COMPARISON BETWEEN MEASURED AND
CALCULATED STATIONARY THERMAL NEUTRON
SPECTRA IN HETEROGENEOUS SYSTEMS
L M. CASPERS
5'35->2r. s v / . ^/.oy
COMPARISON BETWEEN MEASURED AND
CALCULATED STATIONARY THERMAL NEUTRON
SPECTRA IN HETEROGENEOUS SYSTEMS
iilMI 11 nil
^ liililM
'iii liiiiiiniiiti mmêr>
o o o (-•
(> UI ^ fS> U) OJ 00 f-BIBLIOTHEEK TU Delft P 1221 6158COMPARISON BETWEEN MEASURED AND
CALCULATED STATIONARY THERMAL NEUTRON
SPECTRA IN HETEROGENEOUS SYSTEMS
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE
HOGESCHOOL DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS DR. IR. C.J.D.M. VERHAGEN, HOOGLERAAR IN DE AFDELING DER TECHNISCHE NATUURKUNDE, VOOR EEN COMMISSIE UIT DE SENAAT
TE VERDEDIGEN OP WOENSDAG 19 JUNI 1968 TE 16 UUR
DOOR
LEOPOLD MARIA CASPERS
NATUURKUNDIG INGENIEUR GEBOREN TE 's-GRAVENHAGE1968
"BRONDER-OFFSET" ROTTERDAM
DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOR PROF, DR. J . J . WENT.
C O N T E N T S
page
1, GENERAL INTRODUCTION 1 1.1 Purpose of the investigation 1 1. 2 Scope of work involved 3 1. 3 Outline of the following c h a p t e r s 5
2. EXPERIMENTAL TECHNIQUES 6 2 . 1 Introduction 6 2.2 The time-of-flight s p e c t r o m e t e r 7 2. 2 . 1 Principle 7 2 . 2 . 2 Design 8 2 . 2 . 3 Construction 11 2 . 2 . 4 Analysis of data 15 2. 2 . 4 . 1 Background 15 2. 2 . 4 . 2 Calibration of analyser time scale 17
2. 2 . 4 . 3 T r a n s m i s s i o n function of the r o t o r s 19
2. 2 . 4 . 4 Detector efficiency 23 2. 2 . 4 . 5 Other c o r r e c t i o n s 25 2. 2 . 4 . 6 The OWL program 25 2. 2. 5 Accuracy of the m e a s u r e d s p e c t r a 27
2 . 3 Foil-activation techniques 29 2. 3.1 General r e m a r k s 29 2. 3. 2 Automatic foil changer 30 2. 3. 3 Analysis of data 31 2. 3. 4 Accuracy of the measured activations 32
page
CALCULATION METHODS 33
3.1 Introduction 33 3. 2 Formulation of integral t r a n s p o r t theory for isotropic 34
scattering
3. 3 SCAM p r o g r a m for the calculation of the scattering kernel 37
3.4 THIN p r o g r a m for infinite media 41 3. 5 THERMOSLAB p r o g r a m for slab-geometry systems 42
3. 6 THERMOSQUARE p r o g r a m for x-y geometry systems 43 3. 7 THERMOSLAB 3 - an integral transport program for 46
linear-anisotropic scattering
3.8 Probe-tube perturbation 48 3. 8.1 General r e m a r k s 49 3. 8. 2 The PPDCY program 50 3. 8. 3 Some calculated r e s u l t s obtained with PPDCY 53
3. 9 Effect of step size on the accuracy of calculated program 55 r e s u l t s
VERIFICATION OF CALCULATION METHODS BY EXPERIMENTS 59
4 . 1 Introduction 59 4 . 1 . 1 Results to be expected from verifications 59
4 . 1 . 2 Experimental limitations 61 4 . 1 . 3 Deviation yardstick 62 4. 2 Measured infinite-medium s p e c t r a versus THIN r e s u l t s 63
4 . 2 . 1 General r e m a r k s 63 4. 2. 2 Measured and calculated s p e c t r a 66
4. 2. 3 Discussion 67 4. 3 Measured leakage s p e c t r a from slab-geometry s y s t e m s
v e r s u s THERMOSLAB r e s u l t s 69 4. 3.1 General r e m a r k s 69 4. 3.2 Measured and calculated s p e c t r a 72
4. 3. 3 Discussion 72 4 . 4 Measured leakage s p e c t r a from x-y geometry s y s t e m s v e r s u s 75
THERMOSQUARE/PPDCY r e s u l t s
4 . 4 . 1 Measurements and calculations 75
page
4. 5 Space-dependent s p e c t r a measured in slab-geometry 78 s y s t e m s v e r s u s THERMOS LAB/PPIXY r e s u l t s
4. 5.1 General r e m a r k s 78 4. 5. 2 Measured and calculated s p e c t r a 80
4. 5. 3 Discussion 83 4. 6 Final r e m a r k s and conclusions 84
REFERENCES 88
LIST OF SYMBOLS 91
LIST OF ABBREVIATIONS 93
E R R A T A page 8 9 10 14 14 14 18 18 19 20 20-22 22 22 25 line in footnote 20 7 8 13 19 11 4 4 3 _ 15 Fig. 25 2. 14 e r r o r gratefuU m2 ref. 2 . 2 . 4 . 3 Flight tube Electronics Counters r o t o r speed uo= 30.25 s'''' "f(t')g(t-t')dt' t uj/2n / 2 s / r = = 0.00307
m"-*-(jut scale to be multiplied t = c correction grateful 2 m ref. section 2. 2. 4. 3 Counters FUght tube Electronics r o t o r in this period u)/2rr = 30.25 s'"*" t f(t')g(t-t')dt' o 0) s / 2 r ^ = = 0.307 m""*" with 2n ^^C = 27 n(t) 28 29 29 40 41 42 43 45 A 7 4 / 47 48 20 6 6 3 Eq. 3 25 19 1 22 (3.7) considerably better Nal(Th) Table 2.2; 0.208 0.133 0.089 eV, 0.140 eV, 0 . 1 7 4 e V , 0.360 eV V* Z:(v'-.v)$(v')dv' Q maximum THERMOQUARE Beardwoord 3 2AX AX. S t n 1 ik conclusion Molenari's considerably less Nal(Tl) 0.208 0.113 0.089 eV, 0 . 1 8 7 e V , 0.354 eV, 0.533 eV V * S ( v ' - v ) $ ( v ' ) d v ' 0 maximum of THERMOSQUARE Beardwood 3
2^\2iüc^^k
conclusionspage line e r r o r correction 54 56 60 61 66 67 68 83 88 88 89 94 95 3 1 32 14 7 17 Fig. 4 . 8 Table 4. 6 Ref. Ref. Ref. 30 32 10 23 36
allow the prediction neutron-course A$ and Ax for Ee: B 2 = B^ = - 0. 067 cm^ 0 _ 2 B (cm ) 0.067 0.045
footnote missing (sai Neutron P h y s i c s , p.
TDH-H-RF 102 Phys. Rev. , p. 119, 2 (1960)
Lu
zijn iets te hard
3f show neutron-source A9 and Ax for Fe; f(r)B^ = B^ =- - 0.067 cm"^ 2 - 2 B (cm ) - 0.067 - 0.045
ne footnote as under Table 4. 5) 312 Neutron Physics p. 312, 102, 210 THD-H-RF 102 Phys. Rev. , 119, I, p. 872 (1960) 177^ Lu
C H A P T E R 1
G E N E R A L I N T R O D U C T I O N
1.1 PURPOSE OF THE INVESTIGATION
The subject of this investigation, as the title implies, is the experimental verification of calculation models and c r o s s sections used in the determination of stationary space-dependent thermal neutron spectra. The subject is p a r t of a m o r e general n e u t r o n - t r a n s p o r t verification p r o g r a m that is being c a r r i e d out by the Reactor Physics Group of the Physics Department of the Delft Technological University, which group collaborates with and is stationed at the Reactor Instituut, Delft.
Detailed knowledge of t h e r m a l s p e c t r a , a s a fimction of position in a r e a c t o r is in particular important for the determination of flux peaks (caused by i r r e g u l a r i t i e s in the fuel-rod lattice), which often determine the power level at which the danger of burn-out becomes imminent. Moreover, space-dependent t h e r m a l s p e c t r a should a l s o be known for accurate burn-up calculations and for the determination of the t e m p e r a t u r e coefficient during the life-time of the
239 240 241 r e a c t o r . This is because of the formation of Pu, Pu and Pu and of
235
the presence of U in the r e a c t o r fuel, which isotopes have resonances in the t h e r m a l region. Recent evaluations of plutonium recycling in t h e r m a l r e a c -t o r s have fur-ther i n c r e a s e d -the i n -t e r e s -t in -the s-tudy of space-dependen-t -t h e r m a l s p e c t r a .
Existing r e a c t o r codes in this field calculate primarily the neutron s p e c t r a a s a function of position in the r e a c t o r cell [ 1 , 2 ] ; based on these s p e c t r a , v a r -ious s p a c e - a v e r a g e d a n d / o r energy-integrated values a r e then derived. Nearly
all these codes a r e limited to either slab or cylindrical geometry; the latter
a r e based on the Wigner-Seitz r e a c t o r - c e l l approximation.
The ideal way of verifying the calculation models and c r o s s sections used in these codes is to m e a s u r e spectra at various positions in the r e a c t o r cell with the time-of-flight method; the s p e c t r a yielded by other methods, such as activation techniques, have essentially less resolution.
The r e a c t o r cell, in which the s p e c t r a should be measured, does not n e c e s s a r i l y have to be positioned in a lattice. Spectrum m e a s u r e m e n t s in a single mock-up cell, or in a system with a few mock-up c e l l s , which a r e more easily a c c e s s i b l e , also provide a sensitive test for models and c r o s s sections. The practical goal of our verification program was therefore the measurement of s p e c t r a in such mock-up cells using a time-of-flight s p e c t r o m e t e r .
In 1963, when this project was s t a r t e d , this objective still seemed far off. Most spectrum work c a r r i e d out until then concerned "infinite" systems [ 3 , 4 , 5 ] ; leakage s p e c t r a had been measured less frequently [ 3 , 4 ] . Beyster et a l . had reported spectrum m e a s u r e m e n t s in water and polyethylene slabs to verify one-dimensional S,|^ type transport codes [ 3 , 6 ] . Some verification of the cylindrical codes had been and was being c a r r i e d out in an integral way, i . e . by activating foils at various cell positions [ 7 , 8 ] . In this manner only spectrum-integrated values could be verified. Time-of-flight measurements of spectra inside a r e a c t o r cell w e r e considered impractical, a s it was expected that the s p e c t r a would be seriously perturbed by the probe tube, which has to be inserted into the cell to extract the neutrons, and one did not know how to evaluate this p e r -turbation.
F r o m the above it is c l e a r that the key problem in the Delft p r o g r a m , which, a s has just been mentioned, was intended to obtain spectra from r e a c t o r c e l l s , would be how to minimise and/or how to evaluate the perturbation caused by the probe tube. The way in which it was decided to solve this problem i s in principle a s follows.
To minimise the perturbation, a probe tube was chosen of rectangular c r o s s section with one side much s m a l l e r than the other. Figure 1.1 shows such a probe tube together with one with a c i r c u l a r c r o s s section. Both probe tubes have the s a m e c r o s s - s e c t i o n a l a r e a , so that in principle they can yield
the s a m e amount of neutrons. The answer to the question as to why the r e c
-tangular probe tube causes less flux perturbation follows from the consideration of a hypothetical probe tube with an infinitely thin and infinitely long side and the s a m e c r o s s - s e c t i o n a l a r e a . Such a probe tube would not disturb the flux
Fig. 1.1 Two types of probe tube with equal cross-sectional area
at all, and our rectangular probe tube is closer to this limit than the c i r c u l a r one.
A further advantage of a r e c t a i ^ u l a r probe tube, as shown in Fig. 1 . 1 , i s , that with a good approximation it can be considered to have x-y geometry, and the perturbation caused by this tube can be evaluated m o r e easily (by using an x-y t r a n s p o r t code) than the perturbation caused by a c i r c u l a r tube.
The numerical application of x-y transport theory r e q u i r e s the use of d i s c r e t e points or zones. In this thesis d i s c r e t e zones a r e used which a r e infinite-ly long cylinders or rods with their axes in the z-direction and with s q u a r e c r o s s sections (see Fig. 1.2). The choice of the latter shape of c r o s s section facilitates the numerical work, but limits, on the other hand, the program to s y s t e m s that can be composed of such square zones. It is for this reason that in this thesis only slab r e a c t o r cells a r e considered, and not e . g . cylindrical c e l l s .
1. 2 SCOPE OF THE WORK INVOLVED
Having discussed the purpose of this study, a brief enumeration will be given of the various tasks c a r r i e d out to r e a U s e this purpose:
(1) The design and construction of a time-of-flight s p e c t r o m e t e r with an energy resolution sufficient for our purpose (sect. 2. 2. 2).
164 (2) The development of techniques for the activation of foils containing Dy,
176 197
-up Cd Cd -up
I I I I I I I
Fig. 1.2 Division of space around probe tube into discrete zones
of-flight m e a s u r e m e n t s and, moreover, they a r e m o r e suitable for obtaining information on the spacedependency of the flux than the s p e c t r o m e t e r m e a s -u r e m e n t s .
(3) The development of p r o g r a m s for calculating:
- the space-dependent s p e c t r a in the various experimental geometries used in this study,
- the perturbation caused by the probe tube,
- the scattering kernels that a r e used in these p r o g r a m s .
All these p r o g r a m s have been written in Algol, so that they can be used on the Telefunken TR4 computer of the Delft Technological University. (4) The m e a s u r e m e n t of the following types of neutron s p e c t r a :
- infinite-medium spectra. The measurement of spectra in "infinite" media is a useful first step, because some of them (e.g. the water spectrum) a r e well-known and can be used to test and calibrate the s p e c t r o m e t e r . Spec-t r a m e a s u r e d in poisoned waSpec-ter a r e especially useful for checking Spec-the s c a t t e r i n g - k e r n e l program r e s u l t s (sect. 4 . 2 . 3 ) .
leakage spectra flom semiinfinite media and slabs. These spectra a r e not p e r -turbed, because the probe tube does not enter the system. Hence, they s e r v e as a useful check for slab-geometry p r o g r a m s .
- spectra inside slabs and mock-up cells. The measurement of these s p e c t r a has fulfilled our purpose. To verify these s p e c t r a , however, use must be made of the probe-tube perturbation p r o g r a m , and this p r o g r a m , which is based on xy t r a n s p o r t theory, needs in turn verification by some a d -ditional m e a s u r e m e n t s , viz:
- leakage spectra from x-y geometry systems. The geometries of these s y s t e m s have been chosen simple enough to make a meaningful comparison between calculated and measured spectra possible.
1. 3 OUTLINE OF THE FOLLOWING CHAPTERS
Chapter 2 deals with all details of the experimental techniques used and the apparatus involved. The time-of-flight s p e c t r o m e t e r (ref. sect. 1.2, task 1) and the calibration method a r e discussed in detail. F u r t h e r m o r e , a description is given of a program written for the TR4 computer, which t r a n s f o r m s the experimental r e s u l t s of the s p e c t r o m e t e r into neutron spectra. The techniques for activating and countii^ foils such as Dy, Lu, Au, and the c o n -struction of a self-made automatic foil changer, a r e also discussed in this chapter (ref. sect. 1.2, task 2).
Chapter 3 is devoted to a description of the various computer p r o g r a m s developed for this study (ref. sect. 1.2, task 3). These p r o g r a m s a r e based on integral t r a n s p o r t theory for r e a s o n s that will be explained, and a r e based on the assumption of isotropic scattering. This assumption will be verified for a test c a s e by means of a p r o g r a m in which anisotropic scattering is applied. In this chapter the probe-tube perturbation mentioned before is discussed in detail, and a special program developed to evaluate this perturbation is described.
Finally, Chapter 4 outlines the experiments r e f e r r e d to in sect. 1.2 under item (4). The r e s u l t s of the m e a s u r e m e n t s a r e compared with those obtained by calculation using the p r o g r a m s mentioned above; hence, in this chapter the actual verification of calculation models and c r o s s sections is c a r r i e d out.
C H A P T E R 2
E X P E R I M E N T A L T E C H N I Q U E S
2 . 1 INTRODUCTION
This chapter d i s c u s s e s the experimental techniques for determining the e n e r g y - a n d space-dependent neutron distributions in the various s y s t e m s .
Two basically different methods w e r e used, viz:
(1) Measurement of detailed s p e c t r a with a time-of-flight s p e c t r o m e t e r . This method and the s p e c t r o m e t e r constructed a r e discussed in sect. 2. 2. (2) Measurement of s p e c t r u m - s e n s i t i v e quantities by means of activating foils.
Details of this technique and the facilities used a r e given in sect. 2. 3.
It may be useful to compare the m e r i t s of both methods in general t e r m s . In the first method the energy distribution of the neutrons that leave the system via an extraction hole, the probe tube, is measured with good resolution. The quantity m e a s u r e d is the angular flux l ( r , v , 0 ) , Q being the direction of the probe tube, v the neutron velocity, and r the position of the probe-tube bottom. The probe tube p e r t u r b s the flux in the adjacent region, and a c o r r e c t verifica-tion of the experimental r e s u l t s r e q u i r e s that this perturbing effect must be evaluated when calculating the angular flux. One might say that the probe tube tends to reduce spatial effects and the method therefore combines a good energy resolution with moderate spatial resolution.
On the c o n t r a r y , with the second method the spatial resolution is good. The foils can be chosen thin enough for the local flux not to be perturbed. One m e a s u r e s , however, an activity A = S ( E ) , . . . * ( E , r ) d E , with an energy
resolution depending on the resolution with which various detector m a t e r i a l s can distinguish neutron e n e r g i e s . Since there a r e no m a t e r i a l s available with s h a r p resonance peaks in the t h e r m a l region, the energy resolution of the activation method is essentially poor.
As the two methods a r e complementary, they may be considered equally important; it i s only because the second method has already been applied by various investigators [ 7 , 8] for the verification of r e a c t o r codes that in this work the main emphasis is placed on the m e a s u r e m e n t of s p e c t r a with the t i m e -of-fUght method.
2 . 2 THE TIME-OF-FLIGHT SPECTROMETER
2 . 2 . 1 P r i n c i p l e
The principle of the chopper time-of-flight s p e c t r o m e t e r is well-known. A detailed description of the method may be found in, amongst o t h e r s , [ 9 , 1 0 ] ; this section only gives a short description, while reference is made to Fig. 2 . 1 .
H
I collimatorI I light experimental system \yA source
Fig. 2.1 The principle of the time-of-flight spectrometer
Fig. 2.2 The rotor transmission as a function of neutron flight time
The continuous s t r e a m of neutrons leaving the probe tube is transformed by the chopper into short pulses of neutrons. The neutrons in these pulses a r e allowed to t r a v e l a c e r t a i n flight path 1, before they a r e detected. D u r i i ^ this flight the neutrons s o r t themselves out according to their velocity, i . e . faster neutrons will a r r i v e at the end of the flight path e a r l i e r than slower ones. The neutron velocity v follows directly from the measured flight time t = L / v . The slits of the chopper a r e curved and so designed that no neutrons a r e transmitted with flight times longer than the time between two p u l s e s . The neutron beam
should be so coUimated that only neutrons from the source a r e a ( i . e . the bottom of the probe tube) can reach the detector. The time measurement Is performed by means of a time analyser containing an electronic clock, which is started when the neutrons leave the chopper by means of the optical system indicated in Fig. 2 . 1 . The analyser also contains a magnetic-core memory with a number of channels in which neutron counts a r e added. The clock opens these channels one after another for a p r e s e t time interval (the channel width), so that the number of the chaimel in which a particular count is added, is directly related to the neutron flight time. Every half revolution of the chopper this procedure is repeated until a statistically sufficient number of neutron counts have been collected in the analyser m e m o r y . The desired neutron density s p e c -trum n(t) can then be calculated from the memory contents w(t) using the relation
where b(t) = neutron background, T(t) = t r a n s m i s s i o n of the r o t o r , e(t) = efficiency of the detector,
C = constant determined by the dimensions of the s p e c t r o m e t e r , g(t) = correction factor to take into account the effect of the s p e c t r o m e t e r
resolution and the scattering and absorption in m a t e r i a l s present in the neutron beam.
2 . 2 . 2 D e s i g n
The design of the s p e c t r o m e t e r is quite straightforward and for our detailed calculations reference is made to [ 1 1 ] , and to [ 1 2 , 1 3 , 1 4 ] for extensive d i s -cussions on design methods. The main requirements determining our design will be enimierated below.
F i r s t of all it was r e a l i s e d that the mechanical design of a safe chopper would r e q u i r e considerable experience, which we did not have. As no time had to be lost in building up such experience, Dr M . J . Poole, Dr M . S . Coates and others in H a r w e l l * , where s e v e r a l choppers were already in operation, were asked for advice, and their method of construction was adhered to. Our chopper therefore has two typical "Harwell" features (requirements 1 and 2):
(1) K - m o n e l ( 3 0 % C u / 7 0 % N i a l l o y ) a s r o t o r m a t e r i a l . This
m a t e r i a l combines a good tensile strength with a relatively high removal c r o s s section.
(2) A m a x i m u m a n g u l a r s p e e d of t h e r o t o r of 2 0 0 s
(= 1 2 0 0 0 r p m ) , a s can be obtained with a Smith type KM 16 h y s t e r e s i s motor, provided the weight of the rotor does not exceed 9 . 1 kg (Harwell experience).
F r o m the K-monel c r o s s section for fast neutrons (S , « 0. 35 cm ^ removal
for E > about 30 keV),
(3) a r o t o r d i a m e t e r of 2 0 c m could be calculated that would give a neutron t r a n s m i s s i o n of 2 / o o in the fully closed position. Coates has r e ported [ 1 5 ] that with m e a s u r e m e n t s in multiplying s y s t e m s , such a t r a n s -mission r e s u l t s in an angular background (due to neutrons that pass through the rotor) of the s a m e order a s the r e a c t o r background (due to neutrons that pass through the shielding of the detector). It should be noted that spectriun m e a s u r e m e n t s in multiplying s y s t e m s will be included in our future p r o g r a m .
The above r o t o r d i a m e t e r and the maximum weight of 9 . 1 kg determined the sUt height at 24 m m , which followed from a s t r e s s calculation according to the method proposed by Umakantha [16]. The determining factor in this calculation was:
Q
(4) A m a x i m u m a l l o w a b l e s t r e s s of 1 . 2 4 x 10 N / m 2 , which is 1/3 of the minimum 0.2% yield s t r e s s of thermally hardened K-monel.
T h r e e important dimensions, viz the slit width s, the flight path L and the sUt curvature radius R then followed, in combination, from the following t h r e e r e q u i r e m e n t s :
(5) D u r i n g t h e l a s t 1 0 % t o 1 5 % of t h e t i m e b e t w e e n t w o p u l -s e -s o n l y b a c k g r o u n d n e u t r o n -s a r e t o b e c o u n t e d . In the design the c r i t e r i o n used was
1 . 1 5 t = - , (2.2)
c U)
with t being the flight time of the slowest neutron transmitted through the rotor and u) the angular speed of the r o t o r . The time t follows from the t r a n s m i s s i o n function T of the r o t o r , which will be discussed in detail in sect. 2. 2 . 4 . 3. F o r a better understanding at this stage, the essential
t u r e s of this function a r e given in Fig. 2, 2 where T is given as a function of the neutron flight time t. In this figure t = - corresponds to the a r r i v a l of infinitely fast neutrons of the next rotor pulse.
(6) A r e l a t i v e r o t o r t r a n s m i s s i o n of 1 5 % f o r f a s t n e u t r o n s . One can then look through the s l i t s , which may be useful for alignment p u r p o s e s . Moreover, such a t r a n s m i s s i o n makes m e a s u r e m e n t s of a f u l l -range t h e r m a l spectrum in one run possible (ref. 2. 2 . 4 . 3). F r o m the t r a n s m i s s i o n function it follows that this requirement leads to the expression
s i
our
or together with Eq. (2, 2) to
and
s l j « 1.60 r^ (2.3)
If
where t is the flight time of the neutrons that have maximum t r a n s m i s s i o n m
and r is the rotor r a d i u s .
(7) A s p e c i f i c r e s o l u t i o n 6T = At/L of 4 p s / m , which is required 239
to m e a s u r e the Pu resonance at 0. 3 eV with 3. 5% accuracy [ 1 7 ] . This important specification was adopted because of future plans for measuring t h e r m a l neutron s p e c t r a in Pu-containing s y s t e m s .
The total time uncertainty At is mainly determined by the width of the neutron pulse from the r o t o r , which pulse is approximately triangular with a width at half maximum At = s / 2 cur. There a r e , of c o u r s e , other time u n c e r -tainties such a s the analyser -channel width, the time for a neutron to pass through
the detector (detection time) and the time for the r o t o r - s l i t axis to scan the detector
or source surface (sweep time), but these uncertainties can be easily adjusted. It i s good p r a c t i c e to choose all partial time uncertainties approximately equal, s o a s to optimise the counting r a t e . In that case the overall resolution time, which is minimum, may be conservatively estimated at 2 . 5 times the partial
time uncertainties.
Hence,
At/lj = 2 . 5 s / 2 ujr L = 4 x l O ' ^ s m"-*- and s/l^ « 3. 2 x lO"® uur . (2. 5)
Using E q s . (2. 3) and (2. 5) it followed that s = 2 . 60 x l O ' ^ m and 1^ = 6. 20 m, whereas Eq. (2. 4) gave R = 2. 774 m.
After determination of the rotor dimensions and the flight path, the counting r a t e had to be optimised. To obtain a high counting r a t e the distance 1 between
a
the source and the chopper axis should be s m a l l . On the other hand, the chopper should be well shielded, and these considerations led to the choice 1 = 115 cm
a (see also F i g s . 2 . 1 and 2. 3).
F u r t h e r obvious m e a s u r e s to enhance the counting r a t e were to use three p a r a l l e l slits in the rotor and nine detectors instead of a minimum of three (see Fig. 2 . 1 ) . The only remaining means of increasing the counting r a t e was to i n c r e a s e the source a r e a , i . e . the a r e a of the bottom of the probe tube, but, for the c a s e of the space-dependent spectriun m e a s u r e m e n t s the problem of the perturbation caused by this probe tube then immediately a r o s e . As explained before, a probe tube of rectangular c r o s s section, with one side much s m a l l e r than the other, was chosen to alleviate this problem, and the coUimation of the neutron beam was adjusted accordingly. Using the above dimensions and a
2
source a r e a of 6 cm x 0. 8 cm RS 5 cm , a counting r a t e could be calculated with which a spectrum from a pseudo r e a c t o r cell with about 3% s t a t i s t i c s can be m e a s u r e d within 12 h o u r s .
This time was considered reasonable; however, the above-mentioned source flux was based on the expected r e a c t o r power level of 2 MW, whereas at the s t a r t of this investigation this level was only 200 kW (the latter level resulting
9 —2 —1
in a flux in the source region of about 2 x 10 cm s ). To enable spectrum m e a s u r e m e n t s at this low r e a c t o r - p o w e r level, the possibility of reducing the flight path to 3. 20 m was incorporated. With this flight path and the use of a rotor with l a r g e r sUts, about ten times higher counting r a t e s could be obtained, although at the expense of resolution and an increased angular background. The dimensions of this second rotor (rotor II) a r e given in Table 2 . 1 ; this table also s u m m a r i s e s all data on the normal rotor (rotor I).
2 . 2 . 3 C o n s t r u c t i o n
The apparatus has been constructed in the workshops of the Technological University of Delft; the chopper has been made to our specifications by Nonius N. V . , Delft.
Table 2 . 1
Some important design parameters of the spectrometer* Spectrometer arrangement I
n
Flight path 1 a (m) 1.15 1.15 (m) 6.20 3.20 Chopper rotor r (m) 0.10 0.10 s (m) 2 . 6 0 X l o " ^ 4 . 9 4 X l o ' ^ slit height (m) 24 X l o " ^ 24 X l o " R (m) 2.774 1.458 number of slits 3 3Fig. 2 . 3 The mechanical construction of the spectrometer
Figure 2. 3 shows a general outline of the mechanical construction of the s p e c t r o m e t e r . The location of the s p e c t r o m e t e r with r e s p e c t to the r e a c t o r c o r e was dictated by the presence of a hole in the concrete shielding next to the t h e r m a l column. The experimental geometry, the chopper and collimators a r e all combined in one rigid construction, which r e s t s on wheels. This whole construction can be withdrawn from the hole, so that changes in the geometry can be made and maintenance of the chopper c a r r i e d out. All collimators a r e Uned out with a theodolite when the s p e c t r o m e t e r is out of the hole. When moving
• It should be mentioned that in sect. 2. 2 . 4 . 3 effective rotor parameters will be derived which differ from the design parameters given in this t a b l e .
the apparatus into the hole, it should not touch the hole walls, s o that the c o l -Umation of the neutron beam is not disturbed.
Neutron chopper
The construction of the neutron chopper can be seen in Fig. 2 . 4 . In this construction full use has been made of the experience gained by Harwell, where s e v e r a l choppers of this type a r e in operation. The chopper consists of a m i l d -steel tank with holes for the insertion of c o l l i m a t o r s . These a r e provided with aluminium windows, so that the chopper can be evacuated. The tank has a removable lid (on which the motor stator is mounted), so that either of the two r o t o r s specified in Table 2 . 1 can be installed. The slits in rotor I (s = 2. 6 mm) have been made by s p a r k erosion, those in rotor II (s = 4. 94 mm) by cutting.
Fig. 2.4 The mechanical construction of the Fig. 2.5 Lubricating system of the chopper chopper
The r o t o r s a r e fitted with two journal ball b e a r i i ^ s , which a r e lubricated con-tinuously, without breaking the vacuum, by means of the system indicated in F i g . 2. 5. At one end the rotor axis is extended with a double-sided polished m e t a l m i r r o r , which, together with a small light source and a photocell, forms the optical system which provides the starting pulse mentioned above. At the other end of the r o t o r axis a sleeve is mounted, which is the r o t o r of a 100-watt 3-phase h y s t e r e s i s motor (Smith type HM 16). The motor is jKJwered by a
thousand throughout the run. For safety r e a s o n s , deterioration of bearing performance is detected in two ways. The t e m p e r a t u r e of each bearing is m e a s -ured with a thermocouple and recorded continuously. F u r t h e r , the vibrations of the chopper a r e measured with an a c c e l e r a t o r detector (Bruël and Kjaer type 4332), and the mean vibration amplitude is also recorded continuously. Both r o t o r s 1 and II were tested at 233 s (= 14. 000 rpm) in a test pit of the Mechanical Engineering Department of the Delft Technological University.
Flight tube
There a r e nine 5 cm diameter proportional counters filled with BF„ gas 10 to 0. 93 bar (= 70 cm Hg). The boron has been enriched to 96% in the isotope B. The counters a r e , together with their shielding, mounted on a s e p a r a t e truck to facilitate the alignment of all c o l l i m a t o r s .
Electronics
The flight tube consists of three sections; removal of the last two sections r e d u c e s the flight path from 6. 20 m to 3. 20 m. Aluminium windows at both ends of the tube allow the tube to be evacuated. With a backing pump a p r e s s u r e
-3
of less than 10 bar can be obtained in the flight tube as well as in the chopper tank. The flight tube and the colUmating sections a r e lined with borated wax.
Counters
The neutrondetector pulses a r e analysed with a TMC (Technical M e a s u r e -ment Corporation) analyser with 4096 channels and 16 s e p a r a t e inputs. This analyser has been so modified that it can accommodate two time-of-flight experiments independently. One half of the memory has been allocated for a r o t a t i n g - c r y s t a l experiment [18], whereas the other half ( i . e . 2048 channels) with four s e p a r a t e inputs (each with max. 512 channels) has been used for the experiment h e r e reported. Channel widths of 8, 16, 32 and 64 |is have been used. Each BF counter is connected to a separate cathode-follower amplifier. The nine counters a r e divided into three groups, as indicated in Fig. 2 . 1 . The amplifier outputs of each group a r e connected to one of the four inputs of the a n a l y s e r . This makes it possible, in the calculation of the s p e c t r u m , to allocate to each group of counters its proper flight path and, hence, to reduce the time uncertainty in the detection time.
2 . 2 . 4 A n a l y s i s of d a t a
For the calculation of a neutron spectrum from the a n a l y s e r - m e m o r y contents, the following factors must be known:
(1) Number of background neutrons in each channel. (2) Analyser time s c a l e .
(3) T r a n s m i s s i o n of r o t o r . (4) Detector efficiency.
(5) Distortion caused by the resolution of the s p e c t r o m e t e r .
(6) T r a n s m i s s i o n of the m a t e r i a l s present in the neutron beam between s o u r c e and d e t e c t o r s .
In the following sections these factors will first be discussed in m o r e detail; subsequently a description will be given of the OWL p r o g r a m which t r a n s f o r m s the a n a l y s e r - m e m o r y contents into final neutron s p e c t r a .
2 . 2 . 4 . 1 Background
The neutron background may be considered to have two components, which r e s u l t from (1) neutrons that a r e transmitted through the rotor during the interval between two pulses and (2) neutrons that reach the detector after penetrating the shielding of the experiment (general r e a c t o r background).
Since the amount of K-monel in the neutron beam depends on the angle which the slits make with the beam axis, component (1) varies with the rotor position during the time between the p u l s e s . In F i g s . 2. 6a and 2. 7a r e s u l t s a r e given of a graphical determination of this background component for r o t o r s I and II. The macroscopic removal c r o s s section of K-monel is about 1. 3 cm up to about 30 keV, where it falls to about 0. 35 cm ; the above-mentioned two figures show the angledependent relative t r a n s m i s s i o n for these two c r o s s -section values.
The general r e a c t o r background i s , of c o u r s e , time-independent and in F i g . 2. 6a the total background can therefore be found by shifting the curve in vertical direction. This total background has also been determined e x p e r i m e n -tally. A plug of B .C saturated paraffin was inserted into the neutron beam, which only transmitted neutrons with a negligible flight time, and the rotor speed was set to an a r b i t r a r i l y chosen value. The angular distribution of the total background then followed from the a n a l y s e r - m e m o r y contents. Figures 2. 6b
u.
^
o 2 0 4 0 6 0 BO 1 0 0 120 140 1 6 0 IflO 4 0 0 2 0 0 30 6 0 9 0 120 150 " 1B0 f i a a 4 0 0 2 0 0 f b a c k g r o u n d c o u n t s , a r b . scale\
tv.,
J
^
-3 0 6 0 9 0 120 150 1 8 0 l i ^ b k backgro\mii c o u n t s , a r c . s c a l e O^ ' 2 0 ^ b 6 0 8 0 l ü ü 120 140 160 180
Fig. 2 . 6 Background of rotor I a. Angle-dependent relative
transmission
b . Total background determined dynamically
c . Total background determined statically
Fig. 2. 7 Background of rotor II a. Angle-dependent relative
transmission
b. Total background determined dynamically
c . Total background determined statically
and 2. 7b show the total neutron background measured in this dynamical way. The total background has also been determined statically, with the rotor sUts making a fixed angle with the neutron beam, and counting all transmitted neutrons. By varying the angle, the angle-dependent total background has been obtained. The r e s u l t s of such m e a s u r e m e n t s a r e given in F i g s . 2. 6c and 2. 7c; they appear to tally reasonably well with the background functions determined dynamically.
The procedure for determining the background function b(t) in Eq. (2.1) is as follows. After each m e a s u r e m e n t the contents of the analyser back-ground chaimels, which a r e the channels corresponding to rotor angles a between approx. 160 and 180 , a r e plotted and the background curves of F i g s . 2. 6b and 2. 7b a r e made to fit in this region by multiplying the vertical scale by a factor. Values of b read off from F i g s . 2. 6b and 2. 7b for 10 equidistant values between a = 90 and a = 180 , multiplied by the s a m e factor, a r e then
supplied a s input for the data-analyser p r o g r a m (see sect. 2 . 2 . 4 . 6). In this p r o g r a m the background for every a, andhencefor every flight time, is obtained by linear interpolation.
2 . 2 . 4 . 2 Calibration of analyser time scale
The channel width determined by the electronic clock of the analyser could be easily checked and was found to be accurate to 1 to 10 . However, determination of the z e r o flight time t with r e s p e c t to the time scale of the analyser proved to be r a t h e r difficult. This z e r o time corresponds to the moment at which the slits a r e in the "open" position as indicated in Fig. 2 . 1 .
Initial calibrations were c a r r i e d out by measuring the total c r o s s section of aluminium. Because of Bragg reflection, this c r o s s section shows some marked jumps, the most pronounced jump being at 0. 0037 eV, which can be used to calibrate the z e r o flight time (see Fig. 2.8).
W'
Iff' w* 4 0 0 300 2O0 3O0 200 100 30O 200 lOO 3 0 0 2 0 0 counts P(f
. ^...-,
L
T Channel^ • _ . .
••yf-"
• • • • • • • • •.,/f
.,.
1 (rpm mi. . * • * '
32«1 57S4 9000 IligM time in,s too 200 300 « O 500 600 700 800 90O 10OO nOO 1200 1300Fig. 2. 8 The total cross section of aluminium Fig. 2 . 9 High-energy tail of water spectrum measured at different rotor speeds. (The arrows indicate the zero flight time t ).
o
This calibration can, however, only be c a r r i e d out at a rotor speed of 20 s (= 1200 rpm); at higher rotor speeds the neutron transmission of the r o t o r at 0. 0037 eV becomes negligible. It appeared from spectrum m e a s u r e m e n t s at higher rotor speeds that the time calibration is dependent on this speed. This proved to be mainly due to the limited frequency range of the photocell (OAP12), causing some phase shifting of the starting pulse at higher rotor s p e e d s .
An alternative method was therefore developed, which could be used to calibrate the time s c a l e for any r o t o r speed. This method makes use of the fact that the a r r i v a l of the first ( i . e . fastest) neutrons can be made visible on the display of the analyser by the introduction of a suitable electronic delay of the starting XHilse and by turning the m i r r o r on the rotor axis 10 forward with respect to the s l i t s .
In Fig. 2. 9 the step in the neutron counting r a t e , corresponding to the a r r i v a l of the first neutrons, is shown for various rotor speeds. The midpoints of these steps (indicated by arrows) correspond to the z e r o flight time t , a s will be explained below. In Fig. 2.10 the time difference between the starting pulse and t , and the rotation angle covered by the rotor speed a r e shown as a function of rotor speed. The increasing delay in the starting pulse transmission at increasing r o t o r speeds is especially apparent from the latter function.
SOlOO ' 7I$00 ' sok»
—.. rotor speed (rpm) 9 2 ^ 5 8 0 ^ 5 rotor pulse scon
3000 SOOO 7000 9000 —^ rotor speed (rpm) 32 MS chomet w i d t h Fig, 0 20A\a 4 spectrum mg. b 204 HS 204)is StM tlflCti llsplay of a
Fig. 2.10 The flight-time correction as a function of rotor speed
Fig. 2.11 Derivation of analyser response to — spectrum. (The times quoted E
represent base widths).
The step in the counting r a t e in Fig. 2 . 9 , with uu = 30.25 s (1815 rpm), has been further analysed by calculation, a s shown in Fig. 2 . 1 1 . Figure 2.11a shows on the right the pulse shape which can be derived for infinitely fast neutrons at this rotor sjieed. This pulse shape follows from the partial resolution functions, a l s o shown in Fig. 2.11a, such as the nearly triangular rotor pulse (base width 92 ^s) and the rectangular time functions, which correspond to the scanning of 18
the slit axis of the detector bank and the analyser channel width (base widths 80 y,s and 32 ^us respectively). The detection time for these fast neutrons is z e r o . The symbol (x) in Fig. 2.11 can be considered a convolution operator defined by f(t) (x) g(t) = J f(t') g(t-t')dt'. Figure 2. l i b indicates the counting-r a t e function which follows fcounting-rom combining the pulse decounting-rived, with the neutcounting-ron distribution n(t) which corresponds to the 1 / E tail of the s p e c t r u m .
The counting-rate step function derived tallies reasonably well with the m e a s u r e d one, which indicates that the s p e c t r o m e t e r operates as expected. Moreover, as all p a r t i a l time uncertainties used in the analysis a r e s y m m e t r i c a l , it is c l e a r that the z e r o - t i m e point should indeed lie halfway the m e a s u r e d steps shown in Fig. 2. 9.
As a check on the calibration procedure developed, infinite-medium water s p e c t r a , m e a s u r e d a t various rotor speeds, have been analysed using the flight-time c o r r e c t i o n as indicated in Fig. 2 . 1 0 . The neutron t e m p e r a t u r e s of the resulting s p e c t r a did not differ by m o r e than 5 K.
2. 2. 4. 3. T r a n s m i s s i o n function of the r o t o r s
F o r the velocity-dependent t r a n s m i s s i o n T of a parallel neutron beam through a rotor (radius r) with p a r a l l e l - s i d e d curved slits (radius of curvature R, width s) and made from a m a t e r i a l with infinitely large removal c r o s s section ("black" r o t o r ) , Larsson et a l . [ 1 2 ] , and M a r s e g u e r r e and Pauli [19] have derived the following expressions:
T ( Y ) = 1 - | Y ^ , 0 < Y < Ï . T(Y) = 8 ( | Y^ - Y + I Y^) . Ï < Y < 1 .
t-t 1 s Ij
with Y = I , J " I . t = :5= , t„t
-(2.6) t - t I ' m 2u)R ' c m 2 c m r u) t - t As - I m I _ I ,0)1 1 . / s I c m f rT r a n s m i s s i o n of r o t o r I
In Fig. 2.12 curve a r e p r e s e n t s T(üt)t) of rotor I, calculated with Eq. (2. 6) using the design values from Table 2 . 1 for L, s, r and R. (This curve can also be obtained from Fig. 2. 2 by multiplying the horizontal scale by p—)• The value for tut = TT, indicated in Fig. 2.12, corresponds to the a r r i v a l of infinitely fast neutrons from the following rotor pulse. F o r uut values between out and TT, the t r a n s m i s s i o n is z e r o ; thus, only background neutrons a r e counted in this region. According to requirement (5), and Eq. (2. 2) tn section 2. 2. 2, 1.15 ujt = n.
An obvious requirement for a t r a n s m i s s i o n function is that the s p e c t r a from the same medium determined at different rotor speeds should coincide. It was shown that the function of Fig. 2.12 did not fuKil this r e q u i r e m e n t , which turned out to be due to the fact that the rotor sUts had not been lined with cadmium, although this had been specified. Rotor I is therefore not "black" for t h e r m a l neutrons, so that E q s . (2. 6) do not apply. "Grey" r o t o r s , i . e . r o t o r s with a finite macroscopic removal c r o s s section (E ), have been considered
^ ^ r e m '
by Verbinski and J a r r a r d [20] . In this c a s e no explicit expressions for the t r a n s m i s s i o n function a r e found. Reed and R o s s , however, have suggested [21] that E q s . (2. 6) could still be used for " g r e y " r o t o r s , provided r is replaced by an effective radius r fff«r - 1/E . When following this suggestion, coinciding s p e c t r a could still not be obtained, and it was thought possible that R had not
c
been made to specification. A " t r i a l and e r r o r " p r o g r a m , in which R and—g J* w e r e varied, finally yielded the following "best" values:
R = 2. 650 m (design value 2. 774 m),
- | = 0.152 m ^ (design value 0.130 m \ . r
T(u)t) calculated with these p a r a m e t e r s is shown in Fig. 2.12 a s curve b . Infinite-medium water sjiectra obtained using the adjusted t r a n s m i s s i o n function a r e shown in Fig. 2.13 for a few rotor speeds (see a l s o sect. 4. 2 for further experimental details). Considering Fig. 2 . 1 3 , it can be seen that the deviation of the effective r o t o r p a r a m e t e r s from their design values reduces the number of channels for background determination to nil. Direct background determination with r o t o r I is therefore not possible until the slits have been cadmium - lined.
transmission T(iiit) of rotor I
R. 2.650m \P»'"»™'«7*"''^^ r i ' } Oeni water spoctra
,R«2-774m "l design —» 0.130 m'ƒ parameters . , o ' UNITS 1 1 ,o'
"^
n ROTOR T1UNSH 1 0. u u 1 C/
/ / /
/ /
' J •/
Y/\
/ /
1 1
/
V A
'
/^^^^ (-)EXPEWMEHTAL OAU 89*0rpm\l-l"'O«J"ED WITH THIN5«20riini\ \
32«A^\^V,!
/ A \V .
» , 5 ^ \ ^ - - ••v..
n nnnsn inatw -•—ROTDR SPEED
X 7 \ \
/C\\\
/^^"~~^~^^^^^^^
/
,0 — » - NEUTRON ENEROV (eV)
Fig. 2.12 The transmission function of rotor I
Fig. 2.13 Infinite-medium water spectra mea-sured at different rotor speeds (spectro-meter arrangement 1). Note that the same calculated spectrum fits all four experimental spectra
Meanwhile, the bacl^round-determination procedure described in section 2. 2 . 4 . 1 i s used only for m e a s u r e m e n t s at rotor speeds of 33. 3 s (= 2000 rpm) or lower. In these m e a s u r e m e n t s the number of "spectrum neutrons" in the last 10-15% of the channels i s small, a s compared with the number of background n e u t r o n s , s o that a true backgroimd level can b e measured. This latter level i s adjusted in proportion to the monitored total neutron dosage to obtain the back-ground for runs at higher r o t o r s p e e d s .
T r a n s m i s s i o n of r o t o r II
The " t r i a l and e r r o r " p r o g r a m mentioned above was a l s o c a r r i e d out to determine the "best" transmission p a r a m e t e r s for rotor II. The resulting values
R = 1.462 m (design value 1.458 m),
- ^ = 0.262 m ^ (design value 0.247 m ^ ) . r
The slits of rotor II w e r e cadmium-Uned and the "best" values therefore a g r e e reasonably well with the design values (see Fig. 2.14).
Ilight time
o 3520')
a 2 5 6 0 I . . . • 2080 ?«*?*'•'"'«'''*' point» X 176oJ
calculated with eq. (2£) 1 parameters which Agive M- indepen'.t. • 't/v " H J C [ . C M -— ï0262mjd^nt water spectra .R= 1.<58m't design Ai0.2<7m'Y parameters
Fig. 2.14 The transmission function of rotor II
As the t r a n s m i s s i o n function T depends on ujt, one may also determine T by measuring s p e c t r a from the s a m e medium at different r o t o r speeds and comparing the relative intensities of neutrons with the s a m e flight time. In Fig. 2.14 r e s u l t s a r e given of such a determination of T for rotor II, and one may s e e that the experimental points of T found in this manner a g r e e s a t i s -factorily with the curve found by " t r i a l and e r r o r " .
The cadmium lining l o s e s , of c o u r s e , its effectiveness with increasing neutron energy, and the t r a n s m i s s i o n p a r a m e t e r s should be c o r r e c t e d a c c o r d -ingly. In Fig. 2.15 the correction procedure is shown: below 0. 2 eV the above-mentioned "best" p a r a m e t e r s a r e used, above 0. 6 eV r is replaced by r
r - 1
eff 1 2
= , yielding s / r „ = 0. 00307 m ^, whereas between 0. 2 eV and 0. 6 eV r e m
a joining function is used, which has the s a m e trend a s the cadmium c r o s s s e c -tion func-tion. Infinite-medium water s p e c t r a measured at different rotor speeds and analysed using the abovedefined t r a n s m i s s i o n curve, coincide, and m o r e -over they a g r e e , as they should, with s p e c t r a measured with rotor I (compare F i g s . 2 . 1 3 and 2.16).
U J < l
10-^
I T calculated with r^ff
n „ .. r
— final T used for rotor II
• corrected « uncorrected
Fig. 2.
10" E(eV)
15 The transmission correction above 0. 2 eV for rotor II
601|^rpm
/"T^-(^experimental data (-)calculated with THIN
1800 rpm 6012 rpm
"" 3612 rpm 1 ^ — r o t o r speed
Fig. 2.16 Infinitemedium water spectra m e a -sured at different rotor speeds (spectro-m e t e r arrange(spectro-ment II). Note that the same calculated spectrum fits all the experimental spectra shown above and those shown in Fig. 2 . 1 3 .
2. 2. 4. 4 Detector efficiency
The efficiency e(t) of the bank of nine detectors can be calculated from the manufacturer's data regarding the B contents and the geometrical a r -rangement of the c o u n t e r s . In Fig. 2.17 the geometry of the counter bank is given.
When the following absorption probabilities a r e derived,
f^(x,t) = 1 - exp (-6 E^(t) (Vr2^-(r^-x)2+Vr2^-x2)).
f (X, t) = 1 - exp (-6 E^(t) Vr^ -x^),
for neutrons in the beam regions 1 and 2 respectively, shown in Fig. 2 . 1 7 , then e(t) is given by the expression
s(t) = J f ^ ( x , t ) d x + J f2(x,t)dx , (2.7)
where h , is the height of the detector collimator, r is the radius of the BF c o u n t e r s , E (t) = E v / v = E v t / L and E = E (v ), with v = 2200 m / s .
a ^ ' a o a o f a a o ' o o o o
F r o m the gas p r e s s u r e and enrichment quoted by the manufacturer, i . e . 0. 93 bar (70 cm Hg) and 96% ^°B respectively, it follows that E = 0 . 095 cm""*^.
a o
Figure 2.18 shows the efficiency function calculated according to Eq. (2. 7) for this E value. The detector was also calibrated experimentally using
a
° 1 counters the sensitivity of which is known to vary as —. These a r e 1 cm diameter
^ 10 BF„ counters filled to a p r e s s u r e of 0. 93 b a r (70 cm Hg) with 90% B, which means that the counters a r e thin enough in the nuclear sense for their sensitivity to vary a s the boron c r o s s section. In Fig. 2.18 the points indicate the r e s u l t of the calibration. Owing to the low counting r a t e obtained with the s m a l l coimters
detector collimator
Fig. 2.17 The geometry of the detector bank Fig. 2.18 The efficiency of the detector
(three in p a r a l l e l were used), the experimental points show large variations, although the m e a s u r e m e n t has been continued for s e v e r a l weeks. The c a l i b r a -tion should, in due c o u r s e , be repeated after the expected i n c r e a s e in r e a c t o r power, or the bank should be sent to e. g. E u r a t o m ' s CBNM at Geel for calibration.
Meanwhile, in this work use has been made of Eq. (2. 7) and the manufac-t u r e r ' s filling damanufac-ta, i . e . E = 0.095 cm
o
2. 2 . 4 . 5 Other c o r r e c t i o n s
The time resolution of the s p e c t r o m e t e r At causes the neutron distribution n.(t) incident on the chopper to be different from the actual distribution n(t) d e -rived. Neglecting higher derivatives than the second o r d e r . Stone and Slovacek [22] have shown that
"i<^)-°(^) i M _ ' d!nit).
n(t) 12 n(t) • ^^2
A few of our m e a s u r e m e n t s , in which this c o r r e c t i o n could be expected to be relatively high, w e r e evaluated and'a maximum e r r o r of about 2% was found. F o r most of our m e a s u r e m e n t s the e r r o r was < 1%.
The fraction of neutrons removed from the neutron beam by scattering and absorption in the aluminium windows of the evacuated flight tube, in the copper lining of the BF„ counters and in the air between the source and the flight tube has been calculated to be about 15%, but the variation of this fraction between 0. 01 eV and 0. 5 eV, and hence, the spectrum distortion in this region is not m o r e than + 2%.
2. 2. 4. 6 The OWL p r o g r a m
The calculation of the neutron spectrum from the a n a l y z e r - m e m o r y contents r e q u i r e s that the c o r r e c t i o n s described in the previous section must be applied to the counts in each channel. Since t h e r e a r e hundreds of channels, this task is c u m b e r s o m e and a computer p r o g r a m , designated OWL, which can be run on the University of Delft's TR4, has been written which transforms the raw analyser data punched on eight-hole tape into final plotted spectra. Full details of this OWL p r o g r a m a r e given in [ 2 3 ] and [24] . The various calculations c a r r i e d out a r e briefly enumerated below.
(1) The flight time t, pertaining to each channel 1 is calculated using the relation:
tj =(l-è).At^-t^(cu) , (2.8)
with t = channel width and t (ou) = z e r o - t i m e position following from section 2. 2. 4. 2. Equation (2. 8) indicates that the channels a r e r e p r e s e n t e d in the
time s c a l e by their midpoints.
(2) The contents of each channel a r e c o r r e c t e d for background using the method described in 2. 2 . 4 . 1 ,
(3) The counts a r e c o r r e c t e d for any differences in flight path; a s mentioned before, the nine BF„ counters have been geometrically spUt into three groups with flight paths 1, , L and L , and each group is connected to its own group
^1 2 ' 3
of channels in the a n a l y s e r . The neutron counts from different groups, but in corresponding channels, should be c o r r e c t e d for this difference in flight path before they a r e added. This is done in OWL as follows: the time s c a l e s of groups 2 and 3 a r e normalised by multiplying by L / I , and L / l , r e
-*1 *2 1 3 spectively (see Fig. 2.19). The counts of a normalised channel a r e then added to the group-1 channels in proportion to the fractional overlap with these latter channels. So, for instance, in F i g . 2.19 the fractions AB/AC and B C / A C of the counts in channel 4 group 2 a r e added to channels 3 and 4 respectively of group 1.
time scale multiplied by — r - ' . 2 3 4 - 1 - 1 2 . e ^ 3 . 3. i . i A B; C . •< . I s . « f 1(gm time ^ 5 6 . 7 1
"./''.
'<J\
Fig. 2.19 Correction for differences in flight path
(4) Spurious channel counts a r e eliminated.
Incidentally a fault in the analyser may r e s u l t in a very large or z e r o number of counts in one or two particular channels, without affecting the contents of the other channels. In OWL these faulty channel contents a r e then automat-ically replaced by the average of the contents of the two adjacent channels. This is done in view of the procedure to be followed for the determination of the neutron t e m p e r a t u r e (see below).
(5) The neutron density for each t, is calculated using Eq. (2.1), i . e . n(t.) = w ' , / v , T . e , , with w'. being the c o r r e c t e d contents of channel 1 following from the calculations (2) to (4), v^ = 1 / t , , T = T(tj) and e = e(tj). The functions T and e follow from Eq. (2. 6) and Eq. (2. 7) respectively. In this p r o g r a m function g is taken to be 1; hence, if the corrections mentioned in
s e c t . 2. 2. 4. 5 a r e d e s i r e d , these must be made by hand.
(6) The distributions n(v), n(E) , $(v), §(E), Ef(E) a r e calculated using the r e l a t i o n s :
2 3 n(v) = n(t)dt/dv = j — n ( t ) , n(E) = n(t)dt/dE = - ^^ n(t) ,
f., m l ,
^ 1
$(v) = V n(v) and $(E) = v n(E), where m = m a s s of neutron.
(7) The neutron t e m p e r a t u r e T of the Maxwell spectrum M(E) which fits best
^ —E/kT wdth the m e a s u r e d spectrum $(E) is calculated. As M(E) ~ Ee ^, it
follows that In M(E)/E = -ri^ > a^nd the neutron t e m p e r a t u r e is found by Kin 1 determining, with a l e a s t - s q u a r e s fit, the slope -T-^ of the straight Une which can be drawn through points with co-ordinates (ln($,/E,). E,). with *^ = $(E.) and E, = è mv, .
2.2.5 Accuracy of the measured spectra
In Fig. 2 . 1 3 and following figures, showing measured s p e c t r a , the estimated e r r o r s AE in E and AE$(E) in E?(E) a r e indicated for three e n e r g i e s , viz, 0. 01 eV, 0. 05 eV and 0. 5 eV. The horizontal and vertical e r r o r margins indicate r a n g e s E + AE and Ef (E) + AE$(E) respectively.
The first e r r o r AE i s , of c o u r s e , determined by the resolution of the s p e c t r o m e t e r , which is found by combining the p a r t i a l time uncertainties c o n -nected with the scanning of the s o u r c e , the detection time, the channel width and the r o t o r pulse width. F o r an example of how these factors a r e combined, reference is made to Fig. 2.11a and sect. 2 . 2 . 4 . 2 .
As r e g a r d s AE§(E), the following relation may be derived from Eq. (2.1), using n(t)dt = n(E)dE, and E = èml^^/t^:
E § ( E ) - 2 C t ^ ^ ^ ^ ^ ^ ^ ^ .
Hence, the relative e r r o r in E$(E), for a certain energy, equals the sum of the relative e r r o r s in w(t)-b(t), T(t) and e(t).
Considering the method used for the determination of T(t), i. e. by comparing s p e c t r a obtained at various r o t o r speeds, it s e e m s logical that the accuracy of T(t) i s , in fact, the accuracy with which these s p e c t r a have been matched, and from F i g s . 2 . 1 3 and 2.16 this is estimated to be within 3%, 3% and 5% for the
t h r e e above-mentioned e n e r g i e s .
The possible e r r o r in e(t) would be r a t h e r large, if only the calibration m e a s u r e m e n t s reported in sect. 2 . 2 . 4 . 4 were to be considered. However, in Chapter 4 it will be shown that the e r r o r margin due to the combined systematic e r r o r s in e(t) and T(t) cannot be l a r g e r than about 5% (ref. sect. 4. 3. 3).
The e r r o r in w(t) is purely statistical and has been approximated by Vw. The background function has been accurately determined and the statistical e r r o r in b can be neglected, which leads to a relative statistical e r r o r in w-b of Vw/w-b. However, the background function can sometimes not be fitted with sufficient accuracy through the spectrum points in the background channels (see sect. 2 . 2 . 4 . 1 ) . This may lead, especially in runs with a low s p e c t r u m - n e u t r o n / background-neutron r a t i o , to a relative e r r o r —-r-, which should be taken into account.
The e r r o r caused by setting g = 1 in Eq. (2.1), i . e . < 2% (sect. 2 . 2 . 4 . 5 ) , is s m a l l e r than the above e r r o r s and will therefore be neglected in the following.
The total e r r o r AEf (E) can now be obtained from
AE$(E) _Vw , 6e 6T 5b
E$(E) w-b e T w-b '^'^•^>
It should be noted that the statistical e r r o r in Eq. (2. 9) only concerns the indi-vidual channel, corresponding to energy E, and that the e r r o r with which a best fit can be drawn through all measured spectrum points may be considerably better. If one a s s u m e s a pre-knowledge of the spectrum or part of it, then the method of the least squares can be used. So, for instance, it is justified, for most s p e c t r a , to a s s u m e a -^ dependency above 0. 3 eV, and in media with little absorption and leakage it is reasonable to a s s u m e a Maxwellian spectrum below 0.1 eV. If the spectrum is distorted either by absorption or leakage, the latter spectrum assumption can, with approximation, be applied to p a r t s of the s p e c t r u m . In Chapter 4, where calculated s p e c t r a a r e compared with m e a s u r e d s p e c t r a , use is made of such assumptions to obtain a measuring accuracy which is m o r e r e a l i s t i c than that of single-channel contents. Details of this a r e given in sect, 4 . 1 . 3 .
•^.. 3 FOIL-ACTIVATION TECHNIQUES
2 . 3 . 1 G e n e r a l r e m a r k s
The various foil m a t e r i a l s used in this investigation a r e listed in Table 2. 2, together with some relevant isotopic and experimental data. In all c a s e s the integrated number of gamma photons, resulting from the decay of nuclides formed by neutron absorption, was measured with a Nal(Th) scintillation s p e c t r o m e t e r using a fixed lowerthreshold energy. P r i o r to each m e a s u r e m e n t , the g a m m a -energy scale was calibrated with a cesium gamma source to eliminate possible drift a n d / o r t e m p e r a t u r e effects. The lutetium activity was m e a s u r e d three days after the exposure to allow the Lu activity (T^ = 3. 7 h) to decay.
2 2
All isotopes w e r e applied in the form of thin foils (10 x 10 m m ), and their corresponding surface loadings of the natural mixture of isotopes (see Table 2.2) w e r e chosen low enough s o a s to e n s u r e negligible perturbation of the t h e r m a l flux. Dysprosium and lutetium w e r e used in the form of an aluminium alloy.
Table 2 . 2
Some isotopic and experimental data Foil material Dy Au Lu Reaction 164 165 Dy(n,Y) Dy 1 9 7 . , 1 9 8 , Au(n,Y) Au 176, , 177, Lu(n,Y) Lu Main g a m m a energy (MeV) 0.095 0.411 0.208 0.133 Half life z 2.39 h 2 . 7 d 6 . 8 d Threshold energy used (MeV) 0.07 0.30 0.09 Surface l o a d -ing of the natural
mixture of Isotope ( m g / c m ) 2 . 0 100 2 . 7
Dysprosium, which is almost a — a b s o r b e r in the t h e r m a l region, was used to obtain an indication of the integrated-flux level. Gold was activated under cadmium to m e a s u r e the epithermal flux at 4. 9 eV. Lutetium was used in c o m -bination with dysprosium; a s is well-known, the r a t i o of the activities of the two components of this foil pair gives an indication of the " h a r d n e s s " of the
1 Yfi
s p e c t r u m , because of a resonance peak in the absorption c r o s s section of Lu at 0.142 eV (see Fig. 2.20 and amongst others ref. [25]).
oaet (Mriw)
<
^
-y Maxweman neutron v ^ d i s t r i b u t i o n w i t h X T n = 2 9 3 K "Vvy-"«Lu / \ l \ • ^ x 1 o \ \ N ^
\
tor* «(E) arb. units .'rf"Fig. 2. 20 Activation cross sections of Lu and 164py^ Note that a hardening of the spectrum shown (corresponding to a shift to the right) results in an increase in the activation of Lu.
— ^ e(eV)
2 . 3 . 2 A u t o m a t i c f o i l c h a n g e r
The m e a s u r e m e n t of the activation of large s e r i e s of foils is a t i m e c o n s u m -ing task of a m o r e or less routine-like n a t u r e . In order to save time and to
eliminate e r r o r s , a simple automatic foil-changing apparatus has been constructed.
^-T*^
s
Hi
^ photo diocto - : toil ^C3
%
acintlUatJor^
I ^ J ï ^ ^ s ^ ^ ^ ^ perspm plates 1 % s l i g M a o u nc« ^ " ^^
counter^
_
^S
<i^pt
Fig. 2 . 2 1 The automic foil changer
A sketch of the apparatus is given in Fig. 2. 21. It consists of an endless belt on which 24 frames a r e mounted. The foils a r e placed between two perspex plates, which a r e then clamped in the metal frames. The belt, with the frames, i s transported along the window of a scintillation counter by means of an electric motor. A small light source and a photocell a r e mounted on opposite sides of the belt, in line with small holes in the belt which a r e positioned in such a manner that the photocell is actuated when a foil a r r i v e s in the measuring position. The
motor is then stopped, and a counter (Philips PW 4232) and a t i m e r (Philips PW 4260) a r e r e - s e t and s t a r t e d . After a p r e - s e t number of counts or a p r e - s e t t i m e , counting is stopped; the total count and time a r e printed via a printer control (Philips PW 4200). When the printing is finished, the motor is s t a r t e d for a new cycle. The timing of the various actions is further elucidated in Fig. 2. 22. Figure 2. 23 shows a block scheme of the electronics.
The foil changer has been operating successfully and despite its simplicity, has proved t o be very p r a c t i c a l .
e«eark motor indkatjor c o u n t e r / t i m e r
1
1
k
electric m o t o rFig. 2.22 Timing diagram of foil changer Fig. 2.23 Block diagram of foil-changer
elec-tronics
2 . 3 . 3 A n a l y s i s of d a t a
The activation of each foil is c o r r e c t e d for background, for decay since the exposure, for decay during the m e a s u r e m e n t and for differences in the foil
177 165 weight using a s m a l l computer p r o g r a m . In this program the L u / Dy activation r a t i o is normalised with r e s p e c t to the activation r a t i o of a s i m i l a r pair which h a s been i r r a d i a t e d in a known flux. Thus the following relative activation r a t i o is calculated:
<
-177 Lu act. 165 •) 177 Lu act. Dy act. , •' unknown spectrimi i 165 •) Dy act. , •' known spectrumIn L any differences in counting efficiencies for the decay-gamma photons of
the two isotopes a r e eliminated.
2 . 3 . 4 A c c u r a c y of t h e m e a s u r e d a c t i v a t i o n
The e r r o r s in the actual activation m e a s u r e m e n t s were due to: (1) Inaccuracy in the weighir^ of the foils (0.1 mg),
(2) Statistics in the total counting r a t e and background.
A deviation from calculated activity values was further caused by: (3) The inaccuracy in the positioning of the foils in the experimental system.
This last factor proved to be the major source of inaccuracy. The activations w e r e c a r r i e d out in the s a m e s y s t e m s a s used for spectrum m e a s u r e m e n t s ; these s y s t e m s therefore did not contain special r e c e s s e s for locating foils. As a
result, the positioning of the foils, using adhesive tape, could not be done with
good accuracy. In the y-z and x - d i r e c t i o n s , which a r e defined in Fig. 4 . 2 , the maximum e r r o r s a r e approximately 1 mm and approximately 0. 2 mm r e s p e c t -ively.
In our m e a s u r e m e n t s the above c a u s e s led to the following relative e r r o r s (in%): cause: (1) 0 . 3 0.2 0 . 3 _ (2) 0.7 0.4 1.2 _ (3) 3.5 3.5 3.5 _ tota 4 . 5 4 . 1 5.0 3.5 . ., 1 6 5 ^ , in the Dy act. in the [ A u ] _ , act. 177 in the Lu act. . ^, 177^ /165„
in the Lu/ Dy act. r a t i o
The e r r o r s resulting from cause (3) were derived from F i g s . 4. 7a and b and e. g. Fig. 4 . 1 4 . The e r r o r s due to inaccurate positioning in the y-z directions a r e largely eliminated in the activation r a t i o of the lutetium/dysprosium foil
pair. However, some misalignment of these two foils may still occur (0. 3 mm
m a x . ) . Moreover, because of their thicknesses (0.1 mm), the two foils have different x-positions. The e r r o r in the r a t i o quoted above includes an additional 1% to take these factors into account.
