The Bohm criterion in the presence of radio-frequency fields

Abstract

In d.c. discharges the Bohm condition is the condition for sheath formation, the ion velocity at the plasma boundary having to satisfy the condition ½Mv2= ½kBTe, if the spread of velocities is ignored. The model is a good one if the Debye distance is small compared with the relevant scale length. As there is much current interest in radio-frequency (RF) discharges, the question arises as to whether the criterion remains valid in the presence of RF fields. The question has been studied recently by Riemann, following earlier work by Allen who compared the plasma boundary to a sonic surface. Riemann considered a wider range of frequencies and obtained a dispersion relation that was a quartic equation. The present paper examines the complex roots of this equation, using a method developed by Briggs. The results substantiate Riemann's statement that the Bohm criterion is still valid in the presence of RF fields.