Fast and spectrally accurate evaluation of gyroaverages in non-periodic gyrokinetic-Poisson simulations

TL;DR

This paper introduces a fast, spectrally accurate numerical method for evaluating gyroaverages in non-periodic gyrokinetic-Poisson simulations, improving computational efficiency and accuracy.

Contribution

The authors reformulate the gyrokinetic-Poisson system to compute gyroaverages via Fourier and Hankel transforms, achieving near optimal run time complexity.

Findings

Demonstrates geometric convergence of the error

Shows improved computational performance in numerical examples

Validates the method's accuracy and efficiency

Abstract

We present a fast and spectrally accurate numerical scheme for the evaluation of the gyroaveraged electrostatic potential in non-periodic gyrokinetic-Poisson simulations. Our method relies on a reformulation of the gyrokinetic-Poisson system in which the gyroaverage in Poisson's equation is computed for the compactly supported charge density instead of the non-periodic, non-compactly supported potential itself. We calculate this gyroaverage with a combination of two Fourier transforms and a Hankel transform, which has the near optimal run time complexity $O(N_{\rho}(P+\hat{P})\log(P+\hat{P}))$, where $P$ is the number of spatial grid points, $\hat{P}$ the number of grid points in Fourier space, and $N_{\rho}$ the number of grid points in velocity space. We present numerical examples illustrating the performance of our code and demonstrating geometric convergence of the error.