J.-F. Ripoll

On the dynamics of hot air plasmas related to lightning discharges: 1. Gas dynamics

In this paper, we first study the dynamics of hot shocks in air in cylindrical geometry coupled to multiband radiation transport and detailed air chemistry. The wide energy and length scale ranges which are covered herein includes and exceeds the ones of first and subsequent return strokes happening during lightning discharges. An emphasis is put on the NOx production and the optical power emitted by strong shocks as the ones generated by Joule heating of the air from intense current flows. The production rate of NOx, which is useful for atmospheric global modeling, is found to be between 4.5 × 1016 and 8.6 × 1016 molecules/J for all computed cases, which is in agreement with the literature. Two different radiation transport methods are used to characterize the variability of the results according to the radiation transport method. With the exact radiation solver, we show that between 15 and 40% of the energy is lost by radiation, with a percentage between 20 and 25% for averaged lightning energies. The maximal visible peak is between 7 × 108 W/m and 3 × 107 W/m obtained for, respectively, a 19 kJ/cm and a 28 J/cm energy input. The mean radiated powers in the visible range are found between 9 × 106 W/m and 2 × 105 W/m for the energies just mentioned. We discuss the agreement of these values with previous studies.

On the time needed to reach an equilibrium structure of the radiation belts

In this study, we complement the notion of equilibrium states of the radiation belts with a discussion on the dynamics and time needed to reach equilibrium. We solve for the equilibrium states obtained using 1-D radial diffusion with recently developed hiss and chorus lifetimes at constant values of Kp = 1, 3, and 6. We find that the equilibrium states at moderately low Kp, when plotted versus L shell (L) and energy (E), display the same interesting S shape for the inner edge of the outer belt as recently observed by the Van Allen Probes. The S shape is also produced as the radiation belts dynamically evolve toward the equilibrium state when initialized to simulate the buildup after a massive dropout or to simulate loss due to outward diffusion from a saturated state. Physically, this shape, intimately linked with the slot structure, is due to the dependence of electron loss rate (originating from wave-particle interactions) on both energy and L shell. Equilibrium electron flux profiles are governed by the Biot number (τDiffusion/τloss), with large Biot number corresponding to low fluxes and low Biot number to large fluxes. The time it takes for the flux at a specific (L, E) to reach the value associated with the equilibrium state, starting from these different initial states, is governed by the initial state of the belts, the property of the dynamics (diffusion coefficients), and the size of the domain of computation. Its structure shows a rather complex scissor form in the (L, E) plane. The equilibrium value (phase space density or flux) is practically reachable only for selected regions in (L, E) and geomagnetic activity. Convergence to equilibrium requires hundreds of days in the inner belt for E > 300 keV and moderate Kp (≤3). It takes less time to reach equilibrium during disturbed geomagnetic conditions (Kp ≥ 3), when the system evolves faster. Restricting our interest to the slot region, below L = 4, we find that only small regions in (L, E) space can reach the equilibrium value: E ~ [200, 300] keV for L = [3.7, 4] at Kp = 1, E~[0.6, 1] MeV for L = [3, 4] at Kp = 3, and E~300 keV for L = [3.5, 4] at Kp = 6 assuming no new incoming electrons.