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Plasma outflow or wind against a gravitational potential under the influenceof cosmic rays is studied in the context of hydrodynamics. Cosmic rays interactwith the plasma via hydromagnetic fluctuations. In the process, cosmic raysadvect and diffuse through the plasma. We adopt a multi-fluid model in whichbesides thermal plasma, cosmic rays and self-excited Alfven waves are alsotreated as fluids. We seek possible physically allowable steady state solutionsof three-fluid (one Alfven wave) and four-fluid (two Alfven waves) models withgiven the boundary conditions at the base of the potential well. Generallyspeaking, there are two classes of outflows, subsonic and supersonic (withrespect to a suitably defined sound speed). Three-fluid model without cosmicray diffusion can be studied in the same way as the classic stellar windproblem, and is taken as a reference model. When cosmic ray diffusion isincluded, there are two categories of solutions. One of them resembles thethree-fluid model without diffusion, and the other behaves like thermal wind atlarge distances when the waves wither and cosmic rays are decoupled from theplasma. We also inspect the effect of wave damping mechanisms (such as,nonlinear Landau damping). Roughly speaking, the effect is much smaller insupersonic outflow than in subsonic outflow.

Outflows in the presence of cosmic rays and waves