Particle code simulations with injected particles

As problems we are interested in become more complex, we often find our simulations stretching the limits of available computer resources. For example, an interesting problem is simulation of dissipation processes in sub-critical collisionless shocks. To simulate this system our simulation box must contain the shock and its upstream and downstream regions over the entire length of a run. If the shock moves with any appreciable speed the box must then be considerably larger than the shock thickness making it hard to resolve the shock front itself with a reasonable number of grid points. A solution to this problem is to run the simulation in the frame of reference of the shock. Particles are injected upstream of the shock and leave the simulation box downstream. With the shock stationary in the simulation box, we only need to contain enough of the up and downstream regions for the fields, etc., to settle down and separate the shock from the box boundaries. In this tutorial we consider some basic algorithms used in a practical particle injection code, such as the two dimensional WAVE code used at Los Alamos. We will try to present these ideas in a simple format general enough to be easily included in any particle code. Topics covered are:

1. Smoothly Injecting Particles.
2. Generating the Distribution Functions.
3. Time Dependent Injection Density.
4. Boundary Conditions on Fields and Particles.

(Flux and Charge Conservation)