Kelvin's Canonical Circulation Theorem in Hall Magnetohydrodynamics

TL;DR

This paper demonstrates that Kelvin's Circulation Theorem can be valid in Hall MHD when using the canonical ion-flow velocity, restoring the proper connection between current density and plasma flow.

Contribution

It establishes the validity of Kelvin's Circulation Theorem in Hall MHD by redefining the circulation integral with the canonical ion-flow velocity.

Findings

Kelvin's Theorem is valid in Hall MHD with the canonical velocity.

Restoring the connection between current density and plasma flow is crucial.

The canonical ion-flow velocity replaces the usual velocity in circulation integrals.

Abstract

The purpose of this paper is to show that, thanks to the restoration of the legitimate connection between the current density and the plasma flow velocity in Hall magnetohydrodynamics (MHD), Kelvin's Circulation Theorem becomes valid in Hall MHD. The ion-flow velocity in the usual circulation integral is now replaced by the canonical ion-flow velocity.