Electron Density from Stark Broadening

Estimates the electron density of a plasma from the Stark width of an emission line: from the Stark broadening parameters of the line (STARK-B, or a reference width), or from the width of the hydrogen H$\alpha$ line at 656.28 nm.

Usage

electron_density(
  width,
  method = "stark",
  stark = NULL,
  wavelength = NULL,
  temperature = NULL,
  reference_width = NULL,
  reference_density = 1e+17,
  tolerance = 0.5
)

Arguments

width: The measured Stark full width at half maximum, in nm (see Details). A vector is allowed.
method: "stark" (default) or "halpha".
stark: For method = "stark": a tibble returned by starkb_lines(). Alternatively, give reference_width.
wavelength: For method = "stark" with stark: the wavelength of the line, in nm.
temperature: For method = "stark" with stark: the plasma temperature, in K.
reference_width: For method = "stark": the electron-impact Stark width (nm) at reference_density, when stark is not given.
reference_density: The density of reference_width, in cm$^{-3}$. Default is $10^{17}$.
tolerance: For method = "stark" with stark: the largest difference between wavelength and the tabulated wavelength, in nm (see stark_width()). Default is 0.5.

Value

A numeric vector of electron densities, in cm$^{-3}$.

Details

width is the Stark full width at half maximum, in nm, with the instrumental and Doppler broadening removed. The line must be optically thin: self-absorption broadens lines and overestimates the density (see self_absorption()).

For isolated lines (method = "stark"), the Stark profile is Lorentzian: use the Lorentzian width wL of a Voigt fit with peak_fit() or multipeak_fit(), whose Gaussian part absorbs the instrumental and Doppler broadening.
The Stark profile of H$\alpha$ (method = "halpha") is not Lorentzian: use the FWHM of the whole line, for example voigt_fwhm() of the fitted widths, corrected for the instrumental width when it is not negligible (for Gaussian broadening, approximately $\sqrt{w^2 - w_{inst}^2}$).
method = "stark": in the impact approximation the Stark width is proportional to the electron density, $$N_e = N_{ref} \frac{w}{w_{ref}(T)}$$ where $w_{ref}(T)$ is the electron-impact width at density $N_{ref}$. It is taken from stark (a table returned by starkb_lines(), interpolated at temperature with stark_width()), or given directly as reference_width (nm) at reference_density. Tables from other sources can be built with stark_table() or read from saved STARK-B files with read_starkb(). Ion broadening is neglected, which is usually justified for lines of ions and at LIBS densities.
method = "halpha": the computer-simulation fit of Gigosos, González and Cardeñoso (2003) for the H$\alpha$ line, $$w = 1.098\,(N_e / 10^{17})^{0.67823}\ \mathrm{nm},$$ which includes the ion dynamics and depends only weakly on temperature.

References

Gigosos, M.A., González, M.Á., Cardeñoso, V. (2003). Computer simulated Balmer-alpha, -beta and -gamma Stark line profiles for non-equilibrium plasmas diagnostics. Spectrochimica Acta Part B, 58(8):1489-1504.
Konjević, N. (1999). Plasma broadening and shifting of non-hydrogenic spectral lines: present status and applications. Physics Reports, 316(6):339-401.

Examples

# From the H-alpha line: a Stark FWHM of 0.5 nm
electron_density(0.5, method = "halpha")
#> [1] 3.135367e+16

# From a line with known Stark width 0.012 nm at 1e17 cm-3
electron_density(c(0.006, 0.012, 0.024), reference_width = 0.012)
#> [1] 5e+16 1e+17 2e+17