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

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 finite β. It is shown that in the case of a Hall plasma the α effect can exist in the interaction between two waves which propagate in opposite directions and have different phase velocities and several new β-terms are produced by the Hall effect, while in the case of a compressible plasma the α-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.