Ion Microfield Research Articles

Simple multi-particle model of ion dynamical broadening

The existing analytical models of ion dynamical broadening, while working relatively well at high densities, become progressively more inaccurate at low densities. We have developed a new analytical model that is free from this shortcoming and is also simpler than most of its predecessors. Our model is based on dynamic characteristics of the multi-particle ion microfield introduced by Chandrasekhar and von Neumann. These characteristics are used for separating the entire ensemble of microfields into two parts that act differently on radiating atoms/ions: a dynamic part, that is then treated in the impact approximation, and the remaining part, treated in the quasistatic approximation. It turns out that this model not only is simpler and faster than the previous analytical models, but also is practically as accurate as simulation models. The comparison with the experiments shows that our model is universal: it yields a good agreement with the experiments over five orders of magnitude density range where the experimental results are available.

Interference of radiating states and ion dynamics in spectral line broadening

The influence of the plasma coupling between the populations and the coherences on the lineshape is investigated. Ion dynamics is taken into account. The present research is performed within the atomic density matrix formalism. Ion microfield dynamics is simulated by the kangaroo - Poisson stochastic process (model microfield method). Numerical calculations of both lifetimes of radiating states and lineshapes are performed for the spectral doublet (1s - 2s) - (1s - 4p), (1s - 2) - (1s - 4d) of helium-like multicharged ions in hot dense plasmas. It is found that the ion microfield essentially influences the difference of populations of radiating states. Calculation of the lineshape of the doublet (1s - 2p) - (1s - 4d), (1s - 2p) - (1s - 4f) of neutral helium at astrophysical plasma conditions is also performed. The contribution of nonlinear interference effects (NIEF) in both allowed and forbidden components is calculated at various plasma conditions and a comparison with binary adiabatic theory is made. The results demonstrate that it is essential to take account of NIEF in the calculation of lineshapes of multicharged ions, but not essential in the case of neutral helium.

On the time evolution of the ionic microfield in plasmas

The field - field correlation function and the conditional covariance for the ionic microfield in a plasma are calculated within a virial cluster expansion of the two-time generating function. Results for the Debye potential are given. The short-time, high-field behaviour is discussed within a regularization procedure. The evaluated conditional covariance provides direct access to the probability density of a field strength jump which appears in the well known model microfield method. The resulting stochastic process would describe the time evolution of the ionic microfield on the basis of the real motion of the plasma particles instead of assuming Markovian behaviour.

Effective gain and Stark profile calculations in the recombination scheme X-ray lasers

Stark profile functions of Al 10+ lasing lines in recombining plasmas are calculated. Due to electron-emitter collisions and dynamic ion microfields, the 3 d − 4 f and 3 d − 5 f lines at 10.57 and 15.47 nm, respectively, are broadened by a large amount, compared to thermal Doppler broadening. Consistently with experiments, an effective gain is derived from intensity of the X-ray beam, versus plasma length. A lowering of the effective and the spectral peak gains, with respect to the commonly used Doppler gain, is noticed. Effective and peak values differ by less than 13% for transitions at 15.47 nm, and by less than 10% for those at 10.57 nm. Comparison with experimental results is discussed. Calculations seem to indicate that there is no gain at 10.57 nm, due to a large Stark broadening.

A generalized theory of stark broadening of hydrogen-like spectral lines in dense plasmas

An improved semiclassical theory of Stark broadening of spectral lines emitted by hydrogen-like ions is developed in spirit of our previous papers. Compared to the standard theories, the improvement is achieved by taking into account on equal footing a “dynamic” splitting of Stark sublevels caused by one of the components of the electron microfield and a quasistatic splitting of Stark sublevels caused by ion microfield (only the latter was allowed for in the standard theories). The presented generalized theory is developed analytically to the same level as the standard theories and embraces the latter as one of its limiting cases corresponding to relatively low densities of a plasma. However, for dense plasmas the predictions differ: e.g., for lines with intense central Stark components (such as L α , L γ , H α , etc.) the standard theories noticeably underestimate Stark broadening for high density plasmas. For conditions of the experiment by Grützmacher and Johannsen previous calculations ended up with halfwidths of the H α line of Hell that were drastically smaller (by factor of two) than the observed halfwidth of this line. Calculations by our generalized theory result in a better agreement with the experiments.

Frequency-fluctuation model for line-shape calculations in plasma spectroscopy.

A model is developed that permits the calculation of the radiation emitted by complex or highly charged ions in a plasma. The model is based on the usual separation of the plasma-emitter interaction into the homogeneous broadening effects of the fast electrons and the inhomogeneous broadening arising from slow ions. For plasma conditions where the ion motion can be neglected, the spectrum is the usual static line shape. To account for ion dynamics, the frequency-fluctuation model is introduced by decomposing the line shape of each radiative transition into a sum of radiative channels that are associated with the smallest observable inhomogeneities that form the static profile. The fluctuations of the ion microfield, the ion dynamics effect, is modeled by an exchange process between the static radiative channels. This results in both a smoothing and an overall coalescence of the radiative channels and depends strongly on an averaged characteristic fluctuation rate associated with the dynamics of the interaction of the local plasma microfield with the ion. This rate is formally related to the double-time field-field correlation function behavior. This stochastic model of the observed frequency fluctuations permits fast and accurate calculations of the emitted spectral profiles, including ion dynamics emitted by complex ions in a wide range of plasma conditions.

Line Shapes of Multiply-Charged Ions: Ion Dynamics and Concentration Effects

The model microfield method has been applied to the broadening of spectral lines emitted by multiply charged hydrogenic ions in pure and binary mixtures. Special attention is paid to the calculation of the ionic microfield distribution function. Extensive comparisons with other theoretical results are performed. Fine structure effects are shortly discussed. This paper confirms the importance of ion dynamics effects m the line shapes and discusses in detail, in the case of mixture, the dependence of the profile on the concentration of the radiating species

Generalized theory of ion impact broadening in magnetized plasmas and its applications for tokamaks.

A generalized semiclassical theory of ion impact broadening in high-temperature, magnetized plasmas is developed that is free from a shortcoming of the standard semiclassical theories of Stark broadening, which were intrinsically divergent at small impact parameters. The convergence of the present theory is achieved by taking into account, on equal footing, both the "dynamic" splitting of Stark sublevels, caused by one of the components of the ion microfield, and the Zeeman splitting. The results are applied to a novel spectroscopic method for local measurements of an effective charge in tokamaks.

A convergent theory of Stark broadening of hydrogen lines in dense plasmas

A generalized semi-classical theory of Stark broadening is developed that is free from a shortcoming of the standard semi-classical theories of Stark broadening which were intrinsically divergent at small impact parameters. A convergency of the present theory is achieved by taking into account on equal footing both a “dynamic” splitting of Stark sublevels caused by one of the components of the electron microfield and a quasistatic splitting of Stark sublevels caused by ion microfield (only the latter was allowed for in the standard theories). The presented generalized theory is developed analytically to the same level as the standard theories: it substitutes the “broadening” function C ST( Z) of the standard theories by a generalized but still elementary function C( Z). The generalized theory embraces the standard theories as one of its limiting cases corresponding to relatively low densities of a plasma. However for dense plasmas the predictions differ: our results demonstrate that the standard theories overestimate an electron impact broadening for high density plasmas.

Spectroscopy of atomic hydrogen in dense plasmas in the presence of dynamic fields: Intra-Stark spectroscopy.

The Lyman-\ensuremath{\alpha} profile of hydrogen was studied in a gas-linear pinch, the plasma parameters of which were determined by Thomson scattering. The profiles displayed pronounced first- and second-order dips. The theory of dips in profiles of hydrogenlike spectral lines in plasmas containing quasimonochromatic electric fields, e.g., plasma waves or microwaves, is therefore further developed for high-density plasmas. The central point is the allowance of a spatial nonuniformity of the ion microfield that becomes more important with increasing density. Three qualitatively new features of the ``dip'' effect arise: (1) a significant shift of the dip positions (mostly to the blue side), (2) an appearance of dips in profiles of the central Stark components, and (3) an appearance of higher-order dips due to multiquantum resonances (between plasma waves and quasistatic Stark splitting). The measured blueshifts of the first- and the second-order dips are in fairly good agreement with the predictions of the present theory. This shift is much larger than the shift of the spectral line as a whole. The amplitude of the plasma waves as estimated from the measured half-widths of the dips was of the order of 2 MV/cm.

Simulation microfield method for plasma spectroscopy

A computer simulation method has been developed to analyze the effect of the ionic microfield fluctuations on the spectral line shape of hydrogenic emitters. The simple simulation model involves use of independent perturbers interacting with the emitter through a Debye potential and is valid for weakly-coupled plasmas. The dipole autocorrelation function of the emitters are obtained by numerical integration of the Schrödinger equation for the time- evolution operator. For a large domain of plasma parameters, our calculations demonstrate that the ion-broadening mechanism belongs to a regime which is intermediate between the limiting impact and quasistatic approximations. The effect of ion-microfield fluctuations on the redistribution function has also been analyzed. This function enters into radiative transfer calculations and is often approximated by complete redistribution, which assumes that the emission profile is the same as the fluorescence profile. For highly charged emitters, this approximation is no longer valid and we have partial redistribution conditions. The occurrence of partial redistribution depends critically upon competition of the rates of spontaneous emission, Stark shifts, electron broadening, and the rate associated with ion-microfield fluctuations. By using the simulation model for an estimate of the latter rate, it is possible to analyze the role of ion-microfield fluctuations in partial redistributions.

What is meant by low or high densities in the stark broadening of hydrogenic ion lines?

The usual approximations concering the Stark broadening of the Lyman lines emitted by hydrogen or hydrogenic ions are discussed. It is shown by a simple comparison of the relevant time scales associated with the fluctuations of the slowly varying ion microfield and with the damping of the radiating dipole, that the static approximation (valid at high densities) breaks down in the line center at low densities. In this case the perturbing ions and electrons can be described in the same way, i.e., in terms of collisions. Additional effects occuring at low densities such as fine structure, Lamb shift and Doppler effects are also discussed. It is pointed out that a similar discussion may also be followed in the derivation of the rate equations.

Ion correlations and ion microfields at impurities in dense plasmas.

An impurity placed in a plasma modifies the particle-particle correlations in the plasma. This impurity-plasma-plasma correction is relevant to ion-microfield calculations in hot dense plasmas as well as to models of the fractional quantum Hall excitations in terms of impurity-plasma systems. We show how to calculate such impurity-plasma-plasma corrections and apply them to a calculation of the Baranger-Mozer (BM) second-order microfield at He, Li, Be, and B impurities in a hydrogen plasma. Such a calculation for a dense plasma requires a definition of the electric field at the impurity due to an individual plasma ion in the plasma. We show how the traditional uniform jellium background assumption can be transcended via a deconvolution of the electron density obtained from a density-functional calculation for the plasma that incorporates the fully self-consistent nonlinear screening effects. Finally we carry out all-order resummations of the BM series beyond second order using the weighted-chain-sum method and also two models of the adjustable parameter exponential approximation.

Redistribution of radiation by the fluctuating ion microfield

The redistribution of populations due to electric field fluctuations within a Stark-broadened profile of the deuterium line D 6 can be approximately described by master equations. The high-frequency component of the microfield (electrons) is included by using Lorentz-broadened Stark components. The dynamics of the low-frequency component (ions) are characterized by average lifetimes of the microfield strength. The interaction with short laser pulses deforms the microfield distribution (hole burning) in a manner that is analogous to the case of Doppler broadening. In order to obtain a simple survey concerning redistribution, a rate equation system is numerically solved by using time-iterative calculations.

Experimental investigation of saturated laser absorption in the Stark-broadened profile of the Balmer line D6

In an rf-produced deuterium plasma of known electron density ( n e = 2 × 10 19m -3) and temperatures ( T e = 1500 K, T D+ ≅ T D = 700 K), short, narrow-bandwidth laser pulses (pulse duration = 2 nsec) excite the Balmer transition from the level n = 2 to the level n = 6. The time-integrated flourescence intensity F L at the wavelength of the Balmer line D 4( D 5) from levels coupled to n = 6 by collisional and radiative processes is a measure of the population density of the level n = 6 at the end of the laser pulse. The fluorescence intensity F L is detected as a function of the laser power P L and of the distance Δλ of the laser line from the center wavelength of D 6. The reduction of the measured fluorescence is more pronounced in the wings of the Stark-broadened line profile than in the line center as compared with the theory of homogeneous line broadening. The observations can be explained by the influence of the lifetime of the ion microfield on the saturation behavior.

Density-sensitive allowed and forbidden dielectronic satellite line profiles in laser-produced plasmas

Calculations of the spectral line broadening for (2p2)1D to (1s2p)1P and (2s2p)1P to (1s2s)1S dielectronic satellite transitions have been performed for the aluminium He-like emitter in hot and dense plasmas. These calculations illustrate that the ion microfield causes an oscillator strength mixing which significantly alters the spectral intensity of such transitions. A discussion of the effects is presented, with particular emphasis on the appearance of the electric-dipole forbidden dielectronic satellite lines.

Density effects on the spectral intensities of dielectronic satellite line in dense plasmas

In this paper we present a theoretical analysis of the spectral intensity of dielectronic satellite lines in dense plasmas. The ion microfield causes an oscillator strength mixing that alters the spectral intensity of such a transition. Numerical calculations of this high-density effect have been performed for the most intense 2l2l′→1s2l He-like transitions.

Specific Features of Stark Broadening of Helium-Like Multi-Charged Ion Spectral Lines

Recently as a result of more active research on dense high temperature plasmas prominent importance has been acquired by the development of the theory of Stark broadening of multi-charged ions’Spectral lines (SL). This theory must take into account, on the one hand, the presence of fine structures in ion energy levels, and on the other hand, the effects appearing in the dense plasma:(1) dipole as well as quadrupole interaction with plasma ion microfield; (2) plasma polarization shift (PPS) of SL due to the mean electric field where the ion emitter is situated. Over the recent years a number of papers has appeared [1-4] which consider different aspects of the theory for ions with one and with two electrons.

Disalignment of excited neon atoms due to electron and ion collisions.

The laser-induced-fluorescence spectroscopy has been applied to an afterglow plasma (2 torr of 5% neon and 95% helium mixture gas), and we have observed disalignment of the neon 2${p}_{2}$-level atoms under the condition of ${n}_{e}$=5.1\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{m}}^{\mathrm{\ensuremath{-}}3}$ and ${T}_{e}$=2.0\ifmmode\times\else\texttimes\fi{}${10}^{3}$ K. The disalignment rate due to atom collisions has been determined separately. The effect of ion collisions is considered in the approximation of the static ion microfield---the Holtsmark field. This field affects and decreases the initial alignment, and its effective rate is estimated. The disalignment rate coefficient due to electron collisions is deduced to be (4.1\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$ ${\mathrm{m}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. This rate coefficient is found to be consistent with the Stark broadening due to electron collisions.

Disalignment of excited atoms due to electron and ion collisions - Relationship to the stark broadening.

The laser-induced-fluorescence spectroscopy (LIFS) has been applied to a pulsed discharge plasma (2 torr of 95% helium and 5% neon mixture gas), and we have observed disalignment of the neon 2p2-level atoms due to electron and ion collisions under the condition of ne=5.1×1013 cm-3 and Te=2.0×103 K. The effect of ion collisions is estimated in the approximation of the static ion microfield. This field causes effective disalignment, and its rate is calculated. The disalignment rate coefficient due to electron collisions is deduced to be (5.3±1.3) ×10-7 cm3s-1. This rate coefficient is found to be consistent with the Stark width as calculated by Griem.