Understanding the accuracy of Nanbu's numerical Coulomb collision operator

Andris M. Dimits, Chiaming Wang, Russel Caflisch, Bruce I. Cohen, Yanghong Huang

Research output: Contribution to journalArticle

Abstract

We investigate the accuracy of and assumptions underlying the numerical binary Monte Carlo collision operator due to Nanbu [K. Nanbu, Phys. Rev. E 55 (1997) 4642]. The numerical experiments that resulted in the parameterization of the collision kernel used in Nanbu's operator are argued to be an approximate realization of the Coulomb-Lorentz pitch-angle scattering process, for which an analytical solution for the collision kernel is available. It is demonstrated empirically that Nanbu's collision operator quite accurately recovers the effects of Coulomb-Lorentz pitch-angle collisions, or processes that approximate these (such interspecies Coulomb collisions with very small mass ratio) even for very large values of the collisional time step. An investigation of the analytical solution shows that Nanbu's parameterized kernel is highly accurate for small values of the normalized collision time step, but loses some of its accuracy for larger values of the time step. Careful numerical and analytical investigations are presented, which show that the time dependence of the relaxation of a temperature anisotropy by Coulomb-Lorentz collisions has a richer structure than previously thought, and is not accurately represented by an exponential decay with a single decay rate. Finally, a practical collision algorithm is proposed that for small-mass-ratio interspecies Coulomb collisions improves on the accuracy of Nanbu's algorithm.

Original languageEnglish (US)
Pages (from-to)4881-4892
Number of pages12
JournalJournal of Computational Physics
Volume228
Issue number13
DOIs
StatePublished - Jul 20 2009

Fingerprint

Coulomb collisions
operators
collisions
Parameterization
Mathematical operators
Anisotropy
Scattering
pitch (inclination)
mass ratios
Experiments
Temperature
parameterization
decay rates
time dependence
anisotropy
decay

Keywords

  • Collisional plasma
  • Coulomb collisions
  • Lorentz collisions
  • Monte Carlo methods
  • Numerical methods

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

Understanding the accuracy of Nanbu's numerical Coulomb collision operator. / Dimits, Andris M.; Wang, Chiaming; Caflisch, Russel; Cohen, Bruce I.; Huang, Yanghong.

In: Journal of Computational Physics, Vol. 228, No. 13, 20.07.2009, p. 4881-4892.

Research output: Contribution to journalArticle

Dimits, AM, Wang, C, Caflisch, R, Cohen, BI & Huang, Y 2009, 'Understanding the accuracy of Nanbu's numerical Coulomb collision operator', Journal of Computational Physics, vol. 228, no. 13, pp. 4881-4892. https://doi.org/10.1016/j.jcp.2009.03.041
Dimits, Andris M. ; Wang, Chiaming ; Caflisch, Russel ; Cohen, Bruce I. ; Huang, Yanghong. / Understanding the accuracy of Nanbu's numerical Coulomb collision operator. In: Journal of Computational Physics. 2009 ; Vol. 228, No. 13. pp. 4881-4892.
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