Numerical Solution of the Gyroaverage Operator for the Finite Gyroradius Guiding-Center Model

Abstract

In this work, we are concerned with numerical approximation of the gyroaverage operators arising in plasma physics to take into account the effects of the finite Larmor radius corrections. Several methods are proposed in the space configuration and compared to the reference spectral method. We then investigate the influence of the different approximations considering the coupling with some guiding-center models available in the literature.

A 5D gyrokinetic full-f global semi-Lagrangian code for flux-driven ion turbulence simulations

“…This is performed on a finite element formalism and enables therefore high order accuracy by keeping the matricial formulation. In [30] the influence of the interpolation operator (which is of great importance when the quadrature points do not coincide with the grid points) has been studied and it is shown that the cubic splines are appropriate. The direct integration on gyro-circles proposed in [30] has been recently generalized to arbitrary coordinates [113] and implemented in the code.…”

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

“…The Padé approximation approach has the advantage of being fast, but is well known to cause an overdamping of small scales, which limits its accuracy (Steiner et al 2015). A more common approach is to evaluate directly the gyroaverage integral through numerical quadrature, relying on interpolation on points along the gyroring of the function which is gyroaveraged (Jolliet et al 2007;Crouseilles et al 2010;Görler et al 2011;Steiner et al 2015). By choosing high-order interpolation schemes, high-order accuracy can be achieved with this method, but with a larger computational cost than with a Padé based approach (Steiner et al 2015).…”

Gyroaverage operator for a polar mesh

“…This is performed on a finite element formalism and enables therefore high order accuracy by keeping the matricial formulation. In [5] the influence of the interpolation operator (which is of great importance when the quadrature points do not coincide with the grid points) has been studied and has shown that the cubic splines are a good candidate. Some techniques used in [5] taking advantages of the cartesian coordinates properties are no more valid in (r, θ) polar geometry.…”

“…In [5] the influence of the interpolation operator (which is of great importance when the quadrature points do not coincide with the grid points) has been studied and has shown that the cubic splines are a good candidate. Some techniques used in [5] taking advantages of the cartesian coordinates properties are no more valid in (r, θ) polar geometry. In this paper we present a method based on a direct integration of the gyroaverage operator which is directly applicable for global gyrokinetic code in toroidal geometry as GYSELA code.…”

“…The present work is devoted to the numerical computation of the gyroaverage operator for a polar mesh, following a a A part of this work was carried out using the HELIOS supercomputer system at Computational Simulation Centre of International Fusion Energy Research Centre (IFERC-CSC), Aomori, Japan, under the Broader Approach collaboration between Euratom and Japan, implemented by Fusion for Energy and JAEA. previous work which was designed for cartesian geometry [5]. We propose an alternative to the classical Padé approximation, that is especially employed in the gyrokinetic code GYSELA [8,9] and which is known to be only valid for small Larmor radius.…”