A Study on Particle Trajectory Error in Finite-Element Particle-in-Cell Algorithms

• Published in: IEEE transactions on plasma science Vol. 52; no. 4; pp. 1546 - 1554
• Main Authors: Saleh, Haitham H., Teixeira, Fernando L.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Algorithms; Approximation algorithms; Charged particles; Electric potential; Electromagnetic fields; Error analysis; Finite element (FE); harmonic oscillator; Iron; kinetic plasma; Kinetic theory; Magnetic fields; Mathematical analysis; Particle in cell technique; Particle trajectories; particle-in-cell; Plasmas; sparse approximate inverse (SPAI); Sparse matrices; Trajectory; unstructured mesh
• ISSN: 0093-3813; 1939-9375; 1939-9375
• DOI: 10.1109/TPS.2024.3388369

Particle-in-cell (PIC) algorithms are widely used for the simulation of kinetic plasmas. PIC algorithms account for the interaction between charged particles in a plasma and the electromagnetic field in ambient space, including self-field interactions. The objective of this article is to study the error in charged particle trajectories present in finite-element (FE)-based PIC algorithms on unstructured meshes. We study how the trajectory error behaves according to the FE mesh resolution and the matrix solver employed in the FE algorithm. The study is performed by considering a trajectory established by a parabolic electric potential and an axial magnetic force acting on the charged particle. Under a proper choice combination of electric and magnetic field parameters, the 2-D particle trajectories comprise closed orbits. Numerical errors cause small perturbations on the trajectories, with cumulative effects. As a result, the resulting orbital trajectories exhibit distortions including spurious apsidal precession. These distortions provide a clear imprint of the numerical error. We also study the numerical error in a quantitative fashion by computing the distance norm between the trajectories obtained by the exact fields and numerical fields.