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The relativistic dispersion relation including temperature anisotropy and a parallel drift has been derived for electron cyclotron waves of frequency up to third harmonics, and solved for a perpendicularly stratified plasma around the fundamental and second harmonic resonances. For quasiperpendicular propagation, damping of fundamental modes is much more sensitively affected by T∥ than by T⊥. This is also true for the ordinary mode of oblique propagation. The theory has been extended to a bulk thermal distribution with a two‐temperature or three‐temperature tail distribution by a simple summation of each contribution to the dispersion tensor. The effect of a tail distribution is relatively small if the tail is localized in the resonant layer for the bulk electrons. For a nonlocal tail distribution, the existence of a tail becomes important.

Fluid equations with transport effects have been derived from summing up discrete particle effects in the configuration space. The diffusion coefficient takes a form different from, but equivalent to, the Kubo formula. By taking into account the decoherence along the field lines, the diffusive damping in the perpendicular direction, and the finite Larmor radius effect in the cyclotron resonance, it is shown that the diffusion of magnetized 3d plasma has a regime of B−3/2 scaling which lies between the Bohm diffusion of B−1 and the classical diffusion of B−2.

An electromagnetic (EM) wave at the mode conversion layer transfers its energy to the electrostatic (ES) wave whose amplitude can be greatly enhanced due to its slow group velocity near the cut off layer. The large amplitude ES wave produces the density compression, indispensable for the nonlinear coupling in the EM wave, leading to the localized vortex flow. A dc magnetic field, tantamount to the vorticity, is generated as a result of the conservation of canonical momentum.

The equations governing the mode conversion between an electromagnetic wave and the plasma wave are derived from the relativistic Vlasov equation. They are further reduced to a two dimensional matrix equation involving only two electric field components. It is shown that the mode conversion efficiency diminishes to zero at both 0° and 90° of incidence angles, becomes insignificant beyond 45° and tends to improve with higher plasma temperature.

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.