Vlasov model using kinetic phase point trajectories

A method of solution of the collisionless Vlasov equation by following fixed collisionless phase point (“particle”) trajectories (characteristics) in phase space is presented. It solves the coupled Vlasov Maxwell system self-consistently and employs the Leapfrog-Trapezoidal scheme to solve for the characteristics explicitly. It then uses the bilinear finite element interpolation scheme in phase space and maps vital instantaneous phase point information (distribution function) to a fixed background phase space mesh while retaining it at the phase point. The scheme is an enhanced second order one in time and fourth order in space. The code is then used to model a thermal plasma as well as two stream instability using mobile electrons and fixed background ions: the scheme being a momentum conserving one by construction allows energy conservation without assignment of particle shape functions; Langmuir waves are obtained with very good agreement with the Bohm-Gross dispersion relation; the two stream results do not show any numerically induced oscillations attributed to the initial well-ordered velocity distributions. Retention of the characteristics also minimized diffusion. Extensive numerical stability analysis deriving Courant condition for the scheme as well as behavior of computational modes are done in Appendix A, as well as estimating the impact of numerical diffusion in Appendix B. Two to five dimensional versions in phase space exist.