The characteristics of the plasma formed in a low-pressure gas discharge in a magnetic field were studied in this work. The motion of electrons is considered in the diffusion-drift approximation. As for the ions, it is assumed that they leave the gap in free flight mode. Two regimes of discharge operation are considered, which are characterized by negative and positive anode potential fall. Analytical expressions are obtained for the plasma concentration in both regimes. Conditions are found under which there is no anode potential drop, and the plasma is in direct contact with the anode surface. The negative anode fall mode is preferred for use in sources of charged particles and other devices, since the discharge voltage is lower and the energy efficiency is correspondingly higher in this case.