Evaluation of the Bohm Sheath Criterion for Ion Density Determination

Abstract

The Bohm sheath criterion requiring a minimum ion energy [Formula: see text] for sheath formation at a plasma boundary is discussed in connection with ion density determinations for planar, cylindrical, and spherical collection geometry. For truly planar geometry (i.e. an infinite plane collector) the ions must gain a large directed energy in the presheath (e.g., > 3.5 kTc for kTc = 1 eV) which will always exceed the Bohm minimum energy before a sheath is formed. In fact, Langmuir's original ion equation is applicable, and is compatible with the Bohm sheath criterion for the specific case of planar geometry. For cylindrical and spherical geometry, the necessary directed ion energy lies closer to, or may even equal, the Bohm minimum energy; however, uncertainty in the exact amount of directed energy required for sheath formation could lead to ion density determinations involving errors of nearly an order of magnitude in the two cases.