Grid effects on the plasma simulation by the finite-sized particle

Abstract

About the so-called usual models, in which the total momentum is conserved, it is well known that the total energy is not conserved due to the nonuniformity of space caused by spatial grids. It fluctuates and increases in time from a stochastic origin. In order to see the accuracy of the plasma simulations, it is important to evaluate the fluctuation K g , which is more dominant for small errors during the shorter time. We study its standard deviation in t, σ K g , and the correlation time of dK g K · dt, T, τ c about periodic one-dimensional systems, where K is the kinetic energy. We evaluate σ K g by invoking the stochastic theory and obtain a scaling law: σ{K g} K ≅ ( 2 π ) 1 2 · η · {(2M) 1 2 n sλ D} −1 · (tτ cω p 2) 1 2 , where 2 M is the number of the grids per one period, n s , is the electron density, λ D is the Debye length, and ω p is the plasma angular frequency. The coefficient η depends on the magnitude of the unphysical grid force of each model. Our simulations with the usual models (CIC-PIC, modified SUDS, and method 2 2 ) support this scaling law. We obtain the correlation time empirically. It is found that τ c ≅ ΔAt if Δt is sufficiently large, and τ c ≅ built1 4 Δ ν th if Δ (Δt · ν th) > 3 , where Δt is the time step, Δ is the grid distance, and ν th is the thermal velocity of the electron.