### Abstract

The accuracy of first-order Euler and higher-order time-integration algorithms for grid-based Langevin equations collision models in a specific relaxation test problem is assessed. We show that statistical noise errors can overshadow time-step errors and argue that statistical noise errors can be conflated with time-step effects. Using a higher-order integration scheme may not achieve any benefit in accuracy for examples of practical interest. We also investigate the collisional relaxation of an initial electron-ion relative drift and the collisional relaxation to a resistive steady-state in which a quasi-steady current is driven by a constant applied electric field, as functions of the time step used to resolve the collision processes using binary and grid-based, test-particle Langevin equations models. We compare results from two grid-based Langevin equations collision algorithms to results from a binary collision algorithm for modeling electron-ion collisions. Some guidance is provided on how large a time step can be used compared to the inverse of the characteristic collision frequency for specific relaxation processes.

Original language | English (US) |
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Article number | 5475281 |

Pages (from-to) | 2394-2406 |

Number of pages | 13 |

Journal | IEEE Transactions on Plasma Science |

Volume | 38 |

Issue number | 9 PART 1 |

DOIs | |

State | Published - Sep 2010 |

### Keywords

- Algorithms
- collision processes
- computer applications
- numerical analysis
- particle collisions
- plasmas

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Condensed Matter Physics

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## Cite this

*IEEE Transactions on Plasma Science*,

*38*(9 PART 1), 2394-2406. [5475281]. https://doi.org/10.1109/TPS.2010.2049589