Conservative fourth-order finite-volume Vlasov–Poisson solver for axisymmetric plasmas in cylindrical (r,vr,vθ) phase space coordinates

Abstract

A fourth-order finite-volume Vlasov–Poisson algorithm is developed for simulating axisymmetric plasma configurations in (r,vr,vθ) phase space coordinates. The Vlasov equation for cylindrical phase space coordinates is cast into conservation-law form and is discretized on a structured grid. The conservative finite-volume discretization is based on fifth-order upwind reconstructions of the distribution function and a fourth-order quadrature rule that accounts for transverse variations of fluxes along control volume surfaces. High-order specular reflection boundary conditions enable high-fidelity treatment of plasma distribution functions at the axis and at wall boundaries. The numerical method is applied to simulate a confined uniform neutral gas to assess convergence properties for an equilibrium system in which effects of finite-temperature and acceleration due to centrifugal and Coriolis forces are present. The discretization is also applied to a Z-pinch configuration to study electrostatic ion confinement and the dynamics of the associated breathing mode. Simulations show that the ion distribution function exhibits non-Maxwellian features and that a temperature anisotropy develops and is sustained. The finite-volume implementation is demonstrated to converge at fourth-order for both applications.