Spectral line ratios

The emission intensity density of an atomic transition from the upper state to the lower state is:^[1]

$${\displaystyle P_{u\rightarrow l}=N_{u}\ \hbar \omega _{u\rightarrow l}\ A_{u\rightarrow l}}$$ 

where:

• ${\displaystyle N_{u}}$  is the density of ions in the upper state,
• ${\displaystyle \hbar \omega _{u\rightarrow l}}$  is the energy of the emitted photon, which is the product of the Planck constant and the transition frequency,
• ${\displaystyle A_{u\rightarrow l}}$  is the Einstein coefficient for the specific transition.

The population of atomic states N is generally dependent on plasma temperature and density. Generally, the more hot and dense the plasma, the more the higher atomic states are populated. The observance or not-observance of spectral lines from certain ion species can, therefore, help to give a rough estimation of the plasma parameters.

More accurate results can be obtained by comparing line intensities:

$${\displaystyle {\frac {P_{u_{1}\rightarrow l_{1}}}{P_{u_{2}\rightarrow l_{2}}}}={\frac {N_{u_{1}}\omega _{u_{1}\rightarrow l_{1}}A_{u_{1}\rightarrow l_{1}}}{N_{u_{2}}\omega _{u_{2}\rightarrow l_{2}}A_{u_{2}\rightarrow l_{2}}}}}$$ 

The transition frequencies and the Einstein coefficients of transitions are well known and listed in various tables as in NIST Atomic Spectra Database. It is often that atomic modeling^[2] is required for determination of the population densities ${\displaystyle N_{u_{1}}}$  and ${\displaystyle N_{u_{2}}}$  as a function of density and temperature. While for the temperature determination of plasma in thermal equilibrium Saha's equation and Boltzmann's formula might be used, the density dependence usually requires atomic modeling.

• Plasma diagnostics
• Spectral line

• NIST Atomic Spectra Database

• Latimer, I; Mills, JI; Day, RA (1970), "Refinements in the helium line ratio technique for electron temperature measurement and its application to the precursor", Journal of Quantitative Spectroscopy and Radiative Transfer, 10 (6), Elsevier: 629–635, Bibcode:1970JQSRT..10..629L, doi:10.1016/0022-4073(70)90079-8
• Muñoz Burgos, JM; Barbui, T; Schmitz, O; Stutman, D; Tritz, K (2016), "Time-dependent analysis of visible helium line-ratios for electron temperature and density diagnostic using synthetic simulations on NSTX-U", Review of Scientific Instruments, 87 (11), AIP: 11E502, doi:10.1063/1.4955286, OSTI 1259296