On the stability of a liquid layer bordering plasma

Abstract

The surface of a liquid wall (cathode) in contact with plasma is subjected to the electric field and to the bombardment of plasma particles, mostly ions. The stability of electrocapillary waves at the wall surface is considered. In the first part of the paper, the motion of ions inside the sheath and its influence on the electric field distribution are considered in a self-consistent way. The stress exerted on the liquid surface by ions and the electric field is found. This stress is used to describe the liquid motion in the second (hydrodynamic) part of the paper. It allows us to obtain the dispersion relation of the electrocapillary waves and to find the most dangerous wavenumbers and corresponding instability increments. It is shown that disturbances with wavenumbers less than some critical value κ0 = kλ (λ is the Debye length) do not grow. Shorter disturbances grow if E, the electric field, at the wall exceeds a specific Ecrit number. Expressions for κ0 and Ecrit are obtained. The increment of instability for κ > κ0 and E > Ecrit is calculated. It is shown that the instability takes place within an interval of wavenumbers. The higher the electric field, the wider this interval and the higher the increment of the most dangerous instability. Calculations were performed for the liquid wall at floating potential bordering hydrogen and deuterium plasmas. It is shown that the instability takes place in a wider range of wavelengths and has a higher increment in the case of deuterium plasma than in the case of hydrogen plasma.