There are several articles where you may find details of how to do this. I could suggest you, "Particle densities for three hollow cathode discharge configurations" Rev.Mex.Fis. V.38,No.2, pp910, or, "Metal Vapor Lasers" Opt. Pura y Aplicada, V. 26, No. 3, pp783.. By far one of the finest references is the book, "Principles of Laser Plasmas",Edited by, George Bekefi, Wiley Interscience 1976, in particular Chapter 13, "Spectroscopic Diagnostics of Laser Plasmas".

A good way to measure the plasma electron density is by looking at the atomic H-beta line at 486.1 nm. The FWHM of this line is dominated by Stark broadening

I use a look-up table (from Gigosos & Cardeñoso http://iopscience.iop.org/0953-4075/29/20/029 ). Here is the data for the table:

log10ne={20, 20.33, 20.67, 21, 21.33, 21.67, 22, 22.33, 22.67, 23, 23.33, 23.67, 24, 24.33, 24.67} in units of m^-3

fwhm_Hbeta={3.63e-2, 6.19e-2, 1.14e-1, 2.05e-1, 3.59e-1, 6.17e-1, 1.05, 1.77, 2.97, 4.98, 8.49, 14.4, 24.0, 39.9, 65.6} in units of nm

So a plasma with ne = 10^22 m^-3 has a Hbeta FWHM of 1.05 nm.

Electron temperature can be determined from line ratios, but it is model dependent ( is your plasma in an equilibrium or not).

A Doppler broadening measure of neutral H temperature is also possible but it is typically smaller than the Stark broadening requiring a careful deconvolution of the instrument function, the Lorentzian due to the Stark broadening and the Gaussian due the thermal Doppler broadening. This requires very high spectral resolution and low noise on the signal.

As for vibrational modes of H2, I believe that the molecular state can only exist steady state for very cold plasmas < 1 eV, so molecular lines may not be observable unless there is a region with a high rate of influx of cold H2 molecules.

I hope that helps!

You can use for Ne diagnostics a NED (Ne diagnostics) program, which is described in http://dx.doi.org/10.1016/S0584-8547(02)00015-0. If you can not download program, please send me request by mail. Description of this and other methods you can find in http://dx.doi.org/10.1016/j.sab.2004.02.005.

In atomic spectra:

You can calculate electron density by using FWHM of a non-self-absorbed line like the H alpha line at 656.27 nm. It is relatively good spectral line since it is related to air line, this choice is good provided that the analyzed sample doesn't contain hydrogen. FWHM = (2wne)/(10^16) .

Another way for calculation of electron density is using the line shifts provided that your spectrometer be calibrated.

Gas temperature can be calculated from the common methods of 2 lines ratio or Boltzmann plot technique.

The ionic concentrations can be evaluated by Saha-Eggert equations. In equilibrium condition the gas temperature and electron temperature is assumed equal.

For estimating vibrational temperature you must use the data of molecular spectrum.

Furthermore, the details of above calculations is inserted in the books of :

(1) Handbook of Laser-Induced Breakdown Spectroscopy, by Cremers & Radziemski.

(2) LASER-INDUCED BREAKDOWN SPECTROSCOPY (LIBS) Fundamentals and Applications by MIZIOLEK.

(3) Laser-Induced Breakdown Spectroscopy Fundamentals and Applications. by Reinhard Noll.

by using the Boltzman equation or simpler form, i.e. the fokker planck equation.

There are various methods to measure these different parameters. However one needs to be very careful about the validity range (I.e. assumptions behind the methods) of these techniques. There is no way to propose specific methods without any 'a priori' knowledge of the plasma. For instance pressure, power density, driving frequency and so on... which will give ideas about the electron density and temperature, as well as various departures from equilibrium (LTE, Boltzmann for rotational and vibrational states, Maxwellian equilibrium for the electrons and so on).

For instance Stark broadening is valid only for electron densities of 10e19m-3 and above (altough extension are possible towards lower pressures). Boltzmann plots on the other hand are usually dubious. For electronic/vibrational states certainly and for rotational states only the first rotational states can be used to obtained an estimation of the gas temperature... Using the ratio of only two lines should not be done as there is no way to check whether the results have any accuracy and systematic errors are not assessed...

Best regards,

E. Carbone

N Bundaleska, D Tsyganov, R Saavedra, E Tatarova, F M Dias, C M Ferreira , Hydrogen production from methanol reforming in microwave "tornado"-type plasma

International Journal of Hydrogen Energy

Also read on optical emission spectroscopy

http://www.oxford-instruments.com/products/spectrometers/optical-emission-spectroscopy

Stark broadening of H-alpha line for electron density? doi:10.1088/0963-0252/24/3/034001

H-alpha (H𝛼) is the excitation of the atomic hydrogen and emits a wavelength of approximately 656 nm in the optical spectrum that corresponds to the transition of the electron from 𝑛 = 3 to 𝑛 = 2 .

"...línea de emisión del hidrógeno atómico, H𝛼, con longitud de onda de λ=656,3nm. La intensidad de está línea da una idea del grado de ionización del hidrógeno." [Labanca ARC et al.]

Article Simposio A: Reología Y Mecánica de Fluidos y Procesamiento. ...

"H𝛼 is formed when hydrogen is ionized and the peak intensity increases with the DC power" [ Shih-Hao Chan, Shih-Fang Liao, Hung-Pin Chen, Hung-Sen Wei, Sheng-Hui Chen, Cheng-Chung Lee and Chien-Cheng Kuo. Spectral Monitoring CH/C2 Ratio of Methane Plasma for Growing Single-Layer Graphene on Cu. Hindawi Publishing Corporation. Journal of Nanomaterials Volume 2015, Article ID 423237, 5 pages. 2015.]

Understanding the calculation of electron density, electron temperature, gas temperature, species concentrations, vibrational temperature, and atomic hydrogen concentration in non-equilibrium hydrogen plasma requires theoretical understanding, experimental techniques, and computational methods. Diagnostic techniques like Langmuir probes, microwave interferometry, and Thomson scattering are used for electron density and temperature determination. Gas temperature can be measured using rotational or vibrational spectroscopy. Species concentrations are determined using spectroscopic techniques like optical emission spectroscopy for hydrogen. Vibrational temperature is derived from vibrational bands in emission spectra. Atomic hydrogen concentration can be inferred from optical emission spectra. Practical understanding often comes from theoretical knowledge and hands-on experience with experimental setups and data analysis. Online resources and academic journals can provide updates on the field. https://link.springer.com/article/10.1140/epjd/s10053-021-00186-5

https://www.researchgate.net/publication/262000879_Determining_electron_temperature_and_electron_density_in_moderate_pressure_H2CH4_microwave_plasma

https://www.researchgate.net/publication/230985068_An_Easy_Way_to_Determine_Simultaneously_the_Electron_Density_and_Temperature_in_High-pressure_Plasmas_by_using_Stark_Broadening

https://digitalcommons.odu.edu/cgi/viewcontent.cgi?article=1135&context=ece_fac_pubs

https://iopscience.iop.org/article/10.1088/1361-6463/ac5e1c/ampdf