The Runaway of Electrons and the Formation of Beams in Glow Discharges

Analytical methods are used to obtain the criterion defining the boundary between the beam and hydrodynamic modes of motion of electrons in uniform and nonuniform electric fields for Townsend and high-voltage glow discharges. The beam approximation is used to study the electron energy distribution function in view of electrons being produced in gas. The hydrodynamic approximation is used to obtain the criterion which characterizes the runaway of electrons and the criterion of transition to the beam mode of motion. It is demonstrated that the curve of discharge ignition on the $U(pd)$ diagram differs significantly from the boundary line between the beam and hydrodynamic modes of motion of electrons.