The magnetic network, which consists of vertical flux tubes located in intergranular lanes, is dominated by Hall drift in the photosphere–lower chromosphere region (≲ 1 Mm). In the internetwork regions with weak magnetic field, Hall drift dominates above 0.25 Mm in the photosphere and below 2.5 Mm in the chromosphere. Although Hall drift does not cause any dissipation in the ambient plasma, it can destabilize 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 an azimuthal field. Then, torsional oscillations of the azimuthal field, in turn, generate the radial field, completing feedback loop. The maximum growth rate of Hall instability is proportional to the absolute value of the shear gradient, and it is dependent on the ambient diffusivity. The diffusivity also determines the most unstable wavelength, which is smaller for weaker fields.
We apply the results of a local stability analysis to the network and internetwork magnetic elements and show that the maximum growth rate for a kiloGauss field occurs around 0.5 Mm and decreases with increasing altitude. However, for a 120-G field, the maximum growth rate remains almost constant in the entire photosphere–lower chromosphere, except in a small region closer to the surface. For a shear flow gradient ∼0.1 s−1, the Hall growth time is about 1 min near the photospheric footpoint. Therefore, network and internetwork regions with an intense field in the presence of shear flow are likely to be unstable in the photosphere. The weak field internetwork regions could be unstable in the entire photosphere–chromosphere. Thus, Hall instability can play an important role in generating low-frequency turbulence, which can heat the chromosphere.