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A new scheme that evolves the perturbed part of the distribution function along a set of characteristics that solves the fully nonlinear gyrokinetic equations is presented. This low-noise nonlinear characteristic method for particle simulation is an extension of the partially linear weighting scheme, and may be considered an improvement over existing δf methods. Some of the features of this new method include the ability to keep all nonlinearities, particularly those associated with the velocity space, the use of conventional particle loading techniques, and also the retention of the conservation properties of the original gyrokinetic system in the numerically converged limit. The new method is used to study a one-dimensional drift wave model that isolates the parallel velocity nonlinearity. A mode coupling calculation for the saturation amplitude is given, which is in good agreement with the simulation results. Finally, the method is extended to the electromagnetic gyrokinetic equations in general geometry.
Parker et al. (Fri,) studied this question.