Kinetic Alfve‘n wave in the inhomogeneous magnetosphere and general distribution function

Dispersion relation, associated current and growth-rate of the kinetic Alfve‘n wave with general loss-cone distribution function in a low β inhomogeneous plasma in the presence of an inhomogeneous magnetic field have been obtained by investigating the trajectories of the charged particles. The effects of steepness of loss-cone distribution and inhomogeneity of magnetic field are discussed. The treatment of the kinetic Alfve‘n wave instability is based on the assumption that the plasma consists of resonant and non-resonant particles. The excitation of the wave is treated by particle aspect analysis and the wave particle energy exchange method. The results are interpreted for the auroral acceleration region of the earthʹs magnetoplasma.