The hydrodynamic theory of a positive discharge column in an axial magnetic field

The influence of an axial magnetic field on the performance of a low-pressure cylindrical positive discharge column is studied from the hydrodynamic point of view. It is shown that the magnetic field affects the distribution of the plasma density, its speed, and the energy of electrons. The energy of electrons, the concentration and the speed of plasma, and the azimuth speed of electrons and ions as functions of the radius have been found for a helium atom in a magnetic field of varying intensity. It has been noticed that the electron and ion azimuth movement equations should account for inertia. The obtained hydrodynamic results significantly deviate from the ones obtained in the wide-spread diffusion model of a positive column. It is shown that the distribution of plasma concentration and the radial speed in the positive column are generally close to the results using the diffusion approach, if the axial inductance of the magnetic field and the gas density are increased. However, major differences are found near the walls.