The transport of relative canonical helicity

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. I. INTRODUCTIONPrevious treatments of canonical helicity-also known as generalized vorticity 1 , self-helicity 2 , generalized helicity 3 , or fluid helicity 4 -concluded that the canonical helicities of each species were invariant, independent from each other. Assuming closed canonical circulation flux tubes inside singly-connected volumes, and arguing for selective decay arguments in the presence of dissipation, it was shown that canonical helicity is a constant of the system stronger than magnetofluid energy. Generalized relaxation theories could therefore minimize magnetofluid energy for a given canonical helicity and derive stationary relaxed states.It is puzzling that in a multiple-component plasma a species' canonical helicity must be independent from another. Given a general isolated system, the canonical momentum vectors of ion and electron fluid elements trace out different closed helical paths. Both paths are linked, resembling intertwined helical braids directed along a magnetic field line, and define flux tubes of canonical momentum that interpenetrate each other. On scales larger than the ion and electron skin depths, defined as ⁄ where is the speed of light and is the plasma frequency of the species , or when species momentum is negligible, canonical flux tubes are topologically indistinguishable from magnetic flux tubes, so magnetic helicity suffices to describe the quasistatic evolution of the system. But when species momentum is significant or when phenomena involves scales that include ion or electron skin depths, then canonical flux tubes are distinguishable from one another, and because they overlap, any effort to count helicity in the system should consider gauge dependence.

A generalized two-fluid picture of non-driven collisionless reconnection and its relation to whistler waves

“…Section III C shows that the magnetic energy is converted and propagated mainly in the form of Poynting flux, and that the canonical helicity Ð P Á QdV as a whole must indeed be considered rather than just the magnetic helicity Ð A Á BdV. 13,25 Section III D proposes a mechanism for whistler wave generation and propagation associated with reconnection and shows that it agrees with magnetosheath and magnetosphere observations. Section IV summarizes the results and discusses some prospects on 3D-localized reconnection in a similar regime.…”

A field theory approach to the evolution of canonical helicity and energy

“…The framework also shows that a species' canonical helicity is well conserved compared to the species' energy in shallow density gradients but not in steep density gradients (in the simplest case of an isolated, dissipative system). These results suggest that in the edge of multi-species, collisionless, kinetic plasmas, magnetic helicity can couple to ion canonical helicity, spontaneously generating flowing structures when density gradients are of the order of the ion skin depth 20 . These regimes apply to magnetic fusion plasmas.…”

The Mochi LabJet Experiment for Measurements of Canonical Helicity Injection in a Laboratory Astrophysical Jet

“…The strength of this approach is the ability to predict the structures of two-fluid plasmas, for example, in isolated toroidal configurations with significant flows, angular momentum and pressure gradients (Steinhauer & Ishida 1998) or isolated double-Beltrami states in complex multi-fluids with dust (Mahajan & Lingam 2015). Another strength is the ability to predict the threshold for bifurcation in compact torus formation from the merging of counter-helicity spheromaks (You 2014;You 2012) . In the most general form, canonical helicity evolution is also valid in kinetic regimes and relativistic systems (You 2016). This mathematical result opens the door to considering selforganization in realistic regimes beyond the simplest neutral (Moffat 1969), magnetohydrodynamic (MHD) (Taylor 1974) or at best, barotropic multi-fluids (Mahajan & Lingam 2015;Steinhauer et al 2001).…”