Charged dust clouds play an important role in the evolution of sub-stellar atmospheres through electrical discharges such as lightning events or inter-grain discharges. The consequent plasma activation presents an alternative source of disequilibrium chemistry, potentially triggering a set of chemical reactions otherwise energetically unavailable. The aim of this paper is to address the problem of the electrostatic stability of charged spheroidal dust grains in sub-stellar clouds and its impact on inter-grain electrostatic discharges, the available area for atmospheric gas-phase surface chemistry, the particle eccentricity distribution function and observed polarization signatures. This paper has derived the criterion for the allowed values of dust eccentricity that are electrostatically stable as a function of grain size m, floating potential V and tensile strength Pa. As a consequence of electrostatic instability we also calculate the expected electric field enhancement at the spheroidal poles, the increased surface area of a dust grain, the truncation of the particle eccentricity distribution function and the resultant degree of polarization. Dust grains with an eccentricity below a critical value will be electrostatically stable; whereas, grains with an eccentricity above a critical value will be unstable. For example, for a 1 µm charged dust grain with surface potential of 1 V, the maximum allowable eccentricity is 0.987. As a consequence, electric field strength enhancement at the pole is limited to a factor of 3.5; the surface area for surface chemistry and the synthesis of chemical products is increased by a factor of 1.45; and the degree of polarization is reduced by a factor of 0.65. The results presented here are applicable not only to spheroidal dust grains but any non-spherical dust grains where non-uniform surface electric fields or inhomogeneous tensile strengths could be susceptible to electrostatic instability. In this context electrostatic erosion presents a mechanism that may produce bumpy, irregularly shaped or porous grains.
This paper examines the electrostatic stability of charged, non-spherical dust grains in sub-stellar atmospheres. It shows that dust grains with high eccentricity can become electrostatically unstable, leading to electric field enhancement, increased surface area for chemical reactions, and changes in polarization. This is important for understanding lightning, atmospheric chemistry, and dust properties in exoplanet and brown dwarf atmospheres.