The purpose of this chapter is to formulate the self-consistent set of equations (expressed in cgs units) which describe the theoretical behaviour of cyclotron masers operating in a plasma constrained by a dipole magnetic field. Thus the equation of motion of a non-relativistic charged particle is considered; the first adiabatic invariant of motion is the magnetic moment, and the second is the bounce integral. The charged particle distribution function approach is then presented.

The general dispersion relation for electromagnetic waves propagating in a plasma is derived. From this expressions are obtained for the refractive index and polarization parameters of whistler-mode waves and of Alfvén waves. These lead to the wave eigenmodes (natural, or resonant, oscillations) in an operating cyclotron maser. Due to the current of hot particles in gyroresonance with the wave, a monochromatic wave is an evolving wave packet. Its amplitude changes slowly with time; the wave packet propagates at the group velocity.

The theory is derived first for a homogeneous plasma for which the plasma density and the ambient magnetic field do not vary with any spatial coordinate. Secondly it is extended to an inhomogeneous plasma, specifically to plasma and energetic charged particles confined by a dipole magnetic field such as the Earth's.