On the initiation of a corona discharge near the surface of a nonlinearly oscillating liquid layer on the surface of a charged hailstone

An expression is derived for the electric field strength near a wet hailstone in an approximation quadratic in the oscillation amplitude of a charged liquid layer on its surface. It is found that the electric field strength in a small neighborhood of the capillary wave crests grows with the number of a mode governing the initial deformation of the equilibrium (spherical) shape of the liquid layer. Even if the charge is small (when the Rayleigh parameter of the hailstone equals one-hundredth of the value critical for stability against the self-charge), the electric field near the hailstone is high enough for initiating a corona discharge in its vicinity.