Convective instability of longitudinal Electro-Kinetic waves in Magnetised Semiconductor Quantum Electron Plasmas

The spectrum (dispersion and gain characteristics) of longitudinal electro-kinetic waves have been reported for semiconductor quantum plasma embedded in transverse magnetostatic field. The dispersion relation has been derived using well known magnetic field modified QHD model of plasmas. We found that the classical plasma supports the propagation of only four modes whereas quantum plasma supports six modes of propagation. The magnetic field strongly modifies the spectra of all six possible modes and smooths the propagation through the media. It is found that the modes which are contra-propagating are always growing in nature and vice versa. The characteristics conversion from contra-to co-propagation is caused by the presence of magnetic field in most of the cases. The numerical appreciations are made for n-InSb at liquid helium temperature.