Computational Methods for Kinetic Processes in Plasma Physics

Computational Methods for Kinetic Processes in Plasma Physics Ken Nishikawa National Space Science & Technology Center/UAH September 8, 2011 1/39

Context Three-dimensional current deposit by Villasenor & Buneman Zigzag scheme in two-dimensional systems by Umeda

Current deposit scheme (2 -D) y x

3 D current deposit Jx Jx

3 D current deposit Particle moves from between t= − 1/2 and t = +1/2 at t = 0 Jx= Jy at (i+1, j+1/2, k+1) Jz at (i+1, j+1, k+1/2)

The total fluxes into the cell indexed i+1, j+1, k+1 The difference between the particle fractions protruding into the cell before and after the move.

Staggered mesh with E and B

Current deposition seven-boundary move Δx 1=0. 5 −x, Δy 1=(Δy/Δx)Δx 1, x 1=− 0. 5, y 1=y+Δy 1, Δx 2=Δx−Δx 1, Δy 2=Δy−Δy 1

Current deposition ten-boundary move Δx 1=0. 5 −x, Δy 1=(Δy/Δx)Δx 1, x 1=− 0. 5, y 1=y+Δy 1, Δy 2=0. 5 y−y−Δy 1, Δx 2=(Δx/Δy)Δy 2, x 2=Δx 2− 0. 5, y 2=0. 5, Δx 3=Δx−Δx 1−Δx 2, Δy 3=Δy−Δy 1−Δy 2

Current deposit scheme (2 -D) y x

Charge and current deposition Current deposition can take as much time as the mover. More optimized deposits exist (Umeda 2003). Charge conservation makes the whole Maxwell solver local and hyperbolic. Static fields can be established dynamically.

Zigzag scheme in two-dimensional systems i 1 =i 2 and j 1=j 2 J 1 i 1 see Umeda (2003) for detailed numerical method i 2