Oblique Ion Collection in the Drift-Approximation: How Magnetized Mach-Probes Really Work

The anisotropic fluid equations governing a frictionless obliquely-flowing plasma around an essentially arbitrarily shaped three-dimensional ion-absorbing object in a strong magnetic field are solved analytically in the quasi-neutral drift-approximation, neglecting parallel temperature gradients. The effects of transverse displacements traversing the magnetic presheath are also quantified. It is shown that the parallel collection flux density dependence upon external Mach-number is n∞cs exp[−1 − (M‖∞ −M⊥ cot θ)] where θ is the angle (in the plane of field and drift velocity) of the object-surface to the magnetic-field andM‖∞ is the external parallel flow. The perpendicular drift, M⊥, appearing here consists of the external E ∧B drift plus a weighted sum of the ion and electron diamagnetic drifts that depends upon the total angle of the surface to the magnetic field. It is that somewhat counter-intuitive combination that an oblique (transverse) Mach probe experiment measures. Ion collection by solid objects immersed in a plasma is a problem of perennial interest in plasma physics. It provides the basis for the measurement of plasma parameters by electric (Langmuir) probes[1] as well as the charging of dust[2] and spacecraft[3]. The present work addresses the situation where the ion Larmor radius (in the background magnetic field B) is much smaller than the object, so that perpendicular plasma flow is strongly constrained. This problem has important similarities to the solution of the flow of plasma to a plane aligned obliquely to the field, the most obvious example being a tokamak divertor plate. That problem can be formulated[4] as one-dimensional, taking the coordinates in the plane as being ignorable. However, it is well established that no spatially-varying solution of the quasi-neutral plasma equations in one dimension is possible without additional sources of particles (e.g. through ionization) or momentum (e.g. from collisions). Recent studies of this problem of the one-dimensional magnetized plasma and oblique presheath (e.g. [5, 6]) have