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