Why is the mach probe formula expressed as R = Jup/J dn = exp[KM∞]?

Abstract

The normalized drift velocity of flowing plasmas can be deduced using a Mach probe, which has two directional probes at opposite sides. The relationship between the ratio (R) of upstream ion saturation current density (J up) to downstream current density (Jdn) and the normalized drift velocity (M∞ = Vd/√Te/m i/ of plasma has generally been fitted into an exponential form as R = Jup/Jdn = exp[KM∞], where K is a calibration factor depending on the magnetic flux density, collisionality, viscosity, and ion temperature of plasmas. Without going into detailed theories for various conditions of plasmas and probes, a simple explanation is given in terms of decaying current density in the downstream region. Existing theories and experiments of Mach probes in magnetized and unmagentized flowing plasmas are summarized along with key physics and comments.