Test cases for grid-based direct kinetic modeling of plasma flows

Kentaro Hara, Kyle Hanquist

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Grid-based kinetic models are promising in that the numerical noise inherent in particle-based methods is essentially eliminated. Here, we call such grid-based techniques a direct kinetic (DK) model. Velocity distribution functions are directly obtained by solving kinetic equations, such as the Vlasov equation, in discretized phase space, i.e., both physical and velocity space. In solving the kinetic equations that are hyperbolic partial differential equations, we employ a conservative, positivity-preserving numerical scheme, which is necessary for robust calculations of problems particularly including ionization. Test cases described in this paper include plasma sheaths with electron emission and injection and expansion of neutral atom flow in a two-dimensional configuration. A unifying kinetic theory of space charge limited sheaths for both floating and conducting surfaces is presented. The improved theory is verified using the collisionless DK simulation, particularly for small sheath potentials that particle-based kinetic simulations may struggle due to statistical noise. For benchmarking of the grid-based and particle-based kinetic simulations, hybrid simulations of Hall thruster discharge plasma are performed. While numerical diffusion occurs in the phase space in the DK simulation, ionization oscillations are well resolved since ionization events can be taken into account deterministically at every time step.

Original languageEnglish (US)
Article number065004
JournalPlasma Sources Science and Technology
Issue number6
StatePublished - Jun 18 2018
Externally publishedYes


  • Hall thruster
  • Kinetic simulation
  • Vlasov simulation
  • nonlinear plasma waves
  • plasma instability
  • plasma sheaths
  • space charge limited sheath

ASJC Scopus subject areas

  • Condensed Matter Physics


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