Continuous solutions of cosmic-rays and waves in astrophysical environments

The propagation of energetic charged particles and cosmic rays in magnetized thermal plasma is focused. We consider a four-fluid system that consists of thermal plasma, cosmic rays, and two opposite propagating Alfvén waves to investigate the dynamics and energy exchange mechanisms of the system. Additionally, cosmic rays diffusion within the plasma is considered along the magnetic field lines whereas neglected the cross field line diffusion effects. This study is important for understanding of pressure gradients and their impact on the feedback in astrophysical environment. Over the last few decades, this problem becomes important when we discuss the interaction of cosmic rays with plasma in space, such as interstellar clouds or interstellar medium.