Three-wave coupling and weak turbulence of kinetic Alfven waves

The nonlinear dynamics of kinetic-Alfven-wave (KAW) turbulence is studied. Weak KAW turbulence induced by three-wave interaction among parallel-propag ating KAWs has a direct energy cascade in the wavenumber domain k(s perpend icular to) > rho(i)(-1) and an inverse cascade in the domain k(s perpendicu lar to) < rho(i)(-1), resulting in Kolmogorov-type spectra, W-k similar to (k(z))(-1/2)(k(perpendicular to))(-p), with exponents p = 4 and p = 3.5 res pectively. The interaction including antiparallel-propagating KAWs, usually most effective, results in an inverse energy cascade over the whole k(perp endicular to) range and p = 2 (at k(perpendicular to) < rho(i)(-1)) and p = 3.5 (for k(perpendicular to) > rho(i)(-1)) spectra. Three applications con cerning KAW turbulence in flaring loops, in the Earth's magnetosphere and i n tokamaks are considered. It is suggested that turbulent KAW spectra are c ommon in space plasmas.