Identification and Analysis of Atomic and Molecular Superposition Spectra Following Laser-induced Optical Breakdown Alexander C. Woods Christian G. Parigger University of Tennessee Space Institute 411 B. H. Goethert Parkway Tullahoma, TN 37388

Goals Identify specific diatomic spectra Determine micro-plasma parameters such as electron density and temperature Determine temperature in flame Shadowgraph of LIOB in expanding methane flow. Igniter and propellant surface on test bed.

Main Idea LIBS Laser-induced optical breakdown Sample is excited and ionized Plasma is formed Atomic structures cool Molecular species form Flame emission Continuous emission spectroscopy Analyze recorded spectra Superposition spectra Background Variations in combustion

Approach Use Diatomic Quantum Theory to create synthetic spectra Fit the model spectra with collected spectra Use results to infer micro-plasma parameters

Method for Calculating Diatomic Line Strengths 5 step process Numerically solve 1D Schrödinger equation for calculated potential energy curves Calculates Hönl-London factors, r-centroids, and Franck- Condon factors Taylor expand the electronic transition moment containing r-centroids Programs like SPECAIR will calculate spectra for you

Fitting of Synthetic Spectra with Measured Spectra Experimental H-beta line profile fitted with Vidal-Cooper-Smith model corresponding to pressure 2.7x10 5 Pa and time delay 2.1 µs. Experimental H-beta line profile fitted with the computation model from [9] corresponding to 2.7x10 5 Pa and time delay 2.1 µs.

Fitting of Synthetic Spectra with Measured Spectra Measured and fitted H-beta profile, using asymmetric H-beta line shapes for T=10,000K and N e = 1.0  cm -3. Experimental profile corresponds to the pressure 2.7  10 5 Pa and to the time delay 0.9 µs.

Fitting of Synthetic Spectra with Measured Spectra Fitting of measured spectra with synthetic spectra, using non-linear methods/simplices Input includes line-strength file, measured spectra, specified or constant/linear/quadratic fitted background, and spectroscopic parameters

Fitting of Synthetic Spectra with Measured Spectra

Expanding Methane Pulsed expanding methane flow Laser-induced breakdown spectroscopy (LIBS) Hydrogen Balmer series observed LIOB above nozzle used for expanding methane flow.

H-alpha Hydrogen-alpha emission at 2.7 x 10⁵ Pa. Time delay (a)t delay = 0.4 μs, (b) t delay = 0.8 μs, (c) t delay = 1.5 μs, (d) t delay = 2.1 μs.

H-beta Hydrogen-beta emission at 2.7 x 10⁵ Pa. Time delay (a)t delay = 0.4 μs, (b) t delay = 0.8 μs, (c) t delay = 1.5 μs, (d) t delay = 2.1 μs.

H-gamma Hydrogen-gamma emission at 2.7 x 10⁵ Pa. Time delay (a)t delay = 0.4 μs, (b) t delay = 0.8 μs, (c) t delay = 1.5 μs, (d) t delay = 2.1 μs.

C₂ Swan System Treat Balmer series spectra as background Clearly analyze C₂ structure

C₂ Swan System

Measured H-beta and C 2 Swan Band fitted molecular emission. The fitted molecular emission shows a temperature of 0.59  10 4 K, while the electron excitation temperature amounts to 1.0  10 4 K.

C₂ Swan System

Measured H-gamma and C 2 Swan Band fitted molecular emission. The fitted molecular emission shows a temperature of 0.48  10 4 K, while the electron excitation temperature amounts to 1.0  10 4 K.

AlO Flame Test Performed by Fire and Aerosol Sciences, Sandia National Laboratory Data collected along a vertical plume Temperature gathered via two-color pyrometer Temperature inferred via AlO emission spectra Schematic of test setup with propellant on table next to track. Grated floor allows for ventilation and purge of smoke.

AlO Emission Spectra Both Boltzmann plot techniques and Nelder-Mead minimization algorithm (NMT) between synthetic spectra and measured spectra yield temperature.

AlO Emission Spectra

Conclusion

Conclusions It is possible to identify select diatomic spectra superposed to atomic emission spectra. Electron density and temperature may be inferred for both atomic and molecular species at a given time. The continuing development of atomic and molecular synthetic spectra broadens the applications of superposition spectra as a diagnostic tool. Proper identification of background enhances results.

References 1.C. G. Parigger and J. O. Hornkohl, “Computation of AlO B 2 Σ + →X 2 Σ + Emission Spectra,” Spectrochim. Acta, Part A – Molec. Biomolec. Spectrosc. 81, (2011), 2.J. O. Hornkohl, L. Nemes, and C. G. Parigger, “Spectroscopy of Carbon Containing Diatomic Molecules,” in: L. Nemes, S. Irle (Eds.), Spectroscopy, Dynamics and Molecular Theory of Carbon Plasmas and Vapor, World Scientific, Singapore, 2011, I. G. Dors, C. Parigger, and J. W. L. Lewis, Opt. Lett. 23 (1998) J.L. Height, B. Donaldson, W. Gill, and C.G. Parigger, “Measurements in solid propellant plumes at ambient conditions,” Proceedings of IMECE2011, Denver, Colorado, USA, paper IMECE (2011). 5.C. Parigger, G. Guan, and J.O. Hornkohl, “Measurement and Analysis of OH Emission Spectra Following Laser-Induced Optical Breakdown in Air,” Appl. Opt. 42, (2003). 6.C. O. Laux, “Radiation and Nonequilibrium Collisional-Radiative Models,” von Karman Institute Lecture Series , Physico- Chemical Modeling of High Enthalpy and Plasma Flows, eds. D. Fletcher, J.-M. Charbonnier, G.S.R. Sarma, and T. Magin, Rhode-Saint- Genèse, Belgium, Christian Parigger, Alexander Woods, Eugene Oks, James Hornkohl, Jonathan Height, Burl Donaldson and Walter Gill, “Atomic and Molecular Superposition Spectra following laser-induced optical breakdown,” Proceedings of NASLIBS 2011, Jul 18-20, Clearwater Beach, FL, Alexander Woods, Christian Parigger, Eugene Oks, and James Hornkohl, “Analysis of Combined Atomic and Molecular Spectra,” FACSS 2011, Analytical Science and Innovation, Oct. 2-7, Reno, NV, R.Zǐkić, M.A.Gigosos, M.Ivković, M.Á.González, N.Konjević, “A program for the evaluation of electron number density from experimental hydrogen Balmer beta line profiles,” Spectrochim. Acta B Atom Spectrosc (2002). 10.C. G. Parigger, M. Dackman, and J. O. Hornkohl, “Time-resolved spectroscopy measurements of hydrogen-alpha, -beta, and –gamma emissions,”Appl. Opt. 47, G1-G6, C. G. Parigger, “Diagnostics of a Laser-Induced Optical Breakdown Based on Half-Width at Half Area of H-α, H-β, and H-γ Lines,” Int. Rev. Atom. Mol. Phys. 2, (2010). 12.C. G. Parigger, A. Woods, J. O. Hornkohl, “Analysis of Time-Resolved Superposed Atomic Hydrogen Balmer Lines and Molecular Diatomic Carbon Spectra,” Appl. Opt. Submitted Oct. 9, 2011.

Spontaneous Intensity Radiated Intensity across varying wavelengths provides insight into electron number, energy, and temperature. Radiation intensity for transitions between upper and lower levels can be written

Boltzmann Plot Techniques The Boltzmann equation for line intensity may also be used to infer temperature from measured spectra. Rewriting this is in the form of a line, the slope becomes inversely proportional to the temperature.

Method for calculating diatomic line strengths Step 1: Determine the number and numerical values of parameters for upper and lower energy states Predict positions of all spectral lines in the band system Apply selection rules

Method for calculating diatomic line strengths Step 2: Hönl-London factors are calculated

Method for calculating diatomic line strengths Step 3: Potential energy curves are calculated utilizing rotational constants and vibrational term values.

Method for calculating diatomic line strengths Step 4: Numerically solve 1D Schrödinger equation Compute Franck-Condon factors Compute r-centroids

Method for calculating diatomic line strengths Step 5: Taylor expand the electronic transition moment containing the r-centroids. The expanded electronic transition moment, Franck- Condon factors, and Hönl-London factors are combined.