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 the ory. 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 g rowth rate of decay instability varies as k(perpendicular to)(2) in both li mits kappa(2) much less than 1 and kappa(2) much greater than 1. The main t endency of KAWs is towards nonlinear destabilization at very low wave ampli tudes B-k/B-0 less than or similar to 10(-3). Two applications concerning K AW dynamics in the magnetosphere and in the solar corona show that three-wa ve resonant interaction among KAWs may be responsible for the turbulent cha racter of their behaviour, often observed in space plasmas.