The susceptibility tensor of a uniform magnetized plasma with a transverse electric field and the electromagnetic waves propagating parallel to the magnetic 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 unperturbed distribution functions have a common shift in velocity space. In this work the susceptibility tensor is first derived in the laboratory frame for such a situation using the commonly used method of integration along unperturbed trajectory. 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. A qualitative new phenomenon is the appearance of a resonance at the plasma Langmuir frequency if a transverse equilibrium electric field is present.