Analysis of noise in particle codes and the development of a meshless kinetic particle code

Recent work [JCP 440 (2021) 110394] is extended to include time dependent results on the noise and correlations in the density and electric field in particle-based kinetic codes. A meshfree particle code in 1D with electrostatic dynamics is under development. The estimated density is obtained by kernel density estimation (KDE), which does not require a mesh. In this meshfree setting, bias-variance optimization of the density error shows that the number of particles per cell does not have any relevance; instead, the number of particles-per-kernel-width is the relevant quantity. The electric field interpolation is discussed in terms of a partition of unity principle. The conservation properties of such a code are discussed and the relationship with statistical errors is explored. A comparison of Vlasov-Gauss (Vlasov-Poisson) methods and the Vlasov-Ampere approach is shown. Results on the covariance matrix of the electric field, obtained from the density by Gauss's law, also in a meshfree context, are presented and the analogy with the Ornstein-Uhlenbeck bridge of stochastic processes is explained. Comparison and interpretation of the meshfree results is made with a standard PIC code.