The mean electromotive force generated by random hydromagnetic waves in a collisionless plasma

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Abstract
The mean electromotive force generated by random hydromagnetic waves is calculated by using Fourier analysis methods for the cases of an incompressible Hall plasma and a compressible plasma with finiteβ. It is shown that in the case of a Hall plasma theαeffect can exist in the interaction between two waves which propagate in opposite directions and have different phase velocities and several newβ–terms are produced by the Hall effect, while in the case of a compressible plasma theα–effect can exist only in the interaction between the Alfvén mode and the fast or slow magneto-acoustic mode, and not between the fast and slow magneto-acoustic modes. The results are discussed in the context of the substorms in the earth's magnetosphere.