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Transformation of Canonical Helicity under the Collision and Merging of Two Magnetic Flux Ropes


Magnetic helicity, a measure of the linkage of magnetic field lines, has long been used in the contexts of astrophysical and experimental plasmas because, for highly conductive plasmas, it is a conserved quantity. In this experimental study, the dynamics of two magnetic flux ropes and the magnetic reconnection that occurs between them is used as a proving ground for helicity conservation theory. A magnetic flux rope is a twisted bundle of magnetic field lines that is ubiquitous in space and solar plasmas. Two magnetic flux ropes are created in the Large Plasma Device (LAPD) using a lanthanum hexaboride (LaB6) cathode that injects current along a background, magnetic field. The flux ropes are kink unstable, causing them to collide. As they collide, the field lines diverge, and a quasi-separatrix layer (QSL) forms. The QSL is an indicator of magnetic field line reconnection. Helicity conservation is examined inside the QSL. Two types of helicity are considered: relative magnetic helicity, which is a standard formulation, and relative canonical helicity, an extension. Three-dimensional measurements of plasma density (ne), electron temperature (Te), plasma potential (ϕp), the magnetic field (B), and ion flow (vflow) are required to evaluate each terms that appear in the extended formulation of helicity. In the magnetohydrodynamic (MHD) limit, the transport of relative magnetic helicity and the dissipation of relative magnetic helicity do not balance. Using relative canonical helicity, the dissipation of relative canonical helicity is balanced by the transport of relative canonical helicity into the QSL – such that the temporal derivative of the quantity is zero. The electrostatic field is the key term that balances helicity. It is ignored in the standard model of helicity. In this experiment, the electrostatic component of the electric field is large compared to the induced electric field produced by reconnection; and therefore, it should not be ignored in other circumstances.

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