Three-wave coupling and parametric decay of kinetic Alfven waves

The dynamic equation and coupling coefficient of the three-wave interaction among kinetic Alfven waves (KAWs) are derived by use of plasma kinetic theory. Linear and nonlinear effects of finite ion Larmor radius are kept for arbitrary value of the 'kinetic variable' kappa = k(perpendicular to)rho(i). The parametric decay KAW --> KAW + KAW is investigated and the threshold amplitude for decay instability in a Maxwellian plasma is calculated. The growth rate of decay instability varies as k(perpendicular to)(2) in both limits kappa(2) much less than 1 and kappa(2) much greater than 1. The main tendency of KAWs is towards nonlinear destabilization at very low wave amplitudes B-k/B-0 less than or similar to 10(-3). Two applications concerning KAW dynamics in the magnetosphere and in the solar corona show that three-wave resonant interaction among KAWs may be responsible for the turbulent character of their behaviour, often observed in space plasmas.