Model and results of numerical experiments are presented for axisymmetric flows of ionizing gas in the presence of an additional longitudinal magnetic field in the channel of quasi-stationary plasma accelerator considered as perspective electric propulsion plasma engine. A two-dimensional flow model for a three-component medium consisting of atoms, ions, and electrons is based on magnetogasdynamic equations written in terms of the vector potential of magnetic field, taking into account electrical conductivity, thermal conductivity, and radiation transfer. A three-dimensional model of radiative transfer includes main mechanisms of emission and absorption for different parts of the spectrum. Numerical studies of the ionization process and radiation transfer were carried out in an approximation of local thermodynamic equilibrium. The stabilizing effect of flow rotation in the presence of a longitudinal magnetic field and thermal conductivity along the magnetic field on non-stationary unstable flows of ionizing gas, which arise at low discharge currents, is considered.