The electromagnetic waves propagating parallel to the magnetic field in a uniform magnetized plasma with a transverse electric field

In natural and laboratory magnetized plasmas, an equilibrium electric field may exist perpendicular to the background magnetic field. In such a situation all the plasma species experience a common drift and the equilibrium distribution functions have a common shift in velocity space. The susceptibility tensor is derived for such a situation using the characteristics and then the Lorentz transformation method is adopted to verify the results. As an application we give an analysis of the waves propagating parallel to the background magnetic field for a simple electron plus single charged ion plasma. It is predicted that the presence of a transverse equilibrium electric field can drastically change the wave propagation only if the wave frequency is close to the plasma Langmuir frequency.