Sommario
Si considera l'equazione stazionaria del trasporto per neutroni monoenergetici in geometria piana con condizioni al contorno di riflessione speculare e diffusa. Si ricava l'equazione integrale per il flusso partendo dalla equazione integro-differenziale per la distribuzione angolare di particelle; i corrispondenti operatori integrali hanno nuclei di cui si danno le forme esplicite. In entrambi i casi γ/σ è l'autovalore di modulo massimo e le corrispondenti autofunzioni sono costanti. Si dimostra così che esistono soluzioni stazionarie che sono date da flussi costanti e densità angolari costanti se γ=σ.
Summary
We consider the stationary transport equation for monoenergetic neutrons in slab geometry with boundary conditions of perfect and diffuse reflection. The integral equation for the flux is derived starting from integro-differential equation for the angular distribution of particles; the corresponding integral operators have kernels whose explicit forms are given. The eigenvalues of maximum modulus are γ/σ and the corresponding eigenfunctions are constant in both cases. This fact shows that the stationary solutions exist and are given by constant fluxes and constant angular densities if γ=σ.
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Work performed under the auspices of C.N.R., G.N.F.M.
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Bassi, L., De Vito, A. A solution of the stationary transport equation in plane geometry. Meccanica 18, 71–76 (1983). https://doi.org/10.1007/BF02128347
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DOI: https://doi.org/10.1007/BF02128347