Noise and error analysis and optimization in particle-based kinetic plasma simulations.

analysis is restricted to: § Periodic systems (on the interval [0,1]) § Electrostatic (Vlasov-Poisson) § Charge-neutral plasmas § Mobile electrons and immobile ions § Constant and equal weight computational particles § Spatial analysis on uniform grid (non-Fourier models) § Noise and error in the charge density and electric field Density estimation by finite number of particles § Write the density distribution function as § Integrating we have at any spatial point, i.e., continuous § In our analysis, the kernel is generally not the familiar PIC particle shape; it satisfies these conditions: § The normalization to unity assures conservation of total charge in the system.