Electron cyclotron resonant heating: A simpler method for deriving the linear wave equations in a nonuniform magnetic field

In a recent article Cairns et al. [Phys. Fluids B 3, 2953 (1991)] gave a method for the derivation of full wave equations describing propagation through a cyclotron resonance in an inhomogeneous plasma. The simplicity of this method compares favorably with previous derivations, and the damping resulting froin the variation in the magnetic field across a Larmor orbit, described by Lashmore-Davies and Dendy [Phys. Fluids B 1, 1565 (1989)], is included. The effect of the relativistic mass shift on the cyclotron frequency, which plays an important role in the electron cyclotron range of frequencies, was not taken into account, however, and the object of the present work is to remedy this omission. It is shown how equations, valid in the weakly relativistic regime, may be obtained in a rather straightforward way. Results obtained by a number of earlier workers are recovered and can be extended.