Continuous solutions of the hydrodynamic approach to cosmic-ray propagation

A hydrodynamic approach is employed to study a cosmic-ray-plasma system, wh ich comprises thermal plasma, cosmic rays and two oppositely propagating Al fven waves. The hydrodynamic approach is a good approximation in dealing wi th the structure or dynamics of the system. In this paper, we concentrate o n the steady-state structures of the system, in particular, structures with continuous (or smooth) profiles. Three mechanisms are responsible for the energy exchange between different components. They are work, done by plasma flow via pressure gradients, cosmic-ray streaming instability and stochast ic acceleration. The interplay between these mechanisms generates several m orphologically different structures. They may be divided into two categorie s: one looks like the test-particle picture and the other looks like a modi fied shook. Very often the profiles are nonmonotonic, which is in sharp con trast to systems with only thermal plasma and cosmic rays, whose flow veloc ity (and cosmic-ray pressure) profiles are al-ways monotonically decreasing (and increasing).