Equivalence of the method of the kinetic equation and the fluctuating-frequency method in the theory of the broadening of spectral lines

A new expression for the Stark profiles of spectral lines in plasma has been obtained by the method of the kinetic equation taking into account the dynamics of the plasma microfield. The result represents a dynamic line profile in the form of simple functionals of a static profile. The relation of the new solution with the known fluctuating-frequency method has been analyzed. It has been shown that this method is a discrete analog of the method of the kinetic equation and passes to the latter method in the limit of the continuous fluctuations. Simple formulas (4), (5), and (21) for dynamic line profiles provide ultrafast calculations of the profiles of spectral lines taking into account the dynamics of the plasma microfield.     

Description of the line shape of Bragg peak in neutron powder diffractometers taking into account spatial effects

Based on a universal mathematically correct approach previously developed, the compact analytical expression for the line shape of Bragg reflexes taking into account spatial effects has been obtained and a geometrical interpretation is given.     

Angular Velocity Distribution of the Electric Microfield in Plasma

In theory of the spectral line shapes, the conventional scheme use two approximations for the local electric field (microfield) due to all charged particles of the plasma. The quasi‐static approximations for the ions and the impact approximation for the electrons. The first approximation consists to say that the electric field is constant during the characteristic time. In this work we shall transpose the idea of the first approximation, to the angular velocity of the microfield whereas its strength is kept constant and equal to its mean value. We shall use the Holtsmark approach and the independent particles model (due to Margeneau and Lewis) to compute the static distribution function of the angular velocity of the microfield. In the first approach (Holtsmark), the distribution shows a Lorentzian behavior, whereas the second approach (Margenau and Lewis) shows a gaussian behavior. Subsequently, we have applied the obtained static distribution to show the effect on the broadening of Lyman‐alpha line for a plasma composed of He⁺ ions. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contribution to Calculation of Ion Microfield Nonuniformity Effect on the Asymmetry of Lyman‐α Line in Dense Plasma

The high orders of Stark effects on spectral line shapes are examined in the ion‐static and electron‐impact ap‐proximations. At first the distribution functions of the spatial derivative of the ion microfield in He⁺ plasma are calculated for different plasma conditions when the coupling parameter is weak. We present new results about the spatial derivative ion microfield distributions and apply them to show the asymmetry of the Lyman‐α (Ly‐α) line in He⁺ plasma. At the second stage we show that asymmetry is affected by the spatial derivative tensor of the local ion electric field. We have used the Monte‐Carlo simulation (MCS) to compute the distribution functions for all tensor components and use them to solve the evolution equation of emitter whose solution serves to compute and therefore to show the line shape asymmetry. Good agreement of our distribution functions of ion microfield gradients and the line asymmetry with other results are obtained (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Density Measurements from the Asymmetry of the Lyman ζ Line in a Vacuum Spark Lithium Discharge

A lithium spectrum is obtained form vacuum spark discharges using a grazing-incidence flat-field spectrometer. Hydrogen-like lines up to Lyman η are identified in the spectrum. The spectrum is analyzed, and it is found that the experimental line widths increase along the Lyman series. An asymmetry between the blue and red wings appears in the profile of the Lyman ζ line, and becomes significant in the profile of the Lyman ? line. A relatively new method is used to estimate an electron density of 1 ± 0.4 × 10¹⁸cm^?3 from the experimental degree of asymmetry between the blue and the red wings of the Lyman ζ line. This result is compared with an analysis of the experimental widths of two optically thin lines, namely, Lyman δ and Lyman ζ. In this analysis an electron density of 1.2±0.5 × 10¹⁸cm^?3 is deduced. The principal quantum number of Lyman η (n=8) is used in the Inglis-Teller formula for the last line seen before the merging of the lines with the continuum, and the estimated electron density is found to be 2.0 × 10¹⁸cm^?3 for the lithium plasma. Thus, it is demonstrated that the new method employing the asymmetry of the lineshapes in dense plasmas yields results consistent with the analysis of the widths of the lines. However, it requires obtaining the profile of just one spectral line, which is a great advantage. The reference data on the Stark broadening of the Lyman ζ line is also tabulated, which was previously unavailable in the literature.     

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 E₀≈1-9 GV/cm, indicative of a strong Langmuir turbulence. The polarization analysis of the profiles of the Al XIII Lyman γ line has shown that the Langmuir oscillations develop anisotropically, primarily in the direction of the plasma current     

Anharmonic Excitations,Time Correlations and Electric Conductivity

We study the influence of anharmonic mechanical excitations of a classical ionic lattice on its electric properties. First, to illustrate salient features, we investigate a simple model, an one‐dimensional (1D) system consisting of ten semiclassical electrons embedded in a lattice or a ring with ten ions interacting with exponentially repulsive interactions. The lattice is embedded in a thermal bath. The behavior of the velocity autocorrelation function and the dynamic structure factor of the system are analyzed. We show that in this model the nonlinear excitations lead to long lasting time correlations and, correspondingly, to an increase of the conductivity in a narrow temperature region, where the excitations are supersonic soliton‐like. In the second part we consider the quantum statistics of general ion‐electron systems with arbitrary dimension and express ‐ following linear response transport theory ‐ the quantum‐mechanical conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the ion motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. An evaluation of the influenec of solitons predicts for 1D‐lattices a conductivity increase in the temperature region where most thermal solitons are excited, similar as shown in the classical Drude‐Lorentz‐Kubo framework. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On simple quantum theories of pressure broadening: The exact resonance approximation applied to Lyman alpha

Starting from the exact unified quantum expression of the line profile, the exact resonance approximation, which is valid for lα3 in the case of Lyman α, is applied to the calculation of the high partial waves contribution to the broadening. A simple analytic expression is obtained which converges towards the classical limit of Lisitsa and Sholin.⁽¹) The dipolar interaction is taken into account exactly. Analytic expression can be obtained when proper account is taken of the quadrupolar and polarization terms.This example illustrates the non-adiabatic character of the processes as well as the need of accurate quantum results for l < 3 for which-a fortiori-all semi-classical results are completely wrong.     

Excitation of Highly Charged Ions in Plasma by Ultrashort Electromagnetic Pulses

Excitation of highly charged ions in plasmas under the action of ultrashort electromagnetic pulses is investigated theoretically in the frame of perturbation theory. The study is based on analytical expression for probability of bound‐bound transition which is derived for Gaussian pulse and Doppler broadening of spectral line shape of the transition. Electronic transitions from the ground state of hydrogen‐like ions are considered with account for fine splitting of upper energy levels. The main attention is paid to the dependence of the excitation probability on pulse duration for various ion charges and carrier frequencies of the pulse. The results obtained are of interest for plasma diagnostics based on ion excitation from ground state by ultrashort pulses. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

掺有Ni2+的α-Al2O3晶体的基态精细光谱、晶体局域结构和Jahn-Teller效应

应用晶体场理论和不可约张量算符方法构造了3d2/3d8态离子在C3v对称晶场中包含自旋-轨道相互作用、自旋-自旋相互作用、自旋-其它轨道相互作用和其它轨道-其它轨道相互作用四种微观磁效应的45阶可完全对角化的能量哈密顿矩阵.利用该矩阵,计算了Ni2+∶α-Al2O3晶体的光谱精细结构和晶体局域结构,深入研究了Ni2+∶α-Al2O3晶体的自旋-轨道相互作用、自旋-自旋相互作用、自旋-其它轨道相互作用和其它轨道-其它轨道相互作用和它们对光谱精细结构的影响及Jahn-Teller效应.理论计算值和实验值相符合.研究发现,掺杂没有改变晶体的对称性、同时发现并合理解释了Ni2+对α-Al2O3晶体基态精细光谱中Jahn-Teller效应的存在机理.     

Improved Self‐Energy Calculations for Pressure Broadening of Spectral Lines in Dense Plasmas

Pressure broadening of Lyman‐lines of hydrogen‐like lithium (Li²⁺) has been studied using a quantum statistical approach to the line shape in dense plasmas, for details see [1]. In this communication, we concentrate on the electronic self‐energy, which is a basic input to the theory of spectral line profiles. We discuss the effect of strong, i.e. close, collisions which have been neglected so far for Li²⁺ plasmas, but play generally an important role in dense plasmas, as has been shown in [2]. We present a method to calculate an improved electronic self‐energy including strong collisions based on a two‐body T‐matrix and an effective optical potential. The method is tested for level broadening of the ground state of hydrogen (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

高分辨X射线晶体谱仪及其在激光等离子体中的应用

对椭圆型聚焦晶体谱仪配X射线CCD相机的X射线谱测量系统进行了优化设计.优化设计后的椭圆型聚焦晶体谱仪系统的工作距离981.56 mm和摄谱范围0.133～0.756nm,并具有很好的谱分辨本领(λ/Δλ≥1000)和信噪比.新设计的椭圆型聚焦晶体谱仪首次在"神光Ⅱ"X光激光靶室上成功地获得了激光等离子体谱线信息并辨认和归类了一些离子的谱线,同时还给出了实验测定的谱仪能量分辨率.其中一些离子谱线诸如类离子共振线、伴线、互组合线和Ly-α线谱可为下一步诊断激光等离子体的电子温度和离子密度的空间分布轮廓打下了坚实基础.     

Radiative frequency shift without ultraviolet divergency in a two-level hydrogenic atom

Summary By taking into account the retardation effects a finite result for the frequency shift of the Lyman α-radiation from a two-level hydrogenic atom is obtained. This result shows a nonnegligible correction as compared to previous results obtained in the dipole approximation with a cut-off frequency.     

Flame temperature diagnostics with water lines using mid‐infrared degenerate four‐wave mixing

The feasibility of using degenerate four‐wave mixing (DFWM) for hot gas thermometry in the mid‐infrared spectral region is, for the first time, demonstrated by probing molecular ro‐vibrational transitions of water. DFWM spectra of hot water were recorded in specially designed flames, providing a series of temperatures varying from 1000 to 1900 K and, the dramatic spectral structure variations were used as temperature indicator. The intensity ratios between two hot water line groups at around 3231 cm⁻¹ were especially studied and composed into a calibration table for flame temperature measurement using DFWM spectra. The saturation properties of different lines were also studied by recording the line intensity ratios as a function of laser power, and the results indicated that saturated excitation was in favor of reliable temperature measurements. As validation, infrared DFWM spectra in an φ = 1.52 flat premixed methane/air flame were recorded, and a good temperature value was obtained. Moreover, the recently released HITEMP2010 database as well as its previous version HITEMP2000 were adopted to simulate the hot water spectra and to analyze the line intensity ratios. Copyright © 2011 John Wiley & Sons, Ltd.     

Extreme‐ultraviolet compact spectrometer for the characterization of the harmonics content in the free‐electron‐laser radiation at FLASH

The design and the commissioning results of a portable and compact spectrometer for the high harmonics content characterization of the extreme‐ultraviolet radiation of FLASH (free‐electron laser in DESY, Hamburg, Germany) are presented. The instrument is a grazing‐incidence flat‐field spectrometer equipped with two variable‐line‐spaced gratings; it covers the 2–40 nm wavelength region with a spectral resolution in the 0.1–0.2% range. Both spectral and intensity fluctuations of the fundamental emission and the harmonics are monitored.     

Excitation of hydrogen atom by ultrashort laser pulses in optically dense plasma

The features of excitation of a hydrogen atom by ultrashort laser pulses (USP ) with a Gaussian envelope in optically dense plasma at a Lyman‐beta transition are studied theoretically. The problem is of interest for diagnostics of optically dense media. USP have two doubtless advantages over conventional laser excitation: (a) the USP carrier frequency is shifted to the region of short wavelengths allowing exciting atoms from the ground state and (b) the wide spectrum of USP allows them to penetrate into optically dense media to much longer distances as compared with monochromatic radiation. As actual realistic cases, two examples are considered: hot rarefied plasma (the coronal limit) and dense cold plasma (the Boltzmann equilibrium). Universal expressions for the total probability of excitation of the transition under consideration are obtained in view of absorption of radiation in a medium. As initial data for the spectral form of a line, the results of calculations by methods of molecular dynamics are used. The probability of excitation of an atom is analysed for different values of problem parameters: the pulse duration, the optical thickness of a medium, and the detuning of the pulse carrier frequency from the eigenfrequency of an electron transition.     

Cumulative "roof effect" in high-resolution in vivo 31P NMR spectra of human calf muscle and the Clebsch-Gordan coefficients of ATP at 1.5 T

NMR spectra of non-weakly coupled spin systems exhibit asymmetries in line intensities known as "roof effect" in 1D spectroscopy. Due to limited spectral resolution, this effect has not been paid much attention so far in in vivo spectroscopy. But when high-quality spectra are obtained, this effect should be taken into account to explain the quantum-mechanical fine structure of the system. Adenosine 5'-triphosphate (ATP) represents a 31P spin system with multiple line splittings which are caused by J-couplings of medium strength at 1.5 T. We analyzed the ATP roof effect in vivo, especially for the beta-ATP multiplet. The intensities of its outer resonances deviate by ca. 12.5% from a symmetrical triplet. As this asymmetry reflects the transition from Paschen-Back to Zeeman effect with total spin that is largely broken up, the Clebsch-Gordan coefficients of the system can be indicated in analogy to the hyperfine structure of hydrogen. Taking the roof effect into account, the chi2 of fitting in vivo ATP resonances is reduced by ca. 9% (p<0.005).     

Hopping Transport and Stochastic Dynamics of Electrons in Plasma Layers

We investigate the stochastic dynamics and the hopping transfer of electrons embedded into two‐dimensional atomic layers. First we formulate the quantum statistics of general atom ‐ electron systems based on the tight‐binding approximation and express ‐ following linear response transport theory ‐ the quantum‐mechanical time correlation functions and the conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the atom motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. In the last part we derive Pauli equations for the stochastic electron dynamics including nonlinear excitations of the atomic subsystem. We carry out Monte Carlo simulations and show that mean square displacements of electrons and transport properties are in a moderate to high temperature regime strongly influenced by by soliton‐type excitations and demonstrate the existence of percolation effects (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plasma Diagnostics Using K‐Line Emission Profiles of Silicon

Modifications of K‐line profiles due to a warm dense plasma environment are a suitable tool for plasma diagnostics. We focus on Si K_α emissions due to an electron transfer from 2P to 1S shell. Besides 2P fine structure effects we also consider the influence of excited and higher ionized emitters. Generally spoken, a plasma of medium temperature and high density (warm dense matter) is created from bulk Si the greater part of atoms is ionized. The high energy of K_α x‐rays is necessary to penetrate and investigate the Si sample. The plasma effect influences the many‐particle system resulting in an energy shift due to electron‐ion and electron‐electron interaction. In our work we focus on pure Si using LS coupling. Non‐perturbative wave functions are calculated as well as ionization energies, binding energies and relevant emission energies using the chemical ab initio code Gaussian 03. The plasma effect is considered within a perturbative approach to the Hamiltonian. Using Roothaan‐Hartree‐Fock wave functions we calculate the screening effect within an ion‐sphere model. The different excitation and ionization probabilities of the electronic L‐shell and M‐shell lead to a charge state distribution. Using this distribution and a Lorentz profile convolution with a Gaussian instrument function we calculate spectral line profiles depending on the plasma parameters. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)