Piecewise Field-Aligned Finite Element Method for Multi-Mode Nonlinear Particle Simulations in tokamak plasmas

TL;DR

This paper introduces a novel piecewise field-aligned finite element method combined with particle-in-cell techniques for efficient multi-mode nonlinear plasma simulations in tokamak devices, improving accuracy and flexibility.

Contribution

It develops a new numerical scheme that aligns computational grids with magnetic fields using piecewise basis functions, enabling better representation of plasma modes without grid deformation.

Findings

Linear benchmark tests agree with previous results.

Method effectively simulates nonlinear turbulence.

Demonstrates efficiency on unstructured meshes.

Abstract

This paper presents a novel approach for simulating plasma instabilities in tokamak plasmas using the piecewise field-aligned finite element method in combination with the particle-in-cell method. Our method traditionally aligns the computational grid but defines the basis functions in piecewise field-aligned coordinates to avoid grid deformation while naturally representing the field-aligned mode structures. This scheme is formulated and implemented numerically. It also applied to the unstructured triangular meshes in principle. We have conducted linear benchmark tests, which agree well with previous results and traditional schemes. Furthermore, multiple-$n$ simulations are also carried out as a proof of principle, demonstrating the efficiency of this scheme in nonlinear turbulence simulations within the framework of the finite element method.