Certainly the molecules in the immediate vicinity of the discharge will be in a variety of highly-excited states, including ionized, electonically-excited, dissociated or even atomized. However, the fraction of such molecules will drop off quite steeply as you move away from the core of the discharge, so you will quickly be dealing with essentially pure, unperturbed gas molecules. Note that I am talking about the state at some hypothetical t=0 time, occurring a few nanoseconds or so after the discharge, so that "fast" processes like vibrational relaxation and/or dissociation of electronically excited or ionized states is essentially complete, but that bulk phenomena like shock-wave propagation haven't gotten started yet. This *seems like* a logical separation to make, but I am not an expert on shock-waves, and so I may be assuming too much. One guy who has done a lot of work on this sort of thing is Dana Dlott at the University of Illinois .. you might want to look up his papers.

With that caveat, I am happy to speculate a bit, but please realize that these are just educated guesses. I think that a good rough approximation would simply be to define some "hard-cylindrical boundary" and state that outside of it, the gas is unperturbed, and then use whatever model you are using to describe the excited gas molecules. As to what value of gamma to use inside such a "boundary", I am not really sure ... again, as a rough approximation, you could neglect the vibrational excitation and simply use the estimates of 7/5 for N2 and 4/3 for methane (and most of its fragments, if you are explicitly considering species created by dissociation of methane .. but that gets complicated fast), based on the non-vibrational degrees of freedom. Of course, at the high temperatures that you probably need to consider, neglecting the vibrational degrees of freedom is a poor approximation, but at least you could consider those values to be upper limits for gamma. Note that i am also not sure how to combine gamma values for pure gases when dealing with mixtures .. I guess a mole-fraction bases weighting is a good first approximation, but I suppose there could be significant deviations, particularly under extreme non-equilibrium conditions like you are dealing with.

I hope that helps a bit ... I guess my preferred approach would be to treat gamma as a free, temperature-dependent parameter, and then fit my simulations to experimental data, but I understand that not may be possible for you.

David, thanks for your detailed input. Indeed, my shock propagation model assumes, for now, that the gas ahead is unperturbed, allowing for T-dependent vibrational degrees of freedom. In parallel with the shock model, I tried to obtain a plausible value for gamma by including the dissociation-ionization of N2 and CH4. For N2, this is fairly straightforward. For CH4, on the other hand, I think I pushed the limits of "plausibility" by assuming the reaction CH4->C+4H. In that case, I obtained gamma = 1.1 at 30,000K and gamma=1.45 at 95K, for the mixture. Based on answers to another RGate question, I should stop at CH4->CH3+H->CH2+2H. Also, it seems that HCN formation alters the internal energy quite a bit, so I may have to include it.

As for the order in which dissociation and shock formation occur, I am still confused. There is some initial ionization that enables the stepped leader, then the return stroke occurs and the "discharge" (and most probably the shock) starts. I agree that the high discharge energy will break apart and ionize molecules/atoms. But part of that energy is released as photons which, as I see it, may travel ahead of the shock wave and ionize the gas in front of the latter. I could not find any references addressing this.

Also, thanks for mentioning Dana Dlott - I will look up his work.

Andi, with respect to your concern about the photon front, I tried to address that in my first post .. sorry if it wasn't clear. The "hard UV" light you are talking about has a very high cross-section for absorption in the atmosphere (that's why it is also known as vacuum UV), so it will be attenuated much more rapidly than the shock-wave itself. My suggestion was therefore to just set the edge of the "cylindrical boundary" I mentioned at the edge of where the UV intensity has been attenuated to the point where the fraction of ionized or dissociated molecules is basically zero. You can look up some references on propagation of vacuum UV through air to estimate how far the appropriate propagation length might be, but my guess is that it wouldn't be more than a few mm or so (depending on the initial intensity of course). In any case, I would expect that the propagation length of the UV is many orders of magnitude shorter than that of the shock-wave.

Hope that helps clarify my earlier comments.

David, thank you! This bit of information on the UV absorption rates is quite helpful to my model. Knowing that the shock wave propagates into an unperturbed medium helps a lot simplifies the problem.

During my graduate work on sprites, jets, etc, I got interested in excited state chemistry in the middle atmosphere and found the following reference to be really helpful:

Mario Capitelli, Ettore Molinari, "Kinetics of dissociation processes in plasmas in the low and intermediate presssure range" Plasma Chemistry II, Topics in Current Chemistry Volume 90, 1980, pp 59-109. doi: 10.1007/BFb0048494