Hybrid PIC-Vlasov method

Summary form only given. The proposed hybrid numerical method for kinetic simulation of plasmas combines best features of discrete and continuous approaches. The PIC method suffers from statistical noise. Truly stationary solution can not be found in practice. Poor resolution of energetic tail makes it extremely difficult to accurately calculate high moments of the distribution function. For the same reason calculation of certain functions of the distribution (elementary plasma chemistry reaction rates or floating potential of any plasma facing surface element) may be inaccurate for a limited number of particles per computational cell. Another set of problems emerges when an adaptive grid is introduced. In this case the volume of an individual cell may become small, driving statistical error to infinity for a common PIC scheme. Vlasov method on the contrary suffers from large numerical diffusion. Existing methods, which artificially control gradients (aka flux-control methods), require various artificial correcting procedures. It may also lead to negative values of the distribution function and violation of conservation laws of plasma evolution. But Vlasov method guarantees that the grid in which distribution function is defined evenly covers whole phase space. Required mesh, however, might be huge due high dimensionality of the problem complicated by large numerical diffusion. New scheme includes dual representation of distribution function by grid function and by particles, which are typical for Vlasov and PIC methods, respectively. This combination allows to lower required grid sizes and drastically reduces numerical diffusion of the scheme. Relative efficiency of the hybrid scheme versus pure PIC as well pure Vlasov methods is demonstrated for a set of model problems described with any of the following equations. /spl part/f//spl part/t+v/spl part/f//spl part/x-E/spl part/f//spl part/v=0.../spl part/f//spl part/t+v/spl I.oarr//spl part/f//spl part/x/spl I.oarr/- (E/spl I.oarr/+v/spl I.oarr//spl times/B/spl I.oarr/)/spl part/f//spl part/v/spl I.oarr/=C. Method is applicable to important cases with non-zero collisional integral C. Finally, we discuss possibility of using moving adaptive grids in space and/or phase space bundled with new hybrid procedure.