We present the results of the linear analysis for the Parker-Jeans instability in the magnetized gas disks including the effect of cosmic-ray diffusion along the magnetic field lines. We adopted an uni-formly rotating two temperature layered disk with a horizontal magnetic fields and solved the perturbed equations numerically. Fragmentation of gases takes place and filamentary structures are formed by the growth of the instability. Nagai et al. (1998) showed that the direction of filaments being formed by the Parker-Jeans instability depends on the strength of pressure outside the unperturbed gas disk. We found that at some range of external pressures the direction of filaments is also governed by the value of the diffusion coefficient of CR along the magnetic field lines k.

To study the structure and dynamics of a cosmic-ray-plasma system, hydrodynamic approach is a fairly good approximation. In this approach, there are three basic energy transfer mechanisms: work done by the plasma flow against pressure gradients, cosmic ray streaming instability and stochastic acceleration. The interplay between these mechanisms gives a range of structures. We present some results of different version of the hydrodynamic approach, e.g., flow structure, injection, instability, acceleration with and without shocks.