Numerical solution of quasilinear kinetic diffusion equations in toroidal plasmas

One of the main challenges for the realization of a working fusion power plant is an increased detailed understanding of kinetic phenomena in toroidal plasmas. The tokamak is a toroidal, magnetically confined plasma device and is currently the main line towards a power plant. The spatial and temporal scales in a tokamak plasma are extreme and the only tractable path for quantitative studies is to rely on computer simulations. Present day simulation codes can resolve only some of these scales. Nevertheless they still require the largest high performance computing (HPC) resources available in the world. In combination with the increase of computational performance, it is therefore necessary to improve the numerical algorithms used in the simulations. In this thesis we have developed new numerical methods designed for Monte Carlo simulation of plasma kinetic diffusion. Examples are simulation of fast-ion thermalization and radio-frequency heating. The aim has been to reduce the statistical random noise in particle codes, produced by a finite number of particles (or markers). Traditionally the statistical noise is improved by increasing the number of particles (N) or by simulating the perturbation of the distribution (with particles) from a known distribution function. This is the well known δf method. In this thesis we have developed a new type of δf method, which minimizes the number of particles used in a simulation. The computational speedup of the new method is substantial. In this thesis, we have further benchmarked quasi-Monte Carlo techniques that improve the convergence rate from N to N for some cases. In Monte Carlo simulations, error appears also from the time step discretization. Based on the mathematics of operator splitting, a new scheme for the pitch-angle scattering diffusion process has been developed that outperforms the standard methods. Finally this thesis also presents a new code, SELFO-light, for self-consistent simulations of ion cyclotron resonance heating, suitable for routine calculations, which couples a one dimensional FokkerPlanck model with the finite element wave solver LION. Descriptors Fusion plasma, tokamak, Monte Carlo, quasi-Monte Carlo, variance reduction techniques, the δf -method, pitch-angle scattering, RF heating, ion cyclotron resonance heating (ICRH), self-consistent calculations, SELFO-light, LION.