Propagation of cyclotron maser radiation in inhomogeneous magnetic fields.

Cyclotron masers are important laboratory devices~and play a major role in planetary and stellar radio emission. Recently we have shown that a cyclotron maser instability driven by a horseshoe shaped distribution in velocity space~may be responsible for the observations. A long standing problem though is how the radiation generated at frequencies below the upper hybrid resonance, gets onto the higher frequency branch of the dispersion~curve that connects to the vacuum propagation branch. Here we consider some of the dispersion properties of waves in the presence of energetic particle populations in the shape of a horseshoe and ring distribution in velocity space. The analysis is carried out in a homogeneous and~an inhomogeneous magnetic field and demonstrates that the extraordinary mode that is initially driven unstable by the energetic particles can couple to the vacuum regime and escape the region.