Ion Current from a Collision-Dominated Flowing Plasma to a Cylindrical Electrode Surrounded by a Thin Sheath

Abstract

Experimental results for the ion current to a cylindrical electrode in a flowing continuum plasma are compared with the currents calculated from a convection‐dependent thin‐sheath theory obtained by extending the theory of Lam to cover convection rather than diffusion‐generated currents. The relation derived with this theory $$I_i{\text{≈5.3ε}}_0^{\text{1/4}}{e}^{\text{3/4}}{\mu }_i^{\text{1/4}}{r}_p^{\text{1/4}}{v}_f^{\text{3/4}}{n}_e^{\text{3/4}}{V}^{\text{1/2}}\mathrm{l,\hspace{0.17em}\hspace{0.17em}(}\mathrm{mks})$$ where ε₀ is the permittivity of free space, e is the electronic charge, μ_i is the ion mobility, r_p is the probe radius, v_f is the plasma/probe velocity, n_e is the ionization density, V is the probe bias, and l is the probe length, is found, on the average, to predict the experimental currents to within ±30% over ranges of 0.1–5 mm in probe radius, 5×10²−4×10³ cm/sec in probe/plasma velocity, 5×10¹⁶−2×10¹⁸/m³ ionization density, and 10–100 V in probe bias. Further support for a convection‐dependent thin‐sheath model is provided by two experimental observations: (1) The current is observed to vary as V^1/2 as predicted by the convection‐dependent theory rather than to saturate as would be expected of a diffusion‐generated current. (2) Separate measurements reveal a marked asymmetry in the current distribution around the probe surface as expected in a thin‐sheath situation.