Loading non-Maxwellian velocity distributions in particle-in-cell (PIC) simulation

Plasma velocity distribution functions (VDFs) exhibit many different profiles in the heliosphere. They are often loss-cone-shaped in the presence of a dipole field, they sometimes contain a power-law tail in the high-energy part, and they sometimes have ring- or shell-shaped pickup component. Particle-in-cell (PIC) simulations are useful for exploring kinetic processes, but it is not widely known how to generate such non-Maxwellian VDFs in these simulations.

In this contribution, we present Monte Carlo recipes for generating nine non-Maxwellian VDFs by using random variables. We first present two methods for the (r,q) flattop distribution. Next we present recipes for the regularized Kappa distribution. We then propose a simple procedure for the latest Kappa loss-cone model of the subtracted-Kappa distribution (Summers & Stone 2025 PoP). Properties and numerical recipes for the ring and shell distributions with a finite Gaussian width are discussed, followed by their new variants, the ring and shell Maxwellians. Finally, recipes for the super-Gaussian and the filled-shell distributions are presented.

See also: S. Zenitani, S. Usami, and S. Matsukiyo,  JGR Space Physics, in press, arXiv:2510.11890