### 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) |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Condensed Matter Physics
- Nuclear and High Energy Physics

### Cite this

*IEEE Transactions on Plasma Science*,

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

**Time-step considerations in particle simulation algorithms for coulomb collisions in plasmas.** / Cohen, Bruce I.; Dimits, Andris M.; Friedman, Alex; Caflisch, Russel.

Research output: Contribution to journal › Article

*IEEE Transactions on Plasma Science*, vol. 38, no. 9 PART 1, 5475281, pp. 2394-2406. https://doi.org/10.1109/TPS.2010.2049589

}

TY - JOUR

T1 - Time-step considerations in particle simulation algorithms for coulomb collisions in plasmas

AU - Cohen, Bruce I.

AU - Dimits, Andris M.

AU - Friedman, Alex

AU - Caflisch, Russel

PY - 2010/9

Y1 - 2010/9

N2 - 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.

AB - 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.

KW - Algorithms

KW - collision processes

KW - computer applications

KW - numerical analysis

KW - particle collisions

KW - plasmas

UR - http://www.scopus.com/inward/record.url?scp=77956617263&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956617263&partnerID=8YFLogxK

U2 - 10.1109/TPS.2010.2049589

DO - 10.1109/TPS.2010.2049589

M3 - Article

AN - SCOPUS:77956617263

VL - 38

SP - 2394

EP - 2406

JO - IEEE Transactions on Plasma Science

JF - IEEE Transactions on Plasma Science

SN - 0093-3813

IS - 9 PART 1

M1 - 5475281

ER -