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Plasma outflow or wind against a gravitational potential under the influence of cosmic rays is studied in the context of hydrodynamics. Cosmic rays interact with the plasma via hydromagnetic fluctuations. In the process, cosmic rays advect and diffuse through the plasma. We adopt a multi-fluid model in which besides thermal plasma, cosmic rays and self-excited Alfven waves are also treated as fluids. We seek possible physically allowable steady state solutions of three-fluid (one Alfven wave) and four-fluid (two Alfven waves) models with given the boundary conditions at the base of the potential well. Generally speaking, there are two classes of outflows, subsonic and supersonic (with respect to a suitably defined sound speed). Three-fluid model without cosmic ray diffusion can be studied in the same way as the classic stellar wind problem, and is taken as a reference model. When cosmic ray diffusion is included, there are two categories of solutions. One of them resembles the three-fluid model without diffusion, and the other behaves like thermal wind at large distances when the waves wither and cosmic rays are decoupled from the plasma. We also inspect the effect of wave damping mechanisms (such as, nonlinear Landau damping). Roughly speaking, the effect is much smaller in supersonic outflow than in subsonic outflow.
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