Asymmetry reversal of ion collection by Mach probe in flowing unmagnetized plasma

Mach probes derive ion drift velocity in flowing plasma from the asymmetry of ion current collection by measuring upstream and downstream flux. Intuitively it is expected that the ion flux density on the upstream side of the Mach probe is higher compared to the downstream side. Hutchinson's numerical calculation\footnote{I. H. Hutchinson, Plasma Phys. Control. Fusion \textbf{45}, 1477 (2003)} of a sphere in unmagnetized plasma found unexpected result that the downstream flux was higher than the upstream flux for relatively low drift velocity v$_{d}$, comparable Debye length $\lambda _{D}$ to the probe size r$_{p}$, high probe bias V$_{p}$. We found experimental evidence for such a reversal when $\lambda _{D}$/r$_{p}$ $\sim $ 0.18, v$_{d} \quad <$ 2.7c$_{s}$, where c$_{s}$ is the ion sound velocity, and V$_{p} \quad >$ 20T$_{e}$. The experiments were performed in a double plasma system with v$_{d} \quad \le $ 4.5c$_{s}$ and Ar pressure range of 0.3 $\sim $ 0.6mTorr and a plasma density range of 10$^{8} \quad \sim $ 10$^{10}$cm$^{-3}$. The supersonic ion drift was determined from ion beam detection\footnote{Wim. J. Weber, Richard J. Armstrong, and Jan Trulsen, J. Appl. Phys. \textbf{50 }(7), 4545 (1979)} using the upstream planar Mach probe, and the ion beam energy was found to agree with Ion energy analyzer measurements.