We investigate propagation and amplification of the auroral kilometric radiation over the geomagnetic poles using a particular model for the physical parameters in the auroral zone, which takes into account density gradients perpendicular to the geomagnetic field. The propagation of the waves is investigated with the canonical set of equations of the geometrical optics, taking into account thermal effects and considering both the energetic and the background electron populations, with the components of the dielectric tensor calculated in the locally homogeneous plasma approximation. It is shown that the spatial scale of inhomogeneity perpendicular to the magnetic field is an important factor in the amplification, although less favorable than indicated by previous studies using the method of Poeverlein to obtain the trajectory of the radiation.

We investigate amplification of the auroral kilometric radiation over the geomagnetic poles. The physical parameters needed for the calculation are obtained from a particular model that approximately reproduces the conditions in the auroral zone, taking into account density gradients perpendicular to the geomagnetic field and also the parallel magnetic field gradient. The components of the dielectric tensor are calculated in the locally homogeneous plasma approximation, and the dispersion relation is exactly solved with all harmonics and powers of the Larmor radius needed for the convergency of the solution. We also make a ray tracing study in the geometrical optics approximation, using the method of Poeverlein. The ray tracing study shows that the spatial scale of inhomogeneity, perpendicular to the magnetic field, is a very important factor in the amplification and that the distance to obtain a given amplification can be substantially reduced when the density gradient is increased.