## Abstract

One major characteristic associated with collisionless space plasmas is the development of non-Maxwellian velocity distribution that in many circumstances can be represented by the κ function characterized by the κ parameter. This paper discusses the mathematical character and physical origin of the κ function by first showing that the κ velocity function may be expressed in terms of exponential functions multiplied by the kinetic energy and its higher orders. The possible development of κ velocity distribution is illustrated by the problem of low-frequency waves and instabilities in uniform magnetized plasmas with bi-Maxwellian distribution. It is observed that the background and perturbed distribution functions bear the same forms as the zeroth- and higher-order terms of the κ function expanded in the limit of κ→∞. The consequence of assuming κ velocity distribution in inhomogeneous plasmas is illustrated by the Vlasov-Maxwell equilibrium problems that show the nonthermal equilibrium characteristic of nonuniform plasmas. A generalized Grad-Shafranov equation is proposed for two-dimensional Vlasov equilibria with κ velocity distribution.

Original language | English |
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Article number | 110702 |

Journal | Physics of Plasmas |

Volume | 14 |

Issue number | 11 |

DOIs | |

State | Published - 2007 |