Relativistic Doppler Effect and Group Velocity in Homogeneous Nonlinear and Inhomogeneous Plasmas

W e study the variations of the received frequencies (Complex Doppler effect) from a source moving uniformly in a homogeneous isotropic plasma and emitting a uniform EM plane wave with amplitude E0 , as a function of coe/Eo where coe is the plasma frequency. The ratio of the velocity U of the source over the group velocity UgT of the transmitted wave is then calculated from the slope of the Doppler curves. When the plasma is inhomogeneous (one-dimensional stratification) the Doppler effect depends on the particular profile of the refractive index and its higher (even) derivatives with respect to the direction of stratification z. In this case the ratio U/UgT=f(z) is given as the solution of a higher order differential equation with inhomogeneous part depending on the slope of the Doppler curve with respect to frequency. Typical cases involving symmetrical and transition profiles are examined. Harmonic generation in the plasma is not taken into account.