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A theory is presented for the rate of thermal relaxation of a two-dimensional plasma in a strong uniform d.c. magnetic field. The Vahala—Montgomery kinetic description is completed by providing a cut-off time for the time of interaction of two particles which contribute to the collision term. The kinetic equation preclicts that thermal relaxation occurs as a function of the dimensionless time (ωpt) (ωp/Ω) (n0λ2D)−½, where ωp, is the plasma frequency, Ω is the gyrofrequency, and n0 λ2D is the number of particles per Debye square. By contrast, in the absence of an external magnetic field, a two-dimensional plasma relaxes as a function of (ωpt) (n0λ2D)−1.

The thermal relaxation process for a spatially uniform two-dimensional plasma in a uniform d.c. magnetic field is simulated numerically. Thermal relaxation times are defined in terms of the time necessary for the numerically computed Boltzmann H function to decrease through a given part of the distance to its minimum value. Dependence of relaxation time on two parameters is studied: number of particles per Debye square n0 λ2D and ratio of gyrofrequency to plasma frequency Ω/ωp. When Ω2/ω2p becomes ≫[ln (L/2πλD)]−½, where L is the linear dimension of the system, it is found that the relaxation time varies to a good approximation as (n0 λ2D)½ and Ω/ωp.