Semianalytical models of sprite formation from plasma inhomogeneities

A spherical plasma inhomogeneity located at mesospheric altitudes in a thundercloud quasi-electrostatic field is considered as a possible cause of sprite formation. A simple semianalytical model of ionization instability in a quasi-electrostatic field, the value of which is larger than the air breakdown value, is developed on the assumption that plasma ball conductivity is controlled by impact ionization and electron attachment to neutrals. After several simplifications, the problem is reduced to a system of ordinary differential equations for the average conductivity and plasma ball radius. The analytical estimates and numerical simulation indicate that the predicted expansion rate and acceleration of the plasma inhomogeneity boundary are close in magnitude to the values observed during high-speed imaging of sprite development.