Implicit-in-time, finite-element implementation of the bilinear Fokker-Planck collision operator for application to magnetised plasmas.

In continuum kinetic models of quasineutral plasmas, binary collisions between particles are represented by the bilinear Fokker-Planck collision operator. In full-F kinetic models, which solve for the entire particle probability distribution function, it is important to correctly capture this operator, which pushes the system towards thermodynamic equilibrium. We show a multi-species, conservative, finite element implementation of this operator, using the continuum Galerkin representation, in the Julia programming language. A Jacobian-free-Newton-Krylov solver is used to implement a backward-Euler time advance. We present several example problems that demonstrate the performance of the implementation, and we speculate on future applications.