Intrinsic sheath edge conditions for sheath instability in low-pressure electronegative plasmas

The conditions at the sheath edge that could lead to instability in the plasma-wall boundary in low-pressure electronegative plasmas are considered in a comprehensive manner. The relevant range of the ratio of the negative ion density to the electron density at the sheath edge was derived on the basis of a fluid model and it was clarified how the parameter range are affected by the positive and negative ion temperatures, by the geometries of plasmas (plane-parallel, cylindrical, and spherical), by the directions of the positive ion flow (converging or diverging), and by the effects of ionization and momentum transfer collisions. It was found that in any geometry the instability would be induced in conditions that could be realized without difficulty in low-pressure plasmas.