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A sufficient condition for flattening of the thermal neutron flux and some related problems (in onedimensional geometries)
Applications of Mathematics, Tome 14 (1969) no. 2, pp. 134-145
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The main results of this paper, in which the problem of determination of the fuel concentration distribution $M$ inducing a prescribed thermal neutron flux $\Phi$ in the homogenized critical reactor core with given outer reflector boundary is investigated (in the two-groups diffusion approximation), are stated in the theorems 1 and 2. In theorem 1 sufficient conditions are given for the existence of a oneparametrical family of thermal neutron fluxes induced by the Goertzel's type fuel concentration distribution. This theorem enables us to seek for the flux of this oneparametrical family which gives the maximal total output of the reactor. In Theorem 2 the results of Theorem 1 are generalized for the case of such fuel concentration distributions which are not of the Goertzel's type.
The main results of this paper, in which the problem of determination of the fuel concentration distribution $M$ inducing a prescribed thermal neutron flux $\Phi$ in the homogenized critical reactor core with given outer reflector boundary is investigated (in the two-groups diffusion approximation), are stated in the theorems 1 and 2. In theorem 1 sufficient conditions are given for the existence of a oneparametrical family of thermal neutron fluxes induced by the Goertzel's type fuel concentration distribution. This theorem enables us to seek for the flux of this oneparametrical family which gives the maximal total output of the reactor. In Theorem 2 the results of Theorem 1 are generalized for the case of such fuel concentration distributions which are not of the Goertzel's type.
DOI : 10.21136/AM.1969.103216
Keywords: partial differential equations 
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Zezula, Rostislav. A sufficient condition for flattening of the thermal neutron flux and some related problems (in onedimensional geometries). Applications of Mathematics, Tome 14 (1969) no. 2, pp. 134-145. doi: 10.21136/AM.1969.103216

[1] V. Bartošek, R. Zezula: Flat Flux in a Slab Reactor with Natural Uranium. Journal of Nuclear Energy Parts A/B, 1966, vol. 20, pp. 129-134. | DOI

[2] S. Glasstone M. C. Edlund: The Elements of Nuclear Reactor Theory. Toronto - New York - London 1952.

[3] V. Bartošek R. Zezula: Flat Flux in a Slab Reactor with Natural Uranium. Report ÚJV 1310 (1965).

[4] V. Bartošek R. Zezula: Stability of flat thermal flux in a slab reactor. Apl. Mat. 13 (1968), 367-375. | MR

[5] R. Zezula: Sufficient Conditions for the Flattening of Thermal Neutron Flux and Some Related Problems. (in multidimensional geometries). Report ÚJV 1902/67.

[6] M. Hron V. Lelek: Flux Flattening by means of a Non-Uniform Fuel Distribution in a Slab Reactor with Finite Reflector. Report ÚJV 1660 (1966).

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