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The evolution of relative canonical helicity is examined in the two-fluidmagnetohydrodynamic formalism. Canonical helicity is defined here as thehelicity of the plasma species' canonical momentum. The species' canonicalhelicity are coupled together and can be converted from one into the otherwhile the total gauge-invariant relative canonical helicity remains globallyinvariant. The conversion is driven by enthalpy differences at a surface commonto ion and electron canonical flux tubes. The model provides an explanation forwhy the threshold for bifurcation in counter-helicity merging depends on thesize parameter. The size parameter determines whether magnetic helicityannihilation channels enthalpy into the magnetic flux tube or into thevorticity flow tube components of the canonical flux tube. The transport ofrelative canonical helicity constrains the interaction between plasma flows andmagnetic fields, and provides a more general framework for driving flows andcurrents from enthalpy or inductive boundary conditions.

The Transport of Relative Canonical Helicity