  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.
