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The performance of a light-pulser-operated digital stabilizer
NUCLEAR INSTRUMENTS AND METHODS 124 (I975) 235-241;
© NORTH-HOLLAND PUBLISHING CO.
T H E P E R F O R M A N C E OF A LIGHT-PULSER-OPERATED DIGITAL STABILIZER* K. G. A. PORGES Argonne National Laboratory, Applied Physics Division, 9700 South Cass Avenue, Argonne, IlL 60439, U.S.A.
Received 12 August 1974 This note describes the performance of several similar stabilizer systems intended for scintillation counting channels. In neutron time-of-flight spectrometry, the absence of strong and permanent features in the pulse height spectrum necessitates use of a light pulser for stabilization reference purposes. Such a system lends
itself to a description in terms of random walk theory, which is used here to derive the response to a step excursion in gain and the natural gain fluctuation as a function of several adjustable parameters.
1. Introduction
over the error count may be integrated and the error signal thus developed from the integral, rather than from the rate difference. In terms of servo feedback theory, this results in a servo of the second kind which can restore the channel fully to its condition before the gain shift occurred; a rate-operated error feedback signal (servo of the first kind) can only reduce the error to a small fraction of its unstabilized value. Integrating feedback however can result in an oscillating overshoot unless time constants are carefully trimmed. Each system evidently has its advantages in specific situations, as discussed in ref. 2 (which also contains a fairly extensive list of references).
A stabilizer or super-regulator is an external feedback loop through which gain instability in an analog pulse processing channel is counteracted or corrected for. A great variety of such stabilizers has been applied in two somewhat different experimental situations. One of these concerns the measurement of nuclear spectra through energy-sensitive detectors with the best obtainable resolution; the stabilizer serves to preserve the full detail of the spectrum as produced by the detector through runs over several days, and is required to counteract gradual and relatively small drifts in electronic gain. The other chief application of stabilizers is in scintillation counting work, where detection efficiency, defined by a discriminator level or window, must be maintained under often widely varying count rates and other experimental conditions which can cause relatively large channel gain changes. The latter case, of principal interest here, is exemplified by T O F neutron spectroscopy. All stabilizers require some sort of standard of comparison to develop an error signal which is fed back in paraphase at some point. A widely used stratagem which was first used by De Waard 1) compares the upper and lower half of a peak in the signal pulse height spectrum by means of a stable set of discriminator levels; the difference in count rate from windows symmetrically disposed about the peak is turned into a d c error signal through count rate meters. The error signal may be applied, as in De W a a r d ' s circuit, to the dynode voltage divider, or to a voltagecontrollable amplifier section, or to the voltage source from which the comparison levels are tapped. More* Work performed under the auspices of the U.S. Atomic Energy Commission. 235
2. Applications of digital stabilizers in neutron counting In this note, we consider the performance of a stabilizer of integrating type which produces integration by digital means: instead of count rate metering, pulses which are generated whenever the analog signal pulse falls within some specified window region are processed by a simple logic system and fed to an updown counter. The counter, as a memory device, has infinite retention, in contrast to count rate meters or analog integrators (whose retention is necessarily limited and thus requires a specific time constant choice for specific input rates). Consequently, the use of a digital memory results in uniform performance quality over a wide range of input rates. A primitive version of such a device was implemented through an up-down relay3); the availability of IC u p - d o w n sealers and logic units now makes relays, with a very limited number of positions, obsolete. Two stabilizers which feature scaler integration, but differ in other respects have been described in the recent literature4, 5). The circuit described by Lenkzsus and
236
K. G. A. P O R G E S
Rudnick 4) apphes the error signal internally to adjust the comparison levels and also corrects the levels of two other discriminators which can be set to bracket any desired region of the spectrum. The comparison levels are set to define adjacent windows of equal, adjustable width, centered on some prominent peak in the spectrum. The system has the advantage of simplicity, being completely contained in a single unit, but does require a spectrum featuring a suitable peak. The circuit described by Friese 5) uses feedback through a special amphfier whose gain can be controlled by the error signal, and also has a more complex comparison system in which two half-width windows are placed on either side of a central window. This makes the error output independent of varying background counts, superposed on the signal counts, where the background pulse-height distribution may have a slope in the vicinity of the signal peak. This advantage is necessarily bought at the cost of more complexity, as well as somewhat worse performance. Neither system can accommodate large drifts in photomultlplier gain, e.g. for an in-pile channel exposed to widely varying temperatures; for that case, it is clearly most efficacious to steer the dynode voltage, as in de Waard's original circuit1). As regards the comparison system, the absence of suitable peak structures in the pulse height spectrum of a typical organic scintillator exposed to a fast neutron flux makes the simple double window stratagem inapplicable, while the system of ref. 5 still reqmres an inflection point m the spectrum and thus performs poorly when the inflection point is not well-defined.
Moreover, in some experiments the neutron pulse height spectrum will vary from one run to the next. To accommodate these difficult conditions, it is necessary to forego regulation of the whole channel (including the scintillator) and stabilize only the photomultiplier, generally the least stable element m the transducer and analog pulse chain. This requires a light pulser, readily implemented with a LED which can produce hght flashes of nanosecond width and very stable intensity. The light flasher frequency thus becomes another adjustable parameter, independent of the signal; to secure regulation on light pulses only, a relatively straightforward sorting logic can be employed, as indicated in fig. 1 which shows how light pulser regulation might be implemented for a stabilizer similar to the unit described in ref. 4, except that it stabilizes on a single level rather than two windows. In certain in-pile neutron measurements, e.g. a "Feynman reduced variance" measurement of pile subcriticahty, it is not only crucial to maintain detection efficiency throughout a long series of runs, but moreover to keep channel deadtime a very small fraction of the count sampling time. The fractional error of the result of such a measurement varies with the inverse square root of the number of samples taken and may become barely acceptable only for 1 0 6 - 1 0 8 samples, while the time allowed for the measurement is necessarily restricted to a few hours. This leads to a required channel deadtime within, say, 50 ns. Since the comparator circuitry is not amenable to nanosecond pulses and system performance is adversely affected by the relatively strong noise level obtaining
FAST ~CHANNEL
hiv~---.--~~ "~
k
STEP AV
SIG
.J
Fig. 1. Light-pulse-driven stabilizer. PM = photomultlpher, S C I N T = scintillator, LED = light flasher, PG = pulse generator, SC = add-subtract scaler, D A C = digital to analog converter, hi = lower edge o f signal pulse window, h~ = upper edge o f signal pulse window, he = center o f light pulser peak; V = veto.
A LIGHT
DIGITAL
237
STABILIZER
=
COUNT
I
I
i
i
J
Fig. 2. Stabihzer for m i n i m u m deadtime a n d large gain excursions. F o r symbols, see fig. 1; also: H V = high voltage supply, u n regulated; R E G = internal feedback regulator; F T = fast trigger (dmcriminator).
in channels of large bandwidth, it is expedient to provide a fast channel for counting at low deadtime as well as a slow channel for regulation purposes. Both channels can be derived from a wideband preamplifier which integrates dynode signal current pulses; after some amplification pulses are clipped for the fast channel and integrated once more, to remove noise, for the stabilizer. This still leaves the fast discriminator outside the stabilization loop. However, a series of tests involving several commercial as well as ANL-designated fast trigger circuits revealed that the level stability of these units, all of which use a tunnel diode as the trigger element, is largely a function of temperature and can be satisfactorily controlled through air convection. A stabilizer which controls the photomultiplier and pulse amplifier only, through error signal-steering of the hv, is shown in fig. 2. Like the system shown in fig. 1, this unit stabilizes on a single level only; the reason for this design is discussed below. To include the fast trigger stage within the loop, one would have to work with a system as shown in fig. 1, for instance, and provide a specific attenuation factor for the error feedback to the fast trigger level; the attenuation would require adjustment to the precise shape of input pulses and thus involve a certain amount of difficulty when adapting the stabilizer to a specific photomultipher and scintillator. The system shown in fig. 2, while not quite as reliable as a loop encompassing the whole signal channel, is particularly simple and thus should lend itself to multiplexing for a number of input chan-
nels, say for a covariance reactivity measurement or for a TOF system involving a number of detectors or a large scintillator coupled to a number of photomultipliers. The basic rationale of stabilizing in TOF measurements of neutron spectra lies in the strong sensitivity of the overall detection efficiency for neutrons of specific energy to the pulse height bias and/or channel gain. The result of careful and time-consuming cahbration runs with monoenergetic neutrons, or with a known input spectrum, must be maintained for a long time, so as to apply precisely to subsequent runs with unknown spectra (which may involve different detector location, temperature environment and background, as well as widely different input rates). The flight time spectrum, in all this work, is obtained from a fast channel (usually driven by anode pulses) and a time marker generated by the accelerator; before accepting storage of a processed event, however, gating by the slow, pulse-height channel is required to eliminate PM noise and other unwanted background. Thus, the overall detection efficiency is controlled by the slow channel, which thus can be stabilized independently as shown in fig. 1. 3. Performance
The performance of stabilizers is characterized by the loop transfer function, resulting in a certain recovery speed for a step gain change, and, on the other hand, in a certain mean level of fluctuation. These characteristics are determined by a number of
238
K . G . A . PORGES
adjustable parameters such as the light pulser frequency and intensity, window width and step effect on gain. Improper adjustment evidently can result in actually worsening the performance of a count channel through the introduction of large fluctuaUons, and it is therefore necessary to obtain a quantitative understanding of the effect of adjustment on the first and second moment of the level or gain. For a pulser frequency up to perhaps 1 kHz, the system has enough time to adjust all voltage levels in response to a decision before the next test pulse. This makes the performance describable in terms of a quasi-random walk, step by step. Such a model is clearly more realistic than the customary analysis in terms of servo-feedback theory which approximates what is in reality a discontinuous process by a smooth function of the time and thereupon transforms to the frequency regime - only to have to resort once more to yet another processing step to effect a return to the digital regime, for computation. The random walk description of the stabilizer, largely based on the wellknown work of Wang and Uhlenbeck6), may thus be a useful example of a technique which can be applied in a number of other automatic process control problems, including reactor control. We assume that the reference element, the light pulser, delivers a pulse height spectrum which can be adequately described by a Gaussian law with a mean height ho and variance a 0. This spectrum is presented to the comparator, a pulse height discriminator with three levels defining two adjacent windows of equal width w above and below a center level. All levels are
tapped from a reference voltage V, such that adjustment of V adjusts each level proportionately. If the center level is originally adjusted to bisect the Gaussian pulse height spectrum exactly, then the probability that the next test pulse falls into the upper window is given by P + = ½q), where according to the usual definition, • (x) = (2/x/~)
P+ = ½[~(X+aux)
- ~(~o)3,
P- = ½[~(x-~,O
+ ~(Ao)],
pO = 1 -- l [ ~ ( x - ~ - A u x ) -4- ~ ) ( X - - A l x ) ] ,
in terms of the level increments
A.~ = (ho +w) (a/~/2ao), A,x = (ho - w) (a/x/2ao), Ao = (hoa/x/2ao). ho
ho+W
V
w
=
j'
exp ( - t 2) dt,
with x = w/x/2a o. Likewise the probability that the next pulse falls into the window, P - is equal to ½4 while the complementary probability for the pulse to fall outside both windows is given by po = ( 1 - 4 ) , as indicated in fig. 3. Supposing that the first pulse falls mto the upper window, a very small positive step correction v is added to the reference level V, whereupon all window edges are raised by a factor (1 +a), a = v/V. Thus, the apriori probabilities P+, P - , and pO are shifted:
ho. w
a=v/V
fo
/ I I I i
I I I I
I
I
( ho - w)(I -I- o)
ho(l+o)
\ I I I (ho+w)(l*
¥
I I o)
V ( I + (I)
Fig. 3. SchemaUc illustration of gain excursion wtth respect to a set of fixed levels. Pulser peak originally centered on h0; levels at h 0 + w and h 0- w sudden decrease in gain levels appear sh]fted by factor (1 + a). Sudden increase by (1 + a) of the voltage controlling all levels would have the same effect.
239
A LIGHT D I G I T A L STABILIZER
Expanding the error functions, one finds, to first order,
Introducing the time constant through the identity j=ft, re(t) ",~ mo exp ( - t / T ) ,
P+ = ½ ~ ( x ) + q - p ,
(3')
where
P- = ½~(x)+q+p,
T =
pO = 1 - ~ ( x ) - 2 q ,
½pf = ½aYf[1 - exp (-x2)].
Thus, in the limit of increasing test frequency f and correspondingly decreasing correction fraction a, the loop responds to a sudden step offset of the reference, and likewise to a sudden step offset of the channel gain, with a simple exponential following function; initially the response is somewhat faster:
where q = (axlx/z 0 exp ( - x 2 ) , and p = ay I-1 - exp ( - x 2 ) ] , in terms of the level parameters x, defined above, and y = h o / x / 2 n a o. As long as the fractional correction a is very small, the first-order treatment can be applied likewise to the general case where the reference voltage has been displaced by k positive steps; we might further suppose that this condition happens to obtain after some number j of tests. For the last test, we have, P+ = ½~ + k ( q - p ) , e ; = ½ ~ + k(q + v), P°k = 1 - ~ - 2 k q .
This leads directly to a recurrence relation for the probability W k ( j + 1) of finding the reference level k steps v above its center value V after the ( j + 1)st test, in terms of the probabilities W k - 1 (J), Wk (j), and W k ÷ l ( j ) of finding the reference voltage k - 1 , k, or k + 1 steps from V after the jth test: Wk(j + 1) = Wk(j) P°k + Wk +~ (j) Pk+~ + Wk- 1 (J) P~-x" (1)
( 1 - 2 p ) j = e -2v' {1 - [½(2p)2+½(2p) 3 + ...]j + + (2p)4 (~j z) ...} + O {(2p)S(fl)}.
(4)
For a sudden excursion 4-A G of the normal channel gain G, one finds h,(t) - h,(O) [1 +(AG/G)(1 --e-UT)],
(5)
for any particular discriminator level h,. We note that rapid restoration of initial operating conditions, i.e., a small time constant T, results from widening the window such that exp ( - x 2) ~ 0 . The sole purpose of such windows, in fact, is to discriminate against various other structural features of a pulseheight distribution when the stabilizer makes use of some particular line in the input radiation spectrum; for light pulser operation, windows can thus be dispensed with, at some saving in cost. The other factors which render recovery more rapid are best discussed in connection with the mean fluctuation, which we shall develop from the second moment of the distribution: k 2 W k ( j + 1) = ( m 2 ) j + l
Eq. (1) furnishes recurrence relations for the various moments, including the first and second, of the level probability distribution without requiring knowledge of the latter. For the first moment,
+co k W k ( j + l) = (rn)j+l , -co
= • + ( 1 - 4 p ) ( m 2 ) j + 2 q (rn)~_ 1 .
1 "~-
(I --2p) ( r e ) j ,
(2)
which can be iterated, given an initial displacement (step function) m0, to describe the probable or mean behaviour of the system j steps or tests after this initial displacement: ( m ) j = m o ( 1 - 2 p ) j ~- m o exp ( - 2 p j ) .
(3)
(6)
For initial condition Wk(O)=6k0, one finds that (m2)1 = ~ , while ( m ) l = 0. By iteration, one finds the fluctuation (rn2)j = ~ / 4 p - ( 1 - 4 p ) J ( ~ / 4 p ) .
eq. (1) yields (m)j-i.
-co
(7)
The second term arises from the somewhat artificial assumption that the level is known to be exactly zero initially; the first term represents the actual fluctuation. The fractional fluctuation of the inspection level ho amounts to [ ( r n 2) a23 "t- ---- ½(a/y) ~,
(8)
suggesting that the correction step v be made small
240
K.G.A.
and that the test light pulse be placed in the top quarter of the pulse-height range scanned, in order to maximize the natural resolution ho/tr o. The best overall performance, with a small fluctuation as well as rapid recovery from a step gain excursion, calls for small steps and a high inspection ratef. The latter is limited however by the actual system resetting speed, as well as by considerations of pile-up distortion and deadtime loss. If the test pulser frequency exceeds the system resetting rate, fluctuations will increase and an oscillatory response (overdriving) can develop. Within the resetting time of the dc circuitry, the digital system fluctuation level is quite independent of the test frequency - in contrast to analog stabihzers of De Waard type. This property makes a digital stabilizer which refers to a prominent peak in the incident radiaUon spectrum, rather than to a hght pulser, applicable to such tasks as foil counting, where the input decreases with the decay of the activity scanned and input suddenly ceases as foils are changed. When attempting to use analog stabilization for such a task, one finds that fluctuations tend to increase to the extent of throwing the windows entirely out of the peak region, with the consequence that the stabilizer drives the gain all the way up or down when the spectrum reappears. The gain shifts naturally induced in the photomultipher by rapidly changing dynode bombardment make the use of stabilization particularly appropriate for foil counting, as well as for accurate background subtraction in a precise count of some other source. To some extent, the dynode effect, which is particularly strong beyond a certain threshold, can be mimmized through the reduction of dynode voltage or the use of fewer dynodes. The former stratagem, suggested by PalevskiT), reduces the impact velocity of the electron burst and thus the energy transfer per electron; the latter stratagem was recently tested by Cohna); at the last few of a smaller number of stages the number of impacting electrons ~s evidently smaller than at the anode. An argument in favour of a smaller number of stages is the somewhat reduced effect of photomultiplier statistics. Neither method, however, can cope with large intensity changes, nor w~th slow gain fluctuations resulting from temperature variation or aging.
4. Concluding remarks The quasi-random walk treatment discussed in the preceding section, together with some general implications valid for any digitally integrating feedback
PORGES
stabilizing system, leads to the conclusion for the case of a light pulse operated stabilizer that the window logic is not required for that specific stabilizing scheme. Consequently, that feature has been dispensed with in the two versions of light pulse systems shown in figs. 1 and 2, one for general neutron counting at low or medium rates and the other for neutron counting over a wide range of rates, with minimum deadtime, and under conditions where large PM gain drift would be expected. Either system is relatively simple and could be, once designed, reproduced for $200-500; it should be considered that the complexity of the unit is considerably less than that of a typical DVM. A light display of the up-down scaler status, which adds significantly to unit cost, is not required in normal operation, but helpful in setup, testing, and troubleshooting. A practical alternative to including the light display would be to provide BCD readout to an external display, which could be shared by a number of units in a TOF system application involving a number of photomultiplier channels. A very important consideration in light flasher stabilization, which has as yet not been thoroughly explored, IS the stability of the flasher unit9). Since LED flashers deliver a narrow-band red spectrum, they will not protect a system against possible shifts in spectral sensitivity, resulting from severe temperature excursions and/or strong light input in high neutron flux levels. A very slight shift of the red sensitivity of a given photocathode can result in a strong change in output current, since photomultlpliers intended for scintillator use feature strongly sloping quantum efficiencies in the red (670 nm). Green LEDs have recently become available but deliver light with an appreciable exponential tail; while this does not interfere with a stabilizing scheme as shown in fig. 2, the long-term stability of these devices is as yet unknown and will be subjected to a planned series of tests. Any LED, being a diode, inevitably exhibits a temperature coefficient. For an application where the environmental temperature cannot be controlled, a simple series-parallel compensating network can be provided to reduce temperature sensitivity, in principle by an order of magnitude; this unit again has not as yet been fully designed and tested. Other types of light flashers, such as peanut triodes with a ZnS-coated anode, can produce strong flashes in the blue peak sensitivity region of typical photomultipliers, but have a number of drawbacks: triodes require specially stabilized anode as well as heater supplies, filament evaporation gradually deposits a dark layer on the glass envelope, thus decreasing
A LIGHT DIGITAL STABILIZER light transmission, a n d the whole unit is t o o b u l k y to fit conveniently into typical scintillator h e a d structures, thus requiring a light guide. The flash profile f r o m Z n S excitation, as processed by a t r i o d e o f relatively p o o r g a i n - b a n d w i d t h p r o d u c t , exhibits a risetime o f the o r d e r o f 1/~s a n d c o r r e s p o n d i n g tail, as well as some r a t h e r long-tailed c o m p o n e n t s typical o f ZnS. A blue filter is essential to r e m o v e filament glow. Light flashers o f this t y p e have been used with success in some low-level counting systems, a n d could p e r h a p s be a d a p t e d to n e u t r o n counting. References 1) H. de Waard, Nucleonics 13, no. 7 (1955) 36.
241
~) K. G. Porges and A. DeVolpl, ANL-7210 (1966) 308 (unpublished). 3) K. G. Porges and J. Blorkland, Proc. Syrnp. on Nuclear electronics (ENEA, 1964) p. 811. 4) F. R. Lenkszus and S. J. Rudnlck, IEEE Trans. Nucl. SCl. NS-17, no. 7 (1970). 5) T. Friese, Proc. Ispra Nuclear Electromcs Conf. Euratom, (May 1969) p. 221. 6) Mmg Chen Wang and G. E. Uhlenbeck, Rev. Mod. Phys. 17 (1945) 323. 7) H. Palevskl, private communication (1958). s) C. E. Cohn, Reducing gain shifts in photomultipher tubes, (to be pubhshed in IEEE Trans. Nucl. Scl.). a) j. H. Thorrgate and P. T. Purdue, Nucl. Instr. and Meth. 105 (1972) 57.
© NORTH-HOLLAND PUBLISHING CO.
T H E P E R F O R M A N C E OF A LIGHT-PULSER-OPERATED DIGITAL STABILIZER* K. G. A. PORGES Argonne National Laboratory, Applied Physics Division, 9700 South Cass Avenue, Argonne, IlL 60439, U.S.A.
Received 12 August 1974 This note describes the performance of several similar stabilizer systems intended for scintillation counting channels. In neutron time-of-flight spectrometry, the absence of strong and permanent features in the pulse height spectrum necessitates use of a light pulser for stabilization reference purposes. Such a system lends
itself to a description in terms of random walk theory, which is used here to derive the response to a step excursion in gain and the natural gain fluctuation as a function of several adjustable parameters.
1. Introduction
over the error count may be integrated and the error signal thus developed from the integral, rather than from the rate difference. In terms of servo feedback theory, this results in a servo of the second kind which can restore the channel fully to its condition before the gain shift occurred; a rate-operated error feedback signal (servo of the first kind) can only reduce the error to a small fraction of its unstabilized value. Integrating feedback however can result in an oscillating overshoot unless time constants are carefully trimmed. Each system evidently has its advantages in specific situations, as discussed in ref. 2 (which also contains a fairly extensive list of references).
A stabilizer or super-regulator is an external feedback loop through which gain instability in an analog pulse processing channel is counteracted or corrected for. A great variety of such stabilizers has been applied in two somewhat different experimental situations. One of these concerns the measurement of nuclear spectra through energy-sensitive detectors with the best obtainable resolution; the stabilizer serves to preserve the full detail of the spectrum as produced by the detector through runs over several days, and is required to counteract gradual and relatively small drifts in electronic gain. The other chief application of stabilizers is in scintillation counting work, where detection efficiency, defined by a discriminator level or window, must be maintained under often widely varying count rates and other experimental conditions which can cause relatively large channel gain changes. The latter case, of principal interest here, is exemplified by T O F neutron spectroscopy. All stabilizers require some sort of standard of comparison to develop an error signal which is fed back in paraphase at some point. A widely used stratagem which was first used by De Waard 1) compares the upper and lower half of a peak in the signal pulse height spectrum by means of a stable set of discriminator levels; the difference in count rate from windows symmetrically disposed about the peak is turned into a d c error signal through count rate meters. The error signal may be applied, as in De W a a r d ' s circuit, to the dynode voltage divider, or to a voltagecontrollable amplifier section, or to the voltage source from which the comparison levels are tapped. More* Work performed under the auspices of the U.S. Atomic Energy Commission. 235
2. Applications of digital stabilizers in neutron counting In this note, we consider the performance of a stabilizer of integrating type which produces integration by digital means: instead of count rate metering, pulses which are generated whenever the analog signal pulse falls within some specified window region are processed by a simple logic system and fed to an updown counter. The counter, as a memory device, has infinite retention, in contrast to count rate meters or analog integrators (whose retention is necessarily limited and thus requires a specific time constant choice for specific input rates). Consequently, the use of a digital memory results in uniform performance quality over a wide range of input rates. A primitive version of such a device was implemented through an up-down relay3); the availability of IC u p - d o w n sealers and logic units now makes relays, with a very limited number of positions, obsolete. Two stabilizers which feature scaler integration, but differ in other respects have been described in the recent literature4, 5). The circuit described by Lenkzsus and
236
K. G. A. P O R G E S
Rudnick 4) apphes the error signal internally to adjust the comparison levels and also corrects the levels of two other discriminators which can be set to bracket any desired region of the spectrum. The comparison levels are set to define adjacent windows of equal, adjustable width, centered on some prominent peak in the spectrum. The system has the advantage of simplicity, being completely contained in a single unit, but does require a spectrum featuring a suitable peak. The circuit described by Friese 5) uses feedback through a special amphfier whose gain can be controlled by the error signal, and also has a more complex comparison system in which two half-width windows are placed on either side of a central window. This makes the error output independent of varying background counts, superposed on the signal counts, where the background pulse-height distribution may have a slope in the vicinity of the signal peak. This advantage is necessarily bought at the cost of more complexity, as well as somewhat worse performance. Neither system can accommodate large drifts in photomultlplier gain, e.g. for an in-pile channel exposed to widely varying temperatures; for that case, it is clearly most efficacious to steer the dynode voltage, as in de Waard's original circuit1). As regards the comparison system, the absence of suitable peak structures in the pulse height spectrum of a typical organic scintillator exposed to a fast neutron flux makes the simple double window stratagem inapplicable, while the system of ref. 5 still reqmres an inflection point m the spectrum and thus performs poorly when the inflection point is not well-defined.
Moreover, in some experiments the neutron pulse height spectrum will vary from one run to the next. To accommodate these difficult conditions, it is necessary to forego regulation of the whole channel (including the scintillator) and stabilize only the photomultiplier, generally the least stable element m the transducer and analog pulse chain. This requires a light pulser, readily implemented with a LED which can produce hght flashes of nanosecond width and very stable intensity. The light flasher frequency thus becomes another adjustable parameter, independent of the signal; to secure regulation on light pulses only, a relatively straightforward sorting logic can be employed, as indicated in fig. 1 which shows how light pulser regulation might be implemented for a stabilizer similar to the unit described in ref. 4, except that it stabilizes on a single level rather than two windows. In certain in-pile neutron measurements, e.g. a "Feynman reduced variance" measurement of pile subcriticahty, it is not only crucial to maintain detection efficiency throughout a long series of runs, but moreover to keep channel deadtime a very small fraction of the count sampling time. The fractional error of the result of such a measurement varies with the inverse square root of the number of samples taken and may become barely acceptable only for 1 0 6 - 1 0 8 samples, while the time allowed for the measurement is necessarily restricted to a few hours. This leads to a required channel deadtime within, say, 50 ns. Since the comparator circuitry is not amenable to nanosecond pulses and system performance is adversely affected by the relatively strong noise level obtaining
FAST ~CHANNEL
hiv~---.--~~ "~
k
STEP AV
SIG
.J
Fig. 1. Light-pulse-driven stabilizer. PM = photomultlpher, S C I N T = scintillator, LED = light flasher, PG = pulse generator, SC = add-subtract scaler, D A C = digital to analog converter, hi = lower edge o f signal pulse window, h~ = upper edge o f signal pulse window, he = center o f light pulser peak; V = veto.
A LIGHT
DIGITAL
237
STABILIZER
=
COUNT
I
I
i
i
J
Fig. 2. Stabihzer for m i n i m u m deadtime a n d large gain excursions. F o r symbols, see fig. 1; also: H V = high voltage supply, u n regulated; R E G = internal feedback regulator; F T = fast trigger (dmcriminator).
in channels of large bandwidth, it is expedient to provide a fast channel for counting at low deadtime as well as a slow channel for regulation purposes. Both channels can be derived from a wideband preamplifier which integrates dynode signal current pulses; after some amplification pulses are clipped for the fast channel and integrated once more, to remove noise, for the stabilizer. This still leaves the fast discriminator outside the stabilization loop. However, a series of tests involving several commercial as well as ANL-designated fast trigger circuits revealed that the level stability of these units, all of which use a tunnel diode as the trigger element, is largely a function of temperature and can be satisfactorily controlled through air convection. A stabilizer which controls the photomultiplier and pulse amplifier only, through error signal-steering of the hv, is shown in fig. 2. Like the system shown in fig. 1, this unit stabilizes on a single level only; the reason for this design is discussed below. To include the fast trigger stage within the loop, one would have to work with a system as shown in fig. 1, for instance, and provide a specific attenuation factor for the error feedback to the fast trigger level; the attenuation would require adjustment to the precise shape of input pulses and thus involve a certain amount of difficulty when adapting the stabilizer to a specific photomultipher and scintillator. The system shown in fig. 2, while not quite as reliable as a loop encompassing the whole signal channel, is particularly simple and thus should lend itself to multiplexing for a number of input chan-
nels, say for a covariance reactivity measurement or for a TOF system involving a number of detectors or a large scintillator coupled to a number of photomultipliers. The basic rationale of stabilizing in TOF measurements of neutron spectra lies in the strong sensitivity of the overall detection efficiency for neutrons of specific energy to the pulse height bias and/or channel gain. The result of careful and time-consuming cahbration runs with monoenergetic neutrons, or with a known input spectrum, must be maintained for a long time, so as to apply precisely to subsequent runs with unknown spectra (which may involve different detector location, temperature environment and background, as well as widely different input rates). The flight time spectrum, in all this work, is obtained from a fast channel (usually driven by anode pulses) and a time marker generated by the accelerator; before accepting storage of a processed event, however, gating by the slow, pulse-height channel is required to eliminate PM noise and other unwanted background. Thus, the overall detection efficiency is controlled by the slow channel, which thus can be stabilized independently as shown in fig. 1. 3. Performance
The performance of stabilizers is characterized by the loop transfer function, resulting in a certain recovery speed for a step gain change, and, on the other hand, in a certain mean level of fluctuation. These characteristics are determined by a number of
238
K . G . A . PORGES
adjustable parameters such as the light pulser frequency and intensity, window width and step effect on gain. Improper adjustment evidently can result in actually worsening the performance of a count channel through the introduction of large fluctuaUons, and it is therefore necessary to obtain a quantitative understanding of the effect of adjustment on the first and second moment of the level or gain. For a pulser frequency up to perhaps 1 kHz, the system has enough time to adjust all voltage levels in response to a decision before the next test pulse. This makes the performance describable in terms of a quasi-random walk, step by step. Such a model is clearly more realistic than the customary analysis in terms of servo-feedback theory which approximates what is in reality a discontinuous process by a smooth function of the time and thereupon transforms to the frequency regime - only to have to resort once more to yet another processing step to effect a return to the digital regime, for computation. The random walk description of the stabilizer, largely based on the wellknown work of Wang and Uhlenbeck6), may thus be a useful example of a technique which can be applied in a number of other automatic process control problems, including reactor control. We assume that the reference element, the light pulser, delivers a pulse height spectrum which can be adequately described by a Gaussian law with a mean height ho and variance a 0. This spectrum is presented to the comparator, a pulse height discriminator with three levels defining two adjacent windows of equal width w above and below a center level. All levels are
tapped from a reference voltage V, such that adjustment of V adjusts each level proportionately. If the center level is originally adjusted to bisect the Gaussian pulse height spectrum exactly, then the probability that the next test pulse falls into the upper window is given by P + = ½q), where according to the usual definition, • (x) = (2/x/~)
P+ = ½[~(X+aux)
- ~(~o)3,
P- = ½[~(x-~,O
+ ~(Ao)],
pO = 1 -- l [ ~ ( x - ~ - A u x ) -4- ~ ) ( X - - A l x ) ] ,
in terms of the level increments
A.~ = (ho +w) (a/~/2ao), A,x = (ho - w) (a/x/2ao), Ao = (hoa/x/2ao). ho
ho+W
V
w
=
j'
exp ( - t 2) dt,
with x = w/x/2a o. Likewise the probability that the next pulse falls into the window, P - is equal to ½4 while the complementary probability for the pulse to fall outside both windows is given by po = ( 1 - 4 ) , as indicated in fig. 3. Supposing that the first pulse falls mto the upper window, a very small positive step correction v is added to the reference level V, whereupon all window edges are raised by a factor (1 +a), a = v/V. Thus, the apriori probabilities P+, P - , and pO are shifted:
ho. w
a=v/V
fo
/ I I I i
I I I I
I
I
( ho - w)(I -I- o)
ho(l+o)
\ I I I (ho+w)(l*
¥
I I o)
V ( I + (I)
Fig. 3. SchemaUc illustration of gain excursion wtth respect to a set of fixed levels. Pulser peak originally centered on h0; levels at h 0 + w and h 0- w sudden decrease in gain levels appear sh]fted by factor (1 + a). Sudden increase by (1 + a) of the voltage controlling all levels would have the same effect.
239
A LIGHT D I G I T A L STABILIZER
Expanding the error functions, one finds, to first order,
Introducing the time constant through the identity j=ft, re(t) ",~ mo exp ( - t / T ) ,
P+ = ½ ~ ( x ) + q - p ,
(3')
where
P- = ½~(x)+q+p,
T =
pO = 1 - ~ ( x ) - 2 q ,
½pf = ½aYf[1 - exp (-x2)].
Thus, in the limit of increasing test frequency f and correspondingly decreasing correction fraction a, the loop responds to a sudden step offset of the reference, and likewise to a sudden step offset of the channel gain, with a simple exponential following function; initially the response is somewhat faster:
where q = (axlx/z 0 exp ( - x 2 ) , and p = ay I-1 - exp ( - x 2 ) ] , in terms of the level parameters x, defined above, and y = h o / x / 2 n a o. As long as the fractional correction a is very small, the first-order treatment can be applied likewise to the general case where the reference voltage has been displaced by k positive steps; we might further suppose that this condition happens to obtain after some number j of tests. For the last test, we have, P+ = ½~ + k ( q - p ) , e ; = ½ ~ + k(q + v), P°k = 1 - ~ - 2 k q .
This leads directly to a recurrence relation for the probability W k ( j + 1) of finding the reference level k steps v above its center value V after the ( j + 1)st test, in terms of the probabilities W k - 1 (J), Wk (j), and W k ÷ l ( j ) of finding the reference voltage k - 1 , k, or k + 1 steps from V after the jth test: Wk(j + 1) = Wk(j) P°k + Wk +~ (j) Pk+~ + Wk- 1 (J) P~-x" (1)
( 1 - 2 p ) j = e -2v' {1 - [½(2p)2+½(2p) 3 + ...]j + + (2p)4 (~j z) ...} + O {(2p)S(fl)}.
(4)
For a sudden excursion 4-A G of the normal channel gain G, one finds h,(t) - h,(O) [1 +(AG/G)(1 --e-UT)],
(5)
for any particular discriminator level h,. We note that rapid restoration of initial operating conditions, i.e., a small time constant T, results from widening the window such that exp ( - x 2) ~ 0 . The sole purpose of such windows, in fact, is to discriminate against various other structural features of a pulseheight distribution when the stabilizer makes use of some particular line in the input radiation spectrum; for light pulser operation, windows can thus be dispensed with, at some saving in cost. The other factors which render recovery more rapid are best discussed in connection with the mean fluctuation, which we shall develop from the second moment of the distribution: k 2 W k ( j + 1) = ( m 2 ) j + l
Eq. (1) furnishes recurrence relations for the various moments, including the first and second, of the level probability distribution without requiring knowledge of the latter. For the first moment,
+co k W k ( j + l) = (rn)j+l , -co
= • + ( 1 - 4 p ) ( m 2 ) j + 2 q (rn)~_ 1 .
1 "~-
(I --2p) ( r e ) j ,
(2)
which can be iterated, given an initial displacement (step function) m0, to describe the probable or mean behaviour of the system j steps or tests after this initial displacement: ( m ) j = m o ( 1 - 2 p ) j ~- m o exp ( - 2 p j ) .
(3)
(6)
For initial condition Wk(O)=6k0, one finds that (m2)1 = ~ , while ( m ) l = 0. By iteration, one finds the fluctuation (rn2)j = ~ / 4 p - ( 1 - 4 p ) J ( ~ / 4 p ) .
eq. (1) yields (m)j-i.
-co
(7)
The second term arises from the somewhat artificial assumption that the level is known to be exactly zero initially; the first term represents the actual fluctuation. The fractional fluctuation of the inspection level ho amounts to [ ( r n 2) a23 "t- ---- ½(a/y) ~,
(8)
suggesting that the correction step v be made small
240
K.G.A.
and that the test light pulse be placed in the top quarter of the pulse-height range scanned, in order to maximize the natural resolution ho/tr o. The best overall performance, with a small fluctuation as well as rapid recovery from a step gain excursion, calls for small steps and a high inspection ratef. The latter is limited however by the actual system resetting speed, as well as by considerations of pile-up distortion and deadtime loss. If the test pulser frequency exceeds the system resetting rate, fluctuations will increase and an oscillatory response (overdriving) can develop. Within the resetting time of the dc circuitry, the digital system fluctuation level is quite independent of the test frequency - in contrast to analog stabihzers of De Waard type. This property makes a digital stabilizer which refers to a prominent peak in the incident radiaUon spectrum, rather than to a hght pulser, applicable to such tasks as foil counting, where the input decreases with the decay of the activity scanned and input suddenly ceases as foils are changed. When attempting to use analog stabilization for such a task, one finds that fluctuations tend to increase to the extent of throwing the windows entirely out of the peak region, with the consequence that the stabilizer drives the gain all the way up or down when the spectrum reappears. The gain shifts naturally induced in the photomultipher by rapidly changing dynode bombardment make the use of stabilization particularly appropriate for foil counting, as well as for accurate background subtraction in a precise count of some other source. To some extent, the dynode effect, which is particularly strong beyond a certain threshold, can be mimmized through the reduction of dynode voltage or the use of fewer dynodes. The former stratagem, suggested by PalevskiT), reduces the impact velocity of the electron burst and thus the energy transfer per electron; the latter stratagem was recently tested by Cohna); at the last few of a smaller number of stages the number of impacting electrons ~s evidently smaller than at the anode. An argument in favour of a smaller number of stages is the somewhat reduced effect of photomultiplier statistics. Neither method, however, can cope with large intensity changes, nor w~th slow gain fluctuations resulting from temperature variation or aging.
4. Concluding remarks The quasi-random walk treatment discussed in the preceding section, together with some general implications valid for any digitally integrating feedback
PORGES
stabilizing system, leads to the conclusion for the case of a light pulse operated stabilizer that the window logic is not required for that specific stabilizing scheme. Consequently, that feature has been dispensed with in the two versions of light pulse systems shown in figs. 1 and 2, one for general neutron counting at low or medium rates and the other for neutron counting over a wide range of rates, with minimum deadtime, and under conditions where large PM gain drift would be expected. Either system is relatively simple and could be, once designed, reproduced for $200-500; it should be considered that the complexity of the unit is considerably less than that of a typical DVM. A light display of the up-down scaler status, which adds significantly to unit cost, is not required in normal operation, but helpful in setup, testing, and troubleshooting. A practical alternative to including the light display would be to provide BCD readout to an external display, which could be shared by a number of units in a TOF system application involving a number of photomultiplier channels. A very important consideration in light flasher stabilization, which has as yet not been thoroughly explored, IS the stability of the flasher unit9). Since LED flashers deliver a narrow-band red spectrum, they will not protect a system against possible shifts in spectral sensitivity, resulting from severe temperature excursions and/or strong light input in high neutron flux levels. A very slight shift of the red sensitivity of a given photocathode can result in a strong change in output current, since photomultlpliers intended for scintillator use feature strongly sloping quantum efficiencies in the red (670 nm). Green LEDs have recently become available but deliver light with an appreciable exponential tail; while this does not interfere with a stabilizing scheme as shown in fig. 2, the long-term stability of these devices is as yet unknown and will be subjected to a planned series of tests. Any LED, being a diode, inevitably exhibits a temperature coefficient. For an application where the environmental temperature cannot be controlled, a simple series-parallel compensating network can be provided to reduce temperature sensitivity, in principle by an order of magnitude; this unit again has not as yet been fully designed and tested. Other types of light flashers, such as peanut triodes with a ZnS-coated anode, can produce strong flashes in the blue peak sensitivity region of typical photomultipliers, but have a number of drawbacks: triodes require specially stabilized anode as well as heater supplies, filament evaporation gradually deposits a dark layer on the glass envelope, thus decreasing
A LIGHT DIGITAL STABILIZER light transmission, a n d the whole unit is t o o b u l k y to fit conveniently into typical scintillator h e a d structures, thus requiring a light guide. The flash profile f r o m Z n S excitation, as processed by a t r i o d e o f relatively p o o r g a i n - b a n d w i d t h p r o d u c t , exhibits a risetime o f the o r d e r o f 1/~s a n d c o r r e s p o n d i n g tail, as well as some r a t h e r long-tailed c o m p o n e n t s typical o f ZnS. A blue filter is essential to r e m o v e filament glow. Light flashers o f this t y p e have been used with success in some low-level counting systems, a n d could p e r h a p s be a d a p t e d to n e u t r o n counting. References 1) H. de Waard, Nucleonics 13, no. 7 (1955) 36.
241
~) K. G. Porges and A. DeVolpl, ANL-7210 (1966) 308 (unpublished). 3) K. G. Porges and J. Blorkland, Proc. Syrnp. on Nuclear electronics (ENEA, 1964) p. 811. 4) F. R. Lenkszus and S. J. Rudnlck, IEEE Trans. Nucl. SCl. NS-17, no. 7 (1970). 5) T. Friese, Proc. Ispra Nuclear Electromcs Conf. Euratom, (May 1969) p. 221. 6) Mmg Chen Wang and G. E. Uhlenbeck, Rev. Mod. Phys. 17 (1945) 323. 7) H. Palevskl, private communication (1958). s) C. E. Cohn, Reducing gain shifts in photomultipher tubes, (to be pubhshed in IEEE Trans. Nucl. Scl.). a) j. H. Thorrgate and P. T. Purdue, Nucl. Instr. and Meth. 105 (1972) 57.