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|| ⩽ 1 during their lifetime. Because of this they acquire large n⊥ 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|| ⩽ β) of EBWs is analysed in detail. It is shown that the waves with extremely small n|| propagate with no damping and terminate abruptly at a surface shifted by a distance ∼n||2R0 off the resonance.It is demonstrated both analytically and numerically that propagation of EBWs with moderate n|| is satisfactorily described by the dispersion relation with n|| = 0. In the large k⊥ 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|| = 0. An effective algorithm for its fast computing is suggested.