Mach probes

A Mach probe (MP) is an electric probe system to deduce the plasma flow velocity from the ratio of ion saturation currents. Generally, a typical MP is composed of two directional electric probes located at opposite sides of an insulator, which is mostly used as a parallel MP, but there are other MPs such as perpendicular MP (PMP), Gundestrup probe (GP) or rotating probe (RP), and visco-MP (VMP), depending on the shape of the probe holder, location of different probes or the method of collecting ions. For the parallel MP (to be called simply an MP), the relation between the ratio of the upstream ion saturation current density (J up ) to the downstream (J dn ) and the normalized drift velocity of the plasma has generally been fitted into an exponential form (R = J up /J dn ? exp[KM ∞ ]). For the GP or RP, with oblique ion collection, the relation becomes R = exp[K(M ��� ? M ⊥ ?cot?&thgr;)], where K ? 2.3?2.5, M ��� = M<SU M ∞ , M ⊥ is the normalized perpendicular flow to the magnetic field, and &thgr; is the angle between the magnetic field and the probe surface. The normalized drift velocity of flowing plasmas is deduced from the ratio (R m ) measured by an MP as M ∞ = ln[R< ln[R m ]/K, where K is a calibration factor depending on the magnetic flux density, collisionality of charged particles and neutrals, viscosity of plasmas, ion temperature, etc. Existing theories of MPs in unmagnetized and magnetized flowing plasmas are introduced in terms of kinetic, fluid and particle-in-cell models or self-consistent and self-similar methods along with key physics and comments. Experimental evidence of relevant models is shown along with validity of related theories. Calibration and error analysis are also given. For probes other than the typical parallel MP, the relation between the ratio of ion saturation currents and M ∞ can be expressed as a combination of the functional forms: exponential and/or polynomial form of M ∞ for PMP; two Rs of two separate MPs for VMP. Collisions of ions/electrons/neutrals, asymmetries of ion temperatures and the existence of hyperthermal electrons, existence of ion beam, supersonic flow and negative ions can affect the deduction of flow velocities by an MP.The technical support of Hyun-Jong Woo in preparing the manuscript is greatly appreciated. This paper is much improved by the comments, references and suggested phrases of the referees during the review process, which is deeply appreciated. This work is supported by the National R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant number 2009-0082669 and 2012-0005926). This work is partially supported by the Basic Research Program of the National Fusion Research Institute (NFRI) of Korea. It is also partially supported by the Brain Korea 21 (BK21) program under the Ministry of Education, Science and Technology (MEST)