Grid-free particle simulation of a 1D bounded plasma coupled to an external driving circuit

Summary form only given. In this work we consider the extension of a grid-free field solver to the problem of particle transport in a bounded system with an external driving circuit. The field solver is based on a treecode (TC) algorithm, which is a grid-free O(NlogN) method for computing long range interactions. The efficiency of the method comes from replacing particle-particle interactions by particle-cluster interactions, where particles at a distance are treated by a multipole expansion about the center of the cluster. In our preliminary work, we explored the application of the TC field solver to the problem of virtual cathode formation in 1D planar geometry and compared the results to those of both direct summation (DS) and particle-in-cell methods (PIC). The results for the DS and TC simulations agreed to within machine precision while the PIC simulation exhibited numerical artifacts of the mesh. The TC was also extended to 2D bounded domains using a boundary integral method and was applied to the simulation of charged particle dynamics in a Penning-Malmberg trap. The two cases considered were the merger of two clusters of particles and the instability of a ring. In the current work we extend the 1D TC model to include the effect of an external driving circuit, and in addition the algorithm is modified to handle 1D cylindrical and spherical geometries as in. The method is compared with both 1D DS and PIC simulations for planar, cylindrical and spherical configurations. The boundary conditions for the external circuit are coupled to the field solver using Gauss´ law in a similar way to the work in reference. The TC, DS and PIC algorithms are applied to various 1D problems and will be compared on the basis of efficiency and accuracy.