We present a new exact integral form of the fully relativistic dielectric tensor in the electron cyclotron frequency range for plasmas in the presence of a magnetic field. This form is suitable for numerical applications for arbitrary wave numbers since all the integrals that appear in the expressions are 1D ones and, hence, can be evaluated with arbitrary precision. Thus, this new form of the dielectric tensor has interest from the point of view of studying arbitrary fast and slow electron cyclotron waves in fusion laboratory plasmas for the purpose of plasma heating and current drive in magnetic traps, as well as in extremely hot astrophysical plasmas with the goal of further development and understanding the physics of plasma waves. It is easy to see that such fully relativistic approach to studying plasma waves can also be extended into the ion cyclotron frequency range.
Electrostatic ion cyclotron waves in a low magnetized plasma