Recent achievements on KMHD and applications in the ICM
  Collisionless plasmas are ubiquitous in the Universe. In general full kinetic
equations are needed for a correct description of the physics in such
environments. Fluid approximations are, at some special cases, valid. In this
work we present the basic equations under such an approximation and the
implementation of them in a magnetohydrodynamical code. The numerical
simulations are applied for intracluster medium physical properties, i.e. low
density but high temperature plasma. We show that, under specific conditions
firehose and mirror instabilities may be present. The side effects are the
conversion of thermal to magnetic/kinetic energies and the generation of small
scale structures ($\sim 1$kpc). We study the changes in the statistics of
Faraday rotation measurement, and of the synchrotron polarization, when
compared to a standard MHD simulation for the ICM. We conclude that KMHD
numerical simulations are mandatory in order to fully understand the statistics
of the ICM emission.
