Orbit-based representation of equilibrium distribution functions for low-noise initialization of kinetic simulations of toroidal plasmas

This work deals with the initial loading of phase space markers for global gyrokinetic particle-in-cell (PIC) simulations of plasmas that are magnetically confined in a toroidally axisymmetric configuration. A method is presented, which allows to prepare a marker distribution that is independent of time. This is achieved by discretizing the phase space along lines of constants of motion, which allows to load markers on the toroidal surfaces of unperturbed guiding center orbits. On each orbit surface, markers are distributed uniformly in time, so their distribution represents the compressible motion of physical particles. This method allows to initialize global PIC codes with an accurate equilibrium distribution function for charged particles, taking into account prompt losses to the wall. It facilitates simulations with lower noise levels and minimal noise–signal correlation; especially, in the linear regime. The problem considered is the representation of energetic ions in tokamaks, which are characterized by large drifts across magnetic surfaces.