A global collisionless PIC code in magnetic coordinates

Abstract

A global plasma turbulence simulation code, ORB5, is presented. It solves the gyrokinetic electrostatic equations including zonal flows in axisymmetric magnetic geometry. The present version of the code assumes a Boltzmann electron response on magnetic surfaces. It uses a Particle-In-Cell (PIC), δf scheme, 3D cubic B-splines finite elements for the field solver and several numerical noise reduction techniques. A particular feature is the use of straight-field-line magnetic coordinates and a field aligned Fourier filtering technique that dramatically improves the performance of the code in terms of both the numerical noise reduction and the maximum time step allowed. Anoter feature is the capability to treat arbitrary axisymmetric ideal MHD equilibrium configurations. The code is heavily parallelized, with scalability demonstrated up to 4096 processors and 10 9 marker particles. Various numerical convergence tests are performed. The code is validated against an analytical theory of zonal flow residual, geodesic acoustic oscillations and damping, and against other codes for a selection of linear and nonlinear tests.

Parallel filtering in global gyrokinetic simulations

“…On the other hand, Eulerian codes are free from such noise, and influences of the filtering can be clearly estimated by comparing filtered and non-filtered simulations at a fixed number of grid points.Therefore, this work presents the implementation of the Fourier filtering technique in the Eulerian code GT5D [11] and in the PIC code ORB5 [12].…”

“…Indeed, Particle-In-Cell (PIC) simulations may be polluted by high parallel components generated by inherent statistical noise [12]. This has been resolved by applying a Fourier filter specifically designed to remove high k ρ s modes on the perturbed density [12].…”

“…Unfortunately, the field equation is in that case solved with an iterative solver whose convergence is not guaranteed and depends on the physical problem. For these reasons, many of the global gyrokinetic codes [23,11,12,13] still solve the field equation on the poloidal plane with direct solvers. The GT3D code [23] uses a ballooning phase factor to extract analytically the k = 0 structure at a given magnetic surface: the grid resolution of the field equation can be strongly reduced.…”

“…This has been resolved by applying a Fourier filter specifically designed to remove high k ρ s modes on the perturbed density [12]. This scheme has been recently improved by applying the same filtering procedure to the potential [14] and results in massive computational savings in global Particle-In-Cell (PIC) codes: memory is decreased by 2 orders of magnitude, the number of Fourier modes is decreased by one order of magnitude and the number of particles required for a given accuracy is decreased by the same factor as the number of particle per Fourier modes dictates the noise level [15].…”

Nonlinear interplay of Alfvén instabilities and energetic particles in tokamaks

“…The numerical tool adopted for the studies presented here is the nonlinear gyrokinetic particlein-cell (PIC) code ORB5 [13], which now includes all extensions (including the electromagnetic and multi-species extensions) of the NEMORB project [14,15,16,17]. The GK model contains the treatment of the resonances of ions and electrons, which is neglected by fluid models.…”