Relativistic electron cyclotron theory, revisited

The stages of the relativistic theory leading from the Maxwell-Vlasov system to the absorption and emission coefficients for electromagnetic electron cyclotron waves in a thermonuclear magnetoactive plasma are critically followed, with a particular attention to the approximations involved. Simple and general forms are obtained, holding to arbitrary order in the electron Larmor radius expansion. The applicability limits of the lowest order in this expansion are analysed.