Analysis and simulation for a model of electron impact excitation/deexcitation and ionization/recombination

Bokai Yan, Russel E. Caflisch, Farzin Barekat, Jean Luc Cambier

Research output: Contribution to journalArticlepeer-review


This paper describes a kinetic model and a corresponding Monte Carlo simulation method for excitation/deexcitation and ionization/recombination by electron impact in a plasma free of external fields. The atoms and ions in the plasma are represented by continuum densities and the electrons by a particle distribution. A Boltzmann-type equation is formulated and a corresponding H-theorem is formally derived. An efficient Monte Carlo method is developed for an idealized analytic model of the excitation and ionization collision cross sections. To accelerate the simulation, the reduced rejection method and binary search method are used to overcome the singular rate in the recombination process. Numerical results are presented to demonstrate the efficiency of the method on spatially homogeneous problems. The evolution of the electron distribution function and atomic states is studied, revealing the possibility under certain circumstances of system relaxation towards stationary states that are not the equilibrium states, a potential non-ergodic behavior.

Original languageEnglish (US)
Pages (from-to)747-786
Number of pages40
JournalJournal of Computational Physics
StatePublished - Oct 5 2015


  • Boltzmann equation
  • Excitation-deexcitation
  • H theorem
  • Ionization-recombination
  • Monte Carlo method
  • Singular reaction rates

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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