The steady state of a nonisothermal cylindrical discharge in a longitudinal magnetic field is described by three moment equations in the plasma approximation for electrons and ions. Volume generation of electron‐ion pairs by single‐stage ionization, the presence of axial current, and collisions with neutrals are considered. The theory yields radial profiles of the charged particle velocities, density, potential, electron and ion temperatures, and demonstrates similarity laws for the positive column. The results are compared with two‐moment theories and with experimental data on helium, argon, and mercury vapor found in the literature for a wide range of pressures.