FPN-BN, solution and single integral formulation of the BFP equation for neutral and charged particles in ICF reactors

Abstract

In order to develop ICF reactors a model is needed for the anisotropic transport of neutral and charged particles inside a high density hot plasma generated at the centre of a DT pellet by a laser-driven implosion. Two BFF equations in cascade for the F-transformed angular flux (0) (B, E, μ), unperturbed by the continuous deviation tern, and for its correction (1) (B, E, μ), talcing this effect into account, are solved via FPN-BN method, once an appropriate closed-form, but of infinite anisotropy order, expression is found for (0) (B, E, μ). The introduction of suitably generalized F-transformed kernel functions, with respect to the classical ones for usual anisotropic transport integral formulation, and of projections, of both FPN and BN equations, onto a suitable sequence of Paley-Wiener spaces, leads finally to FPN recurrences reducing the two first BN equations to a couple of F-transformed integral equations for the zero-th order moments only of the two unknowns, talcing nevertheless into account the whole flux and scattering anisotropy of the problem. Finally easily computable polynomial series expansions, of such zero-th order moments of the unknowns, with Fourier coefficients solving appropriate infinite algebraic linear systems, are derived, once appropriate relations are found, between boundary angular flux moments, substantially correspondent to the boundary conditions for the problem.