Calculation of the spontaneous cyclotron emissivity using the complete relativistic resonance condition

An expression for the spectral emissivity of spontaneous synchrotron radiation for a plasma which consists of both thermal and suprathermal electron components is derived using the complete relativistic cyclotron resonance condition. The expression is valid over all angles of propagation. The result is applied to the study of the emission of radiation from an energetic population of electrons with a loss-cone distribution in a relatively low-density plasma (i.e., the electron plasma frequency is less than the cyclotron frequency).