Ion current to a spherical probe in a flowing high-pressure plasma under thin-sheath conditions

The current to a large (radius = 2.4 mm) negatively biased spherical probe in a flowing plasma (a propane/air flame) has been measured over wide ranges of plasma-ionisation density (3 × 1015 to 1018 m¿3), probe bias (10¿400V) and probe/plasma relative velocity (3¿40m/s). Under these conditions, the sheath surrounding the probe is thin and the probe current is a function of the probe/plasma velocity. In consequence, the static continuum probe theory of Su and Lam, and the motionally dependent thick-sheath theory of Clemenets and Smy are both found to be in error by at least an order of magnitude. A thin relationship has been derived for the spherical probe which shows excellent agreement with the experimental data: I=12.13(¿¿0)1/4(neevf)3/4V1/2rp5/4 where I = probe current, ¿ = ionic mobility, ¿0 = permittivity of free space, ne = ionisation density, e = electron charge, vf = flow velocity, V = probe bias and rp = probe radius (all in MKS units)