Phase transition theory of sprite halo

Abstract

We present the phase transition theory for sprite halo using measurable lightning parameters (charge moment and discharge time) on the basis of steady state thermodynamics. A halo is located at the upper part of the tree‐like structure of a sprite and is produced through electron impact excitation of neutral species under the lightning‐induced electric field. We proposed in our previous studies that the occurrence criteria for halos and sprites are characterized by the above lightning parameters, and additionally, the intensity of a halo weakens rapidly with an increase in the discharge time T. We assume that this phenomenon is quite similar to the phase transition between the vapor and the liquid states of water; here the analogy is between the accelerated electrons and the water molecules. We demonstrate analytically a phase transition for a simply modeled halo based on the quasistatic theory of lightning‐induced electric field. Choosing the luminosity of a halo as an order parameter, we show that it has a dependence of T−0.25 − Tc−0.25 near the critical point Tc, which is characteristic of the phase transition. Furthermore, the critical time scale Tc ≈ 5.5 ms is provided naturally from our modeling and is somewhat larger than the typical time scale of the halo luminosity in observations. We consider that this kind of formalism is useful in understanding the detailed relationship between lightning activity and occurrence of halos. We discuss this point for future observations along with the possibilities of the transition model of column and carrot structures.