D E P E N D E N C E O F T H E P A R A M E T E R S O F E L E C T R O N U C L E A R

M U L T I P L I C A T I O N U P O N A D M I X E D 239pu A N D 235U

V. S. Barashenkov, A. N. Sosnin, and S. Yu. Shmakov UDC 621.039.667.9

The yield of plutonium nuclei, the heat liberation, and other parameters of the electronuclear process were determined

for natural and enriched uranium in all the work done to date. But considerable quantities of 239pu can accumulate in an

electronuclear reactor, and this significantly increases the number of low-energy fissions and, hence, the plutonium winning rates

and the energy liberation. When the fuel of fuel elements is regenerated with the aid of the electronuclear process, the irradiated

material is highly enriched also with the readily fissile 235U nuclei.

The goal of the present work is to determine the influence of various degrees of 239pu and 235U enrichment upon the

electronuclear multiplication of neutrons.

The Monte Carlo technique was used for the calculations and resonance-type self-shielding of the cross sections was

taken into account in a subgroup approximation. The calculations and the geometrical features of the six-component reactor

were the same as in [1, 2]. The reactor had a diameter of 120 cm and a length of 90 cm. The proton beam was directed onto a

narrow 26 cm long axial slit and was incident on a lead target having a diameter of 8 cm. The chemical composition of the

homogenized electronuclear reactor beyond the lead target was calculated with the equation Zi = ViNi/Zj=I VjNj, where V i

denotes the volume occupied by an element; N i denotes the number (in %) of nuclei of the i-th element per cm 3, namely z38U

+ 239pu or 238U + 235U 22.77, 56Fe: 17.7; 23Na: 13.8; and 160: 45.8. The total concentration of the material undergoing fission

in the reactor was assumed to be constant; only the relative concentrations of the 238U and 239pu or 238U and 235U nuclei were

changed:

(23s/a~) a ~ 23S ,1 = h,(x)/f,v( ~ + ~(X)l --- l + a (238/~- l ) - --~- a,

where a = p(X)/Lo(Z38U) + p(X)], p(X), N(X), and A x denote the density, the number of nuclei, and the mass number of the

element X, respectively.

When the concentration of 239pu and 235U nuclei increases, the number of nuclear interactions of neutrons (nodal

points of the cascade tree, see Table 1) increases sharply and the calculations become more involved. Since the number of

high-energy interactions, which are most difficult to bring into account, remains almost constant (the properties of the plutonium

and uranium nuclei hardly differ in regard to their response to high-energy particles [3]), and since the trajectories of low-energy

neutrons are rapidly calculated when the technique of statistical weights is used, the total computation time hardly changes and

amounts to about 20 min on an SDS-6500 computer for the first 100 1 GeV protons (100 cascade trees).

Enrichment with Plutonium. It follows from an analysis of Fig. 1 and Table 2 that the distribution of the capture

reactions is almost independent of the enrichment, whereas the maximum of the fission reactions is shifted toward layers farther

away from the reactor center when the plutonium concentration rises. This is a consequence of the fact that plutonium fission

results predominantly from very slow neutrons the number of which increases at greater distances from the reactor axis. At a =

2%, the ratio of the number of fissions of e38U and 239pu nuclei is Nfs/Nf9 = 1, whereas it is as high as 2.5 at a = 6%.

The neutron yield per primary proton increases rapidly with increasing enrichment but the number of neutrons leaving

the reactor increases even more rapidly. At c~ = 6-8% the number of such particles already amounts to half the number of all

neutrons produced in the reactor. An even higher enrichment means that the plutonium winning rates are slowed down and at

a >_ 10% (in the reactor geometry under consideration), the number of plutonium nuclei undering fission and radiative capture

Joint Institute of Nuclear Research. Translated from Atomnaya l~nergiya, Vol. 73, No. 5, pp. 411-415, November, 1992.

Original article submitted October 18, 1991.

926 1063-4258/92/7305-0926512.50 ©1993 Plenum Publishing Corporation

TABLE 1. Dependence of the Number of Elastic and Inelastic Interactions of Neutrons with

Nuclei of Admixed 235U

I Enrichment (%) :

Parameter 2

,!,% 0,3 0,3

2 2 3 0

115

2,03 2540

140

4 6 4 ,~ 6 ,~ 32~ 3570

1~ 2 ~

10 12

li),l 12,t 5 4 0 0 4690

360 350

Remark: The number of inelastic interactions includes (n, y) capture, fission, and inelastic (n,

xn) reactions with neutron generation: Nin = N c + Nf + N n.

• % r ~ ...

&el%

5

.-. t/,%

25 -

20

|

5

0 "16 32 40 60 R,c~

Nc t o/

N~ i I

0 t8 36 5÷ 72 90 o cm

Fig. 1. a) Radial and b) longitudinal distribution of the number N c of (n, y) capture reactions,

of the number Nf of fissions, and of the heat liberation Q at an enrichment of 0.3 (U) ( ),

2 (Pu) ( . . . . ), and 6 (Pu) ( . . . . . ).

is greater than the number of newly produced. In this case, the plutonium-winning system is converted into a powerful source of

neutrons. The reactor must be surrounded with an uranium shield for winning plutonium (or with a shield of thorium for

winning 233U). Tile angular distribution of the neutrons leaving the reactor is almost symmetric with respect to the axis of the

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TABLE 2. Average Integral Parameters of the Electronuclear Process under the Influence of 1-

GeV Protons (the statistical error of the calculation is 5-7% per primary proton at a = 0.3%

and 7-10% at a > 0.3%)

Parameter

Number N c of neutrons captured in an (n,~) reaction

Number of 239pu nuclei generated

Number of Nex of neutronsexiting from the reactor

Total neutron yield N = N c + Nex

Nex/N, % Number of fissions

Heat of liberation (MeV):

Ionization losses (Qion)

Fission of nuclei at T > 10.5 MeV • . • ~ 10,5

Total Q

Including the volume Q(Pb) of the. head target ~(Pb)/Q, % Heat liberation Q/N (MeV) per neutron

Asymmetry W( Q<:t/2)/ IV(Q~/2) Yield of ~gpu

0,3

Enrichment ( ~

450 270 690

1410 430 31 33 0,9

29

(U) 2 iPu)

32 33,8

30 31,5

11 15

43 48,8

25 31

6,2 9,5

480 240

1350 2070 440 21 42 l,l

26,5

6 (Pu)

63

50

38

87

43

34

440 320

5290 6040 410

6,7 69 0,9

27

0,6,

0,5

0,9

0,3 c,.

~_ 0,2

0,7

i t , I .

;'8 26 36 S'~ 72 9O Z, cm

Fig. 2. Ratio of heat liberation in the lead target to total heat

liberation in the reactor at various points along the Z axis.

incident beam. The flux in the direction perpendicular to the beam is about three times smaller than the flux in the longitudinal

direction. This ratio is given by the geometry of the reactor and, within the statistical error limits, does not depend upon the

enrichment.

Figures 1 and 2 illustrate the distribution of the heat liberated; this distribution is an overall repeti t ion of the distribu-

tion Nf(R, Z) of the number of fission events. The amount of heat dissipated in the lead target is almost constant and its relative

fraction Q(Pb)/Q decreases from 21% at a = 2% to 7% at a = 6%.

The admixed plutonium nuclei "eat away" the low-energy part of the neutron spectrum; this is particularly clearly visible

in the spectrum of the outgoing particles (Fig. 3). Yet the main part of the spectrum near its maximum changes but little.

Enrichment with Z35U. The three-dimensional distributions of the number of capture events, fissions, inelastic interac-

tions, and of the heat l iberation as functions of the concentration a remain qualitatively the same as in the case of admixed

plutonium. Quantities which depend upon the high-energy part of the cascade, namely ionization losses of energy, heat liberated

in fission at T > 10.5 MeV, heat dissipation in the lead target, are within the statistical errors of the calculations almost

independent of the enrichment and are the same for 235U and 239pu (Table 3). Changes in the particle fluxes and in the heat

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76 20 15 10 5 7 N:.

I0

1

d . . i

o, ! L

a

2.10 "a 7,3.70"e ~*.70"~l,&lo'zlJ 8,5 ~, MeV

I0

. . . . i , , . %

"3

7

~., tJ 1_ i.J

. J

o,,

7 0 - z . . . . . . . . . . . . . . . . . . . . .

1,2~.1o -8, 7,~.#"~.1o*1.&7ozl,7 s,s ~, MeV

Fig. 3. Average energy spectrum a) of the neutrons inside the reactor and b) of the neutrons

leaving the reactor.

TABLE 3. Average Integral Parameters of the Electronuclear Process under the Influence of 1-

GeV Protons

Parameter Enrichment with Z~U, ~0

0,3 2 Total neutron yield 42 51

Number of 2 3 e pu nuclei generated 29 32

Number of inelastic (n,2n) an (n~n') 73 92 reactions

Number of fission events .6 11 Ratio N~ N (%) of the number of neu- 25 31 trons ~citing from the reactor to the total neutron yield

Asymmetry of the exit 0,9 0,9 Heat liberation (MeV):

Ionization losses (Qion) 450 420

Fissionof nucl. ~ > 10,5 MeV 270 280

*, * * • S 10,5 MeV 690 1510 ,Total Q 1410 2220 Including the volume Q(Pb) of the lead 430 420 target

Q(Pb)/Q 31 19 Heat liberation per neutron Q/N (MeV) 33 44

4 6 10 12

64 80 111 121

36 42 61 71

121 150 218 251

19 28 52 63

32 36 35 38

1,0 0,8 1,0 0,7

450 4 4 0 420 490

290 270 290 230 3180 4230 8880 10940 3930 4960 9590 11660

460 420 390 450

12 8,5 4,1 3,9

61 67 83 89

liberation at increasing a result from an increased contribution of low-energy interactions and, above all, of fission. As in the

case of enrichment, the winning of plutonium is first slowed down at larger a values and decreases further on. This effect so far

did not occur, and the intensity of the particle fluxes and, accordingly, the value of Q is in the case of 235U enrichment at a

particular a value much smaller than in the case of plutonium enrichment.

LITERATURE CITED

1 .

2.

3.

V. S. Barashenkov, A. N. Sosnin, and S. Yu. Shmakov, "Neutron yield in fissile targets irradiated with high-energy

protons," At. ]~nerg., 64, No. 2, 133 (1988).

V. S. Barashenkov, A. N. Sosnin, and S. Yu. Shmakov, "The influence of a lead target upon the characteristics of an

electronuclear reactor," At. t~nerg., 71, No. 2, 172 (1991).

V. S. Barashenkov and S. Yu. Shmakov, Nuclear Fission Induced by High-Energy Protons, Dubna, E2-12902 (1979).

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