Collisional dynamics of a strongly magnetized pure electron plasma

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Abstract
For a pure electron plasma in a sufficiently strong magnetic field, there is a many‐electron adiabatic invariant which constrains the collisional dynamics. For the case of a uniform magnetic field, the adiabatic invariant is the total kinetic energy associated with the electron velocity components that are perpendicular to the magnetic field (i.e., ∑j mv2j⊥ /2). Were the adiabatic invariant an exact constant of the motion, no exchange of energy would be possible between the parallel and the perpendicular degrees of freedom, and the plasma could acquire and maintain two different temperatures, T∥ and T⊥. However, an adiabatic invariant is not strictly conserved. In the present case, each collision produces an exponentially small exchange of energy between the parallel and the perpendicular degrees of freedom, and these act cumulatively in such a way that T∥ and T⊥ relax to a common value. This paper provides a calculation of the equipartition rate.