A mathematical model of the multihollow cathode with the supply of the working medium at the axial magnetic field is considered. The processes taking place in the non-equilibrium multicomponent plasma in the hollows, the redistribution of the working medium flow rate over the channels, the partial transmission of electrons through the magnetic field at the walls, the anisotropy of the design characteristics and the decrease of the work function when the working medium is adsorbed on the walls have all been taken into consideration. A relation for the Richardson constant in the case of atom adsorption has been obtained, which is consistent with the experimental data. As a result, the cathode model is represented as a closed system of 54 equations. The calculated characteristics have been confirmed by experimental data.