  Magnetic fluctuations in the solar wind are distributed according to
Kolmogorov's power law $f^{-5/3}$ below the ion cyclotron frequency $f_{ci}$.
Above this frequency, the observed steeper power law is usually interpreted in
two different ways: a dissipative range of the solar wind turbulence or another
turbulent cascade, the nature of which is still an open question. Using the
Cluster magnetic data we show that after the spectral break the intermittency
increases toward higher frequencies, indicating the presence of non-linear
interactions inherent to a new inertial range and not to the dissipative range.
At the same time the level of compressible fluctuations raises. We show that
the energy transfer rate and intermittency are sensitive to the level of
compressibility of the magnetic fluctuations within the small scale inertial
range. We conjecture that the time needed to establish this inertial range is
shorter than the eddy-turnover time, and is related to dispersive effects. A
simple phenomenological model, based on the compressible Hall MHD, predicts the
magnetic spectrum $\sim k^{-7/3+2\alpha}$, which depends on the degree of
plasma compression $\alpha$.

Astrophysics