The parametric interaction of an upper-hybrid pump wave with kinetic Alfvén and electromagnetic waves that propagate in parallel and perpendicular directions to the ambient magnetic field is investigated on the basis of two-fluid magnetohydrodynamics. A nonlinear dispersion relation describing three-wave interaction and instability growth rates are found. The theoretical results are used for the interpretation of satellite observations in the magnetospheric plasma. It is shown that as a result of the decay of an upper-hybrid wave, electromagnetic waves propagating in both parallel and perpendicular directions to the ambient magnetic field are generated. The instability growth rate is much higher in the case of left-polarized electromagnetic wave generation than in the case of ordinary electromagnetic wave generation. The nonlinear parametric processes studied here could also take place during powerful bursts on the Sun, and in the magnetosphere of Jupiter.

The nonlinear dynamics of kinetic-Alfvén–wave (KAW) turbulence is studied. Weak KAW turbulence induced by three-wave interaction among parallel-propagating KAWs has a direct energy cascade in the wavenumber domain ks⊥>ρ−1i and an inverse cascade in the domain ks⊥<ρ−1i, resulting in Kolmogorov-type spectra, Wk∼(kz)−1/2(k⊥)−p, with exponents p=4 and p=3.5 respectively. The interaction including antiparallel-propagating KAWs, usually most effective, results in an inverse energy cascade over the whole k⊥ range and p=2 (at k⊥<ρ−1i) and p=3.5 (for k⊥>ρ−1i) spectra. Three applications concerning KAW turbulence in flaring loops, in the Earth's magnetosphere and in tokamaks are considered. It is suggested that turbulent KAW spectra are common in space plasmas.

The dynamic equation and coupling coefficient of the three-wave interaction among kinetic Alfvén 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’ κ=k⊥ρi. The parametric decay KAW→KAW+KAWis investigated and the threshold amplitude for decay instability in a Maxwellian plasma is calculated. The growth rate of decay instability varies as k2⊥ in both limits κ2[Lt]1 and κ2[Gt]1. The main tendency of KAWs is towards nonlinear destabilization at very low wave amplitudes Bk/B0[lsim]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.