Plasma density profile and electron temperature in discharge positive columns at intermediate pressures: examination of Ingold's approximation

Ingold's model (1978) for the medium pressure positive column is examined and compared with the original quasi-neutral theory of Self (1966). The model for cylindrical geometry is extended to plane and spherical cases, and their plasma balance equations (PBE) are further simplified without loss of accuracy. It is found that Ingold's model is inappropriate to predict the plasma density profiles, producing lower values than the exact curves. For helium plane and cylindrical positive columns, it is shown that the electron temperatures obtained from Ingold's and simplified PBES are accurate within several percent of the exact values and are in good agreement with reported observations.