The development of an implicit full f method for electromagnetic particle simulations of Alfv\'en waves and energetic particle physics

TL;DR

This paper introduces an implicit electromagnetic particle simulation scheme for Alfvén waves and energetic particles, demonstrating its effectiveness in 1D and 3D tokamak plasma models with accurate frequency and growth rate predictions.

Contribution

It develops a novel implicit full f electromagnetic particle scheme with analytical convergence for efficient kinetic plasma simulations.

Findings

Applicable across a broad range of plasma parameters

Successfully simulates toroidicity induced Alfvén eigenmodes

Results agree with previous studies on frequency and growth rates

Abstract

In this work, an implicit scheme for particle-in-cell/Fourier electromagnetic simulations is developed and applied to studies of Alfv\'en waves in one dimension and three-dimensional tokamak plasmas. An analytical treatment is introduced to achieve efficient convergence of the iterative solution of the implicit field-particle system. First, its application to the one-dimensional uniform plasma demonstrates its applicability in a broad range of $\beta/m_e$ values. Second, toroidicity induced Alfv\'en eigenmodes (TAE) are simulated in a three-dimensional axisymmetric tokamak plasma, using the widely studied case defined by the International Tokamak Physics Activity (ITPA) Energetic Particle (EP) Topical Group. The real frequency and the growth (or damping) rate of the TAE with (or without) EPs agree with previous results reasonably well. The full f electromagnetic particle scheme established in this work provides a possible natural choice for EP transport studies where large profile variation and arbitrary particle distribution functions need to be treated in kinetic simulations.