General δf Particle-In-Cell algorithm in the presence of physical boundaries and strong forces*

The Particle-In-Cell (PIC) simulation with δf markers has been widely used to study plasma turbulences because it can effectively represent the evolution of small-amplitude perturbations. However, the δf approach has been considered inadequate for more general situations where perturbations can be large with strong nonlinear dynamics, especially in the presence of physical boundaries and strong forces. We found that the reason the traditional δf approach fails in such a situation is not due to the large amplitude of the perturbation but the vacancy of numerical markers in the phase space of interest. In this work, we present a general δf PIC algorithm that can overcome the existing limitations by appropriately generating new markers that continuously fill the phase space of interest with δf markers. The general δf algorithm can effectively handle arbitrary physical boundaries and strong forces without loss of generality. This algorithm is verified in various 1D problems, such as the two-stream instability and plasma expansion to the vacuum, and can be easily extended to more complex multi-dimensional problems. For example, the global gyrokinetic simulation code GTS successfully simulated thermal quench in a 3D stochastic magnetic field [1, 2] at a much lower computational cost by employing the novel general δf algorithm.

[1] M.-G. Yoo, et al., Nuclear Fusion 61 126036 (2021)

[2] M.-G. Yoo, et al., Physics of Plasma 29 072502 (2022)