Optimization by marker removal for δfδf particle simulations

A marker removal optimization technique is developed for δfδf particle simulations. The technique uses the linear eigenmode structure in the equilibrium constant-of-motion space to construct an importance function, then removes some markers based on the importance function and adjusts the weights of the leftover markers to optimize the marker distribution function, so as to save markers and computing time. The technique can be directly applied to single-mode linear simulations. For multi-mode or nonlinear simulations, the technique can still be directly applied if there is one most unstable mode that dominates the simulation and δfδf does not change too much in the nonlinear stage, otherwise special care is needed, which is discussed in detail in this paper. The technique’s effectiveness, e.g., marker saving factor, depends on how localized δfδf is. The technique can be used for a phase space of arbitrary dimension, as long as the constants of motion in equilibrium can be found. In this paper, the technique is tested in a 2D bump-on-tail simulation and a 5D gyrokinetic toroidal Alfvén eigenmode (TAE) simulation and saves markers by factors of 4 and 19, respectively. The technique is not limited to particle-in-cell (PIC) simulations but could be applied to other approaches of marker particle simulations such as particle-in-wavelet (PIW) and grid-free treecode simulations.