In Chapter 6 the case of a whistler-mode wave with a given amplitude was considered. However, many processes which influence cyclotron maser behaviour demand a selfconsistent approach, which takes into account the feedback effects of gyroresonant electrons on the wave field.

The first step in this approach is an analysis of the linear amplification (or damping) of a whistler-mode wave by electrons with different velocity distributions. This problem was tackled in Chapters 3 and 4 for a monochromatic whistler-mode wave. There it was shown that the cyclotron amplification for a broad velocity distribution function (|Δv∥|/v∥ ∼ 1) is the same for homogeneous and weakly inhomogeneous plasmas (compare Sections 3.2 and 3.4). The situation with amplification by well-organized electron beams (such as a step-like deformation or a delta-function in v∥-velocity space) is more complicated (see Sections 3.3 and 3.5) and strongly differs from the cases of homogeneous and weakly inhomogeneous plasmas. This difference is as follows. First, the hydrodynamic type of instability of a well-organized beam in a homogeneous plasma is replaced by the kinetic-type instability in an inhomogeneous plasma. Secondly, the amplification in inhomogeneous plasmas strongly depends on the spatial gradients of the plasma parameters, specifically the plasma density and magnetic field strength. The amplification of a monochromatic wave is large very close to the equatorial plane of a magnetic flux tube. It decreases sharply (and even changes sign for a delta-function distribution) beyond this interval.