  Turbulence in the weakly collisional intracluster medium of galaxies (ICM) is
able to generate strong thermal velocity anisotropies in the ions (with respect
to the local magnetic field direction), if the magnetic moment of the particles
is conserved in the absence of Coulomb collisions. In this scenario, the
anisotropic pressure magnetohydrodynamic (AMHD) turbulence shows a very
different statistical behaviour from the standard MHD one and is unable to
amplify seed magnetic fields, in disagreement with previous cosmological MHD
simulations which are successful to explain the observed magnetic fields in the
ICM. On the other hand, temperature anisotropies can also drive plasma
instabilities which can relax the anisotropy. This work aims to compare the
relaxation rate with the growth rate of the anisotropies driven by the
turbulence. We employ quasilinear theory to estimate the ions scattering rate
due to the parallel firehose, mirror, and ion-cyclotron instabilities, for a
set of plasma parameters resulting from AMHD simulations of the turbulent ICM.
We show that the ICM turbulence can sustain only anisotropy levels very close
to the instabilities thresholds. We argue that the AMHD model which bounds the
anisotropies at the marginal stability levels can describe the Alfvenic
turbulence cascade in the ICM.
