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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.

Given that the wave numbers of X and O modes merge as they approach the plasma boundary, a pure mode reflected from the plasma by a cut off may excite both modes due to polarization change when it is reflected off the vacuum vessel wall since the tangential components of the electric field change sign. This may explain the good central heating in DIII‐D ECH experiments in which the fundamental X‐mode is launched from the low field side.

A large‐amplitude rf electric field can heat particles at their gyrofrequency and its harmonics despite a significant mismatch between the wave frequency and the gyrofrequency through physical processes analogous to the trapping of particles in large‐amplitude waves. For eE0k0/mΩ2 near unity, the fundamental and the second harmonic resonances may overlap and give rise to stochasticity. The implications for cyclotron heating are discussed.