Frosali, Giovanni and Van Der Mee, Cornelis (1990) *Mathematical study of the runaway process in particle swarms.* Memorie di fisica matematica in omaggio a Giovanni Carini nel suo 70 compleanno, 1. pp. 623-649.

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## Abstract

In this article we study two linear Boltzmann equations which describe the time evolution of the electron distribution in a weakly ionized gas, both of them one-dimensional in the velocity and any spatial variable, and one of them spatially homogeneous. We present two mathematical definitions of electron runaway, one based on travelling wave phenomena and the other one involving the average speed asymptotics. Under suitable assumptions on the collision frequency, we prove electron runaway according to the average speed definition in the spatially homogeneous as well as the spatially dependent case. For constant collision frequency v0 the average speed is shown to relax to a/v0 where a is the electrostatic acceleration.

Item Type: | Article |
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Additional Information: | Atti della Accademia Peloritana dei Pericolanti, LXVIII |

Subjects: | M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali > 1990 > Supplemento 1 M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Medico-Biologiche > 1990 > Supplemento 1 M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Giuridiche, Economiche e Politiche > 1990 > Supplemento 1 M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Lettere, Filosofia e belle Arti > 1990 > Supplemento 1 |

Divisions: | UNSPECIFIED |

Depositing User: | Stage ICCU |

Date Deposited: | 21 Apr 2005 |

Last Modified: | 14 Sep 2012 13:31 |

URI: | http://cab.unime.it/mus/id/eprint/282 |

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