The previous post (Nov. 29), considering the basic principles pertaining to radio astronomy, focused on the (relatively) simple case of propagation of plane EM waves through a medium assumed to be isotropic. That is, the propagation with E, H vectors is the same in all directions. In terms of radio sources this is far too limited to be of practical use, so it is important to also examine propagation of a plane wave in an ionized (e.g. plasma) medium in the presence of steady magnetic field. In this case we expect the propagation to be variable, depending on direction. For this purpose the diagram below can be used:For perspective, note the direction of wave propagation is in the x-z plane and at an angle of φ with respect to the z-axis. Note the electric field E lies in a plane (yz) perpendicular to the direction of wave propagation. The steady magnetic field B is in the z-direction. The relevant force equations involving a particle of charge q and mass m in the presence of a magnetic field are:
Where N is the number of charged particles per unit volume. We assume a movement of the charged particles constitutes a conduction current. The above Maxwell equation can also be expressed in terms of the three rectangular curl components, i.e.