  A phenomenological turbulence model for kinetic Alfv\'en waves in a
magnetizedcollisionless plasma, able to reproduce the non-universalpower-law
spectra observed at the sub-ion scales in the solar wind and the terrestrial
magnetosphere, is presented.The process of temperature homogenization along
distortedmagnetic field lines, induced by Landau damping,affects the
turbulencetransfer time and results in a steepening of the sub-ion power-law
spectrumof critically-balanced turbulence, whose exponent is sensitive to the
ratio between the Alfv\'en wave period and the nonlinear timescale. Transition
from large-scaleweak turbulence to smaller scale strong turbulence is
capturedand non local interactions, relevant in the case of steep spectra, are
accounted for.
