  We study the steady-state expansion of a collisionless, electrostatic,
quasi-neutral plasma plume into vacuum, with a fluid model. We analyze
approximate semi-analytical solutions, that can be used in lieu of much more
expensive numerical solutions. In particular, we focus on the earlier studies
presented in Parks and Katz (1979), Korsun and Tverdokhlebova (1997), and
Ashkenazy and Fruchtman (2001). By calculating the error with respect to the
numerical solution, we can judge the range of validity for each solution.
Moreover, we introduce a generalization of earlier models that has a wider
range of applicability, in terms of plasma injection profiles. We conclude by
showing a straightforward way to extend the discussed solutions to the case of
a plasma plume injected with non-null azimuthal velocity.
