Effect of electron inertial delay on Debye sheath formation

Present contribution deals with the role of weak but finite electron inertia on the sheath formation condition. As reported earlier this becomes effective when the ions’ drift velocity exceeds the phase velocity of the acoustic wave fluctuations. Such situation has natural existence near the sheath edge. Keeping this in mind we have revisited the problem of usual Bohm sheath condition. Analytical and numerical analysis have been performed to re-derive the local condition for plasma sheath formation. It is found that the weak but finite electron inertia reduces the threshold value of ion Mach number that may be, at least in principle, of qualitative value to define the sheath edge boundary. Consideration of finite but weak equilibrium electron flow at the defined sheath edge shrinks the width of non-neutral space charge layer over which major potential drop and charge imbalance occurs. Detailed numerical analysis and results of quantitative and qualitative importance are included in the text.