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Numerical study of the ionizing gas flows with additional longitudinal magnetic field in the channel of the quasi-stationary plasma accelerator (QSPA) is presented. Two-dimensional axisymmetric flows of an ionizing gas are considered using the transfer equations for multicomponent medium consisting of atoms, ions, and electrons, taking into account electrical conductivity, thermal conductivity, and radiation transport. The equations of magnetic gas dynamics are presented in terms of the vector potential of the magnetic field [1]. To calculate the transport of radiation, the 3D formulation of the problem is used in the multigroup approximation, taking into account the main mechanisms of emission and absorption of photons [2]. The study of the process of ionization and radiation transport was carried out in the approximation of local thermodynamic equilibrium. The longitudinal magnetic field leads to the plasma rotation behind the ionization front, which occurs in the ionizing gas flows. The integral radiation characteristics of the medium are determined. Calculations have shown that the ionization front shifts in the direction of the channel outlet with a decrease in the discharge current in accordance with the available experimental data. This is accompanied by oscillations of the ionization front in the narrowest and expanding part of the nozzle-shaped channel at low discharge currents and leads to the appearance of unstable pulsating flows of ionizing gas [3]. As a result of studying the ionization process in the presence of longitudinal magnetic field, it was found that the flow rotation and thermal conductivity along the magnetic field stabilize the instability of the ionization process in the QSPA installation [4]. 1. Kozlov A.N. Basis of the quasi-steady plasma accelerator theory in the presence of a longitudinal magnetic field. // J. Plasma Physics. 2008. V. 74, No. 2. P. 261-286. 2. Kozlov A.N., Konovalov V.S. Numerical study of the ionization process and radiation transport in the channel of plasma accelerator. // Communications in Nonlinear Science and Numerical Simulation. 2017. V. 51. P. 169-179. 3. Kozlov A.N., Konovalov V.S. Empirical stationary condition of two-dimensional flows of ionizing hydrogen in the plasma accelerator channel. // Mathematical Models and Computer Simulations, 2023, V. 15, No. 4, P. 630-642. 4. Kozlov A.N. Flows of ionizing gas in the plasma accelerator channel with longitudinal magnetic field. // Physics of Fluids. 2022, V. 34, No. 10, Ar. 104109.