Topic/Type: 2.2 Kinetic methods, Particle-In-Cell and Vlasov, Poster

### An Adaptive delta-f Monte Carlo Method for Fokker-Planck Models

J. H??k, T. Hellsten

Fusion Plasma Physics, School of Electrical Engineering, Royal Institute of Technology (KTH), Stockholm, Sweden

A new adaptive $\small \delta f$ Monte Carlo method for solving Fokker-Planck equations with application to radio frequency (RF) -heating and transport in fusion plasmas is presented. The method is suitable for models with arbitrary large perturbation from a given zeroth order approximation of the distribution function. For the method to be more efficient than (full-f) standard Monte Carlo requires that $\small \delta f(v)/f(v) < 1$, where the efficiency is measured by $\small [\delta f(v)/f(v)]^2$. This is normally the case in transport studies where the unperturbed part is close to a Maxwellian everywhere in phase space. For distribution functions with a large high-energy tail, as in RF-heating the perturbation becomes locally dominate and the performance of classical $\small \delta f$ method revert back to standard Monte Carlo. Our method compensate large perturbations such that $\small \delta f (v)/f(v) < 1$. This is accomplished by an extended $\small \delta f$ expansion where higher order moment approximation of the distributions are found implicitly through minimization of the source. The source is obtained by inserting the expansion of $\small f(v)$ in the Fokker-Planck equation, which produces an inhomogeneous term. The source term is not positive definite, sources and sinks are present, which is here modeled by adding particles with fixed weights $\small \pm 1$ during simulation at the rate defined by the inhomogeneous term in the Fokker-Planck equation. Because of the continuous increase in the number of simulated particles the simulation needs to be restarted together with annihilation of particles sharing the same regions of phase space with opposite sign. The method is tested on a Fokker-Planck model describing RF-heating and compared against the stationary solution. Different minimization models and some techniques for particle annihilation are presented and tested.