### Abstract

In this paper we describe the anisotropic velocity distribution function of the electron swarm in weakly ionized gases from the three-term spherical harmonic expansion technique of the Boltzmann equation, and a method for solving the coupled integro-differential equations for the electron distribution functions. In the method for solving the equations, we employ a numerical technique using the implicit Gear’s algorithms. Important advantages of using such a numerical technique in the present system are efficiency to solve the stiff equations stably, and appropriateness for obtaining a solution of the equations with poor initial conditions. This analysis is applied to the steady-state electron swarm in helium. Comparative calculation with the conventional two-term Lorentz approximation shows that, not only at high E/N, but even at low E/N, subject to almost spherically symmetric velocity distribution, this procedure gives the results with sufficient accuracy. Also the swarm characteristics in helium are discussed from a viewpoint of the anisotropic velocity distri-butions.

Original language | English |
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Pages (from-to) | 119-126 |

Number of pages | 8 |

Journal | The transactions of the Institute of Electrical Engineers of Japan.A |

Volume | 103 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1983 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*The transactions of the Institute of Electrical Engineers of Japan.A*,

*103*(2), 119-126. https://doi.org/10.1541/ieejfms1972.103.119

**Anisotropic Velocity Distribution Representation of the Electron Swarm in a Weakly Ionized Gas.** / Makabe, Toshiaki; Mori, Tameyoshi.

Research output: Contribution to journal › Article

*The transactions of the Institute of Electrical Engineers of Japan.A*, vol. 103, no. 2, pp. 119-126. https://doi.org/10.1541/ieejfms1972.103.119

}

TY - JOUR

T1 - Anisotropic Velocity Distribution Representation of the Electron Swarm in a Weakly Ionized Gas

AU - Makabe, Toshiaki

AU - Mori, Tameyoshi

PY - 1983

Y1 - 1983

N2 - In this paper we describe the anisotropic velocity distribution function of the electron swarm in weakly ionized gases from the three-term spherical harmonic expansion technique of the Boltzmann equation, and a method for solving the coupled integro-differential equations for the electron distribution functions. In the method for solving the equations, we employ a numerical technique using the implicit Gear’s algorithms. Important advantages of using such a numerical technique in the present system are efficiency to solve the stiff equations stably, and appropriateness for obtaining a solution of the equations with poor initial conditions. This analysis is applied to the steady-state electron swarm in helium. Comparative calculation with the conventional two-term Lorentz approximation shows that, not only at high E/N, but even at low E/N, subject to almost spherically symmetric velocity distribution, this procedure gives the results with sufficient accuracy. Also the swarm characteristics in helium are discussed from a viewpoint of the anisotropic velocity distri-butions.

AB - In this paper we describe the anisotropic velocity distribution function of the electron swarm in weakly ionized gases from the three-term spherical harmonic expansion technique of the Boltzmann equation, and a method for solving the coupled integro-differential equations for the electron distribution functions. In the method for solving the equations, we employ a numerical technique using the implicit Gear’s algorithms. Important advantages of using such a numerical technique in the present system are efficiency to solve the stiff equations stably, and appropriateness for obtaining a solution of the equations with poor initial conditions. This analysis is applied to the steady-state electron swarm in helium. Comparative calculation with the conventional two-term Lorentz approximation shows that, not only at high E/N, but even at low E/N, subject to almost spherically symmetric velocity distribution, this procedure gives the results with sufficient accuracy. Also the swarm characteristics in helium are discussed from a viewpoint of the anisotropic velocity distri-butions.

UR - http://www.scopus.com/inward/record.url?scp=85004271212&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85004271212&partnerID=8YFLogxK

U2 - 10.1541/ieejfms1972.103.119

DO - 10.1541/ieejfms1972.103.119

M3 - Article

AN - SCOPUS:85004271212

VL - 103

SP - 119

EP - 126

JO - IEEJ Transactions on Fundamentals and Materials

JF - IEEJ Transactions on Fundamentals and Materials

SN - 0385-4205

IS - 2

ER -