The relativistic kinetic Weibel instability: Comparison of different distribution functions

Investigations of the relativistic Weibel instability have burgeoned in the last few years because of their potential use in various astrophysical scenarios. In this article, the parameters for the growth rates of well-known distribution functions are provided, based on a recently developed general description. The four distributions to be dealt with are the monochromatic, waterbag, bi-Maxwellian and the kappa distribution. The advantages of this treatment are: (i) One has to solve only one integral to obtain the growth rates, thus (ii) one may compare the different distributions easily. Numerical illustrations of the growth rates for each distribution are given. The growth rates can be classified due to the ansatz of the distributions functions. In addition, some formulas of a previous paper are corrected. (c) 2008 American Institute of Physics.