Polarized radiative transfer in plasmas with sheared magnetic field

The propagation of electromagnetic waves through a (homogeneous) plasma (slab) in a sheared magnetic field is dealt with by adopting a frame of reference which follows the local direction of the magnetic field. The choice of such a local reference frame is particularly appropriate in order to obtain both the dispersion relation and the polarization of the two eigenmodes relevant to the radiative transfer at an arbitrary angle with respect to the magnetic field, and, in particular, so that no linear mode coupling occurs in the limit of uniform shear. The dispersion relation thus obtained is discussed in detail and the conditions for which the true eigenmodes of a sheared plasma can be identified with the extraordinary and ordinary mode in the absence of shear are assessed. Effects due to the non-uniformity of the magnetic shear are also considered in a quasi-optical approximation and the consequent imaginary part of the refractive index is discussed in the context of the transport equation for the electromagnetic energy density.