The relativistic influence on the dielectric behaviour of a plasma near cyclotron resonance

The interaction between an electron plasma and a transverse e.m. wave propagating along a stationary magnetic field exhibits a resonance if the Doppler shifted frequency equals the electron cyclotron frequency. The interaction will become nonlinear if the electric field of the wave is so large, that the variation of the axial velocity, first-order Doppler effect, and the relativistic mass change, second-order Doppler-effect, have to be taken into account. These effects are of comparable importance and will determine the permittivity of an electron plasma near cyclotron resonance if collisions and inhomogeneities of the fields and of the density can be neglected. Here, a method is presented by which the permittivity can be calculated for given values of the wave amplitude, of the density, of the magnetic field strength, and of the applied frequency