Spatial damping of extraordinary-Bernstein wave

The spatial propagation and attenuation of an extraordinary (X) mode wave are investigated by numerically solving the dispersion relation for Maxwellian velocity distribution. The solutions are found by taking the wave vector to be complex but the wave frequency as real, which contrasts to the customary approach of taking complex wave frequency with a real wave vector for a finite number of harmonics. The present alternative approach unveils a hitherto unknown structure associated with the dispersion relation of the X mode wave. This approach is applied to such situations where the incident wave from the outside interacts with plasma, or it is absorbed at the surface. The theoretical aspect of the banded attenuation between the harmonics is discussed, which may lead to uncovering the unforeseen applications for space and laboratory plasmas.