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A two-fluid helicity transport model to explain bifurcation in counter-helicity merging

Author: Setthivoine You
Requested Type: Consider for Invited
Submitted: 2012-12-07 14:26:39

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University of Washington
3795 E Stevens Way NE
Seattle, WA   98195
USA

Abstract Text:
Experiments have observed that, upon merging, two spheromaks with opposite magnetic helicities form one of two single compact torus configurations: another spheromak or a field-reversed configuration (FRC) [1]. The end state depends on whether the initial experimental poloidal eigenvalue, normalized to the Taylor state eigenvalue, is above or below a threshold. The threshold is measured to be proportional to 1/S*, where the size parameter S* is the ratio of the ion skin depth to the system size. A recent model of relative canonical helicity transport [2] derives this measured threshold from first principles by generalizing familiar concepts of magnetic helicity transport to each species' canonical momentum helicity transport. Canonical momentum is the sum of mechanical momentum with the magnetic vector potential. Canonical vorticity is the circulation of canonical momentum, i.e. the sum of flow vorticity and magnetic field. In this model, a tube of magnetized plasma can be thought of as a superposition of a magnetic flux tube and a (flow) vorticity flux tube, or equivalently, a superposition of electron and ion canonical vorticity flux tubes. Any enthalpy difference imposed at the ends of the tubes will inject canonical helicity, and as the size parameter S* increases, a given enthalpy difference will channel canonical helicity increasingly into the magnetic flux tube component. In two-fluid flowing equilibria of compact plasmas, a FRC corresponds to a minimum energy state with finite ion canonical helicity but no electron canonical helicity, and a spheromak corresponds to a minimum energy state with only finite magnetic helicity [3]. A FRC can therefore be represented by a toroidal canonical flux tube dominated by the vorticity flux tube component with a weak magnetic flux tube component. A spheromak is a canonical flux tube dominated by the static magnetic component with a negligible vortex component, so any canonical helicity injection channeled preferentially into the magnetic flux tube will form a spheromak. The size parameter determines the channeling ratio. For a given S*, if the initial poloidal eigenvalue is above the threshold, helicity injection will preferentially be channeled into the magnetic component and result in a spheromak configuration. Otherwise helicity injection will preferentially be channeled into the vortex component and result in a FRC. At high S*, such as for example in large compact torus experiments, the threshold window becomes narrower, so the poloidal eigenvalue has to be set more precisely to make a FRC from counter-helicity merging. The model also suggests a means to find new relaxed states with finite unequal ion and electron canonical helicities as suggested by Steinhauer, Yamada and Ishida [3].

[1] Kawamori et al, Nucl. Fusion, 45, 843 (2005)
[2] You, Phys. Plasmas, 19, 092107 (2012)
[3] Steinhauer, Yamada, Ishida, Phys. Plasmas, 8, 4053 (2001)

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