I have seen in most of the plasma physics textbooks the temperature versus pressure graph as shown attached with this question.
The graph as attached in this question is useful to explain the transition of a non-thermal plasma to thermal plasma. For non-thermal plasma, Te>>Tg whereas for thermal plasma Te~Tg.
The attached graph with this graph is not a real plot. It was sketched for understanding by Prof. Alan Howling. Did anybody try to obtain it through calculations ?
I would be happy for your answers and interested to obtain it with some graphical softwares like MATLAB.
The transition can be shown by plasma simulation with the help of the kappa distribution law.
As the kappa-value tends to infinity, the plasma gets transformed into thermal state (kappa infinite) from the previous nonthermal state (kappa infinite).
Dear Prof. Karmakar,
Looking at your answer, I searched for Kappa distribution law. I have not found the relation that relates temperature with pressure values. Could you please suggest the reference for this plot ?
If you have experience obtaining this plot with some softwares, could you please let me know that ?
That is probably because a pT diagram won't tell you much about the plasma state (i.e. thermal/non thermal). What counts here is rather the collisionality or the mean free paths of your particles in comparison with the lifetime of the plasma. This is because thermalisation needs a lot of collisions that distribute the energy evenly. Also the adiabatic coefficient doesn't help you much because it is only related to the degrees of freedom of the particles that the plasma consist of.
I would generally say (for all the species in your plasma) that the criterion for thermalisation is: tcoll
Dear Prof. Johannes Gruenwald,
Thank you for the explanation. I understand your criterion. But, most of the plasma physicists use this definition for defining the concept of thermal/non-thermal plasma. I want to plot this graph myself. Lets discuss on this issue.
But this graph is totally abitrary without any real physical meaning. If this graph would show a physical law you would not be able to create cnon thermal atmospheric pressure plasma. You have to read the graph like this: If you have high pressure (which means high collisionality) and Te~Ti then you have a thermal plasma. But there is no description of a mathematical nature how you get there.
You can derive the ratio of Te/Theavyparticle via the momentum and energy law as it was originally done by Maecker & Co. Then you obtain a quadratic equation depending on E/p. In other words: If it deals with a discharge then the pressure is not enough and you have to add E (electric field). Te/ThP then depends on repsective cross sections which builds the bridge to the species that you use. The respective equation can also be found in my habilitation (chapter 5) including a list of relevant plasma systems against which I verify the equation (on basis of measured data)
Thanks Prof. Johannes Gruenwald
Dear Prof. Georg Herdrich
Are you talking about this formula (attached with the reply) ?
I have found this formula in some references. But, still wondering how this formula can give the similar plot.
Will you please give us the full reference you are talking about ?
Yes, Georg's answer is in my opinion the best way to go - The works of Maecker are indeed a good starting point.
Yes, but this version appears to be quite simplifies. Either look up Maecker or my Habilitation.......
Dear Dr. Bhagirath Ghimire,
Thanks a lot for your interest.
Please see my RG profile for further details if required.
A good number of works could be found therein.
Please feel free to write to me if and whenever any problem arises in this context.
Kind regards,
Pralay Kumar Karmakar
It is a fact that non-thermal plasmas are indeed inhomogeneous anti-equilibrium in nature due to the presence of diversified gradient force influences. Theoretically, one can see the transition from the non-thermal to thermal plasma nature in a generalized picture even without using any traditional kind of nonthermal non-extensive thermostatistics. It is possible by nullifying all the inhomogeneity effects initially considered in the analytical or numerical calculation schemes. Exploring the reverse case of the simplified-to-generalized transition, however, is not possible.
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