Ion collection by oblique surfaces of an object in a transversely-flowing strongly-magnetized plasma

TL;DR

This paper derives an exact analytic solution for ion collection by oblique surfaces in a strongly magnetized, transversely-flowing plasma, revealing that flux depends solely on surface orientation and supporting the use of oblique Mach-probes.

Contribution

It provides the first exact analytic solution for collisionless plasma flow around arbitrarily shaped objects in strong magnetic fields, validating and calibrating oblique Mach-probes.

Findings

Ion flux depends only on surface orientation.

Exact solution explains previous numerical fits.

Supports use of oblique Mach-probes in plasma diagnostics.

Abstract

The equations governing a collisionless obliquely-flowing plasma around an ion-absorbing object in a strong magnetic field are shown to have an exact analytic solution even for arbitrary (two-dimensional) object-shape, when temperature is uniform, and diffusive transport can be ignored. The solution has an extremely simple geometric embodiment. It shows that the ion collection flux density to a convex body's surface depends only upon the orientation of the surface, and provides the theoretical justification and calibration of oblique `Mach-probes'. The exponential form of this exact solution helps explain the approximate fit of this function to previous numerical solutions.