The fluid equations for an electron beam are used to calculate the equilibrium velocity and density profiles, limiting current and space-charge wave properties of an annular beam undergoing magnetic compression in a gyrotron beam tunnel. Both non-relativistic and relativistic equations are derived. The beam tunnel may have a conventional smooth wall or an absorbing dielectric-loaded wall. Small values of magnetic compression are seen to have large effect on the profiles and the current limit of a given tunnel. Common dielectric-loaded tunnels are also seen to reduce the limiting current by 5%-20%. Limiting current data for a wide range of beam parameters are shown. The dispersion relation for a convective instability arising from the gradient in the equilibrium potential depression profiles is derived using the linearized fluid equations. The growth rate is seen to increase for increasing current and pitch angle, and for increasing wall effects of an absorbing tunnel. The average growth rate is calculated for a typical gyrotron beam and beam tunnel as well as for a beam entering an interaction cavity. Growth rates for all values of k(z) are seen to decrease to zero for a conventional conducting beam tunnel in a constant magnetic field.