Sausage instabilities on top of kinking lengthening current-carrying magnetic flux tubes

Abstract

We theoretically explore the possibility of sausage instabilities developing on top of a kink instability in lengthening current-carrying magnetic flux tubes. Observations indicate that the dynamics of magnetic flux tubes in our cosmos and terrestrial experiments can involve topological changes faster than time scales predicted by resistive magnetohydrodynamics. Recent laboratory experiments suggest that hierarchies of instabilities, such as kink and Rayleigh-Taylor, could be responsible for initiating fast topological changes by locally accessing two-fluid and kinetic regimes. Sausage instabilities can also provide this coupling mechanism between disparate scales. Flux tube experiments can be classified by the flux tube's evolution in a configuration space described by a normalized inverse aspect-ratiok and current-to-magnetic flux ratioλ. A lengthening current-carrying magnetic flux tube traverses thisk -λ space and crosses stability boundaries. We derive a single general criterion for the onset of the sausage and kink instabilities in idealized magnetic flux tubes with core and skin currents. The criterion indicates a dependence of the stability boundaries on current profiles and shows overlapping kink and sausage unstable regions in thek -λ space with two free parameters. Numerical investigation of the stability criterion reduces the number of free parameters to a single one that describes the current profile, and confirms the overlapping sausage and kink unstable regions ink -λ space. A lengthening, ideal current-carrying magnetic flux tube can therefore become sausage unstable after it becomes kink unstable.

Experiments relevant to astrophysical jets

“…https://doi.org/10.1017/S002237781800079X Downloaded from https://www.cambridge.org/core. IP address: 44.224.250.200, on 11 Aug 2020 at 10:11:33, subject to the Cambridge Core terms of use, available at fields shows that the kink is destabilized before the sausage; see von der Linden & You (2017).…”

“…Copyright 2009 by the American Physical Society.] fields shows that the kink is destabilized before the sausage; see von der Linden & You (2017).…”

“…The sausage instability has symmetry whereas the kink has symmetry. A plot of the threshold for sausage and kink instabilities in a plasma having both poloidal and toroidal magnetic fields shows that the kink is destabilized before the sausage; see von der Linden & You (2017).…”

Determination of a macro- to micro-scale progression leading to a magnetized plasma disruption

“…For example, a computational study on current-driven instabilities that used a 3D particle-incell code predicted the possibility of a sausage-to-kink cascade in the context of high energy particle production by a dense plasma focus [17]. Similarly, a recent analytic study by Von der Linden and You [18] suggested a current-driven instability cascade but in an opposite path, i.e., as a kink-to-sausage cascade. These studies suggest that if an MHD cascade results in progressively ner scales, the ion inertia scale and its associated fast non-MHD reconnection might be accessed.…”

Measurements of the Canonical Helicity of a Gyrating Kink

“…Studies suggest that there may also be minimum energy states subject to the conservation of fluid helicity [7] and canonical helicity [8][9][10][11], the weighted sum of helicities of magnetic and flow vorticity flux tubes. The dynamics of these relaxation processes can develop microscales, e.g., when flux tubes undergo instability cascades [12][13][14]. At these microscales, ion inertia, kinetic distribution functions, and finite Larmor radius effects become important, allowing ions and electrons to separate from the magnetic flux, which limits the usefulness of magnetic flux tubes for understanding relaxation dynamics.…”