Reflex discharge has a large number of applications. However, there is no analytical formula allowing for the specified geometry to calculate the current or spatial characteristics of the discharge a priori. To do this, we create two-component model of the discharge in a diffusion-drift approximation in a magnetic field. The conditions of breakdown have been investigated in the framework of the Townsend mechanism. Current-voltage (I-V) characteristics, temporal variation of the discharge current and average ion density, and spatial distributions of ions and electrons have been calculated. I-V discharge characteristics in the absence of magnetic field have been measured. Experiments have been carried out in the discharge with a cylindrical anode with a length of 180 cm, diameter of 90 cm and a flat circular cathode with a diameter of 4 cm. The dependence of discharge current on the applied magnetic field has been determined. The dependence of steady-state discharge current on the order of electric and magnetic field switching has been studied. Comparison of theory with experiment provides qualitative agreement and it confirms the adequacy of the created model.