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.