Model Microfield Research Articles

Path integral approach for Stark broadening of Lyman lines in hydrogen plasma

New results for Lyman lines from hydrogen plasmas are presented using the path integral approach. The influence of plasma components (electrons and ions) on the radiator is analysed separately. The ionic contribution is treated within the path integral approach, while the electronic contribution is estimated by the standard collision operator. The Stark effect, including the ion quadrupole contribution, is considered. The time‐dependent ionic microfield is treated within the path integral approximation using the model microfield method (MMM). The comparison with the quantum statistical approach is performed using a wide range of temperatures (T = 104–107 K) and electron densities (Ne = 1023–1026 m−3). Good agreement is mainly obtained for low density and high temperature.

Electron density determination in the divertor volume of ASDEX Upgrade via Stark broadening of the Balmer lines

In this article we present the development of a new diagnostic capable of determining the electron density in the divertor volume of ASDEX Upgrade (AUG). It is based on the spectroscopic measurement of the Stark broadening of the Balmer lines. In this work two approaches of calculating the Stark broadening, i.e. the unified theory and the model microfield method, are compared. It will be shown that both approaches yield similar results in the case of Balmer lines with high upper principal quantum numbers n. In addition, for typical AUG parameters the influence of the Zeeman splitting on the high n Balmer lines is found to be negligible. Moreover, an assumption for the Doppler broadening of Tn = 5 eV, which is the maximum Frank–Condon dissociation energy of recycled neutrals, is sufficient. The initial electron density measurements performed using this method are found to be consistent with both Langmuir probe and pressure gauge data.

Comparative Study on Ion‐Dynamics for Broadening of Lyman Lines in Dense Hydrogen Plasmas

AbstractBroadening of spectral lines by a plasma surrounding can be used for plasma diagnostics. Full hydrogen Lyman line profiles are calculated with a quantum‐statistical approach. The effects of plasma electrons and ions on the emitter states are considered separately. The influence of electrons is considered in a dynamically screened Born approximation (collision approximation). For the ions, we apply the quasi‐static approximation and two different approaches to account for ion‐dynamics, namely, the model microfield method (MMM) and the frequency fluctuation model (FFM). We compare resulting widths of Lyman lines in the temperature range T = 104 to 107 K and the free electron density range ne = 1023 to 1026 m–3. For Lα, the error made by neglecting ion‐dynamics increases with increasing temperature and decreasing density, and is at least –15%. Due to the double peaked structure of Lβ the situation is less systematic. However, a large region exists, where ion‐dynamics does not affect the line shape of Lβ. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Quantum-statistical line shape calculation for Lyman-α lines in dense H plasmas

We present results for the Lyman-α line of hydrogen in dense plasmas. Full line profiles are calculated within a quantum-statistical method, based on thermodynamic Green's functions. The contributions of plasma ions and electrons are considered separately. Linear and quadratic Stark effect as well as quadrupole effects are taken into account for ions. The model microfield method is used to include ion dynamics. The focus of this work lies on the contribution to broadening and shift by free electrons beyond the Born approximation. The effect of strong collisions can be identified as ladder-like diagrams of the electron-emitter propagator. In an effective two-particle approximation, the electronic self-energy is given in terms of scattering amplitudes, analogous to Baranger's expressions [Baranger, M 1958 Phys. Rev. 112 855]. We obtained scattering amplitudes from convergent close-coupling calculations including medium effects via Debye screening. Additionally, the electronic coupling between initial and final states is taken care of by a vertex correction. In our examples, the free electron density ranges between 1023 and 1025 m−3 at a plasma temperature of 1 and 2 eV, respectively.

A Stark broadening simulation using a renewal process for the electric microfield

Stark broadening of atomic lines in plasmas is investigated by generating the electric microfield with a renewal process. In this model, the microfield is stepwise constant, with jumping times sampled from a waiting time distribution (WTD). Our model is a true simulation of the renewal process, using random number generators for generating different probability density functions (PDF). The use of an equilibrium static microfield PDF and an exponential waiting time distribution reproduces the so called model microfield method (MMM) results. The work presented is an application to the hydrogen Lyman-α line, for which we compare our renewal process model and ab initio simulations calculations, with the aim of studying the role of non exponential waiting time distributions.

Stochastic Processes Applied to Line Shapes

Abstract We present approaches using stochastic processes for the calculation of line broadening in plasmas. The derivation of model microfield methods (MMM) based on analytic formulations is recalled, as well as an approach using a simulation of the stochastic process. We discuss the possibility of an improvement of the stochastic process by comparing our first results to ab initio particle simulations coupled to a numerical integration of the emitters Schrödinger equation.

Hydrogen Stark Broadened Brackett lines

Stark-broadened lines of the hydrogen Brackett series are computed for the conditions of stellar atmospheres and circumstellar envelopes. The computation is performed within the Model Microfield Method, which includes the ion dynamic effects and makes the bridge between the impact limit at low density and the static limit at high density and in the line wings. The computation gives the area normalized line shape, from the line core up to the static line wings.

Spectral line shapes modeling in laboratory and astrophysical plasmas

An overview of several spectral line shapes studies of common interest in astrophysical and laboratory plasmas is presented. For lines dominated by Stark broadening, approaches taking into account the dynamics of numerous perturbers are sometimes required. We briefly recall ab initio simulation techniques and model microfield methods used for such conditions. Together with the impact approximation, such models may also be used for studying the effects on a line profile of a magnetic field of the order of the tesla, allowing the diagnostic of stellar objects or magnetic fusion devices. The problem of the apparent spectral line emitted in a plasma affected by strong fluctuations of the plasma parameters is discussed for the case of optically thin plasmas.

Electron density measurements in the National Spherical Torus Experiment detached divertor region using Stark broadening of deuterium infrared Paschen emission lines

Spatially resolved measurements of deuterium Balmer and Paschen line emission have been performed in the divertor region of the National Spherical Torus Experiment using a commercial 0.5m Czerny-Turner spectrometer. While the Balmer emission lines, as well as the Balmer and Paschen continua in the ultraviolet and visible regions have been extensively used for tokamak divertor plasma temperature and density measurements, the diagnostic potential of infrared Paschen lines has been largely overlooked. We analyze Stark broadening of the lines corresponding to 2−n and 3−m transitions with principal quantum numbers n=7–12 and m=10–12 using recent model microfield method calculations [C. Stehle and R. Hutcheon, Astron. Astrophys., Suppl. Ser. 140, 93 (1999)]. Densities in the range (5–50)×1019m−3 are obtained in the recombining inner divertor plasma in 2–6MW neutral beam heated H-mode discharges. The measured Paschen line profiles show good sensitivity to Stark effects and low sensitivity to instrumental and Doppler broadenings. The lines are situated in the near-infrared wavelength domain, where optical signal extraction schemes for harsh nuclear environments are practically realizable and where a recombining divertor plasma is optically thin. These properties make them an attractive recombining divertor density diagnostic for a burning plasma experiment.

Diagnostics of a current-sheet plasma with the use of helium spectral lines with forbidden components

Results are presented from the first measurements of the profiles of the HeI 447.1-nm and HeI 492.2-nm neutral helium spectral lines emitted by the plasma of a current sheet formed in the CS-3D experimental device. A theoretical analysis of these profiles is performed with the model microfield method. A comparison of the theoretical and experimental profiles shows that the electron density in the peripheral regions of the current sheets amounts to (1.0–2.0)×1015 cm−3.

Stark-broadened hydrogen line profiles predicted by the model microfield method for calculating electron number densities

This report is the first account on the application of theoretical Stark-broadening profiles predicted by the model microfield method (MMM) to estimate electron number density ( n e) in several laboratory plasmas. The determination of n e is accomplished by least-squares fitting of the entire emission profile or the wing portions of the emission profile of the H β line (486.13 nm) to the theoretical Stark-broadened profiles. Experimental profiles obtained for the H β line from argon and helium inductively coupled plasmas (ICP), a glow discharge, and a high-voltage spark are used to test the new MMM profiles. Results are contrasted with data predicted by the traditional ‘Unified Theory’. Compared to the ‘Unified Theory’, the MMM profiles are more accurate in the line center and span over a wide range of temperature (2500–80 000 K) and electron number densities (1×10 10–1×10 17 cm −3).

Balmer-α transition of He II:measurements and calculations

We analyse measurements of the Stark-broadened profile of the HeII Balmer-α transition at densities andtemperatures up to ne = 3×1018 cm-3 andkBTe = 30 eV, respectively, and compare the results withcalculations and existing experimental data. Theoretical spectracalculated according to the frequency fluctuation model(FFM) agree within the measured spectral range with the experimentalones when ion dynamics is taken into account, whereas calculationsaccording to the model microfield method (MMM) underestimate thewidth. Concerning the Stark shift, the present experimental values areconsistent with existing shifts measured at lower temperaturesbut due to the experimental error bars it is not possible to distinguish betweenpredictions based on the MMM or the standard theory, even though these predictions differ bya factor of two.

Asymmetry of Stark profiles

The theoretical basis is presented that allows to compute the Stark broadened line shapes of atomic ions up to the quadrupole terms in the interaction potential between the radiator and the plasma electric microfields and their gradients. The nature of the corrections due to the plasma polarization effects associated with the electron distribution around ion perturbers are carefully analyzed. The relevant universal plasma functions are evaluated in a cluster expansion or by Monte Carlo simulations, and the line shape is calculated with ion dynamic effects by the Model Microfield Method. The asymmetry of the Lyman line of hydrogenic ions is then studied.

Polarised hydrogen line shapes in a magnetised plasma

The general profiles entering the polarised radiation transfer matrix for the hydrogen Ly\(\) line in dense magnetised plasmas are studied. The Stark effect due to plasma electrons is treated by the Unified Theory. The contribution of fine structure is discussed. Ion dynamics effects are studied, by application of the Model Microfield Method (MMM). The validity of a simpler approach, based on the Simplified Unified Theory (SUT) is assessed, by comparison with the MMM.

Hydrogen lines in correlated plasmas

Hydrogen line shapes broadened by Stark effects are calculated for a dense hydrogen plasma created by a Nd:YAG laser focussed into liquid water. The electronic density and temperature deduced from the experiment allow to use a Debye Huckel model for the interaction potential between the plasmas ions screened by the electrons. The Stark broadened line shapes, obtained in the frame of the Model Microfield Method, both for the electronic and ionic contributions, are based upon accurate Monte Carlo hydrogen field distributions functions, calculated on a neutral point together for the electrons (OCP) and for the ions (screened Coulombic field). The theoretical description allows to cover a wide range of thermodynamical conditions and to predict the emissivity (and opacity) of astrophysical and laboratory plasmas.

Diagnostics of dense plasmas from the profile of hydrogen spectral lines in the presence of a magnetic field

A many particle approach to spectral line shapes has been generalized including the influence of a uniform magnetic field. Within this approach the electrons are treated fully quantum mechanically. Ion dynamics have been included via the well-known model microfield method. The developed theory has been applied to calculate the first Balmer lines of hydrogen for plasma parameters as can be found in dense divertor plasmas. It has been shown that the half-width, e.g., of the H β line is a useful tool for the determination of the electron densities in such plasmas.

Accuracy of simplified methods for ion dynamics in Stark profile calculations

To assess the accuracy of simplified methods for the treatment of ion dynamics in Stark-broadening theory, we have compared two such methods, the relaxation theory and model microfield method, against benchmark calculations for the CVI ${\mathrm{H}}_{\ensuremath{\alpha}}$ line. It is shown that both methods show poor agreement at low densities.

On the consequences of a realistic conditional covariance in MMM-calculations

The model microfield method (MMM) may be used to include the effect of ion motion in line shape calculations. This kind of modelling of the time evolution of the microfield as a stochastic process, as is done in this method, yields a short time behaviour of the conditional covariance of the model microfield, which differs considerably from a conditional covariance calculated by considering the real motion of the plasma ions (microscopic conditional covariance). In this work purely ionic broadened hydrogen profiles are calculated using the microscopic conditional covariance within the MMM. It is shown that, depending on the reduced radiator-perturber mass, these MMM calculations may lead to unphysical line shapes. For comparison, hydrogen profiles derived within the MMM using the kangaroo process and from line shape simulations are given.

Quantum Interference in Radiation Redistribution of Highly Charged Ions in Plasmas

The influence of quantum interference effects induced by mixing of coherences and populations in the fluctuating plasma microfield on the redistribution of resonance radiation by HCI is studied in terms of the atomic density matrix. The thermal ion motion is considered within the model microfield method. Results show that the thermal ion motion (ion dynamics) induces QIEF as well, and both are essential in line centres and nearest wings of the scattered radiation.

Model microfield method for partial redistribution of resonance radiation in dense plasmas

The influence of nonlinear interference effects (NIEF) on the radiation redistribution functions is investigated in terms of the atomic density matrix formalism. The ion motion is considered within the model microfield method. The particular calculations have been performed for the spectral doublet , of helium-like ion in hot dense plasmas (T = 350 eV, ). Taking account of both NIEF and ion dynamics is essential in the line centre and the nearest wings of the scattered radiation.