The Transport of Relative Canonical Helicity

TL;DR

This paper investigates how relative canonical helicity evolves in two-fluid MHD, revealing its invariance, conversion mechanisms, and dependence on size parameters, which influence plasma flow and magnetic field interactions.

Contribution

It introduces a model explaining the evolution and conversion of relative canonical helicity in two-fluid MHD, linking enthalpy differences to helicity dynamics and bifurcation thresholds.

Findings

Canonical helicity remains globally invariant.

Conversion between species' helicities is driven by enthalpy differences.

Size parameter influences helicity annihilation channels.

Abstract

The evolution of relative canonical helicity is examined in the two-fluid magnetohydrodynamic formalism. Canonical helicity is defined here as the helicity of the plasma species' canonical momentum. The species' canonical helicity are coupled together and can be converted from one into the other while the total gauge-invariant relative canonical helicity remains globally invariant. The conversion is driven by enthalpy differences at a surface common to ion and electron canonical flux tubes. The model provides an explanation for why the threshold for bifurcation in counter-helicity merging depends on the size parameter. The size parameter determines whether magnetic helicity annihilation channels enthalpy into the magnetic flux tube or into the vorticity flow tube components of the canonical flux tube. The transport of relative canonical helicity constrains the interaction between plasma flows and magnetic fields, and provides a more general framework for driving flows and currents from enthalpy or inductive boundary conditions.