### Abstract

A numerical solution is developed for the time-dependent kinetic equation describing the evolution of arbitrary distributions of electrons injected into a magnetized plasma. Included in the equation are pitch-angle scattering and energy loss because of Coulomb collisions and magnetic mirroring. The numerical code can be easily modified to include other scattering or radiation terms. The numerical results are shown to agree well with known analytic solutions for various simplified configurations such as homogeneous injection in a homogeneous plasma, electron beams moving with small pitch angle with respect to the magnetic field, and injection into a magnetic trap. In general, these comparisons show that the difference between the numerical and analytic solutions is less than 10% in any variable provided that the grid size is one-quarter of the size of the required resolution in that variable.

Original language | English (US) |
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Pages (from-to) | 726-734 |

Number of pages | 9 |

Journal | Astrophysical Journal |

Volume | 354 |

Issue number | 2 |

DOIs | |

State | Published - May 10 1990 |

Externally published | Yes |

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### Keywords

- Numerical methods
- Particle acceleration
- Plasmas
- Radiation mechanisms

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*354*(2), 726-734. https://doi.org/10.1086/168729