Weakly relativistic dielectric tensor for arbitrary wavenumbers

The validity of Shkarofsky's dielectric tensor is extended by taking the strictly weakly relativistic limit and removing, when possible, assumptions on the wavenumbers along and across the ambient magnetic field, kparallel and kperpendicular. An approximation of the time integral is retained, but is shown to be valid under more benign assumptions than those of quasiperpendicular incidence and small Larmor radius. The increased generality with respect to kparallel permits to handle cases of comparable Doppler and relativistic widths of electron cyclotron resonances. The tensor also suits Bernstein waves, as it captures both their natural large kperpendicular and the finite kparallel that is typical of some mode conversions, or acquired as a consequence of the large kperpendicular when propagating in curved magnetic fields. Finally, relativistic corrections to the optimal angle for the ordinary-extraordinary Bernstein mode conversion are presented