What's the difference between the two temperatures in plasmas? Can someone give me the definition? and in which case the two temperatures can be considered equal.? Thank you very much.
Electron temperature in defined to be a temperature of free electrons.
Excitation temperature- coefficient in the Boltzmann distribution across the energy levels.
The temperatures coincide, when the collisions between heavy particles and electrons rule the excitation dynamics for the electronic levels. For atoms, this is incorrect if the radiation has a significant effect on the depopulation of the levels.
The recombination/ionization due to the collisions is more probable for higher levels, and therefor only the distribution temp across them coincides with the temp of the free electrons. If radiation is the only process disturbing the collisional kinetics, you can take that for levels with Ioniz. potential-E>Ecr, temperatures are equal. Ecr[eV]=(Ne[cm-3]/4.5e13)^0.25*(Te[eV]^-0.125)
As Ivan Alexandrovich Moralev mentioned, the excitation temperature is a parameter describing population of excited energy levels by means of Boltzmann distribution. Since non-thermal plasmas (NTP) only can exist if there are either strong spatial gradients or temporal variations (transients) of plasma parameters impeding establishment of thermal equilibrium, the excitation temperature very often does not make any sense in case of NTP, simply because the rates of excitation collisions and superelastic (de-excitation) collisions are far from equilibrium.
In general, the same applies for the electron temperature: The electron temperature is a parameter in the Maxwellian velocity distribution function of electrons. However, in case of NTP the velocity distribution function is not Maxwellian. Often in case of NTP the term "electron temperature" is related to the mean electron energy of the non-thermal distribution function: T_e = 2/3 E_mean. Nevertheless, using this temperature in Maxwellian electron velocity distribution function would be misleading if e.g. electron collision excitation or ionization rates were calculated based on this distribution function.
Thus I would avoid utilizing temperatures for characterization of NTP.
In non-thermal plasmas, also the excitation temperature is misleading, because also internal distributions are not a Boltzmann. In non.thermal plasmas, often the gas temperature is much lower that electron temperature, this is one of the source of non-equilibrium. Another possible source of non-equilibrium is the radiation losses.
In case of non-equilibrium distribution, the temperature is not uniquely defined, and different definition are possible. For level distribution it is possible to define the temperature from the mean energy or from the Boltzmann distribution fitting a group of levels. For electrons another possible definition is the Einstein relation KT=diffusion/mobility.
From the spectroscopical point of view, the assumption that excitation and free electron temperatures are equal is commonly considered.
https://books.google.iq/books?id=ZzmtGEHCC9MC&pg=PA4&lpg=PA4&dq=difference+between+the+electron+excitation+temperature+and+the+electron+temperature+in+plasmas,+especially+in+non-thermal+plasmas?&source=bl&ots=YhkDAdmV7h&sig=ElMZEF_bkklhsd1rLtHd2EFxolI&hl=ar&sa=X&ved=0ahUKEwjCq93K0OPTAhVJCsAKHVXgDckQ6AEIOjAC
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