On the positive column of discharges in helium at intermediate pressures: II. Plasma particle balance and discharge characteristics

Abstract

Corrections on the plasma particle balance owing to deviations from the ambipolar Schottky theory are studied. The effects of ion inertia (transition to free fall theory), deviations from quasi-neutrality (transition to free diffusion theory), and stepwise ionization (Spenke theory) are introduced in the form of a numerical correction factor. Also other effects are briefly considered, i.e., gas heating, dependence of ion mobility on temperature and electric field, conversion of He + into He + 2, electron-ion recombination, and the presence of an axial magnetic field. From the plasma balance various characteristics in a diagram of E/ p against pR are derived with the aid of values of the ionization rate that result from computations in which stepwise processes are taken into account. Here E is the strength of the axial electric field along a cylindrical discharge, p is the filling gas pressure, and R is the inner tube radius. The theoretical results show a good agreement with measurements of E in the positive column of a dc discharge in helium for the range of parameters: p = 0.1–2 torr, E/ p = 300–4000 V m -1 torr -1, current I = 0.01–0.4 A, and R = 0.011 m.