  The results of a numerical study of the magnetic dynamo effect in cylindrical
von K\'arm\'an plasma flow are presented with parameters relevant to the
Madison Plasma Couette Experiment. This experiment is designed to investigate a
broad class of phenomena in flowing plasmas. In a plasma, the magnetic Prandtl
number Pm can be of order unity (i.e., the fluid Reynolds number Re is
comparable to the magnetic Reynolds number Rm). This is in contrast to liquid
metal experiments, where Pm is small (so, Re>>Rm) and the flows are always
turbulent. We explore dynamo action through simulations using the extended
magnetohydrodynamic NIMROD code for an isothermal and compressible plasma
model.We also study two-fluid effects in simulations by including the Hall term
in Ohm's law. We find that the counter-rotating von K\'arm\'an flow results in
sustained dynamo action and the self-generation of magnetic field when the
magnetic Reynolds number exceeds a critical value. For the plasma parameters of
the experiment, this field saturates at an amplitude corresponding to a new
stable equilibrium (a laminar dynamo). We show that compressibility in the
plasma results in an increase of the critical magnetic Reynolds number, while
inclusion of the Hall term in Ohm's law changes the amplitude of the saturated
dynamo field but not the critical value for the onset of dynamo action.
