Theoretical approaches to particle propagation and acceleration in turbulent intergalactic medium

Intercluster medium is expected to be turbulent with turbulence being superAlfvenic at large scales. Magnetic fields substantially modify the turbulent cascade when the turbulence reaches the scales at which the fluctuation velocity gets less than the Alfven velocity. At those scales it is possible to consider three cascades, of fast, slow and Alfven modes with little energy exchange between them. As Alfvenic and slow modes are anisotropic they marginally scatter and accelerate cosmic rays, while fast modes dominate the processes. However, in the presence of cosmic rays the turbulence is modified as cosmic rays transfer the energy of compressible motions (i.e. slow and fast modes) from large scales to the scale of cosmic ray Larmor radius. This results in generation of a new small-scale Alfvenic component which is not a part of the ordinary MHD cascade. This component does scatter and accelerate cosmic rays. In addition, magnetic reconnection in turbulent medium accelerates cosmic rays. The complexity of the intracluster turbulence calls for observational studies. A new technique Velocity Coordinate Spectrum (VCS) is particularly promising for studies of velocity fluctuations with a new generation of X-ray observatories