Efficient Fourier Basis Particle Simulation

Abstract

The standard particle-in-cell algorithm suffers from grid heating. There exists a gridless alternative which bypasses the deposition step and calculates each Fourier mode of the charge density directly from the particle positions. We show that a gridless method can be computed efficiently through the use of an Unequally Spaced Fast Fourier Transform (USFFT) algorithm. After a spectral field solve, the forces on the particles are calculated via the inverse USFFT (a rapid solution of an approximate linear system). We provide one and two dimensional implementations of this algorithm with an asymptotic runtime of $O(N_p+N_m^D\log N_m^D)$ for each iteration, identical to the standard PIC algorithm (where $N_p$ is the number of particles and $N_m$ is the number of Fourier modes, and $D$ is the spatial dimensionality of the problem) We demonstrate superior energy conservation and reduced noise, as well as convergence of the energy conservation at small time steps.

arXiv comment17 pages, 12 figures

References in corpus (4)

• An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm
• The Energy Conserving Particle-in-Cell Method
• Variational formulation of particle algorithms for kinetic plasma simulations
• Finite grid instability and spectral fidelity of the electrostatic Particle-In-Cell algorithm

Cited by in corpus (3)

• Testing the conservative character of particle simulations: II. Spurious heating of guiding centers and full orbits subject to fluctuations expressed in terms of $\mathbf{E}$ and $\mathbf{B}$
• Grid instability growth rates for explicit, electrostatic momentum- and energy-conserving particle-in-cell algorithms
• On Geometric Fourier Particle In Cell Methods