.603 0.678 0.761 0.855 0.962
11.2kO ! 12.6 14.2 15.9 17.8 20.1 22.6 25.3 28.5 32.0 36.0 40.7 4.57 5.08 5.76 6.46 7.26 8.12 9.12 10.35
Zk
r~ (calc)
I
1 23 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3o 31 32 33 34 35 36
1.08 1.22
1.37 1.53 1.73
1.94 2.18 2.44 2.74 3.10 3.46 3.90 4.40 4.92 5.22 5.55 5.88 6.23 6.61 7.01 7.43 7.90
8.38 8.85 9.40 10.0
11.53
13.0 14.66 16.37 17.4 18.5 19.6 20.8 22.0 23.3 24.8 26.3 27.9 29.5 31.3 33.3
69.7 -(2 75.8 85.3 96.0 107.6 121.4 136.5 153.3 172.5 194.1 218.4 247.0 277.5 311.0 351.0 395.5 445 500 563 637 717 812 920 1035 1100 I 175 1250 1330 1415 1510 1607 1715 1830 1935 2075 2222
69.7 £2 6.1 9.5 10.7 11.6 13.8 15.1 16.8 19.2 21.6 24.3 28.6 30.5 33.5 40.0 44.5 49.5 55 63 74 80 95 112 125
,,o
115 115 ) 230
276
L.W. SWENSON
to AE~ = 10.0 V or ct ~, 30 was imposed upon the design. The number of transistors required to realize these conditions is n ~ 30. The values of all other parameters for the circuit of fig. 7 are given in table 1, for A = 0.01 (chosen for convenience), B = 4.5 V, R = 20 kO, R' = 150 kt2 for k = 1-12 and R' = 15 kg2 for k = 12-36. A larger value of R' was used for k = 1-12 to obtain a higher input impedance at the AE input to the multiplier circuit. In an effort to improve the absolute deviation of D k from linearity in the range k = 25 to k = 30 (or AE = 5.22 to 10.0 where the deviations are largest) six more switches were added in this range. The AE intervals between successive switches were then only half as large in this range. The addition although not essential to the circuit design results in a further decrease in the fractional deviation from a linear response in the k = 25-30 range.
MULTIPLIER
LINEARITY
PLOT
7 6
j
_Arnplif!er
=o ==5
:::) =S
;
~
~
;,
~
~
":'
~
4. Multiplier response The product of E and dE/dx is energy dependent due to the logarithmic dependence of dE/dx on E in eq. (1). As first pointed out by Stokes, Northrop and Boyer7), the response of the multiplier may be improved by the addition of a constant term Eo to the energy E before multiplying by dE/dx. The resulting product is then
E dE Cpz2[~--°]log(13"5E 1 dx = \----#--/
ot
~¢-
the divider ratio D, is not to be disturbed. A transistorized amplifier (not shown) was used for this purpose the input stage of which was a Nuvistor cathode follower. Care must be taken in the circuit layout to provide shielding between the r k resistor chain and the AEinput signal. The AE signal is much larger than the signal developed along the rk resistor chain and if this chain is not properly shielded the output pulse will be distorted. Such distortion is characterized by the presence of a negative undershoot on the leading edge of the output pulse.
~
,'o ,',
AE (VOLTS]
Fig. 8. LJnea~ity cm've for multiplier circuit. E pulse was constant
and 10 V. E0 = 0 and K = 0. E and dE amplifiers were commercial RIDL 30-23 models. Input pulse was 1.4 psec in duration. A typical linearity of about 1 ~ for the actual circuit is illustrated by the plot of fig. 8 taken by inserting a pulse of constant pulse height into the E input and a pulse of variable height into the AE input. An additional transistor switch has been added to permit the multiplier to be coincidence gated. A positive 5 V pulse from the fast coincidence circuit is required to gate the input on when the gate switch is in the on position. The gating pulse should be at least as wide as the E and AE input pulses. The E and AE pulses were delay line shaped to 1.4 /~sec, however, the circuit will function satisfactorily with pulses 0.7 psec in duration. The output signal from the multiplier must be delivered to an amplifier with a high input impedance if
(15)
for particles of charge z, mass number # and energy E (in MeV) passing through a silicon dE/dx detector. If an argon proportional dE/dx counter is used the number in the argument becomes 10.7. C is a constant and # -- 1 - 4 for protons, deuterons, tritons and He a, and alpha-particles respectively. The effect the choice of the parameter E o has on the calculated product is shown in fig. 9. The fact that the product is still not completely independent of E results from the incomplete compensation of the log term by the (E + Eo)/E factor in eq. (15). If identification of different particle types is to be effected over a wide range of particle energies a choise of E 0 must be made which makes the product of fig. 9 most nearly resemble horizontal straight lines. If attention is momentarily restricted to the separation of protons and deuterons it appears that Eo = 1.74 is a reasonable choice. Optimum separation of other particle types may dictate another choice o f E o. Particular attention must be given to cases where the energy range extends to low energies (below 3-4 MeV). A 30-stage multiplier circuit has also been constructed is) for use with vacuum tube amplifiers in the 2-100 V range, with a response linear within 1 ~ . The 30-stage circuit has been successfully used to separate over a broad energy range the proton, deuteron and alpha-particle reaction products from 30 MeV alphaparticle induced reactions19'2°). The circuit parameters for the 30-stage circuit are given in table 2.
A CHARGED
PARTICLE
IDENTIFICATION
SYSTEM
WITH
BROAD
ENERGY
RANGE
277
36
Alpha
34
,
32
~
'
.... ~
~
Particles Fz 2= 16
30 28
1
~
....... i / -
He 3
26 -
-
24
o ,+, ,,,
22
x
20
,;"
/
........ ~t-
Eo= 310 MeV
----
= 1.0
// ::k
....
7
,. ",," ' ~ . - . . . .. .~.~-~-"
~ ~
~ . . . . . . . . . . .
'
i
Deuterons
_~ . ~ .---.- " .-"_.-'-
~"~'~'~"~ ° ~ _ _ . . . . .
\
,
2
Tritons
i
Protons FLZ? = I
~
I
6
I
I
I
IO
14
I
I
I
I
18 ENERGY
I
I
22
I
I
26
30
(MeV)
Fig. 9. Calculated multiplier response for protons, deuterons, tritons, I-Ie3 and He4 as a function o f particle energy. The parameter E0 was varied between 1.0 and 3.0 MeV.
250 2000
IJJ Z O~ (3. to ~= 2 0 0
1500
_J--O.-a Z•
. . . . . " ~'--.~.-.-.~-~
~..__
150 I000
_ _ ,~
~
-
Eo= 7.2 M e V I ~
~
~
~
:E
5.4 3.6
! /=~
1.8
|1
0.9
J=
o
o
IO0 500
50
0
4
6
8
I0
ENERGY (MeV)
12
14
'
8
I()
12
14
16
I~1
2'0
ENERGY (MeV)
Fig. 10. Measured response of particle identification system to protons, deuterons and alpha particles as a function of particle energy. The E0 parameter was varied from 0 to 7.2 MeV.
278
L.W. SWENSON
TABLE 2 Table of component values for 30-stage multiplier circuit to be used with vacuum tube amplifiers. (AE)e, Re, Ze and re calculated for multiplier of dE pulse height range 2-100 V. Re = R'AEe[4.5, R" = 15 k-Q, De = L1E/935 and R = 20 k-Q. The brackets grouping resistor values for k > 25 indicate the number of switches were doubled in this range. Precision resistors are necessary only for the re values. In actual construction R' consisted of a 12 k-Q resistor in series with a 5 k.Q, 1 turn carbon pot.
I0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Ee
Re
(volt)
(calc)
2.23 2.55 2.95 3.40 3.92 4.52 5.20 6.00 6.90 8.00 9.22 10.7 12.2 14.1 16.2 18.8 21.7 25.0 29.0 33.2 38.2 44.2 51.0 59.0 68.0 73.0 78.5 84.0 90.6 97.0
10 k-Q 11 13 15 17 20 23 27 31 35 41
Zk 47.7 -Q 54.6 63.1 72.7 83.8 96.7 111.3 128.3 147.6 171.0 197.0 230.5 264.5 306.5 352.5 410.0 475.0 550.0 640.5 736.0 851.5 988.0 1155 1346 1570 1835 2142
rk
(calc) 47.7 -Q 6.9 8.5 9.6 11.1 12.9 14.6 17.0 19.3 23.4 26.0 32.0 33.0 42.0 46.0 57.5 65.0 75.0 92.5 95.5 115.5 136.5 167.0 191.0 112.0 \ I 12.0/) 224.0 133.0 \ 133.0 f 266.0 154.0 \ 154.0/) 308.0
5. System performance The o u t p u t pulse height of the multiplier is shown i n fig. 10 as a f u n c t i o n of incident particle energy E. Monoenergetic protons, deuterons a n d alpha particles were incident u p o n the dE/dx - E telescope o b t a i n e d b y elastically scattering these particles from a A u leaf target. The proton, deuteron a n d alpha particle beams were produced b y the U n i v e r s i t y of P e n n s y l v a n i a t a n d e m V a n de Graaff. The E a n d dE/dx surface barrier detectors used for this m e a s u r e m e n t had depletion depths of 1.3 m m a n d 15/tm respectively. As m a y be seen the measured system response is i n reasonable agreement with the calculated response a n d n o t completely i n d e p e n d e n t of energy for the reason pointed out in the previous section. A choice o f Eo =
1.6 MeV is a reasonable one, a n d permits p r o t o n d e u t e r o n separation over the complete .energy range shown. Particles of higher energy (12-40 MeV) will also be easily identified as the multiplier response is nearly fiat at higher energies. The system resolution was typically 5 - 2 0 ~ , where the system resolution is defined as the full width at h a l f m a x i m u m o f the multiplier o u t p u t spectrum when monoenergetic particles of a single type are incident u p o n the E - dE/dx telescope. The system r e s o l u t i o n is determined primarily by the resolution of the dE/dx detector, which is influenced by the low energy threshold imposed u p o n the system. The low energy threshold determines the m a x i m u m allowable thickness of the dE/dx detector, which i n t u r n establishes the high energy limit if the dE/dx detector signal to noise ratio is to be kept within prescribed limits. The above ment i o n e d detectors set the lower energy threshold at 1.0 MeV for protons, 1.2 MeV for deuterons, 3.8 MeV for alpha particles, a n d m a i n t a i n a dE/dx resolution ( F W M H ) of 5 - 2 0 ~ over the 2-12 MeV p r o t o n a n d d e u t e r o n range or 6-18 MeV alpha-particle range. A p p r e c i a t i o n is extended to R. Chase for c o m m u n i cating his circuit design to the author. The assistance of P. K w o k in developing the formal circuit analysis is gratefully acknowledged. A p p r e c i a t i o n is also extended to the operators of the University of P e n n s y l v a n i a T a n d e m Accelerator for their helpful assistance.
References 1) M. S. Livingston and H. Bethe, Rev. Mod. Phys., 9 (1937) 245. 2) F. A. Aschenbrenner, Phys. Rev., 98 (1955) 657. 3) G. Igo and R. M. Eisberg, Rev. Sci. Instr., 25 (1954) 450. 4) B. Wolfe, A. Silverman and J. W. DeWire, Rev. Sci. Instr., 26 (1955) 504. 5) W. L. Brisco, Rev. Sci. Instr., 29 (1958) 401. 6) R. H. Stokes, Rev. Sci. Instr., 31 (1960) 768. 7) R. H. Stokes, J. A. Northrop and K. Boyer, Rev. Sci. Instr., 29 (1958) 61. 8) L. Wahlin, Nucl. Instr. and Meth., 14 (1963) 281. 9) G. Giannelliand L. Stanchi, Nucl. Instr. and Meth., g (1960)79. 10) C. H. Vincent and D. Kaine, Proc. Eighth Scintillation Counter Symposium 1962 IRE Transactions. 11) j. H. Aitken, Nucl. Instr. and Meth., 14 (1961) 343. 12) Carl E. Anderson, D. A. Bromly and M. Sachs, Nucl. Instr. and Meth., 13 (1961) 238. 13) L. G. Kuo, M. Petravi6 and B. Turko, Nucl. Instr. and Meth., 10 (1961) 53. 14) C. D. Goodman and J. Need, Phys. Rev., 110 (1958) 676. 15) D. Bodansky, R. K. Cole, W. G. Cross, C. R. Gruhn and I. Halpern. Phys. Rev., 126 (1962) 1082. 16) A. Whetstone and S. Kounosu, Rev. Sci. Instr., 33 (1962) 423. 17) R. Chase (private communication). 18) p. C. Kwok, B. S. Thesis, M. I. T. (1961) (unpublished). 19) L. W. Swenson and C. R. Gruhn, Bull. Am. Phys. Soc., 8 (1963) 356. 20) C. R. Gruhn and L. W. Swenson, Bull. Am. Phys. Soc., g (1963) 357.