Bounded Multi-scale Plasma Simulation: Application to Sheath Problems

In our previous paper we introduced the multi-scale method, a self-consistent plasma simulation technique that allowed particles to have independent timesteps. Here we apply the method to one-dimensional electrostatic bounded plasma problems and demonstrate a significant reduction in computing time. We describe a technique to allow for variable grid spacing and develop consistent boundary conditions for the direct implicit method. Also discussed are criteria for specifying timestep size as a function of position in phase space. Next, an analytically solvable sheath problem is presented, and a comparison to simulation results is made. Finally, we show results for an ion acoustic shock front propagating toward a conducting wall.