An Improved Ghost-Point Technique for the Electrostatic Equation with Curved Boundaries and Discontinuous Permittivity in ECR Ion Source PIC Simulations

Abstract

In this paper, we propose an efficient Poisson solver for a two-dimensional axisymmetric domain to simulate plasma in a 2.45 GHz Electron Cyclotron Resonance (ECR) ion source. The solver employs a uniform Cartesian mesh for a curved domain, utilizing an unfitted boundary method. The presence of two Boron Nitride disks inside the plasma chamber creates a discontinuity in permittivity, leading to a Poisson problem with discontinuous coefficients. We discretize the Laplace operator by standard central difference formulas, and apply a ghost-point technique at nodes outside the domain and near the interfaces between the disks and the chamber, enforcing appropriate boundary and interface conditions for the ghost values. This method significantly simplifies and accelerates computations compared to boundary-conforming mesh approaches. The primary objective of this work is to upgrade our Poisson solver (employed in the Particle-In-Cell (PIC) code) from a fitted boundary method, such as COMSOL, to a custom implementation based on an unfitted boundary approach. The performance improvements are substantial, reducing computation time from a minimum of 5 seconds per solution with COMSOL to just 0.062 seconds with our custom solver.