7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Laser-induced breakdown spectroscopy based on thermodynamic equilibrium
and corona equilibrium for estimating atomic composition in powdered milk

Estimated density ratio

Estimated density ratio

In this work, we adopted thermodynamic equilibrium
and corona equilibrium to the optical emission spectra ofa plasma produced by laser ablation of a powdered milktarget. The quantitative analysis of the atomic
composition is an issue of laser-induced breakdown
spectroscopy (LIBS). A standard method in the LIBS
field is to apply the local thermodynamic equilibrium(LTE) to the laser-induced plasma with the electron
density exceeding the McWhirter criterion. However,according to the framework of plasma spectroscopy
developed by Fujimoto [1], the electron density
exceeding the McWhirter criterion (it is called the Griemboundary in plasma spectroscopy) is a necessary
condition but it is not sufficient for LTE. In the case of
an ionizing plasma, the Boltzmann distribution isrealized among the energy levels with principal quantum
numbers lower than the Byron boundary. On the otherhand, the corona equilibrium is expected for the opticalemission spectrum from an ionizing plasma with anelectron density below the Griem boundary. In this work,
we compared the applicability of LTE and the corona
equilibrium to the LIBS spectra observed by the laser
ablation of a powdered milk target [2].
We observed the optical emission spectra at various
delay times after the irradiation of an Nd:YAG laser
pulse, and we evaluated the relative excited-state
densities of Mg, Ca, Na, and K. The Stark broadening
widths of the Balmer-α and β lines of atomic hydrogenindicated that the electron density of the plasma at ashort delay time was higher than the Griem boundary. Inaddition, the optical emission spectrum was dominatedby the line emissions of light elements, suggesting a highelectron temperature. Although the electron density washigher than the Griem boundary, the relative
excited-state densities of Mg, Ca, Na, and K at a shortdelay time (td≤1 µs) were not explained by assuming
LTE for the plasma, suggesting that the Byron boundarycorresponding to the high electron temperature waslower than the effective principal quantum numbers of
the first excited states. This means the difficulty in theestimation of the atomic composition by applying LTE.
The optical emission spectrum changed with thedelay time, and it was dominated by Mg, Ca, Na, and K
when the delay time was longer than td ≥10 µs. The
domination by the alkali and alkaline earth metals
suggests the decrease in the electron temperature withthe delay time. In addition, we can expect an electron
density below the Griem boundary at the long delay time.
We calculated the rate coefficients of electron impact
excitation for Mg, Ca, Na, and K, and we estimated theEstimated density ratio

Koichi Sasaki
Division of Applied Quantum Science and Engineering, Hokkaido University
e-mail (speaker): sasaki@qe.eng.hokudai.ac.jp
108

True ratio

620 µs
25 µs
30 µs
35 µs

42(a) [Ca] / [Mg]0108

True ratio

642(b) [Na] / [Mg]010

True ratio

8642020 µs
25 µs
30 µs
35 µs(c) [K] / [Mg]01234Electron temperature (eV)

20 µs
25 µs
30 µs
35 µs
5Figure 1 Ground-state density ratios of [Ca]/[Mg],[Na]/[Mg], and [K]/[Mg] that result in the ratios of the
optical emission intensities observed at td=20, 25, 30,
and 35 μs.
ground-state density ratios of [Ca]/[Mg], [Na]/[Mg], and[K]/[Mg] that result in the ratios of the optical emission
intensities observed experimentally. Figure 1 shows thedensity ratios that result in the experimental ratios of the
optical emission intensities as a function of the electrontemperature. The dotted lines show the true density ratios,
which were confirmed by inductively coupled plasma
mass spectrometry. As shown in the figure, the density
ratios close to the true values are obtainable by assuming
Te ≈ 1.5, 1.2, and 0.8 eV at td=25, 30, and 35 μs,respectively. This means the corona equilibrium works
well for the optical emission spectrum observed at thelong delay times. Accordingly, the present work indicatesthat applying the corona equilibrium to the low-density
plasma which is observed at a long delay time can work
as an alternative method for quantitative LIBS.
References[1] T. Fujimoto, Plasma Spectroscopy (Clarendon Press,Oxford, 2004).
[2] K. Sasaki and K. Maruyama, Appl. Phys. A 128, 736(2022).