Polarization transfer in relativistic magnetized plasmas
  The polarization transfer coefficients of a relativistic magnetized plasma
are derived. These results apply to any momentum distribution function of the
particles, isotropic or anisotropic. Particles interact with the radiation
either in a non resonant mode when the frequency of the radiation exceeds their
characteristic synchrotron emission frequency, or quasi resonantly otherwise.
These two classes of particles contribute differently to the polarization
transfer coefficients. For a given frequency, this dichotomy corresponds to a
regime change in the dependence of the transfer coefficients on the parameters
of the particle s population. The derivation of the transfer coefficients
involves an exact expression of the conductivity tensor of the relativistic
magnetized plasma that has not been used hitherto in this context. Suitable
expansions valid at frequencies larger than the cyclotron frequency allow us to
analytically perform the summation over all resonances at high harmonics of the
relativistic gyrofrequency. The transfer coefficients are represented in the
form of two variable integrals that can be conveniently computed for any set of
parameters by using Olver s expansion of high order Bessel functions. We
particularize our results to a number of distribution functions, isotropic,
thermal or powerlaw, with different multipolar anisotropies of low order, or
strongly beamed. For isotropic distributions, the Faraday coefficients are
expressed in the form of a one variable quadrature over energy, for which we
provide the kernels in the high-frequency limit and in the asymptotic
low-frequency limit. A similar reduction to a one-variable quadrature over
energy is derived at high frequency for a large class of anisotropic
distribution functions that may form a basis on which any smoothly anisotropic
distribution could be expanded.
