Geometric Electrostatic Particle-In-Cell Simulations on Unstructured Meshes

A geometric electrostatic Particle-In-Cell (PIC) algorithm on unstructured meshes has been developed [1]. Present algorithm treats ions as fully kinetic 6D particles with adiabatic electron response. The algorithm is derived from a discrete variational principle on an unstructured triangular or tetrahedral mesh, or a partially unstructured prism mesh similar to that used in the XGC code.  The discrete variational principle mandates that Whitney 0-forms are used for charge deposition and Whitney 1-forms for field interpolation, which implies that the ‘shape functions’ for charge deposition and field interpolation are different. The Whitney 1-forms on the prism mesh are self-consistently derived. The algorithm has been applied to simulate the Ion Bernstein Wave (IBW) in a 2D circular region with the fixed boundary condition. The spectrum and eigenmode structures of the IBW are obtained from the simulation. We plan to implement an equilibrium of a magnetized plasma with density and temperature gradient in a slab geometry [2] using the unstructured prism mesh and simulate the excitation and growth of the ITG instability.

[1] Z. Wang, H. Qin, B. Sturdevant, C. S. Chang, Journal of Plasma Physics, 2021.

[2] J. Xiao and H. Qin, Nuclear Fusion, 2019.