Abstract. Propagation and amplification of the auroral kilometric radiation (AKR) in a three-dimensional plasma cavity is investigated using the approximation of the geometrical optics, and taking into account both the slightly relativistic electrons propagating inside a cavity and the background cold electrons. It is shown that the global magnetic field inhomogeneity plays a key role in a wave escape from a thin plasma cavity. The main contribution to the AKR spectrum is made by waves initially generated with the component of group velocity directed to the Earth and with the optimum relationship between the wave vector components, controlling the value of the linear grow rate and duration of the ray lifetime inside a source.