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

Hongbin Kim, Soung Yong Yun, Jaeguk Lee, Dong-Yeop Na

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.

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

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.
Paper Structure (40 sections, 56 equations, 32 figures, 4 tables, 2 algorithms)

This paper contains 40 sections, 56 equations, 32 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Self-Consistent Multiscale Circuit--Plasma Formulation with Secondary Electron Emission
  3. Transient circuit analysis module
  4. Manual solver option
  5. PySpice solver option
  6. Kinetic plasma solver module
  7. Field solver
  8. Particle solver
  9. Secondary Electron Emission Module
  10. Secondary electron yield modeling
  11. Energy distribution modeling
  12. Monte Carlo SEE sampling algorithm
  13. Integration of circuit, plasma, and SEE modules
  14. Convection current modeling
  15. Strict coupling mode
  16. ...and 25 more sections

Figures (32)

  • Figure 1: Schematic diagram of the cathodic arc-based $\text{Ti}^+$ ion implantation and deposition system. (Created with the assistance of Nano Banana)
  • Figure 2: Simulation model comprising the simplified Tesla transformer circuit and the physical discharge domain.
  • Figure 3: Probability mass function of emitted secondary electrons for 40keV incident ions.
  • Figure 4: Energy dependence of the mean SEY. Experimental data are taken from Holmen1981Zalm1985.
  • Figure 5: Energy-weighted secondary electron energy spectra adapted from Ruano2008. Here, $N(E)$ denotes the number of emitted secondary electrons with kinetic energy $E$.
  • ...and 27 more figures