An electronuclear reactor as a future breeder

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    P. P. Blagovolin, V. D. Dubinskii, V. D. Kazaritskii, G. N. Karavaev, G. V. Kiselev, M. L. Okhlopkov, and I. V. Chuvilo

    UDC 621.039.516.4

    Fast breeder reactors have been built and operated in this country and in other in- dustrially developed ones. Improvements will no doubt be made, but nevertheless the search for new lines of development continues. There have been numerous researches on the fusion problem [i], in which projects have been formulated for hybrid fusion reactors. It has been suggested that a demonstration system should be built this century.

    A more recent line in fusion research is concerned with pulsed reactors, where the ne- cessary conditions are provided by extreme compression in layered targets [2], which is pro- vided by short pulses from lasers or a heavy-ion accelerator. There is at present no convinc- ing suggestion of how some major problems are to be solved, such as to perform a large number of successive microexplosions. The conditions must maintain a high vacuum, and they require thermal and radiation stability in the structures, which are subject to high-intensity cyclic loading.

    Another idea is to catalyze nuclear synthesis with negative muons [3]. The physical principle is attractive, but the technical difficulties already apparent are too great for the method to be considered at present as at all realistic. Essentially new technologies are needed.

    The electronuclear method [4, 5] is an alternative way of producing neutrons and nuclear fuel; it differs favorably from all the others as regards commercial implementation. Experi- mental and theoretical developments have been carried out in this country, the USA, and Canada which began over 20 years ago. Accelerator advances have attracted fresh attention to the electronuclear reactor. In such a reactor optimized to produce fissile materials, one re- quires a proton accelerator giving 1GeV and a beam current of about 300 mA working continu- ously [6]. Specialists at present consider this possibility as realistic [7].

    The particle energy is converted to neutrons, and fissile isotopes accumulate in a tar- get, which is sometimes called a blanket, by analogy with other breeder reactors. The beam- induced processes are dealt with in numerous papers, where computer experiments have been important. Current fast computers provide detailed models for the conversion. In foreign studies, the HETC/MORSE Monte Carlo suite is often used [8, 9]. At the Institute of Theore- tical and Experimetnal Physics, preference has been given to more economical calculation meth- ods based on an inclusive approach to describing particle-nucleus interaction cross sections [I0]. The MARS4/MMK22 suite [ii] is based on tested Monte Carlo programs: MARS4 [12] gen- erates internuclear cascades above 10-20 MeV, while MM22 [13] simulates the transport of the low-energy neutrons emitted from nuclei excited in the cascade. The suite has been tested in reaction-rate calculations for neutrons in metallic targets [ii, 14]. Usually, the dis- crepancies from measurements do not exceed the experimental error.

    The MARS4 program has advantages, particularly in speed, over programs based on the ex- clusive approach [5, 8], and is designed to give particle fluxes and energy release distribu- tions. MARS4 should be supplemented with an appropriate cross section library for detailed calculations on reaction rates and residue yields. This is handled by a novel software suite written at the Institute of Theoretical and Experimental Physics [15, 16], which enables one to calculate the interaction characteristics for hadrons at incident energies from tens of MeV to 15 GeV. This form of the cascade-evaporation model is based on new measurements and incorporates experience from previous software realizations in this country and elsewhere.

    Translated from Atomnaya Energiya, Vol. 65, pp. 326-329, November, 1988. Original article submitted January 29, 1988.

    0038-531X/88/6505-0889 $12.50 9 1989 Plenum Publishing Corporation 889

  • f(X)


    I t I ~,6 o,s c,o

    10 0


    7 % ~ 0

    '7 Idz o ~., 0000

    o I0~ J~ ~J

    ~.~ 9

    i i i i I l l q l

    10 o 107 ~0z 1o 3 Neutron energy, MeV

    Fig. i Fig. 2

    Fig. i. Distributions for the ratios of the calculated and observed neutron yields for electronclear uranium targets (i) and plutonium for fast critical assemblies (2).

    Fig. 2. Neutron spectra from thin uranium targets on bombardment with 590 MeV protons as calculated from the HETC/KFK program (histogram), D2N2(MARS4) (solid line), and as measured (o).

    At present, concepts on electronuclear breeding have raised a need for new and more ac- curate measurements on neutron and energy yields, which Fig. i illustrates. The distribution parameters (mean and standard deviation) have been calculated from published data for some dozens of measurements with extended uranium targets [14, 16-20], and it also shows the dis- tributions for the ratios of the calculated and measured formation rates for plutonium ob- tained for 18 fast critical assemblies [21]. The standard deviations for these distribu- tions can be interpreted as the accuracy attained in such calculations on targets (about 12%) and on fast-reactor cores (about 3%). The ratio indicates deficiencies in the nuclear data for implementing electronuclear breeding.

    Integral experiments in the main indicate the accuracy attained in the nuclear data (pro- cedures for formal mathematical fitting are not envisaged), while differential experiments on thin targets provide the data in conjunction with theoretical models. Recently, there has been a vigorous discussion of the basis for existing cascade-evaporation models. The measurements concern the double differential cross sections for particle formation in in- elastic collisions beween protons and uranium, lead, tantalum, indium, niobium, iron, alu- minum, and carbon [22]. Figure 2 shows the absolute neutron-yield cross sections at 30 ~ for uranium. Similar or worse results are obtained for other angles and materials. The mea- sured neutron-formation cross sections agree with the theoretical predictions below 20 MeV, while at higher energies, the calculated yields, ours and others [23], are much lower than the measured ones. The importance of the secondary high-energy particles increases steadily as the target is enlarged to reactor size, and the contribution from that error may become appreciable. Also, if the measurements are subsequently confirmed, there is an additional margin for efficient electronuclear breeding.

    These electronuclear target problems and the success in solving them largely govern the performance and possibly the economics of an entire system. Such a reactor operates from an external inhomogeneous anisotropic neutron source provided by the beam. It should meet the specifications for power reactors. The target design should be optimized from the physics and should be intended to produce fissile material at the maximum rate, and it is bound to incorporate constraints on the maximum energy production, radiation damage, cooling, and other characteristics. One approach examined at the Institute of Theoretical and Experi- mental Physics is that many aspects related to choosing an acceptable form are resolved by means of simplified models for transport and transformation in an infinite homogeneous medium.


  • Neglecting boundary effects and certain other details in the interaction enables one to solve the problem in closed form and to estimate the output as regards plutonium, power, fuel con- sumption, and other parameters. The speed is such that a series of calculations on models has been possible.

    Inclusive differential cross sections calculated from the D2N2 and EVAP programs [i0] have provided the necessary interaction characterisics; the data for low-energy neutrons have been taken from the BNAB multigroup neutron cross section library [21]. The MATRIX program from the BESM-6 standard software in the Dubna system has been used to solve the linear-equa- tion system [24]. Without entering into technical computation details, we note that this model retains all the most important characteristics of the target processes there: particle multiplication in the internuclear hadron cascade, low-energy neutron generation by evapora- tion from nuclei excited in the cascade, and neutron moderation and absorption in the medium providing breeding by fission. Particle multiplication in deep-inelastic interactions has been considered on the basis of the ionization losses. The neutron cross sections have been averaged over the resulting multigroup flux spectra to calculate the target isotope composi- tion changes.

    We found that the best reactor is based on fast-reactor metallic fuel pins with sodium cooling [25]. Two modes of operation were examined: an open-cycle converter based on stripped uranium and a closed-cycle breeder whose cycle is analogous to that in a fast reactor with plutonium re-use. The calculations were restricted to low burn-up, about 20 GW'days/ton. The characteristics obtained for these states were:

    Power, GW: thermal electrical (nett

    Excess plutonium production, t/y Stripped uranium consumption, t/y Plutonium concentration, kg/t

    in loaded uranium in unloaded

    Initial stripped-uranium target load, t Thermal efficiency, %

    1.5" 6.5** 0 2 i 2

    20 i00

    0 40 50 60 30 i00 40 40

    *, ** Converter with open fuel cycle and breeder in closed fuel cycle with addition of plutonium correspondingly.

    These results may be compared with standard data for fast reactors [26], from which it is clear that an electronculear reactor is worse than a fast one in producing electrical power because of its own internal consumption (including supplying the accelerator), but it produces more plutonium: almost five times as much per unit installed electrical power. The same fac- tor applies to the electronuclear reactors supplying thermal reactors with fuel in a closed system, to which nuclear power will inevitably have to resort as reserves of cheap uranium are exhausted. Published data on accelerator costs [27] give us estimates for the relative cost of the plutonium from it and show that provided one bears in mind that the estimate is only an approximation, the capital components in the cost of the excess plutonium are the same for the two types of reactor. It is envisaged that the electronuclear reactor should be used in breeder mode.

    The advantages of this approach include the scope for using already researched fast- reactor technology. There are the following essential differences from a fast reactor. Firstly, the target is always subcritical, including during accidents, and secondly, it is possible to start work without a preliminary plutonium load, as stripped uranium alone can be used in converter mode. The first is particularly important because it is related to safety. Nuclear safety becomes very complicated for fast reactors [28] and the more so as one strives to raise the power and increase the output of excess plutonium. Safety in a fast reactor is an acute problem because the proportion of delayed neutrons in the total secondaries is small and the neutron lifetime is short (less by a factor i000 than in a thermal reactor), while there is a positive component in the void coefficient of reactivity, as well as little effect from leaks with a large core, small Doppler reactivity coefficient for metallic fuel, etc. These problems do not exist for an electronuclear reactor, which is always subcritical and therefore there is no danger of prompt-neutron runaway. A moving control-rod system is also not required. There are none of the obstacles characteristic of a fast reactor to rais-


  • ing the unit power, which should enable one to increase the production of excess plutonium to a level almost i0 times that in a fast reactor.


    i. B. B. Kadomtsev and V. D. Shafranov, "Magnetic plasma containment," Usp. Fiz. Nauk, 139, No. 3, 399-434 (1983).

    2. P. R. Zenkevich, V. S. Imshennik, I. M. Kapchinskii, et al., Institute of Theoretical and Experimental Physics Researches on Heavy-Ion Fusion [in Russian], Preprint ITEF-64, Moscow (1981), 8 pp.

    3. L. Bracci and G. Fiorentini, "Some aspects of the muon catalysis of d-t fusion," Nucl. Phys., A364, No. 2-3, 383-407 (1981).

    4. R. G. Vasil'kov, V. I. Gol'danskii, and V. V. Orlov, "Electronuclear breeding," Usp. Fiz. Nauk, 139, No. 3, 435-464 (1983).

    5. V. S. Barashenkov, "Nuclear-physics aspects of the electronuclear method," in: Ele- mentary-Particle and Nuclear Physics [in Russian], Vol. 9, No. 5, pp. 871-921 (1978).

    6. M. Lone, W. Selander, B. Townes, et al., Characteristics of a Thermal Neutron Source Based on an Intermediate Energy Proton Accelerator, Rep. AECL-7839, Chalk River, Ontario (1983), 39 pp.

    7. I. M. Kapchinskii, "High-current linear ion accelerators," Usp. Fiz. Nauk, 132, No. 4, 639-661 (1980).

    8. T. Armstrong and K. Chandler, "HETC: a high-energy transport code," Nucl. Sci. Eng., 49, No. i, ii0-iii (1972).

    9. E. Straker, P. Stevens, D. Irving, and V. Cain, The MORSE Code: a Multigroup Neutron and Gamma-Ray Monte Carlo Transport Code, Rep. ORNL-4585 (1970),

    i0. B. S. Sychev, A. Ya. Serov, and B. V. Man'ko, An Analytic Approximation for the Differ- ential Cross Sections for the Formation of Secondary Particles in Inelastic Nucleon- Nuclear Interactions Above 20 MeV [in Russian], Preprint RTI AN SSSR, No. 799, Moscow (1979).

    ii. V. D. Kazaritskii, Linking the MARS4 and MMK22 Programs to Calculate Reaction Rates for Neutrons Formed in a Medium from High-Energy Particles [in Russian], Preprint ITEF-61, Moscow (1986).

    12. N. S. Baishev, S. L. Kuchinin, and N. V. Mokhov, Monte Carlo Calculations on Three- Dimensinal Hadron Cascades at 20 MeV to 3000 GeV (the MARS4 Program) [in Russian], Pre- print IFVE, 0RI-78-2 (1978).

    13. L. V. Maiorov, "The MMKFK software suite for calculating reactors by Monte Carlo methods, devised by A. D. Frank-Kamenetskii," in: Aspects of Nuclear Science and Engineering, Reactor Physics and Engineering Series [in Russian], Issue 8 (21) (1982), pp. 7-20.

    14. V. D. Kazaritskii, "Monte Carlo analysis of integral experiments on neutron yield pro- duced by high-energy protons," in: Aspects of Nuclear Science and Engineering, Nuclear Constants Series [in Russian], Issue 4 (58) (1984), pp. 11-16.

    15. G. A. Lobov, N. V. Stepanov, A. A. Sibirtsev, and Yu. V. Trebukhovskii, Monte Carlo Simulation of Interactions between Hadrons or Light Nuclei and other Nuclei: the Intra- nuclear Cascade Model [in Russian], Preprint ITEF-91, Moscow (1983).

    16. A. A. Sibirtsev, N. V. Stepanov, and Yu. V. Trebukhovskii, Particle Interactions with Nuclei: the Evaporative Model [in Russian], Preprint ITEF-129, Moscow (1985).

    17. V. S. Barashenkov, V. D. Toneev, and S. E. Chigrinov, "Calculations on the electronu- clear neutron-generation method," At. Energ., 37, No. 6, 475-479 (1974).

    18. R. Alsmiller, T. Gabriel, J. Barish, and F. Alsmiller, "Neutron production by medium- energy (~1.5 GeV) protons in thick uranium targets," Nucl. Sci. Eng., 79, No. 2, 162-166 (1981).

    19. P. Garvey, "Neutron production by spallation in heavy metal targets: experiments and calculation," in: Proc. Meeting on Targets for Neutron Beam Spallation Sources. Report Jul-Conf-34, Julich (1980), pp. 1-15. H. Takahashi, "Analysis of neutron yields form high-energy proton bombardment of uranium targets," Nucl. Sci. Eng., 87, No. 4, 432-443 (1984). L. P. Abagyan, N. O. Bazazyants, M. N. Nikolaev, and A. M. Tsibulya, Group Constants for Reactor and Shielding Calculations [in Russian], Energoizdat, Moscow (1981). S. Cierjacks, Y. Hino, S. Howe, et al., "Differential neutron production cross sections for 590 MeV protons," in: Nuclear Data for Science and Technology, Brussels and Luxem- bourg (1983), pp. 383-386.





  • 23. D. Filges, S. Cierjacs, Y. Hino, et al., Validation of the Intranuclear Cascade Evapora- tion Model for Particle Production, Rep. Jul-1960, Julich (1984).

    24. G. L. Maznyi, Programming the BESM-6 in the Dubna System [in Russian], Nauka, Moscow (1978).

    25. A. G. Samoilov, Heat Production by Reactor Elements [in Russian], Energoatomizdat, Moscow (1985).

    26. A. Walter and A. Reynolds, Fast-Neutron Breeder Reactors [Russian translation], Energo- atomizdat, Moscow (1986).

    27. P. Grand and H. Takahashi, "Breeding nuclear fuels with accelerators: replacement for breeder reactors," Nucl. Instrum. Methods in Physics Research, BI0/II (1985), pp. 454- 459.

    28. G. Hammel and D. Okrent, Reactivity Coefficients in Large Fast-Neutron Power Reactors [Russian translation], Atomizdat, Moscow (1975).


    V. I. Khvesyuk and N. V. Shabrov UDC 533.9.07

    The plasma in open traps is substantially nonuniform in both the axial and radial direc- tions. In this paper we study in detail the axial nonuniformities of plasma in ambipolar systems.

    Formulation of the Problem. Modern ambipolar traps are complex systems, consisting of several mirror machines - cells, each carrying its own functional load - connected in tandem. The central cell is the zone where the thermonuclear reaction itself occurs, the plug creates a confining electrostatic potential, the barrier cell ensures that the "hot" electrons of the plug are thermally insulated, and the anchor cell ensures that the entire trap as a whole is magnetohydrodynamically stable. This complex structure of ambipolar systems is created and maintained by specially shaping the magnetic field, by employing different methods for injecting power (injection of neutral particles; microwave heating), and by varying the pa- rameters of the injection devices (the flux and energy of fast atoms; the power and frequency of the microwave generators) along the length of the system, etc. The parameters of the plasma in the different cells of the trap are substantially different. Because the cells interact with one another, however, particle and energy fluxes that tend to equalize the pa- rameters of the plasma in them arise.

    Because the axial size of a separate mirror machine is much smaller than the mean-free path of the plasma particles the usual differential laws for the particle and energy fluxes (Fick's and Fourier's laws) are not applicable here. For this reason ambipolar systems are calculated by first dividing the plasma in a trap into different particle populations and describing the interaction of the populations. By particle population here we mean a group of particles of a single component (electrons, ions of different types), whose trajectories are localized within a fixed zone. The partitioning of the ~ntire trap into such confinement zones is determined by the position of the maxima of the magnetic and extrema of the electric fields along the longitudinal axis of the system. The confinement zone can be any cell of the trap, a group of cells, or part of a cell. In addition, particles of one type occupy a definite region in velocity space. We introduce the following notation: a(m) are particles of one or another population; a is the type of particle; e are electrons; i Z are ions with charge Z, etc.; m is an index denoting the confinement zone, for example (c), (b), or (p) - the central and barriers cells and the plug, respectively - if the confinement zone consists of one cell and (c, p) if the confinement zone consists of a groups of cells, etc.

    Within each population there are no spatial longitudinal particle and energy fluxes. Particle and energy exchange between populations at different points in space occurs by means of collisions of particles of one population with those of another, giving rise to transfer from one region of velocity space into another. Exchange is characteristic for particles of each population and occurs along the entire length of their confinement zone and with all ~

    Translated from Atomnaya Energiya, Vol. 65, pp. 330-334, November, 1988. Original article submitted April 6, 1987.

    0038-531X/88/6505-0893 $12.50 9 1989 Plenum Publishing Corporation 893


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