Oblique ion collection in the drift-approximation: how magnetized Mach-probes really work

TL;DR

This paper analytically investigates how oblique ion collection in magnetized plasmas depends on flow angles and magnetic field orientation, clarifying the physical principles behind Mach-probe measurements.

Contribution

It provides an analytical solution for anisotropic plasma flow around arbitrarily shaped objects, elucidating how oblique Mach probes measure plasma flows in magnetic fields.

Findings

Derived the flux density dependence on Mach numbers and angles.

Quantified effects of transverse displacements in magnetic presheaths.

Clarified the physical interpretation of oblique Mach-probe measurements.

Abstract

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 $n_\infty c_s \exp[-1 -(M_{\parallel\infty}- M_\perp\cot\theta)]$ where $\theta$ is the angle (in the plane of field and drift velocity) of the object-surface to the magnetic-field and $M_{\parallel\infty}$ is the external parallel flow. The perpendicular drift, $\M_\perp$, appearing here consists of the external $\E\wedge\B$ drift plus a weighted sum of the ion and electron 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.