Moment approach of the multi-species non-linear Coulomb collision operator adapted to particle-in-cell codes

Abstract

In this article an approximated version of the multi-species, non-linear Coulomb collision operator is derived via the use of a truncated moment expansion of the distribution function to compute the Rosenbluth potentials. The evolution of the distribution function due to the collision operator takes the form of a Fokker–Planck equation that can be efficiently solved by a Langevin approach in the particle-in-cell (PIC) framework. This kinetic collision operator is then implemented in the global gyrokinetic PIC code ORB5 while neglecting finite Larmor effects. This collision operator ensures exact conservation of density, total momentum and energy as expected. The neoclassical physics is also successfully retrieved by the code. Numerical aspects such as the noise control and the parallelisation of the code are presented in detail.