Boltzmann plot technique is only an approach to relate the spectra to the level population. This can always be done. What you do not know is the ground state, therefore it is not possible to determine the distribution and as a consequence the temperature. Moreover, you can measure the electron gas properties through Stark broadening, but there is no correlation with the gas temperature. 

Even if you have a Boltzmann distribution from the spectra, you are missing information on the ground state and therefore you cannot say that the plasma is in equilibrium.

I have attached a reference showing the evolution of the distributions in the plasma under LIBS conditions.

Can you please elaborate on what you mean by not being able to see the ground state? We are able to see the dv=0 and dr=0 peaks in our spectra, which should be able to act as ground state for each of their respective transitions. What else do we need to be able to use a Boltzmann plot and extract temperatures from it?

Is the lack of ground state information due to it being nonequilibrium, or is it something inherently missing in OES spectra?

It is inherently missing from OES, because you can see only levels that emit transitions. As a consequence, the ground state, that is the lowest level in the system, does not emit any radiation, therefore you cannot measure it, not with OES. You could youse different techniques like Laser induced Fluorescence. Also other levels cannot be observed, such as  metastable states, that are not optically coupled to the ground state. This is the example of triplet state in He and the triplet A state in N2. 

In any case, you cannot relate the internal temperature to the gas temperature, unless you make and assumption of equilibrium. The paper I attach in the previous answer shows that high level energy follow the boltzmann, but the ground state not.

Moreover, we have shown that internal and gas temperature are not equal.

To elaborate further on what Gianpiero explained in as plain terms as I can :

A plasma may be  'steady-state' or it can be quite transient. In principle collisions will tend to  thermalize it, which means ultimately a Boltzman level distribution with a temperature equal to the electron temperature. But this can take a LONG time on the timescale of the plasma lifetime, i.e. it may NEVER materialize. 

You may have heard of LTE and coronal regimes; these are two extremes, LTE means a fully thermal local thermodynamic equilibrium(high density, low T, collision dominated plasma) and coronal(high T, low density, radiation dominated) means practically all population is in the  ground state. In real life high n levels tend to follow LTE(because collisions are stronger-in very simple terms it is easier to  hit an extended target than a more compact one as the ground state) and low-lying ones tend to follow coronal. Otherwise said, high n levels tend to equilibrate(reach LTE) quickly and low-lying ones very slowly or never. So this means that in theory you might be able to use a Boltzman plot from high levels alone. Practically however the quastion is : Do you have enough population in these  high levels to observe anything?

Gianpiero, back to your first statement. You state that the Boltzmann plot technique relates the level populations to the spectra but without the ground state the distribution cannot be found (and the subsequent temperature). But I thought the whole reason you were to use the Boltzmann plot technique was to find gas temperature? From my understanding of what you have said, why would anyone use the Boltzmann plot technique? (I think/know I'm misunderstanding you)

And my original question I guess goes beyond just the Boltzmann plotting technique. I'm also wondering, if I know I have a non-equilibrium plasma can I use programs like BOLSIG+ to gain information about the electron mobility, etc.? 

S. Alexiou, one of our plasma systems is a corona discharge, which is not at all LTE like BUT I've seen authors use the Boltzmann plotting technique to measure the gas temperature (they also do it on DBDs and spark discharges). Their justification is that the collision frequency is much greater than the radiative decay probability of the excited state. Is this the same thing as the McWhirter criterion? Is it not then LTE if it satisfies this (which we know DBDs, coronas and sparks are not)? 

And yes, the intensity of light is very low. This is an onward battle. 

Dear James,

You are posing many problems, all related to the non-LTE, but discussing different aspects. The theoretical approach related to Boltzmann plot technique is the collisional-radiative model, you find an example in the paper I have attached in my first answer.

Doing research, both theoretical and experimental people have to make approximations. In most of the cases these approximations are not the same. This is the case Boltzmann plot technique and collisional radiative models. In the first one, the LTE is considered when conditions allow it, in particular when the density is large enough. 

In collisional radiative models, the internal transitions are leaded by electron collisions and radiative decays (also recombination should be included). Therefore the level population is related to Te and not to Tgas. To match these two points of view, a further assumption is made i.e. Te=Tgas, because, transitions induced by atom-atom interactions have smaller rate with respect to the corresponding transition induced by electron collisions. People making experiments observe a Boltzmann distribution using the Boltzmann plot technique. From this conditions they consider LTE. But there are levels that are not observed such as the ground state and metastable states. As I have shown in my paper, this extension is not possible. What can you deduce from this? LTE is not a valid assumption. Moreover in the paper I have shown you, we have seen that assuming Te=Tgas, does not lead to the right ionization degree. Now, there are many possible reason, not only the one I was suggesting that Te

James, like I said  high enough levels are probably LTE  AMONG THEMSELVES (not with the ground state!) even at very low densities. (whether they have enough intensity, i.e. population to be observed is another question as discussed)

The  comment on the collision frequency(though I 'm not sure what exaty you are referring to) is to be understood as follows: A 'collision'

means  a particle coming close enough to have an appreciable probability of inducing a transition, e.g. n=5->n=6. Because such states  have a large wavefunction extent and are rather loosely bound, they basically have large cross-sections for such events. 

So yes, you can have  high n levels in LTE among themselves, e.g. the  RELATIVE populations of n=5 and n=6  agreeing with a Boltzman prediction and low-lying levels in corona among themselves.

That, however does NOT mean that

if population of n=6/population of n=5=exp(-DE_65/KT)

then population of n=5/population os GS =exp(-DE_50/kT)

with DE_ij the energy difference

If now you have  reliable measurements from say n=5,6,7 and 8 and your data support a Boltzman LTE hypothesis, then you can say that high n levels are in LTE with such a 'Temperature'

For any plasma parameter measurement, LTE criteria must be satisfied that is

most basic McWhirter's criterion must be satisfied, that says

ne ≥ 1.6 *10^12 T^(1/2) ∆E^3