An Accurate Numerical Method to Solve the Linear Fokker-Planck Equation Characterizing Charged Particle Transport in Spherical Plasmas

The time-dependent linear Fokker-Planck equation governing the transport of fast ions in a spherical host medium is solved in the suprathermal energy range, including both continuous slowing down and angular diffusion. Because of the parabolic nature of the angular dispersion term, an implicit time-centered scheme is proposed. On the other hand, a second-order diamond approximation in energy and space is chosen to avoid the spurious numerical diffusion driven by the usual first-order methods. The last variable, the pitch angle cosine, is discretized by centered finite differences. Good accuracy is demonstrated when comparing the results of the proposed method with the “exact” values given in the literature for some benchmark problems or by checking energy and particle balance equations. A numerical code (CIRCE) based on this scheme has been developed; it can be coupled to standard one-dimensional hydrodynamics codes after a few straightforward modifications.