Pulsed neutron method for non-destructive and simultaneous determination of the 235U and 239Pu contents of irradiated and non-irradiated reactor fuel elements

NUCLEAR

INSTRUMENTS

AND

METHODS

73

(I969)

13-33;

©

NORTH-HOLLAND

PUBLISHING

CO.

PULSED NEUTRON METHOD FOR NON-DESTRUCTIVE AND SIMULTANEOUS DETERMINATION OF THE 23SU AND 239pu CONTENTS OF IRRADIATED AND NON-IRRADIATED REACTOR FUEL ELEMENTS* H. K R I N N I N G E R ,

S. W I E S N E R ? a n d C. F A B E R

INTERA TOM, Internationale Atomreaktorbau GmbH, Bensberg bei Kdln, Germany Received 16 April 1969 T h e p r o c e d u r e investigated for t h e n o n - d e s t r u c t i v e d e t e r m i n a t i o n o f the fuel c o n t e n t o f irradiated or n o n - i r r a d i a t e d reactor fuel elements based on detecting the p r o m p t n e u t r o n s released by induced nuclear fissions. T o differentiate between the two fissile isotopes 2aau a n d 239pu a n d for quantitative analysis, their different energy-dependent fission cross sections are used. F o r this p u r p o s e the fuel element to be investigated is successfully exposed to two externally generated n e u t r o n fluxes with different m e a n n e u t r o n energies, i.e. 0.3 eV a n d 0.025 eV. T h e p r o m p t

fission n e u t r o n s are detected by a p r o t o n recoil scintillation counter. A lead spectrometer serves for p r o d u c i n g the different n e u t r o n fluxes. With t h e m e t h o d described, called the slowingd o w n - t i m e m e t h o d , t h e fuel c o n c e n t r a t i o n s N5 ( n u m b e r o f 2z5Ua t o m s / c m 3) and N9 ( n u m b e r o f 239pu a t o m s / c m a) in each individual fuel rod could be d e t e r m i n e d with an accuracy o f ~< 5% by one m e a s u r e m e n t lasting 30 m i n u t e s in each case for t h e used experimental set up.

1. Introduction

elements of light water moderated reactors in all realistic burn-up states. Both a graphical and a numerical procedure were developed for evaluation of the measured results.

The work covered by this report was carried out between 1.6.1966 and 31.12.1967 within the scope of a research contract between the European Atomic Community (Euratom) and Imeratom, Bensberg, Federal Republic of Germany1). Preliminary studies on the applicability of this measuring procedure for non-destructive fuel analysis were started by Interatom as far back as 1959 and led to patents being granted in a number of countries2). The procedure investigated for the non-destructive determination of the fuel content of irradiated or non-irradiated reactor fuel elements based on detecting the prompt neutrons released by induced nuclear fission reactions. To differentiate between the two fissile isotopes 235U and 239pu and for quantitative analysis, their different energy-dependent fission cross sections are used. For this purpose the fuel element to be investigated is successively exposed to two externally generated neutron fluxes with different mean neutron energies, i.e. 0.3 eV and 0.025 eV. The prompt fission neutrons are detected by a proton recoil scintillation counter. A lead spectrometer serves for producing the different neutron fluxes. The method was tested on specially manufactured UO2-PuO2 fuel rods. The fuel contents of the UO2-PuO2 fuel rods were selected in such a way that they are characteristic for the fuel content of the fuel

With the method described, called the slowingdown-time method, the fuel concentration N s (number of 235U atoms/cm 3) and N 9 (number of 2 3 9 p u atoms/cm 3) in each individual fuel rod could be determined with an accuracy of ~< 5% by one measurement lasting 30 minutes for the used experimental set up in each case. The applicability of the slowing-downtime method for the control of the fuel content of non-burnt-up fuel rods in monitoring the flow of fissile materials in the field of peaceful uses of atomic energy was confirmed at the "Gesellschaft fiJr Kernforschung, Karlsruhe"3). Various applications of this method are discussed towards the end of this report. 2. Description of the method For a given neutron flux, the number of fissions taking place in a fuel element depends on the fuel concentration. It is therefore obvious that a method should be used in which a parameter is measured that is proportional to the number of fissions. The prompt fission neutrons emitted during nuclear fission offer themselves for this purpose. In an irradiated fuel element the fuel content consists of the 235U still present after a certain burn-up time and the 2 a a p n and heavier Pu isotopes formed from the 238U during this time. The fission cross-sections of these isotopes differ from each other. In the measurement mentioned

* This work was s u p p o r t e d by E U R A T O M , Bruxelles, C o n t r a c t No. 084-66-5 T E E D. t N o w at Arbeits- u n d Sozialministerium des L a n d e s N o r d rhein-West falen, Dfisseldorf.

13

14

H. KRINNINGER et al.

above the measured value is proportional to the sum of the fissions taking place in all the fissile isotopes. It is hence not possible to determine either the total fuel concentration or the relative proportions of the isotopes by one single measurement. Therefore it is necessary to utilize additionally a parameter which differs in a known and measurable manner for the fissile isotopes 235U and 239pu chiefly present. The energy-dependent fission cross sections for 235U and 239pu meet this requirement. This is particularly applicable to the energy region below 10 eV, in which 239pU exhibits a pronounced resonance at 0.3 eV, which is used to differentiate between the two isotopes. The procedure used for separate determination of the 235U and 239pu contents consists in consecutively irradiating the fuel element being examined in two neutron fluxes having different mean energies, i.e. 0.025eV and 0.3eV, and using as criterion for the total number of fissions the number of prompt fission neutrons detected. The required fuel concentrations can then be calculated from the two fission rates so determined. A socalled reference measurement

with a calibration element of the same type (e.g. a non-irradiated element) with known fuel contents obviates the need for direct determination of the intensity normalizing factors for the two neutron spectra. For generating the different neutron spectra a lead spectrometer is used which utilizes the effect that in a material of high atomic weight the slowing-down time of fast neutrons to the energy E is proportional to E -~. When a brief pulse of fast neutrons is injected into a lead pile, there is a fixed relation between the mean energy of the slowed-down neutrons and the time following cessation of the neutron pulse. It is hence possible to determine the fission rates during the irradiation of the sample with the two different neutron spectra by measuring the counting rate of the p r o m p t fission neutrons at two different time intervals following shut-down of the primary neutron pulse. The time intervals of measurement are selected so that they correspond to mean neutron energies of 0.3 eV and about 0.025 eV. Since the p r o m p t fission neutrons as criterion for

Timp

j

n- source strenght

t

°1'v I

~ ~.-/~

~ fission ne,trons

\ \"~,~

~ i ~ 1 ~ - - - F~X'~%~ ",","\,1"~.~

E.:, thermal region

-I I t

g I

I

I

I I

..9 .~

t

I I

t'~

L.

Td2 -~ Tk2 I-

I

I

o

I I

~= I

t Tdl

_t_

-T-

Fig. 1. Schematictimepatternof two consecutivemeasuringcycles.

Tkl

J

-'

PULSED

NEUTRON

the fissions that have taken place are measured practically without delay time, the entire process can be repeated periodically up to a m a x i m u m frequency of 200 Hz, which is determined by the life-time of the thermal neutrons in lead. The schematic time sequence of two successive measuring cycles is shown in fig. 1. The counting rate D~ to be anticipated in the detector is made up cumulatively from the fission rates in the 235U and 239pu. Here the index i characterizes the two different neutron spectra; i = 1 is attributed to the thermal spectrum, while i = 2 corresponds to the spectrum having a mean energy of 0.3 eV. If self-shielding is neglected, the countivg rates are given by (l)

O 2 = B E ( N 5 a52 -1- N 9 a 9 2 ) ,

(2)

with the fission integrals defined as follows: (i = 1,2) ; (2a)

,

15

/~5, /~9

= efficiency of

the detector for neutrons from z35 U and 239pu ;

Bi

= normalizing factor intensity (i = 1, 2);

4~i

= differential neutron flux.

for

the

fission neutron

To obviate direct determination of the normalizing factors B 1 and B2, the fission rates Dlo and D20 have to be determined in an identical measurement for a non-irradiated fuel element with the known concentration Nso of 23~U:

D 1 = Bl(Nsa51+N9a91),

asi = % f a f s ( E ) ' ~ i ( E ) d E

METHOD

Dlo = B1N50a5t ,

(3)

D20 = B 2 N s o a52 .

(4)

By combining eqs. (1)-(4) one obtains the required atomic densities Ns and N 9 from the four measured values D 1, Dlo, D 2 and D20 as follows:

(5)

g 9 = {(02/020 ) - (Ol/Olo)} (Nso/Aa),

N 5 = {(D1/Dlo ) (a92/a52) - (D2/D20) (a9a/a51)} x

a9i = eo f O'f9(E)" 4 ~ ( E ) d E ,

(i = 1, 2) ;

(2b) x

Ns, No = atomic density o f 235U and 2 3 9 p u ; err5, crt9 = microscopic fission cross-sections of 23sU and 2 3 9 p u ;

ANs Ns

(6)

where Aa is (6a)

Aa = (a92/a52) - ( a 9 1 / a s O .

os~/osl

-- 1

DI

DI

A(D2~ ID2

N

(Nso/Aa),

i~)l ~

"

._

"

~ "I.

10

7.5

~

oszlosz =2

5.0

~"',--~.~O

2.5

S2=4

,

a*a2/as2 = 8

as21os2 =12 -'"

0

0.5

1.0

1.5

Ng N~

2~

Fig. 2. Relative error o f the particle density N9 as a function o f the ratio No/N5 ; parameter: fission integral ratio a92/as"~at 0.3 eV.

16

et al.

H. KRINNINGER

2.1. ERROR DISCUSSION By differentiating eqs. (5) and (6) and going over to the difference quotient, the dependence of the relative errors AN5/N 5 and AN9/N 9 on the fission integrals a92 , a9D a52 and a51 and on the measured counting rates D2, D2o , D 1 and Dlo can be calculated. Assuming a91/a51 = 1 o n e obtains:

,.52

L

+

+ D2/D2o. ,d (D2/D2o)l N s + N 9 DI/D1o DE/D2o J N9

(7)

I

ANs _ (a92_ l) -I Fa92.A(D1/Dlo) + N5 \a52 La52 D1/Dlo D2/D2o A(Dz/D2o) 1 Ns+No

+

J

(8)

N-----S'

where:

D2/D2o Da/Dao

1+

(a92/a52) (N9/N5) 1 + (N9/Ns)

(9)

Figs. 2 and 3 show the characteristic errors derived from eq. (7) and (8) as a function of N9/N5 for various

values of a92/a52. These diagrams are valid on the following premises:

{A (D,/D,o)}/(D~/D,o) = 1 % ,

(10)

{A (Dz/Dzo)}/(Dz/D2o)

(11)

= 1%,

a91/a51 = 1.

(12)

The first two requirements are fulfilled if each of the four counting rates D1, Dlo , D E and D2o is measured with an accuracy of 0.5%. a91/ast is determined by the ratio of the thermal fission cross-sections of the isotopes 239pu (Gf9 "~' 740 b) and 235U (af5 580 b), so that the third assumption is nearly justified. From figs. 2 and 3 it can be seen that in order to obtain high accuracy as large as possible a92/a52 values are necessary. It is characteristic of the error pattern that the isotope which is present in only a low percentage can only be determined with a relative large error. For the 239pu isotope, which is only produced in the course of burn-up by conversion of 238U, in the considered example the error limit of 5% is not undershot until the particle density N9 amounts to more than 20% of the particle density N5. The special significance specifically attributable to the fission integral ratio a92/a52 also becomes clear. If the afore-

Q91/051 =1

Ns

I ,tp - -

& D~

[°/o]

--:

Dlo

1%

a {'D2~/D2 : 1o/.

\D'#/ D~O l0

I •

I

25

. ~ I / I

2.5

I o

0.5

1.o

Fig. 3. Relative error of the particle density N5 as a function of the ratio

1.5

N_Z9 Ns

2.0

Ng/Ns; parameter: fission integral ratio a92/a52at

0.3 eV.

PULSED NEUTRON METHOD

mentioned requirements are fulfilled, the attainable accuracy for a given ratio Ng/N 5 of the fissile isotopes 235U and 2 3 9 p u is only dependent on the magnitude of the fission integral ratio a92/as2. 2.2.

DETERMINATION OF UNKNOWN FUEL

17

anticipated. This is taken into consideration by the fact that the detectors used for fast neutron measurement are separated from the surface of the fuel element by a layer of several centimeters of lead which reduces the gamma dose rate at the detector to admissible value for the latter.

CONCENTRATIONS

The separate determination of the particle densities N5 and No of the 235U and 239pUcontained in the fuel elements from the measured total fission rates, eqs. (5) and (6), is possible if the fission integral ratios a9i/asi (i = 1, 2) are known. Because of the existing slowingdown-time dependent energy distribution of the slowed-down neutrons in the lead spectrometer, the fission integrals defined in accordance with eqs. (2a) and (2b) are parameters which are specific to the spectrometer, i.e. dependent on the operating conditions of the lead spectrometer which are the source pulse duration Tjmp and the pulse interval T = l/fz. Similarly, the fission integral ratios a9i/asi are also dependent on the settings Td, and Tk, (fig. 1) of the single channel time analyzers. In order to obtain a clear picture and simplify the discussion of errors, eqs. ( 1 ) - ( 9 ) do not take into consideration the self-shielding effect in the fuel. Actually, however, there is a considerable dependence of the self-shielding on N 5 and N 9 which cannot be neglected for the measurement. If fuel rods of different diameters are analyzed, the geometrical dependence of self-shielding must also be considered. Finally, when complete fuel elements are being examined, the shielding of the inner zones of the element by the outer zones must be additionally discussed. For practical application of the procedure it is hence necessary to select calibration samples suitable for the considered problems and to go over from the analytical method, eqs. (5) and (6), to a graphical or numerical procedure to determine the unknown fuel concentrations N 5 and Ng. 2.2.1. Perturbationby the 9amma activity of the

fission products The proposed method is also intended for analysis of fuels which, after being removed only temporarily from the reactor for determination of their burn-up are then replaced again in the reactor. When this procedure is followed there is generally insufficient time available to wait for the decay of the gamma activity of the fission products, so that an activity of 10*-105r/h at the surface of the fuel elements during burn-up measurement is to be

3. Experimental set-up The experimental set-up, consisting of a lead spectrometer 2s) in a measuring cell surrounded by heavy concrete walls and a neutron generator. 3.1. LEAD SPECTROMETER

The moderator block of the slowing-down-time spectrometer consists of lead bricks which were built up on a supporting structure to form a cube with an edge length of 1.60 m (fig. 4). In the horizontal mean plane, two measuring channels having a cross-section of 10x 10 c m 2 a r e arranged at right angles to each other and pass completely through the cube. In one of the measuring channels the fuel rods are arranged in the middle of the lead cube, i.e. in the position of the highest neutron flux. From the other end of this channel the target tube of the neutron generator is introduced and the target is positioned about 20 cm from the centre of the cube. In the second measuring channel two detectors of the same type are located whose distances from the fuel rods can be varied along the axis of the measuring channel. All cavities remaining in the measuring channels are filled with shaped lead bricks. Except for the underside of the lead cube, which is shielded by a coating of Cd 1 mm thick, all cube faces are clad with a coating of boric acid 15 mm thick in aluminium containers for shielding against backscattered neutrons. 3.2. NEUTRON GENERATOR For producing the neutron pulses, a neutron generator built by Interatom is available which, ill design and performance, corresponds to the Type N G 250 generator described by Eyrich9). The generator produces 14 MeV neutrons by the D-T reaction in the form of rectangular pulses with a source strength of 1011 neutrons/sec in the pulse. Maximum pulse widths of 80--I00/~sec are possible with a pulse repetition frequency of 200 Hz. 3.3. DETECTORSFOR FAST NEUTRONS The first requirement of the detectors to be used is that they should exhibit an efficiency for fast

18

H. K R I N N I N G E R e t a l . h

~ / /

shielding wall

(concrete)

-..,

1,6rn ° lead cube (/,7 t ) .

~\~C~,x.\\'.(~\

.

.

.

i

\ \ -,-., \ ? ~ \ \ \

\\

/

.

~Ooo ° , o

I

_//

.

.

.

.

.

..""2--_

~oo°o°°d~°~l Fig. 4. Scheme of the measuring cell with the lead spectrometer.

TABLE 1 Efficiencies of various detectors for PoBe-neutrons (en) and for O°Co g a m m a radiation (el').

Detector

Organic N E 150 N E 213 N E 451

scintillators: (2" dia. x 16 mm) (2" dia. x 2") (2" dia. x 16 m m )

aHe counter '~38U fission chamber 237Np fission chamber

Literature, manufacturers' information en(cps/FE)

2 2 0.5 5 x 10-a 3.4 x 10-4* 2.9 x 10-4*

* M a x i m u m value for commercial type of fission chamber.

Detection probability experimental en e l' (cps/FE) (cps/mr. h)

0.1 0.2 0.3

0.002 0.008 10-5

1.5 x 10-3

Dymax (r/h)

Notes

0.1 0.025

pulse shape discr. pulse shape discr. pulse height discr.

0

~10

pulse height discr.

0 0

104 104

E

IP"

PULSED NEUTRON METHOD

19

In t h e case of the N E 150 and N E 213 scintillators the sensitivity loss for e, as compared with the data found in the literature is caused by the pulse shape discrimination process applied. Pulse height discrimination against thermal neutrons reduces the sensitivity of the 3He counter tube to fast neutrons. Table 1 shows that detectors with good efficiency for fast neutrons en also exhibit high g a m m a sensitivity, whereas g a m m a insensitive detectors also exhibit a poor %. With the exception of the fission chambers all detectors require lead shielding about 20 to 25 cm thick to reduce the high g a m m a dosage rate at the surface of irradiated fuel elements to the admissible m a x i m u m dosage rate D~max. Since the g a m m a attenuation in lead is several orders of magnitude greater than the neutron attenuation, detectors with high efficiencies for fast neutrons are prefered for the slowing-down-time method.

neutrons as high as possible. On the other hand the detector must be insensitive to thermal and epithermal neutrons simultaneously present and causing the fissions. A third criterion for selection of the detectors arises from the requirement for also being able to investigate the fuel content of irradiated fuel elements and this demands that the detector be insensitive to g a m m a radiation up to high dosage rates. Since none of the conventional types of detector for the detection of fast neutrons, e.g. plastic scintillation counters, 3He counters or fission chambers, simultaneously fulfills all three conditions, first of all a comparison was made of these detectors in respect of their applicability for the problem concerned. The criteria are the experimentally determined neutron and g a m m a sensitivities of various plastic scintillation counters and of a 3He counter as well as manufacturers' data on different fission chambers. The most important data for these detectors are summarized in table 1. The dosage rate Drm,, is defined as that threshold value above which the g a m m a sensitivity of the relevant detector strongly increases above the value stated in table 1, as a result of pile-up.

3.3.1. Selection of the most suitable detector The detector type was sought which, for a given surface g a m m a activity Do of the fuel element to be investigated, supplied the highest fission neutron

10 -1

"~" " ' -

~..~10 ~'-

5

r/h (8, = Q 2 7 c p s / F E )

I r/h (S, = 0.42 c p s / F E ~ "

~

plastic

~'~.~...

NE 451

scintillat0r

----- .............., -..,. ~ 10 -z

d

liquid scintillator

~ -.....,,=__ ~.~ ~ "-----..._ 01 r / ~ " " ~ - ~

~

--.....

NE

213

0.025 r/h ~" "" • -

5 plastic scintillator

o

N E 150

~--._..._

~'

10-3

~

.

~

3

.

~

. ~

..-.~

N P 2 3 7 - fission chamber ~ . ~ .

10 ~ r / h

I0 _I.

~ 3 r/h ~

~

~

5 103

5

10~

5

10s

5

---.

106

"-'-'-Do [r/h_] 5 I0 ?

Fig. 5. Products of efficiencyfor fission neutrons en and geometry factorfg for various types of detectors as a function of the surface gamma dose of irradiated fuel elements.

20

H. KRINNINGER et al.

counting rate with the smallest possible background counting rate. For a given fission neutron flux at the surface of the fuel element, the efficiency e, multiplied by a geometrical factor fg, which represents the attenuation of the neutron flux as a function of the thickness of lead between the surface of the fuel element and the detector, is directly proportional to the fission neutron counting rate. The product f g . e n was calculated, using known attenuation factors for a typical gamma spectrum of fission products in lead1°), the measured attenuation factor fg for fission neutrons in lead and the e, values from table 1 for the various detectors: The geometry factor f * is dimensionless and normalized so that it assumes a value of 1 at the surface of the fuel element. The dependence of the product f * ' e n on the 7dosage rate D O at the surface of the fuel element is shown in fig. 5. The corresponding gamma dosage rate at the point where the detector is located is given for each curve in this diagram. Fig. 5 shows that independent of the surface activity of the fuel element the N E 451 plastic scintillation counter always provides the highest fission neutron counting rate. It is on the average, indeed, five times higher than those of the N E 150 plastic scintillation counter and the liquid scintillation counter N E 213. Both 3He counter tubes and fission chambers are more than one order of magnitude less sensitive than all organic scintillation counters. A further advantage of the scintillation counters which is not directly apparent from fig. 5 is the fact that they hardly influence the neutron flux at the position of the fuel element, since because of their gamma sensitivity they have to be arranged on the average some 20 to 30 cm from the surface of the fuel element. 3.3.2. Background countin9 rates of the N E 150, NE 213 and NE 451 scintillation counters in the lead spectrometer The experiments with the N E 1 5 0 and N E 2 1 3 scintillation counters did not lead to a satisfactory result, inasmuch as the signal to background ratio, i.e. the ratio between the fission neutron counting rate detected by the scintillation counter and the background counting rate simultaneously present, was much smaller than unity. The relatively high gamma sensitivity of these scintillation counters together with the slowing-down-time dependent gamma background in the lead spectrometer and the decay of excited energy levels in the scintillator seem to be responsible for this result. Possible causes of the gamma background are

(n,y) processes in the cadmium layer surrounding the scintillation counters for shielding against the primary neutrons, (n,),) processes in the lead or its contaminants, or isomeric states in one of the lead isotopes which are induced by non-elastic collisions with fast neutrons. The measurements with the NE451 scintillation counter supplied good results. For the slowing-downtime region of the 2 3 9 p u r e s o n a n c e at 0.3 eV and optimal threshold setting on the linear amplifier with integral discriminator and the pulsed neutron generator operating with maximum source strength a background counting rate of 0.2 cps per detector was obtained, of which 0.05 cps are attributable to the natural background counting rate. In the same energy region the calibration sample 24 (table 2) gave a fission neutron counting rate of 20 cps, so that a value of about 100 was obtained for the signal to background ratio. TABLE 2 U-Pu calibration samples.

Sample no.

1 2 3 4 5 6 7 8 9 10 I1 12 13 14 15 16 17 18 19 20 21 22 23 24

Enrichment (wt %)

Weight (g)

235 U

289pu

235 U

239pu

0.4 0.4 0.4 0.72 0.72 0.72 1.0 1.0 1.0 1.5 1.5 1.5 2.5 2.5 2.5 0.4 0.72 1.0 1.5 2.5 5 5 5 5

1.0 0.6 0.3 1.0 0.6 0.3 1.0 0.6 0.3 1.0 0.6 0.3 1.0 0.6 0.3 ------0.3 0.6 1.0

0.569 0.538 0.547 0.970 0.966 0.982 1.340 1.346 1.352 1.997 2.002 2.018 3.289 3.609 3.318 0.551 0.986 1.349 2.018 3.340 6.866 6.825 6.751 6.770

1.801 1.017 0.5•4 1.706 1.014 0.514 1.697 1.017 0.509 1.686 1.010 0.506 1.666 1.000 0.500 ------0.506 1.005 1.690

Fission isotope density 102°/cms N(235U)/V(239pu)

0.646 0.612 0.621 1.104 1.104 1.118 1.527 1.537 1.545 2.282 2.289 2.298 3.752 3.765 3.782 0.628 1.117 1.545 2.301 3.804 7.791 7.735 7.670 7.692

1.831 1.036 0.523 1.737 1.037 0.523 1.731 1.040 0.520 1.724 1.033 0.516 1.701 1.018 0.510 ------0.513 1.022 1.716

3.4. SINGLECHANNELTIME ANALYZER The single channel time analyzer permits separate setting of delay time (Td) and measuring time (Tk)

PULSED

NEUTRON

21

METHOD

within the range from 50 psec to 6 msec. The delay time starts with the triggering pulse of the neutron generator. During this time no detector pulses are counted. The delay time Td is followed by the measuring time

has been developed as frequency standard. It permits the time settings Td and Tk to be measured accurately to 1 p s e c .

71 (fig. 1).

3.5. MEASURING EQUIPMENT Fig. 6 shows the block diagram of the measuring equipment. The essential features of this apparatus are: 1. Two standard scintillation counters with a lucite light pipe whose output signals are added in a mixer are employed. 2. Two identical channels consting of linear amplifier with integral discriminator, single channel time analyzer and electronic scaler record indepen-

The single channel time analyzer is equipped with micrologic circuits. This enables high counting frequencies, low susceptibility to faults, high switching speed and low temperature dependency. The delay time and the measuring time set on the single channel time analyzer must be precisely known and adjustable. For this purpose an additional time base circuit with quartz-controlled 1 Mc/s oscillator

monitor

I monitor II

i I pro-

amplifier

neasuring cell

I

channe] ..... lyzer J I [- . . . . . . . .

single

I

[

i ........

single channel analyzer "t

counter monitor II

d _

sin]l= channel time ~mllyzer

time analyzer

J

counter ?

printer read-out control I l =

X-Y-plotter

I !

--il

I

monitorIII

adapter l rl . . .i. . . multi channel analyzer ] i read'°ut unit ! ! I

ter

....

!, !

J

m

I

single channel time analyzer

monitor I

I

counter 1

measuring room

~ I

. . . . . . . . .

I °r'°'er I

counter /timer)

ST"2T

~ n- gen. |

pulegenerator neutron generator I puncher

Fig. 6. Block diagram of the measuring equipment.

I

]

22

H. KRINNINGER et al. dently of each other the fission rates which are induced in the fuel samples by the 0.3 eV spectrum and the thermal spectrum. 3. Each measurement is controlled by two monitors a long counter in a fixed position outside the lead spectrometer (monitor I) and a BF3 counter tube of the type 5 EB 40 (20 th Century Electronics) in a defined position inside the lead spectrometer (monitor II). In order to be able to eliminate dead-time effects, the pulses of the latter monitor are additionally recorded by a single channel time analyzer (monitor III) whose delay time Ta is set to 200/~sec (measuring time Tk = 5000/~sec). 4. Following the starting signal from a central pulse generator in the control desk of the neutron generator, measurements are performed automatically until stopped by monitor channel II on which a certain number of pulses was preselected. The stop signal simultaneously commands a printer with a read-out unit to request the counting rates recorded by the two electronic scalers and to print the results.

During the investigations, which were spread over a period of about 4 month, the background counting rate was practically constant. The fluctuation of the number of counts recorded by monitor III when 2 x 106 pulses were always preselected by monitor II was smaller than 0.5%. 4. Calibration samples The calibration samples were manufactured by the "Europ~iisches Institut fiir Transurane, Karlsruhe". The isotopic mixtures for the 24 calibration samples listed in table 2 were selected so that they roughly characterize the fuel enrichments in common used for light water moderated reactors and their burn-up states usually concerned. Specification of the U-Pu calibration samples: Fuel: UO2 in powder form, PuO2 (91% z39pu) in powder form, The homogenous distribution of the PuO2 in the pellets was checked by Pu analyses and autoradiographs. Pellet diameter: 12.0 +_0.05 mm, Pellet column height: 200 + 0 mm - 0 . 1 mm, Fuel density: 6.7- 6.8 g/cm 3. Canning and CrNi steel 2025, Nb stabilized end plugs:

(in accordance with British Standard), Outside diameter: 13 mm, Wall thickness: 0.4 mm. 5. Fission rates in the U-Pu calibration samples 5.1. OPTIMIZATION OF THE SETTINGS OF THE MEASURING EQUIPMENT

The criterion for optimization of the measuring apparatus was the requirement that the fundamental error limit in the determination of the particle densities N 5 and N 9 be kept substantially below 5% which requires for a92/a52 a value of > 4 according to section 2.2. A further requirement was a maximum statistical error of 0.5% for the number of counts in the two single channel time analyzers ZEK1 and ZEK2. At least 40 000 events therefore had to be recorded in each of the two measuring channels. Optimization consisted than in attaining this number of counts with a minimum of measuring time by fulfilling the requirement a92/as2 >=4. In principle the total measuring time can be reduced by increasing the primary neutron pulse frequency fz, the primary neutron pulse width Timp and the measuring time Tk of the relevant single channel time analyzer. It was investigated in detail to what extent these parameters can be increased without infringing the requirement a92/a52 ~ 4. The decay of the thermal neutron flux in the lead pile fixes a maximum primary neutron pulse frequency offz = 175 Hz. For reducing the measuring time there hence remained only variation of the primary pulse width Timp and of the settings (Td, Tk) on the single channel time analyzers. These investigations showed that with the maximum attainable primary pulse width of Timp = 85 ~sec obtainable with the Interatom neutron generator the following settings just fulfill the requirement a92/a52 >~ 4: ZEK2: Delay time: Measuring time:

Td2 = 530/~sec, Tk2 = 270 ~sec.

In order to attain the same detector counting rate with smaller primary pulse width Timp, for a given measuring time the channel width Tk2 would have to be increased so much that the requirement a92/a52 >= 4 would no longer be fulfilled. The setting of the "thermal" single time channel analyzer Z E K I , on the other hand is not critical, since the sole condition to be met is that a91/a5~ ~ 1 (section 2.2). Here the following values were laid down,

PULSED

which resulted in a fission integral ratio a91/as ~ = ZEKh Delay time: Td, = 1 2 0 0 / ~ s e c , Measuring time: Tk, = 2 8 0 0 # s e c .

5.2.

NEUTRON

1.3:

D E P E N D E N C E OF THE FISSION RATES IN THE U - P u CALIBRATION SAMPLES ON N 9 , N 5 A N D dpb

These measurements formed the basis for producing a calibration diagram. All settings of the measuring apparatus (fig. 6) were selected in accordance with the optimization of the method considering that the detected fission neutron counting rate of the two detectors is not only determined by the dependence on the various enrichments of 235U and 239pu, but also by the dependence on the geometry of detector and calibration sample. Figs. 7 - 9 show the fission neutron counting rates recorded by the single channel time analyzers ZEK1 and ZEK2 with various geometries of the calibration sample to the detectors as a function of the fuel isotope densities N5 (parameter: N9).

23

METHOD

All the counting rates shown in the diagrams are background-corrected and related to the same monitor counting rate ( 2 x 106pulses in monitor II). The background measurement was carried out with the pulsed neutron generator without fuel rod in the lead pile. All U-Pu calibration samples - with the exception of the natural uranium sample series (calibration specimens 4, 5, 6 and 1 7 ) - w e r e inserted in the lead spectrometer. If one compares in figs. 7, 8 and 9 the measurements with different geometries (dpb = 0, 10 and 20 cm), the pattern of the ZEK2 counting rate against N5 becomes a straight line for dpb = 10cm and dpb = 20 cm. In the single channel ZEK2 there is hence no increase in the self-shielding caused by the absorption in the 238U by the addition of 235U as fig. 7 would initially lead one to suspect. This simulated selfshielding is rather an effect caused by the detectors. Actually it is only for the samples with the highest enrichment that the absorption in the 235U (S,5) ZEK 2 : Taz = 5 3 0 psec ~ Tk2 : 2 7 0 I1S¢C

146C0

,,2, .... ~°.o~,q

12000

tO3

+ .

0,52

2~i

Y)03o

,+

~

o.s2

8000 6000

Ti~,~ = 85P.$¢C ~tektor NE 451 Z~..,.~. = 2'10 r'

4000

Tim p = 551J.S¢c

Deteldor NE 451 ZMonlt~ll = 2-~0 II dpb = 10 cm

dp b = 0era

2C00 0

0

,

2

ZEK1

~

.

5

: T~, =1200p.sccl Tk,

+

,

~ + + ~.o., + , ]

'it s, 0

1

I

',

m

L

I'

2

3

4

5

6

,'

7

=2800psec

ZEK1 : IOC00

2s00- .r

1

2000-

/ !

!,.~ ,+,. I;o-.~ 1.03 052 0

8CC0

1500-

6000 Ti,,~= 85Psec Deteldor NE 451 Z,,,.mt.,..it • 2.10 I de~=O cm

40OO

_

~

t~-

.

Td, =1200¼s¢c;

~

Tk,=2800pSeC

I

,

1

f

I ~ . I -

/__._.I~'"

/@....~/~....~

1

4

5

7

810

ENu z~s • c m ' ~

Fig. 7. Fission neutron counting rates in the single channel time analyzers as a function of the fuel content N(ZZsU); lead thickness between fuel sample and detector dpb = 0 cm; parameter:

N(Z39Pu).

~0Z°'crr~

Ti.p= 851~

i - "I"~""~"f' ~ J

o .--"L

0

1.72N . . . . 1.(~ 0.52 0

Det~ktor NE 1.51

''''a~

...... 1 . . . . . .

ZMenilorlI ¢ 2.10 dPb =10cm

2OOO

0

, 8.10z° [Nu 23s • cm'~

0

1

[ 2

i 3

4

5

6

7

+10" ~.o,,, °~'l

Fig. 8. Fission neutron counting rates in the single channel time analyzers as a function of the fuel content N(2asU). Lead thickness between fuel sample and detector dpb = 10cm; parameter: N(2Zapu).

24

H. KRINNINGER et al.

becomes comparable with the absorption in 2 3 a u (.FaS), so that a noticeably increasing self-shielding effect is not to be anticipated until still higher particle densities N5 are attained. On the other hand, there is a noticeable increase in self-shielding in the epithermal energy region (ZEK2) because of the 0.3 eV resonance in the 2 3 9 p u (right-hand diagram in figs. 10, 11 and 12, which shows the counting rate in the ZEK2 as a function of N9). Already with the lowest enrichment o f 2 3 9 p u , depending on the sample we have Z~a9 ~_~ (Z~aS+~a8). With increasing enrichment, absorption in the 239pu increases further, so that for the calibration samples with 1% o f 2 3 9 p u by weight we have 2fa9 > 3 (Za5 + Sa8). If one considers the counting rate in the thermal energy region ZEK1 against the fuel density N 5 (figs. 7 and 8) an increasing self-shielding is again observed here, but this time by the 2aSU. In actual fact, for an enrichment of 2.5 wt % of 23SU we already have

~a5 ~-~ (~a8 "[-Z~a9); according to what has been said in the foregoing, this is a criterion for the marked increase in self-shielding. The measurements with dpb = 20 cm (fig. 9) do not appear to confirm this result. Against this it must be said that in the first place the statistical error of the counting rates is the largest in this case and in the second place, depending on the sample, the background counting rate (which has been subtracted) was always more than 50% of the total counting rate, which further increases the error. Accordingly, it should be anticipated that more accurate measurements would also indicate the characteristic pattern of the ZEK1 counting rate for dpb = 20 cm for increasing self-shielding. There is constant selfshielding in single channel ZEK1 and in the region of particle density N9 covered by the calibration samples (left-hand diagram in figs. 10, 11 and 12); this is to be anticipated, since we have X,9 < (~a8 + XaS)" 5.3. RESULTS OF THE BACKGROUND MEASUREMENTS

800

ZEK2:

_T

600

Taz : 5301J.sec ; Tk2 * Z?01aSec 1.,2

I

f

r

f f

/

1.03

/

. /

Table 3 lists the absolute background counting rates per detector for the optimum settings of the experimental set-up.

0.52

TABLE 3

Background counting rate per detector in the ZEK1 and ZEK2 with pulsed and switched-off neutron generator (detector: NE 451).

/

/ I

~

0 Tim~=BSlZsec Oetektor NE 451 ZMealtorI I : 2"10 II

!

Settings

Counting rate (cps)

E (eV)

dw*b= 20 cm

0.3 eV regio~

pulsed n-generator

0

I

2 ZEKI:

3

4

6

7

8.10 zQ ~Nu,., cnn'~ L . . J

Tt I =12G)l~Sec; T% =2800t~s¢c 1.72 N puz31EOZS.cm')-I 103 0.52

400

natural background

Z E K I (Td~ = 1200/tsec, Tkt = 2800/~sec)

0.04

0.035

0.025

ZEK2(Td 2 = Tk,. =

0.2

0.06

0.3

530/~sec, 270/~sec)

,

Ti~ = 85 llsec

E is the average neutron energy in slowing down spectrum.

Detektor NE/.51

200

Zl4onllel I = 2"10 -8

- /

"

deb =20cm

/

thermal reglon

m

2

3

4

5

6

7

8.102o INu2]s.cm "~]

Fig. 9. Fission neutron counting rates in the single channel analyzers as a function o f the fuel content N(235U). Lead thickness between fuel sample and detector dpb = 2 0 c m ; parameter: N(289Pu).

Because of the different sensitivities of the two measuring channels the natural background counting rates of the two single channels differ somewhat. In the " t h e r m a l " single channel ZEK1, practically no increase in the background counting rate can be observed even with the pulsed generator. In the single channel ZEK2, however, the background counting rate which is greater by a factor of five in pulsed operation is attributable to the processes in the lead

PULSED

NEUTRON

25

METHOD U.3 eV

Timp : 85 psec Detektor HE 451 ZMonitor II : 2106 dpb=0 crn

reqion

ZEK 2 : Td2:530Psec T

14000I

Tk2=270ps,¢ ....... Nun, ~OZ°'crn')

, ooo! I

ZEKI: Tdl: 1200psec Tkl= 2800 usec

I'

thermal region

I 1000C T

3E UJ N

!

Nun~ ~.0Z°.cm") 1,54

0.63

2O00

o!

0

I

1.0

0.5

[--Npu239"cm'3]

0 [

Z0.1020

0

1.5

i

~Pu 239,'cm-~

0,5

1.0

1.6

2,0.1020

Fig. 10. Fission n e u t r o n c o u n t i n g rates in the single c h a n n e l time analyzers as a f u n c t i o n o f the fuel c o n t e n t N(239pu). Lead thickness between fuel s a m p l e a n d detector dpb = 0 c m ; parameter: N(2s5U).

1i.3 el/ reqlon

Timp =85 psec Detektor NE 451 ZMonitor II = 2.106 dpb=10 cm

I

th, rm:] r~ llon ZEK 1: Tdl =1200psec Tk1=2800 psec

[

I

I N 2000

i

"

~

3500

I! Nuns ~0'"cm-~ I

N

I 2500

ZEK2 Td2=5301Jsec Tk2= 270 psec

3000

.....

t

L /

~70

?

"

~

3.77

I

I

~Pu23i'cm-3]

1,0

1.5

l_/[Y

2500

,

b0-.cm,~ ~

7170

• 3.77

~

2000 1500

1000

oi 0

, 05

1,0

1.5

2.0-1020

500

0,5

2,0.1020

Fig. 11. Fission n e u t r o n c o u n t i n g rates in the single channel time analyzers as a function o f the fuel c o n t e n t N(ZagPu). Lead thickness between fuel sample a n d detector dpb = 10 c m ; parameter: N(2ssU).

H. KRINNINGER et al.

26

Timp =85psec Detektor NE/,51 ZMonitor i I = 2.106 dpb=20cm

ZEK 1: Tdl =1200psec Tkl=2800psec c

ZEK2 :Td2 =530 psec Tk2 =270 psec

Nuzzs~0ZO.crr~']i l

- - - ~

7.70

/ < . .77

400

0.3eVregion

I

/ 1000

[

~

800

i

30O

i'/'/

,

Lo/

~0

.7 0

I,

200

m

.....

100 ~_ 3 u -239.cm-3 l [ / 0

0

0.5

1.0

1.5

2.0.1020

~

o,

0

N

m~

P

I

0.5

~_ ] Nu 239.cm-3 p

]

1.0

J

1,5

2.0-1020

Fig. 12. Fission n e u t r o n counting rates in the single channel time analyzers as a function of the fuel content N(289Pu). Lead thickness between fuel sample and detector dPb = 20 cm; parameter: N(2asU).

spectrometer itself or in the detector material as described earlier. Because of the slowing-down-time dependent background the background counting rate in Z E K 2 is further dependent on the settings Td2 and Tk2. 5.4.

AXIAL RESOLVING POWER OF THE EXPERIMENTAL SET UP

As criterion for the axial resolving power the half width H of the counting rate distribution was taken which results when an aluminium rod of length L clamped between 2 identical fuel rods is shifted along the axis of these fuel rods. The condition L/H <~ 1 could not be fulfilled for intensity reasons. L varied for various thicknesses dpb of lead between 4 and 20 cm. The half width H determined in this way was between H = 1 4 c m for dpb = 0 c m and H = 30 cm for dpb = 20 cm. 6. Procedure for the determination of the unknown fuel concentrations N9 and N 5 The unknown atomic densities Ns and N 9 c a n be directly calculated from the four counting rates D I ( Z E K I ) , D l o ( Z E K 1 ) , D2(ZEK2) and D2o(ZEK2) with the aid of the eqs. (5) and (6) when the fission

integral ratios a9i/asi are known. Initial considerations assumed that for the content of 235U and 2 3 9 p u characteristic for light water moderated reactors no significant self-shielding was to be anticipated in the fuel rods, so that a9i/asi would be constant and spectrometer specific parameters. The results of measurement contradict this assumption, so that modification of the method characterized by eqs. (5) and (6) for the determination of the unknown fuel densities N5 and N 9 became necessary. The modified method is based on the following facts: With fixed fuel rod/detector geometry and the same monitor preselection the counting rates measured in the timing channels ZEK1 and Z E K 2 for the calibration samples each defines a one-parameter family of curves with the particle density N 5 as abscissa and the particle density N9 as parameter and vice versa. If one presupposes a knowledge of the two characteristic curve d i a g r a m s - which at the moment only applies for the region of enrichment of 235U and 239pU covered by our U-Pu calibration samples and for their g e o m e t r y - t o g e t h e r with the ZEK1 and ZEK2 counting rates recorded for an unknown sample one then has a uniquely determined and graphically solvable system (section 6.2).

PULSED

NEUTRON

6.1. CALIBRATION DIAGRAM The semilogarithmic representation of the counting rates in the timing channels ZEK1 and ZEK2 in the form of one-parameter families of curves in only one diagram is termed the calibration diagram. The semilogarithmic co-ordinates make all measurements for the determination of unknown fuel concentrations independent of the monitor counting rate with which the calibration diagram was recorded. The ratio from the monitor counts of the measurement and the monitor counts of the calibration measurements defines the factor by which the ZEK1 and ZEK2 counting rates must be multiplied in comparison with the calibration measurement; on the semilogarithmic scale this means the addition of a constant, i.e. only a shift of the two families of curves parallel to the ordinate axis. The calibration diagram was constructed for the measured results for dab = 0 because with this

1 2

3

4

5

7.103

6

7

B

9

27

METHOD

geometry every investigated sample was inserted several times in the lead spectrometer and the counting statistics are particularly good. Fig. 13 shows calibration diagram 1 in which the ZEKI and ZEK2 counting rates are plotted against N(235U)/cm 3 [parameter: N(239pu)/cm3]. The straight line c u r v e s N( 235 U)/cm 3 constant are numbered 1 through 10 with increasing enrichment of 235U, while the curves N(239pu)/cm 3 = constant are designated by small letters in alphabetical order. The points of intersection of the straight line curves (1), (3), (4), (6) and (10) with the curves (a), (c), (e) and (g) are obtained by measuring the calibration samples. The curves (d) and (f) are found by interpolation from the calibration diagram 2 (fig. 14) still to be discussed. =

In principle, the calibration diagram 1 suffices for graphical determination of the unknown fuel concentration. However, reading off the enrichment N(239pu)/ cm 3 from this diagram is not accurate enough; this

U'"~

N . . . . . ]I020 " C'~'~

I0

,0,__1.72

i

."

(el - - 1 0 3

k75

(el - - 0 5 2

2.3 1.5 77

( 9) . . . . ~ (e) . . . .

1.72 1.03

{o c --

052

0.6 3.75 2.3 15 0.6

2

g

•

t

f c

/

e

1039

/

/' ,// " // i /" //

d

/'

c

// / ,:, j

7

1 6

~ 2 • 'E ~ "

a

Z=or£tJr :: :." C C l ~ r l ' :a~ :r y: J, ,ci ~st;:! w,r;:i ,:,~:

/

~

. r "IH

; r ~ z c , l J ',:r ir ,ti ~

",

S"S='__7

!

o

3

0

o

I

3

Fig. 13. Calibration diagram channel analyzers ZEK1 and content N(235U); parameter: graphical determination

4

5

6

7

8"10~ EN . . . .

0,2

0~4

0,6

oJJ

!.0

L2

1.4

1JB

I~

2.0402Q

r.~f '1

1: Counting rates in the single Z E K 2 as a function of the fuel N(2aapu); demonstration of the of u n k n o w n fuel densities.

Fig. 14. Calibration diagram channel analyzers ZEK1 and content N(239pu); parameter: graphical determination

2: Counting rates in the single Z E K 2 as a function of the fuel N(235U); demonstration of the of unknown fuel densities.

28

H. K R I N N I N G E R et

can be obviated if one uses the calibration diagram 2 (fig. 14) in which the ZEK1 and ZEK2 counting rates are plotted semilogarithmically against N ( 2 3 9 p u ) / c m 3. 6.2.

GRAPHICAL PROCEDURE FOR THE DETERMINATION OF THE UNKNOWN FISSION ISOTOPE DENSITIES N 5 AND N 9 FROM THE CALIBRATION DIAGRAM

The graphical procedure is now explained by using a measurement with sample l0 (table 2) as an example. The background corrected ZEK1 and ZEK2 counting rates are plotted as horizontal straight line curves in fig. 13 and fig. 14. Perpendiculars are dropped from the points of intersection of the ZEK2 counting rate with the ZEK2 family of curves (solid curves in fig. 13) to the corresponding ZEK1 family of curves. The perpendicular hence joins curves having identical designations [e.g. curve (g) from the ZEK2 family with the curve (g) from the ZEK1 family]. The perpendicular points of intersection with the ZEK1 family again themselves describe a curve whose point of intersection with the horizontal of the ZEK1 counting rate gives the required enrichment. Tbe fuel density N ( E a s u ) / c m 3 c a n simply be read off from the abscissa. To determine N(E39pu)/cm 3 it is recommended employing the ZEK1 and ZEK2 background corrected counting rates in conjunction with calibration diagram 2 and proceeding analogously (fig. 14). A comparison of the graphically determined fuel concentrations with the nominal values shows in this case that despite poor statistics of the measured values and the calibration values an error of better than 6% was attained for the fuel concentrations. Table 4 shows a comparison of the fuel densities N5 and N 9 graphically determined for a number of calibration samples with the actual enrichments present. When the procedure is employed for routine burn-up measurements, evaluation is carried out as follows: A calibration measurement is carried out on the fuel rod which has not been burnt up and has a known enrichment of 235U. After the preselected monitor counts have been attained, the counting rates of the single channels ZEK1 and ZEK2 are read off. The background corrected counting rates are then plotted on transparent sernilogarithmic paper against the known enrichment of 235U (same abscissa scale as in calibration diagram l) and the ordinates of the transparency superposed on that of calibration diagram 1. If the transparency is now shifted along the ordinate until the ZEK1/ZEK2 counting rate touches

al. TABLE 4

C o m p a r i s o n of the fuel isotopic densities as graphically determined with the enrichments of 2a5U and 239pu actually present in the analyzed samples listed in table 2. Experiment data: N e u t r o n generator Timp = 85/~sec;fz = 175 Hz; Target ion current : 150 /tA. Single-channel time-analyzers: Z E K I : Tdl = 1200/tsec; Tkx = 2800/~sec. Z E K 2 : T d 2 = 530/~sec; Tk2 = 270/~sec. Detectors: 2 × N E 451 with lucite light pipes. Zmonitor 11:2 × 106 pulses (Tmeas. ~, 1800 sec). Geometry: dab = 0 cm.

Calibration sample no.

4 8 11 13 23 24

N o m i n a l values according to table 2 1020/cm 3

Graphical determination 102°/cm 3

N5

N9

N5

1.10 1.34 2.29 3.289 7.67 7.69

1.73 1.017 1.032 1.66 1.00 1.71

1.05 1.45 2.17 3.45 8.10 7.3

N9 1.56 0.99 1.1 1.77 1.12 1.70

the curve (a) of the corresponding family of curves, the position of the transparency is fixed with respect to calibration diagram 1. This fix also applies with respect to calibration diagram 2. After the ZEKI and ZEK2 counting rates have been recorded for a burnt-up sample of the same type with the same monitor counting rate as during the calibration measurement, after making the background correction graphical evaluation can be carried out directly by following the procedure just described. 6.3. NUMERICAL PROCEDURE FOR THE DETERMINATION OF THE UNKNOWN FISSION ISOTOPE DENSITIES N 5 AND N 9 FROM THE CALIBRATION DIAGRAM

At first sight it appeared appropriate to represent the families of curves of the calibration diagram in analytical form in a similar manner to that described in section 6.2 and then to solve the resulting set of equations for the unknown particle densities N 5 and N 9. As a result one would then have two equations of the form N i = NI(DI, D2, D1o, D2o) (with i = 5,9) in which the measured fission rates D~o and D2o of the non-irradiated element and D1, D 2 for the same element, but after irradiation could be substituted to obtain the required particle densities. Because of self-shielding, for a power series set-up

PULSED NEUTRON METHOD

for the families of curves at least the quadratic term has to be additionally included. However, solution of this set of equations then leads to a conditional equation of third degree for N5 and N9, i.e. N s and N 9 can no longer be represented as a closed function ot the four counting rates D~, DE, D~o and D2o. Consequently, a computer program was developed which calculates the particle densities N5 and N 9 in two steps by the aforementioned procedure. To describe the families of curves the modified equation below is employed O i = °~i N 5 q- {(fli N 9 -k e.i Ns)/(1 + ~i N5)) + ~'iN9,

( i = 1, 2).

03)

The first part of the program uses the Gaussian method of least square error to calculate from the measured values of the calibration diagram the best values for the 10 parameters cti, ei, 7i, 6i and fit, the so-called fitting parameters. In the second part of the programme, after feeding in the fitting parameter and the 4 measured counting rates D1, D 2 Dxo and D20 it is later intended that the particle densities N 5 and N 9 be directly calculated and printed out. An iteration process is used for solving the set of eq. (13). ~ T o test the numerical procedure the 10fitting parameters were computed with the programme for the calibration diagram with dpb = 0cm. For a number of samples the Ns and N9 values were then determined from their fission rates, using the aforementioned set of eq. (13). In all cases the deviation of the calculated from the actual particle densities was less than 5%. 7. Calculations concerning the slowing down process in the lead cube and the influence of a heterogeneous arrangement of 235Uand plutonium in cylindrical fuel rod samples on the fission rate to be anticipated The build-up of the neutron flux during injection of fast neutrons into the lead cube as well as the decay and the change in the energy distribution of the flux with respect to time during the slowing-down process after switching off the source were computed by means of a simple, zero-dimensional energy group balance programme. Exclusively energetic downward scattering was presupposed, so that computation supplied meaningful results only down to an energy of about 0.1 eV. The MUF T 4 set of data for lead was used for the non-elastic scattering at high energies. The program essentially employed the equation: V k x d t P k / d t = - z~'tk~Ok

-~- E q)j~jk-~-Sk(t)' j
(14)

q~k k

29

is the energy flux density as function of the energy and the slowing down time t; is the energy group index and increases with decreasing energy;

£tk

is the total cross section for the group k and includes absorption, downward scattering and an approximate D B 2 correction for the leakage from the finite lead cube;

vk

is the neutron velocity in energy group k;

2;jk

is the removal cross section of group j to group k >j;

sk

is the neutron source strength.

The program was first used for computing absorption rates in boron and fission rates in 235U and 239pu. The measurement of these parameters enabled the computation to be tested; again, this could be employed for checking the measurements. Very good agreement of the relevant reaction rates was obtained. Equally satisfactory results were obtained for the relation between mean neutron energy and slowing-down time, the decay of the neutron density with respect to the slowing down time and the reduction of the energy width of the neutron pulse with increasing slowing-down time. In irradiated UO2 rods the concentration of 235U and plutonium is not spatially constant. The influence of such a heterogeneous arrangement of the fissile materials on the fission rate for the entire fuel rod could only be determined by computation, since the available fuel rod samples contained only homogeneous mixtures of the isotopes. The slowing-down program was employed for this calculation. It supplies the undisturbed energy flux pattern for any time in the slowing-down region, i.e. above about 0.1 eV, for example also for the time at which the maximum of the flux distribution is at 0.3 eV. This special undisturbed flux distribution supplied by the slowing-down program was impressed in a multigroup S, computation on the lead block at a distance of a few scattering path lengths from the cylindrical fuel rod sample. The attenuation of the group fluxes in the vicinity (lead) of the rod and in the rod itself was then derived from the transport computation. By means of the mean group fluxes in the fuel rod sample the fission rates integrated over the entire rod were then computed. The computation was carried out for various spatial distributions of the isotopes with the same total quantity of the various fissile isotopes (homogeneous mixture; various degrees of heterogeneous distribution).

H. KRINNINGER et al.

30

7.1. INFLUENCE OF HETEROGENEITY ON THE FISSION RATE IN A METALIC U - P u FUEL ROD SPECIMEN The basis for the c o m p u t a t i o n s was a metal U - P u fuel r o d sample h a v i n g the following specification: 4 at % 235U, 2 at % 2 3 9 p u ,

Fuel enrichment:

Fuel rod diameter: 10 m m , Fuel rod length: 200 m m . The fuel r o d was subdivided into two zones of equal v o l u m e ; with c o n s t a n t total c o n t e n t of fissile material, three different distributions of the fissile materials in the fuel rod zones (table 5) were investigated. T o the two model cases o f a h o m o g e n e o u s a n d a n extremely heterogeneous sample i n which the 235U a n d 2 3 9 p u a r e completely separated f r o m each other spatially, was added a case with m e d i u m heterogeneity in which the two fissile isotopes were a s s u m e d to be only partially separated.

n o r m a l i z e d to the fission rate for the case with h o m o geneous fuel distribution. The result of this e v a l u a t i o n shows that even i n the extremely heterogeneous a n d unrealistic case the total fission rate increases by only some 2 % c o m p a r e d with the h o m o g e n e o u s case. The m e a n case, which m u c h more approximates to the distributions for actual b u r n up, o n the other h a n d shows indeed only a deviation of less t h a n 1% as c o m p a r e d with the h o m o g e n e o u s case.

7.2. T H E INFLUENCE OF HETEROGENEITY ON THE FISSION RATE IN A U O 2 - P H O 2 FUEL ROD SPECIMEN

The fission rate for the h o m o g e n e o u s mixture a n d several heterogeneous distributions of the fissile atoms i n the fuel rod were determined in a n entirely analogous m a n n e r for the fuel rod no. 24 (table 2) actually used. I n each case the total q u a n t i t y of fissile material in the fuel rod was the same. Table 6 lists the various cases a n d the relevant fission rates, n o r m a l i z e d to the fission rate for the h o m o g e n e o u s mixture.

TABLE 5

Normalized fission rates in a metallic fuel rod with spatially different distribution of the fissile isotopes 235U and 2agPu for a mean energy of 0.3 eV for the incident neutron spectrum. V1 is volume between r = 0 ... 0.353 cm, //2 is volume between r = 0.353 ... 0.5 cm,

I,'1=1/2.

Sample

Volume V1 Volume 1/2 285U 289pu 235U 239pu (at %) (at %)

Total fission rate (sec-1)

TABLE 6 Normalized total fission rates in a fuel rod with different spatial distribution of the 2asU and 2agPu atoms for a mean energy of 0.3 eV for the incident neutron spectrum.

Characteristics of the fuel rod specimen Case VI:V2:V3

homogeneous heterogeneous extremely heterogeneous

4 6

2 1

4 2

2 3

1 1.008

8

--

--

4

1.021

The total fission rate i n the fuel rod for the relevant 0.3 eV s l o w i n g - d o w n spectrum is o b t a i n e d b y multiplication of the spatial d e p e n d e n t group flux with the macroscopic fission cross section Z r of the g r o u p a n d i n t e g r a t i o n over the v o l u m e of the fuel a n d the energy of the n e u t r o n spectrum. W e have T o t a l fission rate =

f

~'f(E, r) ~0(E, r) d VdE,

td

fuel volume and s1~ctrum

05) where Xf = Xf,5 "[-Xf,9" The results are s u m m a r i z e d in table 5. T o provide a clearer picture, the total fission rates have been

V1 V2 1/8

239pu(wt %) //1 1/"2 V3

5

1

285U (wt %)

1

homogeneous

2 3 4

mixture 1:1 - 3:1 - 1 : 1:1

10 0 6.67 0 6 6

--3

0 0 0.5

2 4 1

Total fission rate (sec 1)

1

--1.5

1.02 1.034 1.01

I n table 6 Vi m e a n s the v o l u m e of the fuel rod zone i. Indexilxg c o m m e n c e s with i = 1 for the central fuel rod zone a n d follows in n u m e r i c a l sequence for the s u b s e q u e n t zones. The isotopic c o m p o s i t i o n of the p l u t o n i u m c o n t a i n e d in the calibration samples (91% 239pu, 9 % 24°pu) was t a k e n into consideration in the calculations. As in the foregoing section, here too there is merely a slight dependence of the fission rates o n the spatial d i s t r i b u t i o n of the fissile materials in the fuel rod.

PULSED

NEUTRON

In the very unrealistic case 3 with pronounced heterogeneity the difference in the fission rate as compared with that for a homogeneous mixture is 3.4%, however only 1% in the realistic case 4. 7.3.

INFLUENCE OF ADDITIONAL ABSORPTION BY FISSION PRODUCTS ON THE FISSION RATE

Fission product contamination in fuel rod no. 24 was simulated by the addition of an absorption cross section with 1/v dependency to the 11 group absorption cross sections for the homogeneous mixture of the fissile isotopes (case 1 in table 6). This assumption appeared admissible for an initial evaluation. Two cases with macroscopic " p o i s o n " cross sections at Vo = 2200 m/sec of Z a = 0.05/cm and z ~ a : 0.01/cm were calculated. The ratio of the relevant fission rates to the fission rate in the unpoisoned case of homogeneous mixture is given in table 7. TABLE 7 Normalized total fission rates in a fuel rod with h o m o g e n e o u s fissile material distribution and various contamination with a 1/v absorber. Fisson rate [sec- 1]

0 0.01 0.05

1 0.998 0.991

The assumed absorption cross sections of the additional 1/v absorber correspond, according to a simple estimate using the Y A N K E E core H) to a burn-up of about 1000 and 8000 MWd/t. According to the results listed in table 7, additional absorbers in the fuel rod - in contrast to heterogeneous fissile material distribution - cause a reduction in the fission rate, while the magnitude of the change is of the same order. Since both effects-heterogeneous fissile material distribution and fission product accum u l a t i o n - always occur together during the course of burn-up, their influence on the fission rate should partially compensate each other, so that deviations in the fission rates f r o m those in equivalent homogeneous non-poisoned cases should remain within the magnitude of 1%. More exact predictions than those provided by the results of computations to date would require still further refined computation models, taking into consideration, for example the heterogeneous distribution of the fission products.

31

8. Outlook on potential applications of the slowingdown-time method 8.1.

NON-DESTRUCTIVE ANALYSIS OF THE FUEL CONTENT OF SINGLE IRRADIATED FUEL RODS

The results described in sections 6 and 7 justify the conclusion that the slowing-down-time method can be used to determine the burn-up of irradiated fuel rods. With one single measurement the unknown fuel concentrations N 5 and N9 can be stated with an accuracy of better than 5%. The measuring apparatus used at present can be further improved in several respects regarding duration of measurement, which is necessary to obtain a given accuracy. These improvements require changing and/or supplementing of some components (neutron generator, lead cube, number of detectors). It is to be expected that with an improved measuring apparatus the fuel densities Ns and N 9 of irradiated fuel rods with a burn-up of the order of 1000 MWd/t can be determined with an accuracy of 5% in one single measurement lasting some 5 to 10 minutes. 8.2.

Xa, 2200 [cm- 1]

METHOD

NON-DESTRUCTIVE ANALYSIS OF THE FUEL CONTENT OF IRRADIATED FUEL ELEMENTS AND SUBASSEMBLIES

In principle there is no obstacle to employing the slowing-down-time method for measuring the burn-up of irradiated fuel elements and subassemblies. Because of the substantially greater quantity of fuel used in comparison with a single fuel rod, with an improved measuring apparatus N 5 and N 9 can be measured in times of about 1 minute with an accuracy of better than 5%. If N9 and N 5 are to be determined for a number of positions along the axis of the fuel element a corresponding multiple of the measuring time is necessary, because the axial resolving power of the measuring apparatus is about 30 cm. Determination of N5 and N9 by the slowing-downtime method presupposes a knowledge of the calibration diagram, which is at present known only for the calibration samples used (table 2). To obtain a calibration diagram valid for fuel elements, a sufficient number of calibration samples of the same type and an assortment of calibration samples would have to be available so that different fuel element models and different burn-up states for each model can be simulated. Such a comprehensive measuring program could be dispensed with to the extent that suitable experiments would demonstrate that quantitative transfer of the measured results for single fuel rods to complete fuel elements is possible, which would obviate the need to measure new calibration diagrams.

H. KRINNINGER et al.

32

8.3. CONTROL MEASUREMENTS DURING MONITORING THE FUEL CYCLE

Indirect methods of measurement intended to be used for monitoring the flow of fissile material in the peaceful uses of nuclear energy must fulfill the following conditions13): 1. It must be possible to determine the total fuel content of a single fuel rod or a subassembly; 2. It must be possible to differentiate between different fissile isotopes, in particular 235U and 239pu, as well as to determine their content in each fuel rod or subassembly; 3. The measuring procedure must be proof against trickery, i.e. it should not be possible by adding resonance absorbers to simulate a lower fissile material content or by adding neutron sources to simulate a larger fissile material content than actually contained in the fuel element. The slowing-down-time method meets these requirements; for fulfillment of the third conditions one can use detection of the capture gamma radiation in a separate detector channel3), deviation of the fission integral ratio or the deviation from the cosine pattern of the fission rates along the axis of the fuel rod in comparison with the nominal rod. The employment of the slowing-down-time method gains special importance for fast breeder reactors and with a view to international control agreements. In these reactors, because of the more favourable breeding rate fuel elements of depleted uranium with high enrichments o f Z39pu ( 1 0 - 3 0 % ) , / 4 ° P u ( 5 - 1 0 % ) and 2 4 1 p u ( 0 . 5 - 2 % ) are employed, the main interest being concentrated on the determination of the 2 3 9 p u content. In addition to the determination of the fuel density N9 at various irradiation a check o f the initial enrichment o f 239pu in the fuel element is also possible. The following procedure should be used for this purpose: During manufacture of the fuel elements the exact composition of a fuel element is determined by chemical analysis. This fuel element then serves as calibration element for the slowing-down-time method. By simple comparison of the fission neutron counting rate in the 0.3 eV slowing-down spectrum recorded for a fuel element being investigated with that for the calibration element the 239pU content of the former can be stated immediately, the error AN9/N9 now being determined by the statistics of the two counting rates. In order to be able to say something about the accuracy of the N9 determination for a given measuring time, however, a supplementary experimental program

must be carried out, because with higher plutonium densities than those dealt with in this report the selfshielding effect plays a much more important role. Probably the procedure would have to be modified for this purpose by using the higher energy resonances of the 239pu fission cross section instead of the 0.3 eV resonance for determining Ng. The 24°pu content (of the order of 5 - 1 0 % in breeder fuel elements) can be determined with the measuring equipment and switched off neutron generator using spontaneous fission as criterion. An analogous procedure could be followed to that described in section 3 for determining the 241Pu content. Instead of separate and absolute determination of 235U and 239pu we here have to determine the enrichment of 241pu with simultaneous high enrichment of 239pu in the fuel element. If one compares the fission cross sections of the two isotopesX2), the 2*~pu resonance at 4.6 eV appears the most suitable for this purpose. This resonance is sufficiently isolated, so that it should be resolved by the lead spectrometer. This is important, because by analogy with the error discussion in section 3.1 the attainable accuracy N(241pu)/N(239pu) becomes greater with increasing ratio of the fission integral specifically defined for the slowing-down-time method (here a241/a239 at E = 4.6 eV). The 4.6 eV resonance of the 241pu is also adequately isolated from the next resonance of the 2 3 9 p u at about 8 eV, so that no interference is to be anticipated from this. Previous experience suggests that an error of < 5% for the 241pu content should be attainable. The autors wish to acknowledge the very considerable assistance by E. Ruppert (Interatom) and G. Boggio (Euratom, Bruxelles) in planning the previous experimental program and analysing the results. References 1) H. Krinninger, S. Wiesner and C. Faber, Verfahren zur zerstrrungsfreien Analyse des Spaltstoffgehalts bestrahlter Brennelemente, I N T A T 73 (Interatom, Bensberg, 1968) final report to Euratom, Bruxelles. 2) K. Einfeld, U.S. Patent no. 3 222 521, dated 17.10.59; Canadian Patent no. 666 943, dated 17.10.59; DAS no. 1 275 794. 3) D. Stegemann and H. Seufert, Application of the slowingdown-time spectrometer for the control of fissionable material, Am. Nucl. Soc. Meeting (Washington, D.C., Nov. 1968); Am. Nucl. Soc. 11, no. 2 (1968) 658. 4) A . A . Bergman, A. I. Isacoff, I . D . Murin, F . L . Shapiro, I. V. Shtranikh and M. V. Cazarnovsky, A neutron spectrometer based on measuring the slowing-down-time of neutrons in lead, A/Conf./P/642, vol. 4 (Geneva, 1955) p. 136.

P U L S E D N E U T R O N METHOD 5) F. Mitzel and H.S. Plendl, Messung von (n-~)-Wirkungsquerschnitten und Resonanzintegralen mit einem Bleispektrometer, INR-Report no. 81 (Gesellschaft far Kernforschung, Karlsruhe, 1964). 6) R. Ramana and P . K . Iyengar, A feasibility study of the method of non-destructive assay of 235U and 239pu in irradiated fuel slug, IAEA-R-92-F, NP-15688 (1965). 7) K. Chandramoleshwar, M . P . Navalkar, D. V. S. Ramakrisha, R. Ramana and K. R. Subbaramu, A feasibility study of non-destructive assay of 239pu in irradiated fuel rods using slowing-down-time spectrometer, A/Conf. 28/P/785 (Geneva, May 1964).

33

s) A. A. Bergman, A. I. Isacoff, M. Cazarnovsky, P. Popov and F. L. Shapiro, Moderation of neutrons emitted by a pulsed source and neutron spectrometry based on slowing-downtime, STI/PUP/104, vol. 1 (1966) p. 671. 9) W. Eyrich, Nukleonik 4 (1962) 167. 10) A. Perkins and K. King, Nucl. Sci. Eng. 3 (1958) 726. ix) C . G . Poncelet, Effects on fuel burnup on reactivity and reactivity coefficients in Yankee core, WCAP-6076 (Pittsburgh, Pa., 1965). 12) D.J. Hughes and I.A. Harvey, Neutron cross sections, BNL-325. la) D. Gupta and W. H~ifele, Atomkernenergie 13, no. 4 (1968) 229.