A Numerical Approach for Nonlinear Transmission Line Analysis with Bidirectional Coupling to Lumped-element and Particle-In-Cell Models

In this article, an iterative method for nonlinear transmission lines (TLs) based on the Lax-Wendroff method has been established to describe a bidirectional coupling model of nonlinear lumped-element models, nonlinear transmission line models, and particle-in-cell (PIC) models. The proposed self-consistent global circuit model is achieved through the introduction of the charge conservation equation at the upper plate as the Robin boundary condition and its coupling with the PIC method used for plasma simulation. The effectiveness of the proposed model is validated through five numerical experiments, including nonlinear transmission line coupling to lumped circuits, and the most general case of plasma-TLs-lumped elements model (LEM) coupling systems. This non-linear global circuit coupling model provides a powerful tool for simulating the complex behavior of various physical systems, including but not limited to capacitively coupled plasmas, vacuum electronic devices, and Z-pinches.