Geometric Electrostatic Particle-In-Cell Algorithm on Unstructured Meshes

We present a geometric Particle-in-Cell (PIC) algorithm on two-dimensional (2D) unstructured meshes for studying electrostatic perturbations in magnetized plasmas. In this method, ions are treated as fully kinetic particles, and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms, and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the Ion Bernstein Wave (IBW) in 2D magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a 2D circular region with the fixed boundary condition, the spectrum and eigenmode structures of the IBW are determined from simulation. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

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