Random number generation in kinetic plasma simulation: flattop and gamma distributions

A flattop distribution is one of the most characteristic non-Maxwellian velocity distributions in space plasmas. It is often observed in collisionless shocks and reconnection sites in near-Earth space. In this contribution, we discuss a numerical approach to study a flattop plasma in particle-in-cell (PIC) simulations. Specifically, we propose two numerical methods for randomly generating flattop-distributed velocities: a piecewise rejection method and a transform method from a gamma-distributed random number. Their usability is briefly compared.
Gamma-distributed random numbers are useful for generating flattop and other distributions. However, random number generators (RNGs) for gamma distribution may not be always efficient. Here, we propose a novel RNG algorithm for gamma distribution with shape parameter less than unity, based on the generalized exponential distribution and the squeeze method [1]. Numerical tests show that the proposed method is one of the best two in this category.

[1] S. Zenitani, Economics Bulletin, 44, 1113-1122 (2024), arXiv:2411.01415