Transfer of radiation in astrophysical plasmas

Abstract

In the previous section 3.1 the so-called “ray treatment” of the geometrical optics approximation has been considered. According to this approach, a set of waves with wave vectors k _j from a phase space element d³k or wave packet, propagates along the rays, the curves tangential to the group velocity vector υ _gr . This vector in isotropic plasma is collinear with energy flux, or Poynting, vector. In magnetoactive plasma the time-average of the Poynting vector is parallel to υ _gr . In astrophysics a wave packet propagating along a ray is called “radiation” and characterized by the specific intensity I_ω This value has been introduced and defined in the section 1.2. As soon as the ray pattern in a medium is known,¹ the problem arise to find the radiation intensity at any point along a ray. Of course, I_ω is constant along a rectilinear ray in a homogeneous, non-emitting, and non-absorbing medium. An inhomogeneity leads to the variation of the radiation intensity with the coordinate l along the ray. This variation which, generally, can also be caused by emission, absorption and scattering of radiation in the medium, is described by the so-called radiation transfer equation. The form of this equation and its solutions are given in the section 4.1.