Grid-free plasma Simulation techniques

A common approach to modeling kinetic problems in plasma physics is to represent the plasma as a set of Lagrangian macro-particles which interact through long-range forces. In the well-known particle-in-cell (PIC) method, the particle charges are interpolated to a mesh and the fields are obtained using a fast Poisson solver. The advantage of this approach is that the electrostatic forces can be evaluated in time O(NlogN), where N is the number of macro-particles, but the scheme has difficulty resolving steep gradients and handling nonconforming domains unless a sufficiently fine mesh is used. The current work describes a grid-free alternative, the boundary integral/treecode (BIT) method. Using Green´s theorem, we express the solution to Poisson´s equation as the sum of a volume integral and a boundary integral which are computed using particle discretizations. The treecode replaces particle-particle interactions by particle-cluster interactions which are evaluated by Taylor expansions. In addition, the Green´s function is regularized and adaptive particle insertion is implemented to maintain resolution. Like PIC, the operation count is O(NlogN), but BIT avoids using a regular grid, so it can potentially resolve steep gradients and handle complex domains more efficiently. We applied BIT to several bounded plasma problems including a one-dimensional (1-D) sheath in direct current (dc) discharges, 1-D virtual cathode, cold two-stream instability, two-dimensional (2-D) planar and cylindrical ion optics, and particle dynamics in a Penning-Malmberg trap. Some comparisons of BIT and PIC were performed. These results and ongoing work will be reviewed.