Propagation and damping of electron Bernstein waves with small n∥ in inhomogeneous plasma

Electron Bernstein waves (EBWs) produced via the linear conversion of incident electromagnetic modes have moderate parallel refractive index n(parallel to) less than or equal to 1 during their lifetime. Because of this they acquire large n(perpendicular to) in the electron cyclotron resonance vicinity. Using this fact, an approximate dispersion relation valid regardless of the resonance harmonic number is proposed. It is expressed in terms of a modified plasma dispersion function whose real part is readily calculated numerically and the imaginary part is given by a simple analytical formula. The relativistic case (n(parallel to) less than or equal to beta) of EBWs is analysed in detail. It is shown that the waves with extremely small nil propagate with no damping and terminate abruptly at a surface shifted by a distance similar ton(parallel to)(2)R(0) off the resonance. It is demonstrated both analytically and numerically that propagation of EBWs with moderate n(parallel to) is satisfactorily described by the dispersion relation with n(parallel to) = 0. In the large k(perpendicular to) approximation this relation is rather simple and convenient for tracing waves, however, it breaks down far off the resonance and must be replaced by the exact dispersion relation with n(parallel to) = 0. An effective algorithm for its fast computing is suggested.