A model for the non-universal power-law of the solar wind sub-ion scale magnetic spectrum

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.