McWhirter Criterion for Local Thermodynamic Equilibrium — mcwhirter

Computes the minimum electron density required for local thermodynamic equilibrium (LTE) by the McWhirter criterion, and checks a measured density against it.

Usage

mcwhirter_criterion(temperature, delta_e, electron_density = NULL)

Arguments

temperature: The plasma temperature, in K.
delta_e: The largest energy gap between adjacent levels, in eV.
electron_density: An optional measured electron density, in cm$^{-3}$.

Value

A tibble with the temperature, delta_e, minimum_density (cm$^{-3}$) and, if electron_density is given, the density and whether the criterion is satisfied. The inputs are recycled to a common length.

Details

$$N_e \geq 1.6 \times 10^{12}\, T^{1/2} (\Delta E)^3\ \mathrm{cm^{-3}}$$ with $T$ in K and $\Delta E$ (eV) the largest energy gap between adjacent levels of interest. The criterion is necessary but not sufficient: in transient and inhomogeneous plasmas such as those of LIBS, LTE also requires that equilibration be faster than the plasma evolution and diffusion (Cristoforetti et al., 2010).

References

McWhirter, R.W.P. (1965). Spectral intensities. In Huddlestone, R.H., Leonard, S.L. (eds.), Plasma Diagnostic Techniques, Academic Press, New York, pp. 201-264.
Cristoforetti, G., et al. (2010). Local thermodynamic equilibrium in laser-induced breakdown spectroscopy: beyond the McWhirter criterion. Spectrochimica Acta Part B, 65(1):86-95.

Examples

mcwhirter_criterion(temperature = 10000, delta_e = 3.12, electron_density = 1e17)
#> # A tibble: 1 × 5
#>   temperature delta_e minimum_density electron_density satisfied
#>         <dbl>   <dbl>           <dbl>            <dbl> <lgl>    
#> 1       10000    3.12         4.86e15             1e17 TRUE