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)     

Distribution Function of Spatial Derivative of the Ion Electric Microfield Using the Independent Particles Model in Plasmas

In this work the distribution function of spatial derivative of parallel component of quasistatic ion electric microfield in plasma is calculated. Some physical approximations are used in these calculations, where only interactions between charged emitter and perturber ions are taken into account, as first step. This approximation is known as the independent particles model. Some special functions and series are used in these calculations. It is deduced that the distribution function of spatial derivative of the ion microfield may be depend more on the probability of finding the microfield rather than the microfield value itself (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

不同微场分布函数下的光谱线型

根据光谱学,总的光谱线型是各种加宽机制的卷积结果。考虑到等离子体中的离子碰撞,Stark加宽本质上是一种非对称的光谱线型, 其中微场分布函数对光谱线型起着非常关键的作用。该文利用不同的微场分布函数研究了微场分布函数对总的光谱线型的影响。研究结果表明,在电子加宽参数和离子加宽参数很小时,不同微场分布函数对整个光谱线型的影响基本相似,但随着离子加宽参数的增加,3种不同的微场分布函数对Stark光谱线型的影响逐渐增加; 随着电子加宽参数的增加,不同的微场分布函数对Stark光谱线型的影响也逐渐增加; 但总体上Holtsmark分布和Nearest-Neighbor场分布下的光谱线型差别较小,但是Mayer模型对光谱线型影响较大。特别是,当离子加宽参数较大时,Mayer模型对光谱线型的影响异常明显,这也正说明离子间碰撞剧烈时对光谱线型的影响很大。该结果对等离子体参数诊断有一定参考价值。     

Distribution of the Coulomb microfield within an ion cluster

The microfield distribution function in clusters was studied by simulation using the molecular dynamics and Monte Carlo methods. The results obtained were compared with microfield distributions in infinite plasma. It was shown that the calculated distributions have the same asymptotics. However, the position of the maximum and the existence of additional extrema depend on the cluster type and size. The dependence of the microfield expectation and variance on the number of cluster particles was also studied.     

Theory of Stark broadening—II exact line profile with model microfield

A semi-classical theory of Stark broadening is presented which differs basically from current theories. No attempt is made to improve existing approximations. An exact solution is given using a model of the actual microfield incorporating all the essential information, i.e. the probability distribution and the covariance of the fluctuating microfield. Calculations can be carried out completely without approximations and no divergences are encountered. It is shown that the correct profiles are obtained in both the high- and low-density limit. Results are presented for hydrogen and helium lines.     

Das Mikrofeld im Plasma

By taking full account of the Coulomb interaction and energy conservation, the probability distribution of the electric and magnetic microfield in an ionized gas is calculated. It results a Gaussian distribution instead of the hitherto used Holtsmark function and its variants which exhibit certain deficiencies. The mean square electric field is found to be proportional to the temperature, in analogy to the Nyquist formula. The probability of finding an atomic charge in the vicinity of another is established. With this, the time correlation function of the microfield and an average of the correlation time is deduced. Applications to the theory of transport phenomena and spectral line broadening are briefly discussed.     

Elementary Many‐Particle Processes in Plasma Microfields

The effect of electric and magnetic plasma microfields on elementary many‐body processes in plasmas is considered. As detected first by Inglis and Teller in 1939, the electric microfield controls several elementary processes in plasmas as transitions, line shifts and line broadening. We concentrate here on the many‐particle processes ionization, recombination, and fusion and study a wide area of plasma parameters. In the first part the state of art of investigations on microfield distributions is reviewed in brief. In the second part, various types of ionization processes are discussed with respect to the influence of electric microfields. It is demonstrated that the processes of tunnel and rescattering ionization by laser fields as well as the process of electron collisional ionization may be strongly influenced by the electric microfields in the plasma. The third part is devoted to processes of microfield action on fusion processes and the effects on three‐body recombination are investigated. It is shown that there are regions of plasma densities and temperatures, where the rate of nuclear fusion is accelerated by the electric microfields. This effect may be relevant for nuclear processes in stars. Further, fusion processes in ion clusters are studied. Finally we study in this section three‐body recombination effects and show that an electric microfield influences the three‐body electron‐ion recombination via the highly excited states. In the fourth part, the distribution of the magnetic microfield is investigated for equilibrium, nonequilibrium, and non‐uniform magnetized plasmas. We show that the field distribution in a neutral point of a non‐relativistic ideal equilibrium plasma is similar to the Holtsmark distribution for the electrical microfield. Relaxation processes in nonequilibrium plasmas may lead to additional microfields. We show that in turbulent plasmas the broadening of radiative electron transitions in atoms and ions, without change of the principle quantum number, may be due to the Zeeman effect and may exceed Doppler and Stark broadening as well. Further it is shown that for optical radiation the effect of depolarization of a linearly polarized laser beams propagating through a magnetized plasma may be rather strong. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

自聚焦棒透镜准直系统的装配误差引起的附加耦合损耗分析

Latex particles are general samples used for electron holography. Electrostatic field outside charged latex particles has been investigated. The observation of electrostatic microfield inside charged latex particles (0.31 μm) is reported. Digital reconstruction is employed to decode the electron image holograms. Experimental results are presented. Correspondent analysis is also given.     

不同微场分布函数对Stark加宽和频移的影响

分别采用Holtsmark,Neutral Point,Nearest-Neighbor和Mayer模型微场分布函数对Stark线型进行了研究,进而得到相应微场函数下的Stark加宽和频移,研究了4种不同的微场分布函数对Stark加宽和频移的影响。研究结果表明,在电子加宽参数不变时,4种微场分布函数对Stark加宽和频移的影响随离子加宽参数的增加而增加;在离子加宽参数不变时,4种微场分布函数对Stark加宽和频移的影响随电子加宽参数的增加而增加;特别是,当离子加宽参数较大时,Mayer模型微场分布函数对Stark加宽和频移的影响异常明显。这说明,微场分布函数对谱线的加宽和频移的影响在离子与离子碰撞剧烈的等离子体环境中尤其显著, 在这样的等离子体环境中,进行等离子体诊断时,选择合适的微场分布函数非常重要。结果对等离子体诊断有一定参考价值。     

Broadening of free-bound radiation thresholds in plasmas—II. Quasistatic theory for negative ions

Broadening and shifts of the long wavelength thresholds of the affinity continua of negative ions are investigated. A quasistatic theory is developed which treats the broadening as a plasma effect. The threshold shape is determined by convolution of the undisturbed negative ion cross-section with the distribution function of a component of the electric plasma microfield. This concept explains the absence of threshold shifts and shows that threshold broadening is proportional to the mean Holtsmark field strength in the plasma. Comparison of theory with experimental data shows good agreement.     

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)     

Die Verteilungen des elektrischen und magnetischen Mikrofeldes im relativistischen Plasma

The probability distributions of the electric and magnetic microfield at a fixed space point in a relativistic, non-degenerate, homogeneous, and isotropic plasma in thermodynamic equilibrium are determined using the Markov-method and neglecting the particle interaction. They are found to be Holtsmarkians like the electricnon-relativistic microfield distribution, but the characteristic field strengths are increasing functions of temperature which are calculated.     

The Lowering of the Spectral Series Limit of Hydrogen and Carbon in a Plasma

The lowering of the ionization potentials of hydrogen and carbon atoms immersed in a high temperature and high density thermal plasma generated in a wall stabilized arc have been estimated from the advance or shift of their respective series limits in the vacuum ultraviolet region of the spectrum for different electron densities and temperatures. Results show a close agreement with those theoretical calculations in which the effects of both microfield and polarization terms are added. However, our electron densities are lower by about two orders of magnitude than the critical electron densities required by theory for the inclusion of the microfield term. The question of validity of a critical electrom density will be discussed.     

Line shapes in nonlinear spectroscopy

The shape of the spectral lines of an optically active system interacting with one or more strong radiation fields in the presence of a perturbing bath is studied. A method based on the statistics of the fluctuation of the interaction between the radiator and the perturbing environment (the model Markov microfield theory) is used. This method permits the foundations of line shape theory in modern statistical mechanics to be seen clearly. Multiphoton processes and homogeneous, inhomogeneous, and power broadening mechanisms are included in the analysis. The correlations between radiative and collisional processes which arise in nonlinear spectroscopy are included explicitly. A discussion of the new information that is obtained from these correlations in nonlinear spectroscopy is also presented. Several model systems are presented as illustrative examples of the theory.     

An analysis of Markovian model microfield methods for stark broadening

Stark broadening theories which concentrate on the statistics of the plasma electric microfield rather than the dynamics of collisions have come to be known as Model Microfield Methods. In the present paper we present an analysis of Stark broadening problems based on Markovian model microfield statistics. Our derivation permits an easy comparison with traditional Stark broadening theories such as the impact and unified theories; this comparison is used to clarify the physical nature of the approximations employed by Markovian models. The strengths and weaknesses of various models are discussed, emphasizing the kangaroo process of Brissaud and Frisch, and methods are suggested for improving the current model microfield approach.     

Electric Microfield Distributions in Dense One‐ and Two‐Component Plasmas

The electric microfield distributions have been calculated using an integral‐equation method for one‐component plasmas proposed by Iglesias [1] and the coupling‐parameter integration technique for two‐component plasmas proposed by Ortner et al. [2]. Electric microfield distributions are studied in the frame of the Kelbg pseudopotential model, taking into account quantum‐mechanical effects (diffraction, quantum symmetry effects) and screening effects. The screened pseudopotential is represented in a numerically approximated form. The results are compared with simulation results obtained by other authors. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inhomogeneity tensors of ion microfield in Debye plasma at neutral emitter

A method of calculation of inhomogeneity microfield tensors in Debye plasma, using the Mayer-Mayer cluster expansion, is presented. The octupole inhomogeneity tensor of the ion microfield at a neutral emitter has been calculated for the first time. The quadrupole inhomogeneity tensor of the ion microfield at a neutral emitter has been recalculated. We have performed numerical calculations for plasma consisting of atoms, electrons and singly or doubly charged ions.     

Drei-Teilchen-Reaktionen und Partialwellen

A formal scattering theory for reactions with three outgoing particles is developed. The transition amplitude is written as an expansion of partial waves numbered by the generalized angular momentumλ in the six-dimensional space and by the ordinary angular momentum. For potentials of finite range only a limited number of partial waves is important. The dependence of the cross section on the position of the decay plane is investigated as well as the distribution of the particle energies in the Dalitzplots. Symmetry with respect to permutations of identical particles is taken into account.     

Electron contribution to quasistatic stark broadening

The contribution of quasistatic electrons to linear Stark broadening is evaluated by means of convolutions. A modified normalized microfield distribution including these electrons is derived. Hydrogen line profiles are calculated on this purely quasistatic basis. Comparisons with experimental results for Lyman-α and H_β yield satisfactory agreement in the line wings.     

Cooling kinetics of a granular gas of viscoelastic particles

The evolution of a granular gas of viscoelastic particles in the homogeneous cooling state is studied. The velocity distribution function of granular particles and the time dependence of the mean kinetic energy of particles (granular temperature) are found. The noticeable deviation of the distribution function from the Maxwell distribution and its non-monotonous evolution are established. The perturbation theory with respect to the small dispersion parameter is elaborated and the analytical expressions for the asymptotic time dependence of the velocity distribution function and the granular gas temperature are derived.