NEUTRON YIELD IN FISSILE TARGETS IRRADIATED WITH HIGH-ENERGY PROTONS

V. S. Barashenkov, A. N. Sosnin, V. N. Sosnin, and S. Yu. S]%makov

UDC 621.039.667.9

The construction of meson factories and of other high-energy particle accelerators of high currents has made it possible to build extremely intense (~101s-1018 sec -I) sources of neutrons which are generated by multiplication of currents of particles produced in high- energy splitting reactions [1-3] in fissile targets. These sources can be used in nuclear physics experiments, materials science research, and other applications [2, 4]. Some labor- atories have made experimental measurements of the neutron fluxes and the liberation of heat in various blocks at neutron energies of up to 1.5 GeV; for example [5, 6], the results agree with the theoretical calculations of [3, 7-10]. But these experiments were made at low in- tensities of the beams of the generating protons when a coolant, reducing the heating, and structure elements which can substantially reduce the intensity of the neutron beam need not be introduced into the target. The neutron flux is also reduced when oxides or carbides are used in the fuel elements of the targets.

The goal of the present work is to assess how the neutron yield and other characteris- tics of the system change in the transition from a target in the form of a homogeneous fis- sile block to a target containing a liquid-metal coolant and structural members.

Let us consider a beam of i Geu protons irradiating a cylindrical target with a diam- eter of 120 cm, a length of 90 cm, and a narrow axial slit with a length z 0 = 26 cm, onto which the primary proton beam is directed (such a target was considered in [3, 7, 8]). The same statistical (Monte Carlo) model which was used in [8, i0] is employed in our calcula- tions; a difference arises only from the use of a more precise subgroup representation of the constants describing the behavior of the neutrons in thelow-energy (reactor) region

~ 10.5 MeV so that resonance self-shielding of the neutron cross section [ii] can be taken into account (the accuracy of calculating the inner-nuclear cascade accompanied by evapora- tion and fission of the excited residual nucleus was discussed in [12]).

The calculations were made for two cases: for a homogeneous target of depleted uranium (the 235U isotope admixture amounted to 0.3%) and for a target of the same structure and com- position as the breeding zone in a fast neutron reactor (Fig. i) [13].* Cylindrical UO 2 fuel elements with a stainless steel cladding (85% Fe and 15% Cr) were uniformly distributed over the target volume parallel to the target axis and the direction of the proton beam. The space between the fuel elements was filled with liquid sodium. The composition of the target with the coolant was taken from [13]:

Nucleus Concentration, % 238 U 22,72 ~3~U 0 ,{~6916 5BFe t4,49 ~Cr 3,tt9 a~Na 13,82 160 45,78

For the sake of simplifying the calculations, we assume that all six nuclear components of the target were uniformly distributed over the target volume. This is a rather good approx- imation because the diameters of the fuel elements and their spacing are much smaller than the neutron range. The results of the calculations are compiled in Figs. 2 and 3 and Table i.

Obviously, in the transition to a complex target which contains a significant percentage of nonfissile elements, the distributions of the majority of parameters as a function of the space coordinates become smoother. As in the case of a homogeneous uranium target, the max-

*The authors thank P. L. Kirillov for discussing questions related to the problem under con- sideration.

Translated from Atomnaya ~nergiya, Vol. article submitted August 14, 1986.

64, No. 2, pp. 133-137,~February, 1988. Original

158 0038-531X/88/6402-0158512.50 �9 1988 Plenum Publishing Corporation

O, EF

Fig . 1. Arrangement of the cooled target (the dimensions are expressed in millimeters).

15

12

0

~ 8 g

E2

24

8

IO

~ 2o

to

I L-- I I I

I .

L . ~ ""

16 52 48 R, cm

Fig. 2. Distribution of the number N c of (n, y) captures, of the number Nf of fissions, and of the heat Q liberated in a cylindrical layer of thickness AR = 4 cm at the dis- tance R from the target axis: ---) target of depleted uranium; ) target cooled by sodium; ..... ) target of large dimensions, cooled with sodium; -x-x-) data ob- tained when the coolant had been removed from the target.

imum in the longitudinal distribution is located at z ~ z0 + lin/2, where %in denotes the average nuclear range of the primary protons before their inelastic interaction (lin = i0 cm for uranium and %in = 30 cm for the target with a coolant). The maximum in the radial dis- tribution of the number Nc(R) of the captures is situated at the distance R ~ 3~tr, where %tr denotes the average transport range of low-energy neutrons (for the uranium block and the target with the coolant, %tr is 4 and 6, respectively).

At the same time, the heat dissipation in the complex target proceeds in a less uniform manner than in the uranium block. Owing to the increased ionization losses of the energy of the charged particles (the fraction Qion/Q of such losses increases almost three times when one switches to the target with the coolant), in the distribution Q(z) there develops a peak near the entry point z = z 0 of the primary proton beam into the target material (see Figs. 3 and 4). About 40% of the total heat are liberated in the central part of the target, though this part forms only 0.4% of the total target volume.

159

/2 r . J I , - 1

g r J - . J ~ ' | I

~ 8 ! r - - ~ - ~ - ~ i

i L.

r . ~ . _ _ j r ? J l _ . 1 L . . , ' . - -= I JL._J j -~ , L. - -u~ , q i , , i i , i t i i I t I I i f i i

i ..~.,

r , L . . I I "II--,, I I r t 3 I ! L., , . , i I I t . .... -i

9 .x4 r.-rx!t

~ x l ' 3

. - . , , - 4 - ~ , , , 'r. , , , , , , , , , ' r ' 7 ~ . 0 t8 if8 54 72 z, cm

Fig. 3. Distribution of the number N c of (n, ~) captures, of the number Nf of fission events, and of the heat liberation Q in a layer-of thickness Az = 4.5 cm in the direction of the target axis. See Fig. 2 for notation. The arrow denotes the end z 0 of the entry channel.

2 , o

~t51

o,5

r I I l " I I I - - - J< '~

I wX

~ - ~ I I I t . - - A- "-J I - -

~-X- I

) ' I

' t I ~ ' ' t 1 i r i I l , ~ I i I ,

0 ~8 36 ~ ~ ~ cm

Fig. 4. Relative fraction of the heat liberated in the central part of the target with the radius R & 4 cm. Q denotes the total heat liberation (see Table i). For the notation, see Fig. 2. The arrow denotes the end z 0 of the entry channel.

Figure 5 illustrates neutron spectra inside and outside the target. Replacing the uranium block by a target with coolant substantially increases the fraction of low-energy neutrons in the spectrum but the maximum maintains its position in an interval of a few tenths of a mega-electronvolt.

By contrast to a nuclear reactor in which the criticality requirement of the system im- poses important limitations, relatively slight changes in the composition of the material in an electronuclear system can substantially change the form of the neutron energy spectrum by either suppressing or enhancing parts thereof.

160

TABLE i. Average Integral Parameters of the Interaction of a I-GeV Proton Beam with Various Targets,* Calculated per Primary Proton (statistical error 3-5%)

Parameter l I! I l l

No. of neutrons captured in (n, y)zreactions

including 238Unuclei No. Nem of neutrons �9 emitted from the target Nem/(N c + Nem), % No. Of fission events:

fort > 10_5 MeV for % < fO.5 MeV

A~. energy (MeV) of the neutrons in a 26- group spectrum: inside the target emitted fromtheta~g@t

Heat dissipation (MeV) Ionization losses Qion Fission of nuclei at T > I0.5 MeV

Fission of nuclei at I T ! 1.05 MeV I

Total Q I Inc luding those in a I cylinder with R = 4 ~l cm, Q(R ~ 4 cm)/q , % I

I

8r 37

8(; t 35 4 13

5 28

5,g I 3,2 14,5 I 5,2

o,!)21 1,37 0,341 0,53

322 437

954 532

239t 859

36(;8 t828 39 37

54

52 ()

t)

4,2 7,2

t ,21

445

(;92

t t90

2327 4O

*I relates to the target of depleted uran- ium; II target with coolant (same dimensions as target I); III refers to a very large tar- get with coolant. %The capture of neutrons by 235U nuclei

amounts to only 0.6%.

Number of the group

N(T),Z "4 __~

10 r I _7

1o 0

I(J " 7 " 1

r _ l I

"/0 "~ 2,5.10 -8 ~0 -~ 10 -s 10 -4 fo '~ 10 -2 10 -1 1,t+ "r, (HeVJ

Fig. 5. Energy spectrum of the neutrons: ---) neutrons inside a target of depleted uranium; -+-+) spectrum of the neutrons emitted from this target; ) neutrons inside the sodium-cooled target; -x-x-) spectrum of the neutrons emitted from this target; ..... ) neutrons inside a sodium- cooled target of very large dimensions. The energy intervals were chosen in accordance with the 26-group approximation of [14].

The introduction of a coolant into the target and the structural members significantly (almost two times) reduce the intensity of the flux of the neutrons generated: N = N c + Nem- However, the number of the neutrons leaving the target increases but these are neutrons with

161

~0

T

'

i ,7 i

L 4 - ~ - - - J

i , i ..... 1 - ~ - - I ] . . . . . L . . . . = - . . ~ - - - i I

Fig. 6. Angular distribution of the neutron flux outside the target (relative to the direction of the primary proton beam): ---)" target of depleted uranium (0.76 • 0.06); ) target with coolant (1.46 • 0.03). The target geometry is the same in both cases. The statistical errors of the calcula- tion are indicated.

N(~Z)

10o

8o

7o o

~7

W// /

/ /

1 /

I ..... i

Fig. 7. Dependence of the neutron yield upon the concentration of the 2~SU iso- tope in the uranium block.

a very low energy which do not multiply in z38U; therefore an increase in the size of the target increases the number N c of (n, 7) captures but hardly affects the total neutron yield N.

It follows from Figs. 2, 3, and 5 and Table I that an increase in the target dimensions only very weakly affects the other parameters of the system, and the dependence upon the di- mensions is important only in the case of small targets with dimensions close to %in"

Losses of coolant have only little influence upon the physical properties of the elec- tronuclear system under consideration. In this case the total neutron yield is practically unchanged (AN = -2 • 10%) while the number of radiative captures slightly decreases (AN c = -15 • 10%) and Nem increases (ANem = 27 • 10%). The heat dissiPation remains on its value within the limits of the statistical accuracy of the calculation (AQ = 2 • 10%).

Figure 6 illustrates the angular distribution of neutrons emitted from the target. The asymmetry of the emission (N/N) increases sharply when the channel length z 0 is significantly increased and when the target is reduced to dimensions which are close to Xin"

Let us note that all the results stated refer to the case in which the proton beam enters into the bulk of the target through a narrow channel (z0/Xin ~ I). When the front face of the target is directly irradiated with protons, completely different results are obtained. Though the total neutron yield N = N c + Nem remains almost unchanged (AN = -8 • 10%), the number of (n, ~) captures is reduced to almost a third (AN c = 36 • 10%), and the number of neutrons emitted from the target increases by a factor of almost 7. The major part of these neutrons is emitted into the rear hemisphere.

The yield of neutrons and the heat dissipation increase sharply when the concentration of the 23SU isotope in the target is increased (Figure 7).

162

LITERATURE CITED

i. Proc. of the Seminar on Intense Neutron Sources, Sante Fe, New Mexico (1966). 2. Yu. Ya. Stavisskii, Pulsed Neutron Sources on the Basis of the Proton Beam of a Meson

Factory, Preprint of the Physics Power Institute F~I-389 [in Russian], Obninsk (1973). 3. V. S. Barashenkov, El. Chast. At. Yad., 2, 871 (1978). 4. Proc. of the Intern. Conf. of Emerging Concepts in Advanced Nuclear Energy Systems Analy-

sis, Atomkernenergie, 32, No. i (1978). 5. P. Tunnicliffe, B. Chidley, and J. Fraser, in: Proc. of the Intern. Conf. on Accelerators,

Chalk River, Ontario (1976). 6. R. G. Vasil'kov et al., At. ~nerg., 29, No. 3, 151 (1970). 7. V. S. Barashenkov and V. D. Toneev, At. ~nerg., 35, No. 3, 163 (1973). 8. V. S. Barashenkov, V. D. Toneev, and S. E. Chigrinov, At. ~nerg., 37, No. 6, 475, 480

(1974). 9. I. Nakahara and H. Takahashi, At. ~nerg., 47, No. 2, 83 (1979).

i0. V. S. Barashenkov and S. Yu. Shmakov, At. ~nerg., 5__O0, No. 2, 150 (1981). ii. V. F. Khokhlov, M. M. Savos'kin, and M. N. Nikolaev, Problems of Atomic Science and Tech-

nology, Nuclear Constants Series [in Russian], Vol. 3, No. 8 (1972). 12. V. S. Barashenkov and S. Yu. Shmakov, Commun. of the Joint Inst. of Nucl. Research E2-

12902 [in Russian], Dubna (1979). 13. A. I. Voropaev, A. A. Van'kov, and A. M. Tsybulya, At. ~nerg., 45, No. 6, 419 (1978). 14. L. P. Abagyan et al., Group Constants for the Calculation of Nuclear Reactors [in Rus-

sian], Atomizdat, Moscow (1964).

STCo AND l~ PHOTON-RADIATION SOURCES FOR X-RAY FLUORESCENCE

ANALYSIS

N. A. Konyakhin, B. V. Zatolokin, V. G. Meshcheryakov, and G. V. Tyamin

UDC 621.039.8.002

X-ray fluorescence analysis (XFA) employs an ionizing-radiation beam with simultaneous characteristic x-ray recording from the sample [i]. If an x-ray or soft y-ray source is used, e.g., from a radionuclide, the characteristics must meet the following requirements:

i) the minimum detection limit requires that the exciting photon energy should not greatly exceed the characteristic value for that element (usually, the photon energy exceeds the lat- ter by not more than a factor 2-3);

2) the spectrum should not contain any lines falling within the test-element range or appreciable hard y rays that would make it difficult to shield the user and detector;

3) the photon yield at the appropriate energy should be high enough to make the source economical;

4) the half-life should be comparable with the total time required to make the source, transport it to the user, and perform a given number of analyses; and

5) the production technique should provide the necessary specific activity, radiochemi- cal purity, and cost.

These requirements are met by the widely used SSFe, STCo, i~ iS3Gd, 2SSPu, 241Am; also, recommendations have been made on using ?iGe, llgSn, 12sI, 145Sm, 17~ 2~ 24~Cm. The characteristics [2, 3] show that a minimal set SSFe, STCo, 1~ 2~IAm provides for analyzing for the elements from magnesium to californium.

The working conditions require the sources to be used sealed, which must meet the fol- lowing conditions:

i) the source shape and size should correspond closely to the particular XFA method;

Translated from Atomnaya Energiya, Vol. 64, No. 2, pp. 137-140, February, 1988. Original article submitted January 19, 1987.

0038-531X/88/6402-0163512.50 �9 1988 Plenum Publishing Corporation 163