An analytic treatment of the bounded and free presheaths with arbitrary viscosity in magnetized flowing plasmas

Analytic solutions are derived from one-dimensional fluid equations with arbitrary shear viscosity for the free and bounded presheaths in the strongly magnetized flowing plasma. Plasma density and flow velocity are obtained analytically in terms of position along the field line, Mach number (M∞), normalized viscosity (α), and size of bounded presheath. Simple analytic relations between the ratio (R) of sheath current and the flow Mach number [M∞ ≡ Vd/√(ZTe+Ti)/mi] are derived as R=exp(M∞/Mc), where Mc = 1/[1 +√α2/1+α arctan√1+α], with less than 5% accuracy for 0≤M∞≤0.5. By generating two free and two bounded presheaths by two Mach probes within two free presheaths generated by a larger object than Mach probes, one can measure α and M∞ simultaneously. The allowed range of α in terms of M∞ is obtained, and comparisons with previous numerical analyses are also made