An External Circuit Model for 3-D Electromagnetic Particle-In-Cell Simulations

In this paper, for the first time, second-order accurate algorithms for coupling external circuit elements to 3-D electromagnetic (EM) particle-in-cell (PIC) simulations are developed and introduced. The circuit equation including an external voltage or current source, resistance, inductance, capacitance, and a dynamic EM and/or plasma load is solved simultaneously and self-consistently with the EM PIC updaters through an instant measured voltage V across the system to obtain the supplied current I for feeding into the system. This external circuit model has been demonstrated and implemented in a 3-D conformal finite-difference time-domain PIC code, Vorpal. The integrated simulation model can be widely used in the vacuum electronics community as well as in the plasma processing community if one wants to consider the effects of a power supply on operation of microwave tubes or plasma reaction chambers.