A Synthetically Accelerated Weighted Diamond Scheme for Charged-Particle Transport Calculations

A new weighted diamond scheme is developed to solve the linear Fokker-Planck equation for suprathermal charged-particle transport. Such a scheme is based on the preservation of the asymptotic behavior of the linear discontinuous finite element scheme previously proposed. A simpler steplike scheme has been also considered. The results show that the weighted diamond scheme is as accurate as the linear discontinuous one, preserving the energy-position-angle correlation of charged-particle slowing down with less calculational effort. On the contrary, the steplike scheme does not preserve this coupling, giving results similar to those obtained by multigroup methods. A spectral analysis of the iteration of the scattering term shows that the convergence process can be unacceptably slow when the momentum transfer cross section is dominant. Consequently, the weighted diamond scheme has been accelerated by the S₂ synthetic method, significantly improving its convergence rate. Finally, the results show that the accelerated weighted diamond scheme is highly effective for electron transport calculations.