Hannover 2016 – scientific programme
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P: Fachverband Plasmaphysik
P 23: Helmholtz Graduate School for Plasma II
P 23.2: Fachvortrag
Thursday, March 3, 2016, 14:55–15:20, b302
Particle in Fourier Discretization of Kinetic Equations — •Jakob Ameres1,2 and Eric Sonnendrücker1,2 — 1Zentrum Mathematik, Technische Universität München — 2Max-Planck-Institut für Plasmaphysik, Garching
Particle methods are very popular when it comes to the discretization of kinetic equations. They are easy to implement and embarrassingly parallel. In plasma physics the high dimensionality (6D) of the problems raises the costs of grid based codes, favouring the mesh free transport with particles and its inherent adaptivity by following characteristics. The Particle in Cell (PIC) scheme couples the particle density to a grid based field solver using finite elements or finite differences. Finite elements yield an energy conserving scheme, whereas finite differences exclusively conserve momentum by the absence of particle self force. In this particle mesh coupling the stochastic error appears as noise, while the deterministic error leads to e.g. aliasing, inducing unphysical instabilities. By projecting the particles onto a spectral grid, we derive an energy and momentum conserving, aliasing-free scheme, Particle in Fourier (PIF). This method allows us to investigate the aliasing and stochastic errors of a B-spline based PIC code in case of the turbulent kinetic electrostatic electron nonlinear (KEEN) waves. In electrostatic problems governed by a strong magnetic field the anisotropies are transported along the magnetic field lines. These anisotropies can often be resolved with few Fourier modes. Here, PIF allows for the selective calculation of these relevant field aligned Fourier modes in a tokamak model, hence reducing the computational complexity.