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

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 $O(N_{\rho }(P+\widehat{P})\log (P+\widehat{P}))$, where $P$ is the number of spatial grid points, $\widehat{P}$ 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.