Aims. We investigate the the stability of a cosmic-ray plasma system using the hydrodynamic approach. Methods. The system we are considering comprises cosmic rays and two oppositely propagating Alfvén waves. The thermal plasma flow is treated as a background, such that the feedback of the cosmic rays and waves is neglected. Steady-state solutions exist for the system, and when two waves are present, the steady state is non-uniform. Linear stability analysis on the steady-state solutions shows that for short wavelengths, large cosmic ray energy density, and small wave energy density the system is stable.Results. We present in detail the case of uniform background flow. The system is most unstable in the upstream region and becomes stable in the downstream region in the linear regime for short-enough wavelengths. We also speculate on the implication of the instability.

We study the stability of a four-fluid cosmic-ray-MHD system which comprises magnetized thermal plasma, cosmic rays, forward and backward propagating Alfvén waves. The coupling between the plasma, cosmic rays, and waves depends on the energy density of the waves. Local short-wavelength small perturbation analysis is performed on a background steady state. The magnetoacoustic modes of the plasma are modified and intertwined with cosmic ray and wave modes, while the plasma Alfvén mode is unaffected. The parameter space is large and the stable/unstable regions of the system are complicated. We discuss some special cases analytically and work out some general cases numerically. Roughly speaking, the system is more likely to be stable if the perturbations have very short wavelength, not propagating at large angle with background magnetic field, large cosmic ray energy density, not too small energy density for both waves and large thermal energy density (and no self-gravity).

This study investigates Parker instability in an interstellar medium (ISM) near the Galactic plane using threedimensional magneto-hydrodynamic simulations. Parker instability arises from the presence of a magnetic field in a plasma, wherein the magnetic buoyant pressure expels the gas and cause the gas to move along the field lines. The process is thought to induce the formation of giant molecular clouds in the Galaxy. In this study, the effects of cosmicray (CR) diffusion are examined. The ISM at equilibrium is assumed to comprise a plasma fluid and a CR fluid at various temperatures, with a uniform magnetic field passing through it in the azimuthal direction of the Galactic disk. After a small perturbation, the unstable gas aggregates at the footpoint of the magnetic fields and forms dense blobs. The growth rate of the instability increases with the strength of the CR diffusion. The formation of dense clouds is enhanced by the effect of cosmic rays (CRs), whereas the shape of the clouds depends sensitively on the initial conditions of perturbation.

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