Density versus temperature freeze out of NO_x

Goldenbaum and Dickerson [1993] have recently suggested that the previously accepted mechanism for NO_x formation, whereby a high concentration of NO_x is frozen out by a rapid drop in temperature is not appropriate for lightning. They suggest that NO_x is frozen out by a rapid drop in density in the core region, causing the time constant for approach to chemical equilibrium (tau_equil.) to increase significantly. It was also suggested that the key parameter for determining the NO_x yield was the energy per unit volume deposited by the discharge and not the energy per unit length; further, they found a strong dependence of NO_x yield per unit energy on the energy density. These conclusions were based on an analysis of numerical simulations using a hydrodynamic model coupled to a chemical model consisting of the three main Zel'dovich reactions.

However we believe their conclusion that NO is frozen out by a rapid drop in density, not temperature, is not appropriate for lightning for the following reasons. Their conclusion relies on there being a rapid drop in density in the core at the temperatures at which NO could form, say 3000 - 6000 K. This was achieved in their calculations by starting the simulation with a finite energy density over a given radius. This leads to an initial temperature in the region of ca. 6000 K, combined with a high (ambient) gas density. The resulting high pressure causes a shock wave to move away from the discharge, carrying most of the gas from the channel with it. This causes a slow reduction in the temperature and a rapid drop in gas density in the core. The total NO produced rose rapidly to a peak in ca. 1 µs then dropped slowly. The calculated chemical lifetime of NO increased rapidly, freezing out a high concentration in the first few microseconds; the increase in lifetime is caused by the rapid drop in density following the onset of the integration, and not the much slower decrease in temperature of the core.

In a lightning discharge however, the rapid drop in gas density in the core is accompanied by very much higher temperatures (over 20,000 K) than found in Goldenbaum and Dickerson's calculations. For example, Plooster's calculation [1971] of the gas behaviour following a spark discharge found that shortly after the time of maximum current flow, the core temperature was 30,000 K, with a core density already as low as 1/20th of ambient. Consequently the drop in core density in lightning is accompanied by a large rise in temperature, so the lifetime of NO will actually be decreasing rapidly as the density drops, precluding any freezing out of NO at this stage of the discharge process. Therefore we would maintain that NO_x is formed by a freeze out mechanism due to the reduction in temperature in the core region.