Hyper Dimensional Phase-Space Solver and Its Application to Laser-Matter

摘要

A new numericla schem for solving the hyper-dimensional Vlasov-Poisson equation in phase space is described. At each time step, the distribution function and its first derviatives are advected in phase space by the Cubic Interpolated Propagation (CIP) scheme. Although a cell within grid points is interpolated by a cubic-polynomial, any matrix solutions are not required. The scheme guarantees the exact conservation of the mass. The numerical results show good agreement with the theory. Even if we reduce the number of grid points in the v-direction, the scheme still gives stable, accurate and reasonable results with memory storage comparable to particle simulations. Owing to this fact, the scheme has succeeded to the generalized in a straightforward way to deal with the six-dimensional, or full-dimensional problems.