Absorbing boundaries for space plasma simulations

For the simulation of plasma phenomena in infinite space one must surround the computational domain by boundaries which absorb radiation. For spherical computational domains a rigorous absorbing condition can be formulated and implemented. This requires working in spherical polars and expanding surface data in spherical harmonics. A history of the past L steps must be kept for each L-th order harmonic in order to predict its value at the next step. For Cartesian meshes and box-shaped boundaries, Lindman's method can be applied on each of the six surfaces. It becomes very accurate if taken to high enough order. However it is arithmetic-intensive and it still leaves problems in the eight corners. Opting for the lowest order Lindman scheme and restricting angles of incidence to less than 45 degrees from vertical already achieves albedos (reflected/incident power) lower than 0.00003. Since finite differences methods for Maxwell's equations in vacuo are highly efficient, one can afford a wide buffer region between radiating plasma sources and boundaries, thereby reducing angles of incidence. In this paper, a simple PC program using the low-order method is used to demonstrate how an expanding wave is apparently fully absorbed at the boundaries