Self-Consistent Numerical Framework for Multiscale Circuit-Plasma Coupling with Secondary Electron Emission

TL;DR

This paper introduces a self-consistent numerical framework that models multiscale circuit-plasma interactions including secondary electron emission, improving the predictive accuracy of voltage breakdown simulations in high-voltage vacuum systems.

Contribution

It develops a novel integrated approach incorporating ion-energy-dependent secondary electron emission into circuit-plasma co-simulations with both monolithic and partitioned integration schemes.

Findings

SEE significantly affects surface charge and voltage evolution.

The framework accurately predicts voltage collapse and plateau.

Results are consistent across different coupling schemes.

Abstract

Voltage breakdown in high-voltage pulsed vacuum systems arises from nonlinear multiscale interactions among circuit dynamics, kinetic plasma evolution, and ion-induced secondary electron emission (SEE) at electrode surfaces. Although circuit-plasma co-simulation frameworks couple lumped circuits with particle-in-cell (PIC) solvers, most neglect energy-resolved SEE and its feedback to both plasma and circuit, limiting predictive capability. We present a self-consistent framework for multiscale circuit-plasma coupling that incorporates ion-energy-dependent SEE into the electrode boundary of an electrostatic PIC solver. The emitted electron flux is included in the surface charge update, leading to a modified Poisson boundary condition that couples plasma and circuit within a unified formulation. Two integration strategies are developed: (i) a fully implicit strict coupling scheme solving the plasma-circuit system monolithically, and (ii) a weak coupling scheme based on operator splitting, compatible with SPICE solvers and enabling partitioned time integration with one-step lag. The framework is applied to a Tesla-transformer-driven vacuum capacitor with ion injection. Results show that SEE alters surface charge evolution, triggering rapid voltage collapse and sustaining a near-zero-voltage plateau, while SEE-free models fail. Agreement between strict and weak coupling confirms robustness. The method provides a unified framework for predictive simulation of multiscale circuit-plasma interactions.