Theory of the resonance escape factors of plasma resonance lines basing on the exact Voigt profile

In this paper, based on the exact Voigt profile we obtained, we derive the theory of resonance escape factors of plasma resonance lines, for both Lorentzian profile and Voigt profile. The oscillator strength, the number density of the absorbing atoms in the ground state, and the optical depth in the line center are discussed. As an example, the helium He I 1083.0 nm, lithium Li I 670.970 nm and carbon C I 111.74 nm are discussed for infrared, visible and ultraviolet regions. The results we calculated are in good agreement with the experimental results. These calculations will be significant in the theoretical analysis of plasma.     

Calculation of the escape probabilities of Fe XVII resonance lines for the Voigt profile

Using the Voigt profile we obtained, we calculate the escape probabilities of Fe XVII resonance lines at 15.02, 13.28, 12.12, 11.13, 11.02 and 10.12 Å for optically thick plasma, both for slab and cylindrical geometry. The oscillator strength, the number density of the absorbing atoms in the ground state, and the optical depth in the line center are discussed in this calculation. Results show that the escape probabilities for the slab geometry are larger than that for the cylindrical geometry. This calculation is useful for the study of the Fe XVII resonance lines.     

Calculation of the escape probabilities of Fe XVII resonance lines for the Voigt profile

Using the Voigt profile we obtained, we calculate the escape probabilities of Fe XVII resonance lines at 15.02, 13.28, 12.12, 11.13, 11.02 and 10.12 ? for optically thick plasma, both for slab and cylindrical geometry. The oscillator strength, the number density of the absorbing atoms in the ground state, and the optical depth in the line center are discussed in this calculation. Results show that the escape probabilities for the slab geometry are larger than that for the cylindrical geometry. This calculation is useful for the study of the Fe XVII resonance lines.      

佛克脱光谱线型干涉图的理论及其应用研究

在一般压强的条件下,佛克脱光谱线型(高斯光谱线型和洛伦兹光谱线型的卷积)是最接近实际的光谱线型,但由于其没有具体的表达式,所以在实际应用中常采用各种近似来表示佛克脱光谱线型。文章未采用任何近似,计算了佛克脱光谱线型干涉图的具体表达式,表明虽然佛克脱光谱线型没有具体表达式,但其干涉图是可以严格求解的。而且其变换结果为一实函数,与高斯光谱线型和洛伦兹光谱线型的变换结果的表达式非常相似,因而可以进行谱线综合展宽的各种计算,而不是像有的文献所预言的有实部和虚部两部分,给计算带来困难。计算结果与实验结果一致。作为应用的一个实例,作者指出了其在大气风场测量中的重要应用。此计算对气体展宽在傅里叶变换光谱仪中的应用方面具有非常重要的意义。     

The mean probability of photon capture of resonance radiation in atomic absorption spectroscopy

The mean probability of photon capture Ψ, obtained via an approximation to the complementary escape factor Λ, for calcium and zinc resonance lines at 4226.73 and 2138.56 Å have been determined from their atomic absorption measurements. Calculations are performed for Gaussian, Lorentzian, and Voigt spectral line shapes. Tabulations and graphical plots of the mean probability of photon capture, Ψ, with the optical depth in the center of Doppler profile, τ_D, and the number density of free atoms in the ground state N, are provided.     

Principle of temperature,velocity and pressure of upper atmospheric wind measurement for the Voigt profile

Using the accurate expression of the Fourier transform of the pure Voigt spectral line profile, we present the principle of the passive optical method to measure temperature, velocity, and pressure of atmospheric wind for the Voigt profile. Through discussion, from the Gaussian, Lorentzian and Voigt profiles, we find that velocity will not be affected, pressure can be derived for Lorentzian and Voigt profiles, and temperature will be affected greatly. By simulation and comparison, we find that temperature derived from the Voigt profile is greater than that from the Gaussian profile, and it is less than that from the Lorentzian profile. This discussion will be significant in accurate upper atmospheric wind measurement.     

Comment on The exact expression of the Voigt profile function

The recent paper by Di Rocco [The exact expression of the Voigt profile function. JQSRT 2005;92:231-7] claims that an exact and closed-form expression for the Voigt profile function is found. We show that these claims are wrong and the proposed expression is in fact the Type VII Pearson density. We additionally show by numerical computations that the expression proposed by Di Rocco cannot serve even as a good approximation for the Voigt profile in practical applications.     

Calculation of the self-absorption of laser induced Mg I 285.2127 nm spectral line

In order to study the self absorption of laser induced plasma, using the escape factor, we study the self absorption of laser induced magnesium plasma at 285.2127 nm in this paper. The theoretical total radiance, the escape factor and the real radiance for Gaussian and Lorentzian profiles are discussed. The self-absorption of the Mg I 285.2127 nm line is explained, and some useful conclusions are drawn. This study is significant in the analysis of self-absorption of laser induced plasma.     

佛克脱线型HeⅠ 1 083.0 nm的有效后向散射截面的理论研究

考虑到碰撞展宽导致的洛伦兹线型,理论上研究了佛克脱线型(高斯线型和洛伦兹线型的卷积)HeⅠ 1 083.0 nm辐射线的后向散射截面和有效后向散射截面,HeⅠ 1 083.0 nm辐射线实际上由三条非常接近的1 083.034,1 083.025和1 082.908 nm辐射线组成,文章给出了此3条辐射线的有效后向散射截面的曲线及其峰值,得到的10-16数量级与预言的数量级相一致。此研究比以前假定HeⅠ 1 083.0 nm辐射线为高斯线型更接近实际,从而为共振雷达探测热成层亚稳态He提供了更全面翔实的理论基础。文章还给出了HeⅠ 388.9 nm和HeI 318.8 nm辐射线的有效后向散射截面的曲线及其峰值,得到它们的有效后向散射截面比HeI 1 083.0 nm辐射线的小,此结论与实验结果相一致。     

Voigt线型函数及其最大值的研究

研究了多普勒和洛伦兹线型函数卷积形式的Voigt线型函数, 给出了它的最大值.结果表明, Voigt线型函数是关于中心频率的对称函数, Voigt线型函数的最大值由多普勒和洛伦兹线型函数的半宽度决定, 与中心频率无关, 且比洛伦兹和多普勒线型函数的最大值都小.提出了利用Voigt线型函数最大值和半宽度获得多普勒线型函数和洛伦兹线型函数的方法, 并利用Monte Carlo方法进行了验证. 关键词： Voigt线型函数 半宽度 最大值 傅里叶变换     

Voigt线型两翼拟合非均匀流场吸光度的方法研究

在吸收光谱领域特别是可调谐半导体激光直接吸收光谱(dTDLAS)技术中, 需要精确测量吸收光谱的积分吸光度值以精确反演出流场温度、组分浓度等参数。对于非均匀流场,单光路吸收光谱测量时,由于沿测量路径的谱线展宽随流场状态的变化而变化,见诸文献的研究主要采用Voigt或Lorentz线型对吸光度曲线拟合处理或直接对吸光度曲线数值积分获取积分吸光度值,针对方法可能引入的误差进行了模拟分析,并提出Voigt线型两翼拟合吸光度的方法来获取吸收光谱的积分吸光度值,以减小拟合误差。采用流场测量中常用的H₂O作为目标气体,选取了8条具有不同低态能级的吸收线,以实验室平焰炉为原型建立两种非均匀流场模型,并通过分段法对流场非均匀性进行等效处理。分别采用Voigt线型拟合法、数值积分法和Voigt线型两翼拟合法模拟计算两模型的积分吸光度值,通过与理论积分吸光度值对比得出各方法的误差大小,从而确定出在不同的非均匀流场情况下相适应的积分吸光度值获取方法。     

Exact analytical formula for Voigt spectral line profile

An analytical formula for the Voigt spectral line profile has been derived. The obtained formula is the solution of the second-order differential equation of the Voigt profile. The obtained results using the new analytical formula are in perfect agreement with the published results obtained by numerical calculation methods for a wide range of the line damping parameter (a) . The accuracy of the obtained formula is found to be 100% for all ranges of the line damping parameter (a).     

Absorption line profile recovery based on TDLS and MEMS micro-mirror for photoacoustic gas sensing

A novel and efficient absorption line recovery technique is presented. A micro-electromechanical systems (MEMS) mirror driven by an electrothermal actuator is used to generate laser intensity modulation through the mirror reflection. Tunable diode laser spectroscopy (TDLS) and photoacoustic spectroscopy (PAS) are used to recover the target absorption line profile which is compared with the theoretical Voigt profile. The target gas is 0.01% acetylene (C2H2) in a nitrogen host gas. The laser diode wavelength is swept across the P17 absorption line of acetylene at 1535.4 nm by a current ramp, and an erbium-doped fibre amplifier (EDFA) is used to enhance the optical intensity and increase the signal-to-noise ratio (SNR). A SNR of about 35 is obtained with 100 mW laser power from the EDFA. Good agreement is achieved between the experimental results and the theoretical simulation for the P17 absorption line profile.     

Asymmetry and speed-dependent effects on the 748.8 nm self-broadened neon line

Using an interferometric method, detailed analysis of the self-broadened 748.8 nm Ne line shapes emitted from the glow discharge of neon was performed, where departures from the ordinary Voigt profile were observed. These departures are shown to be consistent with fits of the speed-dependent asymmetric Voigt profile to experimental profiles. It was shown that neglecting the correlation between Doppler and collisional broadening may cause errors in determined line shape parameter values. Coefficients of the pressure broadening, shift and collision-time asymmetry are determined and compared with those calculated in the adiabatic approximation for the van der Waals and Lennard-Jones potentials.     

Low-threshold parametric decay instabilities in the experiments on the electron cyclotron resonance heating in tokamaks and stellarators

The experimental conditions have been analyzed for a significant reduction of the threshold of the reflective parametric decay instabilities under electron cyclotron resonance heating (ECRH) of a plasma in magnetic devices in the absence of the upper hybrid resonance for the pump wave. The role of the nonmonotonic profile of the plasma density near the O point of the magnetic island, which allows for the localization of ion Bernstein waves in the direction of the density gradient and the suppression of convective losses from the decay region has been discussed. It has been shown that the threshold of the instability of the induced backscattering near the local maximum of the density profile is decreased by four orders of magnitude and is easily exceeded in present-day ECRH experiments at a power of several hundred kilowatts.     

Infrared HCN Lineshapes as a Test of Galatry and Speed-Dependent Voigt Profiles

Absorption lineshapes of the ν₂ infrared band of HCN in collision with He, Ne, Ar, Kr, Xe, N₂, HCN, and CH₃Br have been considered. Observed lineshapes differ significantly from the usual Voigt profile and are characteristic of line narrowing processes. The Galatry profile fairly reproduces lineshapes observed in the low-pressure regime, but leads to unexpected nonlinear behavior of optical diffusion rates in the high-pressure regime and strongly fails with the heaviest perturbers. On the other hand, fair results are obtained for all experimental conditions by using a speed-dependent Voigt profile that includes a pressure-dependent narrowing parameter. These observations are discussed by consideration of the polarization correlation functions related to considered line profiles and of the optical and kinetic radii involved in collision processes. It is shown that observed line narrowings primarily result from the dependence of relaxation rates on molecular speeds and that diffusion processes show up with the two lighter perturbers only, He and, to a small extent, Ne. Finally, it can be claimed that, for atmospheric applications, deviations from the Voigt profile must be taken into account by a speed-dependent Galatry profile that reduces to a speed-dependent Voigt profile in most cases.     

Optical Escape Factors for Bound-bound and Free-bound Radiation from Plasmas. I. Constant Source Function

Optical escape factors for bound-bound and free-bound radiation have been calculated by solving the equation of radiative transfer with the assumption that the corresponding source functions are space-independent. The general expression for bound-bound transitions yields for large optical depths—within a correction factor of order unity—Holstein's asymptotic expressions for the two limiting cases of a Doppler and a dispersion profile. Application to the more general case of a Voigt profile leads to an analytical formula which permits a rapid estimate of the escape factor for any optical depth. Numerical application to the resonance lines of neutral helium-which are broadened by Stark and Doppler effects—shows that under certain plasma conditions most of the higher members of the resonance series remain optically thin.—The general expression obtained for the escape factor of free-bound radiation has been applied to the resonance continuum of neutral helium. The numerical results show that the resonance continuum remains optically thin as long as the optical depth in the center of the He resonance line (λ = 584 Å) remains smaller than 10⁴ to 10⁵. A similar result is obtained for atomic hydrogen.     

The influence of the background interference on the escape of photons in atomic absorption measurements

The influence of the background interference on the escape of photons in the determination of Nickel by atomic absorption analysis for a wide range of concentrations between 10 and in an air-acetylene flame have been investigated. Assuming Doppler, Lorentzian and Voigt line profiles for the resonance lines, the resonance escape factor of the Ni-resonance lines at 2320 and have been calculated with and without the effect of the background, in terms of two main parameters, the optical depth in the line center and the number density of absorbing atoms in the ground state. The effect of the background interference due to the presence of the SO₂-molecular band can cause a change in the escape factors values. The dependence of the escape factor for the Voigt distribution on the damping constant is also discussed.     

Some effects of radiative and collisional broadening on line emission in a spherical,laser-heated plasma

We have generalized our treatment of resonance-line radiation from a spherical, laser-heated plasma by including the effects of radiative and collisional line broadening in representing the line-emission and absorption profiles by a Voigt function. We find that the emitted profiles are broadened by factors of five or more, depending on the magnitude of the damping constant. It is also shown that the Al(XIII) to Al(XII) line ratios are seriously affected by the different escape probabilities associated with Doppler and Voigt profiles. We also find that plasma cooling via resonance-line radiation is accelerated relative to that calculated with a pure Doppler profile, and that use of the Voigt profile decreases the density of excited states relative to the Doppler values. These phenomena are analyzed in terms of the differing profile shapes and widths.     

温度和压强的变化对谱线线型峰值的影响

谱线线型是用于气体浓度测量中的一个重要参数。本文基于温度(压强)变化会引起相应压强(温度)的变化这一点,考虑温度和压强同时变化对气体线型峰值的影响。通过分析氟化氢的吸收谱线,发现可用Lorentzian线型来计算峰值吸收系数的温度和压强范围都扩大,而Gaussian线型在绝大数情况下不能用来计算峰值吸收系数;在一定的温度范围和压强范围内,如果只考虑压强或温度的变化,由此计算的三种线型峰值(Gaussian,Lorentzian和Voigt)的相对误差大于0.1。因此,在计算线型峰值时,需考虑压强和温度同时变化对线型峰值的影响。最后分别讨论了甲烷、二氧化碳、一氧化碳及一氧化氮,得到与氟化氢结论相似的结论,结论的不完全相同是由于每种气体在波数、压力展宽系数、相对分子质量及温度系数上的不同而导致。