### 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 language | English (US) |
---|---|

Pages (from-to) | 4881-4892 |

Number of pages | 12 |

Journal | Journal of Computational Physics |

Volume | 228 |

Issue number | 13 |

DOIs | |

State | Published - Jul 20 2009 |

### Fingerprint

### 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

*Journal of Computational Physics*,

*228*(13), 4881-4892. https://doi.org/10.1016/j.jcp.2009.03.041

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

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 228, no. 13, pp. 4881-4892. https://doi.org/10.1016/j.jcp.2009.03.041

}

TY - JOUR

T1 - Understanding the accuracy of Nanbu's numerical Coulomb collision operator

AU - Dimits, Andris M.

AU - Wang, Chiaming

AU - Caflisch, Russel

AU - Cohen, Bruce I.

AU - Huang, Yanghong

PY - 2009/7/20

Y1 - 2009/7/20

N2 - 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.

AB - 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.

KW - Collisional plasma

KW - Coulomb collisions

KW - Lorentz collisions

KW - Monte Carlo methods

KW - Numerical methods

UR - http://www.scopus.com/inward/record.url?scp=68649113293&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=68649113293&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2009.03.041

DO - 10.1016/j.jcp.2009.03.041

M3 - Article

AN - SCOPUS:68649113293

VL - 228

SP - 4881

EP - 4892

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 13

ER -