Spectral Line Shape Model Research Articles

Finding the bulk viscosity of air from Rayleigh-Brillouin light scattering spectra.

Spectral line shape models can successfully reproduce experimental Rayleigh-Brillouin spectra, but they need knowledge about the bulk viscosity ηb. Light scattering involves GHz frequencies, but since ηb is only documented at low frequencies, ηb is usually left as a free parameter, which is determined by a fit of the model to an experimental spectrum. The question is whether models work so well because of this freedom. Moreover, for light scattering in air, spectral models view "air" as an effective molecule. We critically evaluate the use of ηb as a fit parameter by comparing ηb obtained from fits of the Tenti S6 model to the result of Direct Simulation Monte Carlo (DSMC) for a mixture of Nitrogen and Oxygen. These simulations are used to compute light scattering spectra, which are then compared to experiments. The DSMC simulation parameters are cross-checked with a molecular dynamics simulation based on intermolecular potentials. At large values of the uniformity parameter y, y ≈ 4, where the Brillouin contribution to spectra is large, fitted ηb are 20% larger than the ones from DSMC, while the quality of the simulated spectra is comparable to that of the Tenti S6 line shape model. At smaller y, the difference between fitted and simulated ηb can be as large as 100%. We hypothesize the breakdown of the bulk viscosity concept to be the cause of this fallacy.

Introduction to spectral line shape theory

Spectral line-shape models are an important part of understanding high-energy-density (HED) plasmas. Models are needed for calculating opacity of materials and can serve as diagnostics for astrophysical and laboratory plasmas. However, much of the literature on line shapes is directed toward specialists. This perspective makes it difficult for non-specialists to enter the field. We have two broad goals with this topical review. First, we aim to give information so that others in HED physics may better understand the current field. This first goal may help guide future experiments to test different aspects of the theory. Second, we provide an introduction for those who might be interested in line-shape theory, and enough materials to be able to navigate the field and the literature. We give a high-level overview of line broadening process, as well as dive into the formalism, available methods, and approximations.

Stark–Zeeman line-shape model for multi-electron radiators in hot dense plasmas subjected to large magnetic fields

We present a Stark–Zeeman spectral line-shape model and the associated numerical code, PPPB, designed to provide fast and accurate line shapes for arbitrary atomic systems for a large range of plasma conditions. PPPB is based on the coupling of the PPP code—a Stark-broadened spectral line-shape code developed for multi-electron ion spectroscopy in hot dense plasmas—and the MASCB code developed recently to generate B-field-dependent atomic physics. The latter provides energy levels, statistical weights, and reduced matrix elements of multi-electron radiators by diagonalizing the atomic Hamiltonian that includes the well know B-dependent term. These are then used as inputs to PPP working in the standard line-broadening approach, i.e., using the quasi-static ion and impact electron approximations. The effects of ion dynamics are introduced by means of the frequency fluctuation model, and the physical model of electron broadening is based on the semi-classical impact approximation including the effects of a strong collision term, interference, and cyclotron motion. Finally, to account for polarization effects, the output profiles are calculated for a given angle of observation with respect to the direction of the magnetic field. The potential of this model is presented through Stark–Zeeman spectral line-shape calculations performed for various experimental conditions.

Fast approximations of spectral lineshapes to enable optimization of a filtered Rayleigh scattering experiment

Measuring the properties of scattered light is central to many laser-based gas diagnostic techniques, such as filtered Rayleigh scattering (FRS). Alongside the measurements, a model of the scattered light’s spectral lineshape is often used to extract quantitative information about the flow field like pressure, temperature, and velocity. In particular, the Tenti S6 or S7 model are frequently used to model the lineshape of Rayleigh–Brillouin (RB) scattered light. While accurate, it is well attested in the literature that these models can be computationally expensive when evaluated many times, for example, as part of iterative estimation or optimization routines. To overcome this, approximations of these spectral lineshape models can be used instead. In this paper, we develop a method called support vector spectrum approximation (SVSA). This method uses support vector regression and singular value decomposition to create efficient, accurate, and well-conditioned approximations of any existing spectral lineshape model. The SVSA framework improves upon existing approximation methods by allowing quick calculation of spectral lineshapes for arbitrary flow regimes with any number of input parameters over a wide range of values. We demonstrate the efficacy of SVSA in approximating coherent and spontaneous RB scattering spectra. In application, we use SVSA to optimize the design of a filtered Rayleigh scattering experiment of a complex shock-dominated flow. SVSA allows us to comprehensively minimize expected measurement uncertainty of number density and temperature for this experiment. It does this by enabling a high-resolution design of experiments that is otherwise intractable.

Dispersion and relativistic corrections to the spectral line-shape models

We investigate the influence of dispersion and relativistic effects on the spectral line-shape models on an example of simple Gaussian and Voigt profiles. We show that dispersion and relativistic corrections can affect the line shape even at the relative level of 10–5.

Spectral line-shapes of oxygen B-band transitions measured with cavity ring-down spectroscopy

Results of line-shape measurements of self- and N2-broadened P9 P9 transition of the oxygen B band are presented. Spectra were acquired using the optical frequency comb- assisted Pound-Drever-Hall-locked frequency-stabilized cavity ring-down spectrometer (PDH- locked FS-CRDS). In the line-shape analysis the line narrowing described by Dicke narrowing or/and the speed dependence of collisional broadening were taken into account. The multispectrum fitting technique was used to minimize numerical correlations between line-shape parameters. Collisional broadening and shifting coefficients are reported with sub-percent uncertainties. Influence of the spectral line-shape model used in data analysis on determined line intensities and collisional broadening is discussed.

Influence of the line-shape model on the spectroscopic determination of the Boltzmann constant

Recent high-resolution spectroscopic experiments demonstrated the possibility of measuring the Boltzmann constant directly from the Doppler width of atomic or molecular lines; however, both experimental setups and data analysis methods still need to be improved to compete with the best acoustic methods. In this paper, the influence of choice of spectral line-shape model for data analysis on systematical error of the Doppler-width determination is analyzed on the example of the oxygen line near $\ensuremath{\lambda}=687$ nm. Profile simulations were performed for many different models at pressures ranging from 0.012 Pa to 120 kPa, taking into account such line-shape effects as the speed dependence of collisional broadening and Dicke narrowing. We discuss limitations of an applicability of the Voigt profile for purposes of the Boltzmann constant determination. The influence of the model line-shape profile and the gas pressure range on the Doppler width extrapolated to the zero-pressure value is investigated.

Frequency dependent electron collisional widths for opacity calculations

It is shown that theoretical Rosseland mean opacities are sensitive to spectral line shape models. Due to computational constraints, however, opacity codes typically use Voigt or Lorentz profiles. Both of these profiles have an incorrect far wing behavior that can significantly overestimate the photon absorption. A new line profile is proposed, based on second-order line broadening theory, which is both more physical and relatively fast to compute.

Speed-dependent line-shape model analysis from molecular-dynamics simulations: The collisional confinement narrowing regime

A critical analysis of the speed-dependent spectral line-shape models is presented. With this aim, a comparison of these models is done with molecular-dynamics results for ${\mathrm{H}}_{2}\ensuremath{-}X$ gaseous mixtures. This allows us to get a clear understanding of the consequences of the assumptions underlying these models on the line profile. This proves the requirement to introduce, in the collisional confinement regime, distinct treatments for the velocity-orientation and velocity-modulus memory mechanisms. Such a requirement applies when the goal is to get both a high accuracy with experimental stimulated Raman profiles and a high consistency with molecular dynamics (i.e., with first principles).

Speed-dependent line-shape models analysis from molecular dynamics simulations: The collision regime

A spectral line-shape model accounting for the speed dependence of the relaxation parameters has been proposed for the collision regime [D. Robert et al., Phys. Rev. A 47, R 771 (1993)]. In this model, the speed class exchanges are governed by a memory parameter playing a crucial role. It has been exhaustively used to accurately describe the observed inhomogeneous features of ${\mathrm{H}}_{2}$ vibration line profiles in various mixtures with respect to concentration and temperature. Molecular dynamics calculations of the characteristic memory parameter are performed in order to test this model from first principles. The resulting data are in remarkable agreement with those deduced from experiments through the model.

Correlation effect in spectral line shape from the Doppler to the collision regime

The spectral line shape model recently proposed by the present authors [J. Chem. Phys. 109, 8283 (1998)] is extended in order to account for correlation between velocity- and phase-changing collisions. The possible additional source of asymmetry due to the finite duration of collision is also included. In this implemented form, the model is consistent with previous exhaustive experimental studies in the collision regime for H2–rare gases and H2–nitrogen mixtures and has been shown to also accurately describe the observed spectral features at lower pressure for H2–Ar. It should be pertinent for various other molecular systems in a wide range of pressure and temperature, in particular for optical diagnostics.

An analytical model for collisional effects on spectral line shape from the Doppler to the collision regime

A spectral line shape model accounting for both the collisional confinement narrowing of the Doppler distribution and the inhomogeneous effects due to the radiator speed dependence of the collisional broadening and shifting parameters is proposed. The velocity changes are assumed to be induced as well by hard as soft collisions. Doppler-collision correlations and speed-class exchanges are taken into account. A comparison with the previous models used for the Doppler regime and for the collisional one is done. The present model also applies for the intermediate regime where the two above mechanisms are simultaneously efficient. The spectral line shape characteristics are exemplified through the H2–Ar and C2H2–Xe prototype molecular systems.

JavaFit: A platform independent program for interactive nonlinear least-squares fitting using the Levenberg—Marquardt method

The JavaFit program is a package for carrying out interactive nonlinear least-squares fitting to determine the parameters of physical models from experimental data. It has been conceived as a platform independent package aimed at the relatively modest computational needs of spectroscopists, where it is often necessary to determine physical parameters from a variety of spectral lineshape models. The program is platform independent, provided that a Java runtime module is available for the host platform. The program is also designed to read a wide variety of data in ASCII column formats produced on DOS, Macintosh and UNIX platforms.

Diagnostics of Langmuir oscillations in a superdense plasma

The level and the angular distribution of Langmuir oscillations in a dense plasma produced on the Phoenix plasma radiation source (PRS) were measured. Line profiles of several lines in the Lyman series of Al XIII were measured using crystal spectrometers. A spectral line shape model was used, which attempted to take into account all significant broadening mechanisms. The parameters of the plasma and the Langmuir oscillations were found by generating profiles using the model and comparing these profiles to the experimental spectra. The strength of the Langmuir oscillations was found to be E/sub 0//spl ap/1-9 GV/cm, indicative of a strong Langmuir turbulence. The polarization analysis of the profiles of the Al XIII Lyman /spl gamma/ line has shown that the Langmuir oscillations develop anisotropically, primarily in the direction of the plasma current.

New Method for Spectral Line Shape Fitting and Critique on the Voigt Line Shape Model

In this work we introduce a new method for testing spectral line shape models and optimizing the parameters in any parametric model. Given some general parametric line shape and a piece of a spectrum, the method finds the optimal values for the parameters and gives a number which tells how well the spectrum under consideration is explained by that model. The number of spectral lines under analysis may be more than one, and their exact locations need not be known. This characteristic follows from the property that the method does not need the information about line positions and amplitudes at all. Thus, in the absence of a singlet line, a set of overlapping lines can also be analyzed. The analysis is carried out in the signal domain by utilizing linear prediction. Application examples of the method to a molecular spectrum measured in gas phase are given. The results suggest that the Voigt line shape, despite its common use, is not a correct model in molecular spectroscopy. Its limitations become evident when one is trying to enhance the resolution by linear prediction, which requires detailed knowledge of the line shape. Instead a stochastic model, which is also tested, turns out to be rather promising.

Spectral line shape considerations for limb temperature sounders

The sensitivity of radiative transfer calculations to spectral line shape models is investigated for two CO2 spectral regions used by instruments aboard the Upper Atmosphere Research Satellite for making low‐altitude temperature and pressure retrievals. Line shape models have been tested by comparing calculated spectra with observations made by the Atmospheric Trace Molecule Spectroscopy experiment. Spectral line mixing is discussed and shown to be important at the 617 cm−1 Q branch where its inclusion in the radiative transfer model can lead to differences of more than 2 K in brightness temperature at low tangent heights. The sub‐Lorentzian line wings of the CO2 ν2 band must be correctly modeled in calculations at the 791 cm−1 Q branch otherwise equivalent brightness temperatures for a 15 km limb view will be in error by as much as 10 K.