  The Warm-Hot Intergalactic Medium (WHIM) is thought to contribute about 40-50
% to the baryonic budget at the present evolution stage of the universe. The
observed large scale structure is likely to be due to gravitational growth of
density fluctuations in the post-inflation era. The evolving cosmic web is
governed by non-linear gravitational growth of the initially weak density
fluctuations in the dark energy dominated cosmology. Non-linear structure
formation, accretion and merging processes, star forming and AGN activity
produce gas shocks in the WHIM. Shock waves are converting a fraction of the
gravitation power to thermal and non-thermal emission of baryonic/leptonic
matter. They provide the most likely way to power the luminous matter in the
WHIM. The plasma shocks in the WHIM are expected to be collisionless.
Collisionless shocks produce a highly non-equilibrium state with anisotropic
temperatures and a large differences in ion and electron temperatures. We
discuss the ion and electron heating by the collisionless shocks and then
review the plasma processes responsible for the Coulomb equilibration and
collisional ionisation equilibrium of oxygen ions in the WHIM. MHD-turbulence
produced by the strong collisionless shocks could provide a sizeable
non-thermal contribution to the observed Doppler parameter of the UV line
spectra of the WHIM.
