A system for stabilizing the efficiency of scintillation detectors with weak photocathode illumination

NUCLEAR

INSTRUMENTS

AND

METHODS

77 (197o)

lt2--t24;

©

NORTH-HOLLAND

PUBLISHING

CO.

A SYSTEM F O R S T A B I L I Z I N G T H E E F F I C I E N C Y OF S C I N T I L L A T I O N D E T E C T O R S W I T H WEAK P H O T O C A T H O D E I L L U M I N A T I O N J. S. H E W l T T * a n d J. W A L K E R

Department of Physics, University of Birmingham, Birmingham 15, England Received 2 September 1969 A system for stabilizing the effective bias level in a large class of scintillation detectors to within 0.1% is described in detail. The system, which e n c o m p a s s e s all drift-prone c o m p o n e n t s in the feed-back loop, including the operating discriminator, employs a stable pulsed light source to generate the reference line in the scintillation spectrum. T h e r m i s t o r s driven by binary signals provide the highly stable feed-back coupling which is essential w h e n the reference line is severely broadened due to photo-

electron fluctuations a c c o m p a n y i n g weak p h o t o c a t h o d e illumination. This requirement is given a quantitative basis in the control theory presented. T h e analysis also permits the prediction of the stabilization factor, stabilization rate, a n d statistical fluctuations for different detectors to which the stabilizer m a y be coupled. The analytical results m a y also describe other stabilizers obeying proportional control theory, including proportional control spectrometer stabilizers.

1. Introduction

Under these circumstances the distribution of reference pulses may even overlap appreciably with the pulseheight spectrum of the photo-tube noise. These conditions place stringent demands on the stabilizing circuits and on the reference pulse source, as will be explained later in this paper. Although one might expect the instabilities from photomultiplier fatigue 4) to be minimal under conditions of small photomultiplier current, unwanted intense radiation often contributes intermittently to fatigue as, for example, during accelerator bursts. The present paper describes a system which has greatly improved the stability of several different types of scintillation detector operated in the biased mode, including some with low photocathode illumination. The reference peak is generated in the scintillation spectrum by means of a highly-stable pulsed light source 5) coupled to the detector optical system with fibre-optical light-guides. This facility enhances the versatility of the system because it can be applied to a variety of detectors and operating environments. The stabilization loop encompasses all system components, including the discriminator used to set the bias level for the detection of wanted events. The system dynamics are described by proportional control with phase lag. The main advantages of systems obeying proportional control 2) over those obeying integral control 3) (our classifications) are that they can withstand gross gain changes without risk of losing control permanently, and the rate of recovery after a gain jump is independent of the reference pulse rate. Proportional control, moreover, has simpler circuits and is therefore likely to be more reliable and less costly, important considerations in multi-detector arrangements. One disadvantage of proportional

In the two decades since the first 1) reported application of servo-mechanism principles to the stabilization of nuclear detection systems, a number of variations of the original concept have appeared in the literatureZ'3). Most of the developments described have concentrated on stabilizing the calibration of scintillation or solid state spectrometers, while little attention has been paid specifically to stabilizing the efficiency of those scintillation detectors which are simply biased as, for example, in proton-recoil detectors for fast neutrons, in lithium or boron-loaded neutron detectors of glass or plastic, and in other scintillation detectors for measuring precisely the intensity of radiation of known quality. Most of these detectors produce a continuous pulse spectrum and therefore have drift-sensitive bias characteristics but even a nominal line spectrum may be rendered similarly sensitive by broadening as a result of low light collection. Additional complications in the stabilization problem are apparent when the illumination of the photocathode is so low that only a few photoelectrons are produced in each event. This condition is present in detectors for measuring low-energy radiation (e.g. from tritium or carbon-14), in the detection of low-energy 12erenkov radiation, or in systems where light collection efficiency is necessarily low. For these detectors a reference line, when superimposed on the scintillation spectrum at a point corresponding to the desired bias level (as required for comprehensive stabilization), becomes severely broadened as a result of statistical fluctuations in the number of photoelectrons prodtmed. * Present address: D e p a r t m e n t of Physics, University of Toronto.

112

STABILIZING THE EFFICIENCY OF SCINTILLATION DETECTORS

residual drift has been virtually eliminated from the present system t h r o u g h the use of circuits in which the heating elements o f thermistors incorporated in the gain controllers are governed by digitally controlled binary wave-forms in such a manner that the most important drift effects cancel and operation is at the same time rendered independent of the reference pulse rate. The remainder of this paper describes the system and its operation and performance. The

control is that drifts occurring in normal system components result in a finite residual drift which, however, can be made arbitrarily small by increasing the feed-back gain. It will be shown in section 3.6 that the previous proportional control systems, having been designed to stabilize spectrometers would, in general, be vulnerable to drifts in the feed-back components themselves if applied to bias stabilization when the reference peak is broadened. This source of FROM EMITTER o FOLLOWER

~ A M P l

1~--

~

TO MAIN AMPLIFIER -

I ~

~ "f

/

I P

'

"

FROM DISCRIMINATOR

TD

DR VER

!

I

I

~

I BINARY

r \

-

No° : l N

I

TO TRIGGER ~ LIGHT SOURCE

~

l

_1 .

| L--:

No I

~ ~

I

.

ET

I

]

I~

~/

[

I I IFLZP~FLORI L .... ]

I I FLIP-FLOP

IVARIASLEI I DELAY

VARIABLEI DELAY I

I ~

I ~

h ] r MULTIYIBRATOR~__________~._~FLIP_FLOPI A

I

TO SCALER

|

SE

~ ~I-~ Z I I 8INASY THERMISTOR 0 ~ / I ~ - - -BR,VEF~v'' ~ NOR ~/ A ~G L

113

[ NOI ::~

~--

/':v~

I No2

I

I

I

> ~ - ~

No 3

Fig. 1. Block diagram of stabilizing system.

I] A~ fl 11 rl 811 II 11 fl C111 11 11 DJh 11 I-I#l /151 ILl El 11 11 M I] F_n

J]

I1

11

I1

0 R

I-1 n fl

n

11

N

rl LIGHT SOURCE TRIGGER

FI

n

FL

I1 J-1 i1

I1

I"I I"I I-I 0

H

[~

I

I

HI

I

I ........

I I

I

I

1--

G ..1

__

~ _K_---I KJ - - - - - ]

LJ q o] ~-1

I-I--

I--1 __L___ I I

I

I I

I-I--

0

DISCRIMINATOR OUTPUT ANTI-COIN COIN

_

~77L___ I-------I ,CURRENT TO L------.--JLFEEDBAC K THERMISTOR _

I

I

---L_~J'CLJR RENT TO I .... IINPUT THERMISTOR

Fig. 2. Schematic of wave forms generated in the stabilizer by a representative number of reference pulses. Pulse widths in waveforms A-F have been exaggerated to illustrate role of variable delays.

114

J. S. H E W I T T

control theory used in section 3 to analyse the system and to interpret the tests on it is sufficiently general to be applied to any proportional control stabilizers2).

A N D J. W A L K E R

Vo-V' J{ zo E(J-V' Zsfz/

[

,o

] GV___2

vL

Z'lm ,

2. The system 2.1. DESCRIPTIONOF OPERATION The block diagram of the stabilizer system is shown in fig. 1 and its operation can be best understood by referring to the wave-form diagrams in fig. 2. The multi-vibrator periodically triggers the pulsed light source 5) used as reference, and also operates the coincidence and anti-coincidence gates which separate the nuclear counts from the reference pulses. The discriminator bias-level is set initially to accept about 50% of the reference pulses, the reference source intensity having been adjusted to peak at the desired bias level. Each coincidence count, which corresponds to the appearance of a reference pulse above the discriminator level, alternately sets the two driver binaries, while signal B resets any driver binary left in the set state at the instant when another reference pulse can be expected. (For this, the delay number 1 must be adjusted so that signal B determines the rise of F). This mode of operation yields, at the output of the OR gate, a binary signal whose mean is proportional to the fraction of reference pulses exceeding bias level and operation is therefore independent of the reference pulse rate. The current analogue of the binary signal is used to control the heat supplied to the indirectly heated thermistor serving as the feed-back element in the control stage, which has an operational amplifier configuration. Correspondingly, the output of the NOR gate, being complementary to that from the OR gate, controls the heat supplied to the input element of the controlled stage. For thermistors with negative thermal coefficients of resistivity, both thermistors contribute to the negative feed-back of the stabilized system, but the effects of ambient temperature changes and of aging in the thermistors and their driver circuits cancel, as do the effects of signal heating. The smoothing time constant of the feed-back network is the 18 sec thermal time constant of the thermistors. The feed-back gain of the system can be increased by adding more gain controlled stages with the signal leads in series and the heaters in parallel. 2.2. CIRCUITS The stabilizing unit is composed of standard logic units, such as binaries and coincidence gates, and some analogue circuits of special design. Details of only the analogue components will be given.

~] AMPLIFIER CURRENTI~ OF GAIN G

I ! i

f

Fig. 3. Equivalent circuit for the controlled stage.

2.2.1. Controlled stage In order that the controlled stage should perform as described, care was taken in the design to ensure that the gain would follow the ratio of the thermistor values over the signal frequency range of interest. It was important, furthermore, that steps should be taken to ensure that drift, and the corrective action, should have little effect on the shape of the pulse being processed. This condition, intended to reduce the sensitiv'ty of the stabilizer performance to imperfect simulation of phosphor pulses by the light pulser, is expected to be well approximated if the discharge time of the phototube anode is large compared with the duration of both the phosphor and the reference light-pulses, and if the differentiation time-constant in the main amplifier is of the same order as the discharge time. To be consistent with this scheme, the controlled stage must possess a band-width adequate to transmit the pulses to the main amplifier with good fidelity. To gain a quantitative insight into the design requirements, an expression for the overall gain of the controlled stage has been derived. The model on which the derivation was based is shown in fig. 3, where Z' is the input impedance of the current amplifier of gain G, and Z s, Z~, Z0 and ZL are, respectively, the impedances of the source Eg, the input thermistor circuit, the feed-back thermistor circuit, and the load. The current amplifier was chosen for this model since it is most suitable for representing the transistor amplifier in which the characteristically low impedances are compatible with the operating impedances ( ~ l k~) of the thermistors. It is, furthermore, advantageous to use low impedance circuits to minimize the coupling through the 20 pF capacitance between the iheating wave-form and the signal circuits of the thermistor. Win fig. 3, current contilmity relations at the input

STABILIZING THE EFFICIENCY OF SCINTILLATION DETECTORS and output of the current amplifier are: V'

Eg-

V'

Z'

Zs-}- Z i

Vo -

V'

(la)

Z0

and 6 v' --

Z'

-

Vo + Vo - V' -

ZL

-

(lb)

Z0

Whence, by eliminating V' and assuming that the amplifier inverts polarity, we can obtain the overall gain for the circuit: Vo Eg

Zo Zi

1+

three C64 transistors* form a dc coupled amplifier. The dc feed-back loop provided by the 56k is intended to preserve the bias conditions in the presence of high count rates. The thermistors used are of type B55'. The 16/tF capacitors in series with the thermistors are large enough for the combinations to appear purely resistive to pulses of up to 20/~s duration. The amplifier has a current gain of approximately 2000 and the output impedance is a few tens of ohms. Applying the values to eq. (2) yields a coefficient of Zo/Z i within 0.1% of unity. The device responds linearly to pulses up to +200 mV in amplitude and the rise time is about 1 0 0 ns.

1+

(2)

+[(1 +Z 7

115

Zs+Zi/

+ZLJJILZ'

In general, the Z's and G are complex (i.e. they contain phase information), and are frequency dependent. It is clear from an inspection ofeq. (2) that the overall voltage gain is proportional to Zo/Zi only if the coefficients of -Zo/Zi can be made to approximate unity for all important frequencies. After deciding on the operating values for the thermistors, it follows from further inspection of eq. (2) that the impedence of the source driving any of the cascaded stages must be small, and that an inverting amplifier of considerable gain is essential. The controlled stage circuit is given in fig. 4. The

-¢vwvvv,

B55

2.2.2. The thermistor driver The thermistor driver, for which the circuit is given in fig. 5, supplies current to a pair of thermistor heaters connected in series if operated by one of the gates shown. The voltage across the heating elements is determined by the OAZ 200Zener diode +. If the pre-set potentiometer is adjusted to give a mean collector current in the O.C. 139 transistor of 20 mA, the Zener potential is about 5.4 V which produces 19 mA rms current in the thermistor heaters for a counting fraction of 50%. The driver is designed for use with driver binaries whose collectors swing between - 3 V and the supply voltage. When the driver is turned off, the base-emitter junction is reverse biased. The mean-voltage monitor is fed to a protection circuit.

* Supplied by S.G.S. Fairchild Ltd. ? Supplied by Standard Telephones and Cables Ltd. Supplied by Mullard Ltd.

16uf. II*

56K

r

_L

75

i6"8 K ~f. 11~750

o

Output

t lO0 16of. BSS _ |/+11 II

IlK

I0 pf. //

~.64

Input

!f'~O

O.luf.

t~ - 16uf, 12 K

47~ 560

T

[email protected].

OAZ200

Fig. 4. Circuit diagram for the controlled stage.

-IOVDC,

116

J. S. H E W I T T

NOR. GATE

AND

"'01~" G~TE

J.

WALKER

MEAN- VO LTAGE MONITOR

DRIVER

- I 0 VDC. F r driver

~

C

...4,

II I

.\

I

680

A d~r'~'~r

_ , ~ 3.9 K Pro tection i r e l ~ i

@

0CI39

"1 J

o-vvyv j j,,,

r

'

: ,oo' °Az Thcmtstor hcat¢ r s.

_1_

Fig. 5. Circuit diagram for a thermistor driver showing the OR gate and the NOR gate.

-I0 v. ÷

6.3 VAC (

O

Prom meancurrent monitor,. 5K

S

x¢ SCHMITT TRIGGER

-- -IOVDC

I RELAYS or L nor L~'- To gates

Fig. 6. Schematic of the protection circuit. 2.2.3. Protection circuit For maximum loop gain per controlled stage, the thermistors are operated at nearly their maximum heater current. Accordingly, a counting fraction exceeding 55% will produce excessive current in the number 2 thermistor and a value less than 45% will cause excessive current in the number 1 thermistor. Thus, a protection circuit has been incorporated to make the thermistor drivers inoperative for a counting fraction lying outside these limits. This action also eliminates the possibility of unbalanced aging between the thermistors and the heating circuits. The protection circuit is shown schematically in fig. 6. The outputs from the mean-voltage monitors of the thermistor drivers are connected to the 5k potentiometer which is adjusted so that if the rated current in any of the thermistors is exceeded, the Schmitt trigger performs the following operations by energizing the set of relays shown:

I. Breaks the earthing connections and thereby renders the gates incapable of turning on the thermistor drivers. 2. Provides a dummy input to the trigger circuit. After the canse of the "trip" is removed, this input is disconnected by momentarily opening switch S. 3. Disconnects the front-panel indicator-lamp which, when connected, signifies normal operation. The speed of response of the protection circuit is determined by the 1 s time-constant of the meanvoltage monitor. This value is such that the system working initially at a counting fraction of 1 will cut out in 100 ms if the fraction changes suddenly to 1 or to 0. While being rapid enough to protect the thermistor and their drivers from over-load damage, this response is slow enough to prevent spurious trips arising from statistical fluctuations in the counting fraction.

xt t r i g

~F

OOl

in

nucl¢or

pUI~GS

~FRACTION

7

cxt trig

out

E. light source tri 9. p to neutron source

--

~- from disc

E

-'ig. 7. S c h e m a t i c o f c o m p l e t e s t a b i l i z e r c i r c u i t .

'1 I

DECA DE DIVIDER

-:F

TEST

C O N T R O LI

MONITOP, ~ 1

MEAN

I

I

I

"10

F OIL

lr

m

/a

"3

Z

--i

Z

"3

"3 .<

"rl

..]

Z

J. S. HEWITT AND J. WALKER

118 2.3. COMPLETESYSTEM

The schematic of the working version of the stabilizing system is shown in fig. 7; the basic components given in fig. l can be readily identified here. Two controlled stages have been employed. In addition to the basic components, the final unit also contains a variable triggering system which is particularly useful in accelerator-based experiments; the system provides for either internal or external triggering. Internal repetition periods can be selected and circuits are provided for beginning the accelerator cycle l0 ps after the reference pulse has been sent through the detector system. The external trigger provides for reducing the accelerator repetition rate in case it should exceed the maximum of the reference pulses. During setting up, the function switch is advanced from the " t e s t " to the " s e t - u p " position. In the " t e s t " position a 50% counting fraction will be evident on the 100 pA meter unless there is a fault in the thermistors, their drivers or the logic circuits. In the " s e t - u p " position the reference pulse is adjusted to give a 50% counting fraction after the coincidence delays have been appropriately adjusted. Before advancing to the "control" position the protection circuit must be set. In the event of a protection circuit trip, the function switch must be returned to " s e t - u p " for 30 s before attempting to reset.

3. Analysis of control system In this section, control theory techniques are used to study the dynamics of stabilizer systems obeying proportional control, including the one described in section 2. Haun and Kamke 2) have

°';°

previously analysed a stabilizing system with proportional control, but their work did not include the effects of different sources of drift and of statistical fluctuations. 3.1. FORMULATIONOF TttE PROBLEM Following control theory techniques, the stabilizer system is represented by a set of transfer functions and the various sources of drift are represented as driving functions. The fractional change in loop gain, dG/G, has been chosen as the controlled variable, and it is the role of the stabilizer to minimize this variable. The effects of the residual drift on the experiment can then be deduced from a knowledge of the detector bias curve. A control diagram for the stabilized detector is given in fig. 8. The symbols used are defined as follows: dlnG = dG/G, the fractional change in system gain about the operating gain G. This term accounts also for discriminator bias-level drift; the equivalence is stated for small drifts as dG/G = -dV/V.

dr,

the change in the counting-fraction induced by a gain-change of dlnG. The bar signifies that the change is that based on the observation of a very large number of the standard pulses both before and after the change dlnG is introduced. K = df/dlnG, the transfer function associated with the combination of detector'and standard lightsource. 6[(s), the Laplace transform of the statistical fluctuations in the counting fraction about the mean [. This need not be defined for short time-inter-

DETECTOR (including I~ M., amplifier, disc, • puled li(:Jht-sourc¢,} IC • volav

Ing C ONTI~OLLED STAG ES ~"~ (s) = N;~ '

4

I l"

s

dI

dl

T HDEI~/SET~O~

L:

~

I I

Fig. 8. Control diagram representing present stabilizer and other stabilizers obeying proportional control theory.

STABILIZING

THE

EFFICIENCY

vals since the high frequency components of this function will not be transmitted by M(s). Y, the equivalent noise generator for generating 6f(s). d F = df+6f(s), total counting fraction change. di, the change in the rms thermistor current induced by deviation, dF, from the nominal counting fraction F. L = di/dF, the thermistor-driver transfer function. 6i(s), represents the Laplace-transformed time-dependent drift in the feed-back network. This is defined to include equivalent drift in the characteristics of the controlled stage as well as those changes in the driver output. Z, the feed-back drift generator. d l = di+6i(s), total change in current to the controlled stage. d lny, the change in detector gain executed by d l through M ( S ) . M ( S ) = d In g/dI, the controlled stage transfer function. This is written as a function of s to account for the reactive response of the thermistors. 6 ln g(s), denotes the transformed time dependent drifts associated with the components of the conventional detector system. 3.2.

EVALUATION

OF THE T R A N S F E R F U N C T I O N S

P(v-vp)dv

Inserting numerical values in (5) leads to df = - 0.93 R dv/% ~- - Rdv/vp ,

-½erf

P(v-%)dv.

2x/(ln2)[V-Vp[ , v > %,

Ii+~-erfp'/(ln2) Avp

where R equals Vp/AVp, a measure of the resolution for the reference line. Since each small variation in bias level can be represented by an equivalent variation in system gain, we obtain by replacing dv/vp with

-dG/G: d f = R dG/G.

(7)

Therefore K = df/d In G "~ R

=

Vp/Avp.

(8)

3.2.2. The thermistor-driver transfer function The thermistor driver generates a binary wave-form with amplitude Io and a duty ratio equal to the counting fraction F. The mean current is therefore given by

] = Flo,

(9)

i = x/(F)lo.

(10)

and the rms current by

(3)

(11)

which becomes L = / .max ...

(12)

when i is set equal to Im~x the maximum current rating for the thermistors, and F is set to its nominal value at 1. The maximum amplitude of the binary wave-form is therefore Io = \ / ( 2 ) 1 r ~ .

lv-vpl],v< %.

(4a)

(4b)

d---v-" = v~v, d--vv :~-~-

L

For the two identical thermistor-controlled stages in cascade, the gain is g -

Av,

A%

x~o \

2' RI

(14)

where Ro is the feed-back resistance and R~ is the input resistance in each stage. By differentiating this expression. we obtain

z 2v/(In2) lira ( d e r f ( x ) ] .

2"

(I 3)

3.2.3. The controlled-stage transfer function

The sensitivity of the counting fl'action to changes in c is given in the region of % by

= -

(6)

0

Eq. (3) can be written in terms of the error function:

f=

ll9

DETECTORS

L = di/dF = lo/(2\.'F ) = i/(2F),

To determine this transfer function we assume that the reference line, as it appears in the output pulse spectrum, obeys a Gaussian distribution p ( v - r p ) with a peak at % and a width (fwhm) of Avp. The mean counting fraction as defined in section 2.2 will then be given by

v

SCINTILLATION

Differentiation yields the transfer function

3.2.1. The detector transfer function K

f(v) =

OF

dx

/

(5)

dlng -

2dR1 2dRo -+ - Ri Ro

(15)

120

J. S. H E W I T T

AND

If we remember to control the heater currents to the input and output thermistors in a complementary fashion, this expression reduces to dR dlng = N--, R

(16)

where d R / R is the magnitude of the relative resistance change in each thermistor and N is the number of thermistors involved. For small signals, the thermistor characteristics are well represented by the equation dR

Each drift in to one of the studied 3.4.

of the three terms in expression (20) for net the stabilized system accounts for the response of the three driving functions. The response system to each function can therefore be independently of the others.

DYNAMIC RESPONSE TO A STEP-CHANGE IN THE DETECTOR GAIN

By substituting the transfer functions (8), (12) and (18) into the partial control eq. (21), we obtain

2di -

R

(17)

dlng_ di

-2N. l + Ts

dlnG = 6 lnf(s) + M (s) L K (dlnG) '+ M (s) 6i (s) + (19)

Upon closing the loop, the two (dlnG) expressions are identical and we can then write the closed-loop expression (20)

where

dlnG]rBdlnG]s-

ling(s) , 1 - M ( s ) LK M(s)ai(s) , 1 - M (s) L K M(s)L6f(s) . 1 -M(s) LK

(24)

where

H ~- K(s)" L(s).M(s)]s= o = - N2lrm"~R.

(25)

To determine the response of the system to a stepchange in detector gain equal to 61n9 in amplitude, we replace ,~lng(s) in (24) by (61ng)/s and obtain dlnG(S)]D = 61n9

(s+ I/T)

.

(26)

s[s +(I-t + l )/T]

d l n G ( t ) ] D = 6 1 n g ( 1 - -1 +H

(21)

(22) (23)

+

H I+H

'e

-t.(t+u)/r)

. (27)

Inspection of this equation reveals that, at the instant of the step, the net gain-change is equal to the step and decays with the reduced time constant T/(I + H), to a residual value equal to the step diminished by the feed-back factor 1 + H. 3.5.

RESPONSE TO A STEADY DRIFT IN THE DETECTOR GAIN

To determine response when a steady drift is imposed, beginning at t - - 0 , we replace 61ng(s) in eq. (21) by D/S 2 where D is the fractional increase in gain per unit time. By inverting the transform, we obtain d In G(t)]o

dlnG]o -

, Ts)

Taking the inverse transform we find the following function of time t:

To obtain the control equation, we hypothetically open the loop at the point S in fig. 8. The value of dlnG coming from the adjacent adder is the linear combination of all generator signals in the loop, including the fictitious value of (d In G)' which we impose upon the detector, dlnG is thus given by

dlnG = dlnG]D+dlnG]va+dlnG]s,

1 + H/(I +

(18)

3.3. THE CONTROL EQUATION

+ M (s) L~f(s).

61n9 (s)

dlnG]D -

l+Ts'

where 2 is the sensitivity of the thermistor with respect to the rms heater current, Tis the thermal time constant and s is the Laplace transform variable. The validity of this representation of the time-response of the system can be shown by forming the Laplace transform of the differential equation governing the temperature of the thermistor element. By combining eqs. (16) and (17), we obtain the controlled stage transfer function: M(s)-

J, W A L K E R

-

- Dt H+I

+

- DTH (1-e (H+I) 2

-t

.(l +H)/r).

(28)

The first term on the rhs represents the accumulated drift due to a drift rate D being in effect for time t. This term corresponds to the first term in eq. (27), and, as before, the effect of the accumulated drift is diminished by the feed-back factor. The second term becomes significant only after the

STABILIZING

THE EFFICIENCY

steady drift has been applied for a time greater than the order of the reduced time-constant contributed during the steady drift and will return to zero in a similar time after drifting ceases. The drift is approximately equal to D T / H which is simply the product of the drift-rate and the reduced time constant. These results are useful when considering, for example, the magnitude of the temporary gain change induced while the phototube is progressing from one gain level to another when undergoing fatigue.

3.6.

OF S C I N T I L L A T I O N

3.7.

121

DETECTORS

STATISTICAL FLUCTUATIONS IN GAIN GENERATED BY THE FLUCTUATIONS IN THE COUNTING FRACTION

The position of the reference peak in the amplifier output is well defined at a particular instant only if the light-pulse repetition rate is very high. Since high rates are impractical, owing to the difficulty of producing a suitable light source and to the loss of detector live time, the exact position of the peak over a finite time will be uncertain. To study the effect of the randomness with which the light-source pulses appear at the discriminator output, we examine eq. (23). By writing this equation explicitly, we obtain

RESPONSE TO DRIFT IN THE FEED-BACK NETWORK

The drift induced by the signal ai(s) is represented by eq. (22). Since i(t) is expected to vary little over a reduced time-constant (particularly for the present ;ystem where only aging effects are contributory), we may set s = 0 in the transfer functions. On doing this and assuming H + l ,~ H, as must be the case in a useful stabilizer, eq. (22) becomes

dlnG(t)]v. ~- - (l/R) di(t). max

(29)

Irms

This expression can be shown to apply to any proportional control stabilizer deriving the feed-back signal in digital form from a pulse height selector operating on the output spectrum. In such cases &'/Irmm"x corresponds to the relative drift in the feed-back network measured at the point where the digital information has just been converted into an analogue form. An important contrast can be made here between the way in which drift in the proportional control system affects a spectrometer and how it affects a biased detector. in the spectrometer, the relative line shift is given, by rearranging eq. (29), as

dG/G

Av/%

6i max /rms

(30)

which states that the expected fractional line shift equals the fractional drift in the feed-back network, and hence to reduce feed-back drift to less than, say, 10% is not essential unless one is measuring energies to better than 10% of a line width. Such a large tolerance does not apply for biased detectors, particularly when the reference line is broad; if, for example, the reference line width is 50% which is not unrealistic, a 10% feed-back drift, according to eq. (29), will set the effective bias in error by 5%, an unacceptable situation in many experiments.

,51nG(s)]s_N)oL

l

H+I

(

T/(H+I)

1 1

i))hf(s)"

s+ T/(H+

(31)

The bracketted factor in this expression has the form which can be identified with the frequency response function of a simple rate meter having a time constant T / ( H + 1). To obtain the relative rms gain fluctuation contributed by statistical fluctuations in the counting fraction, we use the result given by Evans 6) for the standard deviation in a single instantaneous rate meter reading and modify it by x/2 to allow for the definition of counting fraction. Hence:

N2L 61nG]rms = - -

1

H+I

x/{rT/(H + l)}

,

(32)

where r is the reference pulse rate. Rearrangement of (32) gives

N2L I 61nG] .... = \/(H + 1)• v/(rT) ,

(33)

which shows that the magnitude of the statistical fluctuations are reduced by the factor x / ( H + l ) compared with that which would be generated with the feed-back loop open. This differs from the results of Gilland and Ried 2) who, however, did not include the effects of feed-back. By making the approximation H + I -~ H we can modify eq. (33) to yield the fractional line broadening at the reference peak for the spectrometer system, viz.

AV/Vp

-

~

.

(34)

4. Performance

4.1. TEST CONDITIONS Performance tests were carried out with the stabilizer connected to a gamma-ray detector probe. The probe

122

J. S. H E W I T T

consisted of a s-~" thick x ~1" diameter anthracene disc, optically coupled to an E M I 9524S photo-tube by means of a long light-guide. The light-guide was a fused silica rod, 2 feet long and ½ inch in diameter. With this arrangement, the intensity of photo-electrons produced is only a factor of approximately two higher than the noise level in the photo-tube. Furthermore, the bias curve is rather steep, since essentially all g a m m a interactions with the small phosphor are of the Compton type. Thus, the tests were carried out under conditions as extreme as are likely to be encountered in most applications. The output pulses from the photo-tubes were passed through an emitter-follower and led to the controlledstage input of the stabilizer. The main amplifier employed a clipping time of 1.2 kts. The light source described elsewhere s) consisted of a hollow-cathode glow discharge tube coupled by means of a fibre optical light guide to the main light guide at a point several inches from the photo-cathode, to ensure a common effective area of photo-cathode for both types of light. The pulse repetition rate of the light source was !00

S -1

.

,sL

I

I

I

I

i

8

A

Z <

N

A

Operating O bias

oo

oF 0

© \ I

Io

A number of discriminator bias curves indicating the test conditions are shown in fig. 9. Curve A is the integral bias curve for the detector when exposed to a 137Cs gamma-ray source. This is the open-loop curve obtained with the stabilizer in the "set-up" mode. A curve of identical shape would be obtained in the absence of a stabilizer. Curve B corresponds to the photo-multiplier noise and background. The bias level was set at 20 V before proceeding to adjust the light pulse amplitude to the correct level corresponding to a 50% counting-fraction. The open-loop bias curve belonging to the appropriately adjusted light-source is represented by curve C. The ordinate of this curve will approach the light-pulse repetition rate, r, as the bias, v, approaches zero. Avp/vp was obtained from this curve using the formula J _

R

Av_. _ -

Vp

V(~ '9-

V ( k ,')

V(½ r)

,

(35)

and was found to be equal to 0.7. This large width is due mainly to the statistics of photo-electron production, for the spread in lightpulse amplitudes was less than 4% when the pulses were analysed using a more efficient coupling between the source and the photocathode. Using this value of Avp/Vp, the feed-back factor H was calculated from eq. (25) and N = 4, 2 = 0.64 mA-1 and lr~ ~ = 18 mA. The resulting value of the feedback factor is H = 67, which is consistent with the factor by which the slope of the closed-loop detector bias curve D in fig. 9 is reduced compared with that of the open-loop curve A. 4.2. TESTS

\

0 "iv

A N D J. W A L K E R

20 30 BIAS (volts)

~ 40

O 50

60

Fig. 9. Bias curves showing test conditions and the effectiveness of the stabilizer in flattening detector bias characteristic. A: bias characteristic o f small anthracene p h o s p h o r and aaTCs source, B: photomultiplier noise, C: light source bias curve, D: transformed detector bias curve.

The transformation of the detector bias curve as illustrated in fig. 9 provides a measure of the resistance of the system to drifts in discriminator level, high voltage supply, and amplifier gain. Other sources of drift not covered by this test, however, are drifts in the reference light pulser and in the feed-back elements themselves. Upper limits were determined for these sources by setting up the stabilized detector to monitor the intensity of g a m m a rays from a radioactive source, and subsequently sampling the count-rate over an extended period of time. The data collected in this way are given in fig. 10. The number of cotmts obtained during successive 50-min intervals is plotted in the upper histogram. The broken lines indicate the rms deviation levels predicted from considerations of

STABILIZING

THE E F F I C I E N C Y

OF S C I N T I L L A T I O N

TABLE 1

counting statistics. A visual inspection of the fluctuations in observed counting-rate reveals that the fluctuations can be attributed to counting statistics alone. An improvement in statistics, with a corresponding loss of time resolution, was realized by combining consecutive counts into groups of 5. The results of the first grouping operation are shown in fig. 10C. Again it is seen that the fluctuations can be attributed to counting statistics for which the expected rms deviations are indicated. It is easily shown that variation in count-rate due to system drifts are related to variations in the effective bias by the expression dv v

_

1

-

--, N

(36)

where dN/N is the fractional change in counts caused by dr~v, the fractional bias change. S is the y-intercept of the tangent drawn to the operating point in the detector bias curve and W is the ordinate at this point. For the bias curve of fig. 9, (S/W)- 1 is found graphically to be equal to 0.7. Using this value, the information displayed in fig. 10 is summarized in terms of the effective bias-level in table 1. An upper limit on the rms deviation in the bias level is thus tabulated for each of the counting or sampling times represented

~

2 36 t

i

0 2351-

]

]

]

i

]

I

]

i

I

i

A _

c23

_

___~_ 1 . 1

O

232[

0.4o/0-

B

L

23 l

__

~

_ t_.....~__

L

J

0.18o/,

-~23aj-

C

4

233 O

O.OBO/o

233308

0232 ~231

M~tan

I

I 500

Counts-

,

I I000 TIME

,

2333

1 1500

26

h

per

I 2000

50

I

rain.

I 2500

(min.l

Fig. 10. Results of stability test.

I

3000

123

DETECTORS

Observed stability in the effective bias level. Sampling (counting) time (rain)

Number of samples

Time spanned by sampling (h)

Upper limit of rms deviation in bias level

50 250 1250

53 10 2

51 42 42

0.27% 0.13% 0.06%

in fig. 10. We can conclude from the data presented in table l that the stability of the effective bias level is better than + 0 . 1 % including long term drifts. Operating experience using the stabilizer has been consistent with this figure. By contrast, the typical drift rate of the system operated without the stabilizer and under ideal conditions (constant photo-multiplier current) was 2% per hour. Thus under these conditions the stability of the system is improved by a factor of at least 20; improvements up to the value of the feedback factor ( H -- 67 for present detector), are realized when varying count rates induce phototube fatigue. 5.

Conclusions

A system for stabilizing the effective bias in a large class of detectors has been described in detail. Design criteria, which are established by the control theory of section 3, have been satisfied by using binary-controlled thermistor circuits. As a result, long term stabilization to better than 0.1%, even for cases where photocathode illumination is weak, has been achieved without interfering with normal detector function. The analysis also allows prediction of the system performance, with regard to stabilization factor, stabilizing rate, and statistical fluctuations for any detector to which it may be coupled. The analytical results, including those for spectrometers, may be applied to any proportional control stabilizer. This work is part of a programme of neutron physics supported by the Science Research Council, London and we are grateful for the support. One of us (J.S.H.) thanks the British Board of Trade for an Athlone Fellowship and the National Research Council of Canada for a Special Scholarship. The final stages in the preparation of the paper were carried out while the other (J.W.) held a Canadian Commonwealth Fellowship at the University of Ottawa.

124

J. S. H E W I T T

References 1) D. H. Wilkinson, J. Sci. Instr. 27 (1950) 36. z) S. H a u n a n d D. K a m k e , Nucl. Instr. a n d Meth. 8 (1960) 331; K. W. Marlow, Nucl. instr, a n d Meth. 15 (1962) 188; P. F. Hinrichsen, I E E E Trans. Nucl. Sci. NS-11 (1964) 420; A. P a k k a n e n and F. S t e n m a n , Nucl. Instr. and Meth. 44 (1966) 321 ; J. R. Gilland and L. Ried, IEEE Trans. Nucl. Sci. NS-16 (1969) 277. 3) j. A. L a d d a n d J. M. K e n n e d y , A.E.C.L.-1417 (Chalk River, C a n a d a , 1961);

A N D J. W A L K E R M. N a k a m u r a a n d R. L. LaPierre, Nucl. Instr. and Meth. 32 (1965) 277; L Dixon, NucL Instr. a n d Meth. 25 (1963) 26; R. A. Dudley and R. Scarpatetti, Nucl. Instr. and Meth. 25 (1964) 297; A. M. C o m u n e t t i , Nucl. Instr. and Meth. 37 (1965) 125; M. K. Efimchik et al., Instr. Exp. Tech., no. 3 (1967) 540. 4) I. Cantarell and I. A l m o d o u a r , Nucl. Instr. and Meth. 24 (1963) 353. 5) J. S. Hewitt and J. Walker, Nucl. Instr. and Meth. 77 (1970) 105. 6) R. D. Evans, The atomic nucleus (McGraw-Hill, New York, 1965) p. 804.