Electrostatic instability of non-spherical dust in sub-stellar clouds

Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mn>0.2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1.8</mml:mn> <mml:mo stretchy="false">]</mml:mo> <mml:mtext> </mml:mtext> <mml:mi>μ</mml:mi> </mml:mrow> </mml:math> m, floating potential <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>ϕ</mml:mi> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>10</mml:mn> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> </mml:math> V and tensile strength <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">Σ</mml:mi> <mml:mrow> <mml:mtext>s</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> 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 µ m 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.