Generalized weighting scheme for δf particle-simulation method

An improved nonlinear weighting scheme for the δf method of kinetic particle simulation is derived. The method employs two weight functions to evolve δf in phase space. It is valid for quite general, non-Hamiltonian dynamics with arbitrary sources. In the absence of sources, only one weight function is required and the scheme reduces to the nonlinear algorithm developed by Parker and Lee Phys. Fluids B 5, 77 (1993) for sourceless simulations. (It is shown that their original restriction to Hamiltonian dynamics is unnecessary.) One-dimensional gyrokinetic simulations are performed to show the utility of this two-weight scheme. A systematic kinetic theory is developed for the sampling noise due to a finite number of marker trajectories. The noise intensity is proportional to the square of an effective charge qeff=̇q(w̄/𝒟), where w̄ ∼δf/f is a typical weight and 𝒟 is the dielectric response function.