Hall instability of solar flux tubes

Abstract

The magnetic network which consists of vertical flux tubes located in intergranular lanes is dominated by Hall drift in the photosphere-lower chromosphere region ($\lesssim 1Mm$). In the internetwork regions, Hall drift dominates above $0.25Mm$ in the photosphere and below $2.5Mm$ in the chromosphere. Although Hall drift does not cause any dissipation in the ambient plasma, it can destabilise the flux tubes and magnetic elements in the presence of azimuthal shear flow. The physical mechanism of this instability is quite simple: the shear flow twists the radial magnetic field and generates azimuthal field; torsional oscillations of the azimuthal field in turn generates the radial field completing feedback loop. The maximum growth rate of Hall instability is proportional to the absolute value of the shear gradient and is dependent on the ambient diffusivity. The diffusivity also determines the most unstable wavelength which is smaller for weaker fields. We apply the result of local stability analysis to the network and internetwork magnetic elements and show that the maximum growth rate for kilogauss field occurs around $0.5Mm$ and decreases with increasing altitude. However, for a $120G$ field, the maximum growth rate remains almost constant in the entire photosphere-lower chromosphere except in a small region of lower photosphere. For shear flow gradient $\sim 0.01s^{-1}$, the Hall growth time is 10 minute near the footpoint. Therefore, network fields are likely to be unstable in the photosphere, whereas internetwork fields could be unstable in the entire photosphere-chromosphere. Thus the Hall instability can play an important role in generating low frequency turbulence which can heat the chromosphere.

8 page, 4 figures

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• Evolution of small-scale magnetic elements in the vicinity of granular-size swirl convective motions
• Can Hall effect trigger Kelvin-Helmholtz instability in sub-Alfvenic flows?
• The non-ideal finite Larmor radius effect in the solar atmosphere
• Surface Wave Propagation in non--ideal plasmas
• Alfven wave coupled with flow-driven fluid instability in interpenetrating plasmas
• Surface Waves in the paritally ionized solar plasma slab
• Viscous Heating and Instabilities in the Partially Ionized Solar Atmosphere
• Hall-magnetohydrodynamic waves in flowing ideal incompressible solar-wind plasmas: Reconsidered