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On the approach to equilibrium of a homogeneous plasma in a uniform magnetic field Haggerty, Michael John

Abstract

The theory of Prigogine and Balescu has been applied to a homogeneous single-species plasma in a static uniform magnetic field. A kinetic equation has been obtained for the one particle velocity distribution, which is assumed initially isotropic in directions perpendicular to the field. The only stationary solutions of the kinetic equation are the Maxwellian equilibrium distributions, and an H- theorem has been established. The neglect of "collisions" of the order of duration of one cyclotron period or less (a strong magnetic field approximation) modifies the kinetic equation so that it no longer predicts any relaxation of the velocity components parallel to the magnetic field. An equation for the binary correlation function has been obtained in terms of the one particle velocity distribution, which is in turn determined toy the kinetic equation. Equations for the binary spatial correlation function and the binary correlation function for the guiding centers have also been obtained. It is demonstrated that the binary spatial correlation function represents the well-known Debye-screened equilibrium correlations when the one particle velocity distribution is the equilibrium distribution. The assumptions and approximations of the theory are clearly stated, and are discussed in some detail.

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