Plasma In Local Thermodynamic Equilibrium Research Articles

Influence of detailed line treatment on the opacity of iron plasmas in the 2p-3d energy region.

The transmission spectrum has been calculated using a detailed-level-accounting model for iron plasmas in local thermodynamic equilibrium in the 2p-3d excitation energy region. The calculation is motivated by the large difference between the theories obtained by statistical methods such as unresolved transition array and superconfiguration transition array and the experiment reported in the literature. Detailed studies have been carried out on the effects of the width of individual lines and configuration interaction. The results show that the saturation of individual lines is evident in the transmission. These effects should be considered carefully to obtain an accurate opacity or transmission. In view of the uncertainties in the experiment, rather good agreement is found between our theoretical result and the experiment when these effects are taken into account in the calculation.

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Radiative opacities and configuration interaction effects of hot iron plasma using a detailed term accounting model

We have calculated the radiative opacities of iron plasma in local thermodynamic equilibrium using a detailed term accounting model. The extensive atomic data are obtained by multiconfiguration Hartree-Fock (MCHF) method, with Breit-Pauli relativistic corrections. Extensive configuration interaction (CI) has been included based on LS coupling to obtain energy levels and the bound-bound transition cross sections. A detailed configuration accounting model is applied to evaluate the bound-free absorption cross sections. We simulate two experimental transmission spectra [G. Winhart et al., Phys. Rev. E 53, R1332 (1996); P. T. Springer et al., J. Quant. Spectrosc. Radiat. Transf. 58, 927 (1997)] to verify our calculation model, one is at a temperature of 22 eV and a density of 10(-2) g/cm(3) and the other is at a temperature of 20 eV and a lower density of 10(-4) g/cm(3). It is shown that the strong CI can effectively change the oscillator strengths in contrast to the single configuration HF method. For both of the two simulated transmission spectra good agreement is obtained between the present MCHF results and the experimental data. Spectrally resolved opacities and Planck and Rosseland mean opacities are also calculated. For the isothermal sequence of T=20 eV, when the density decreases from 10(-2) to 10(-5) g/cm(3), the linewidth also decreases so that the iron transition arrays show more discrete line structures and the linewidth becomes very important to the Rosseland mean opacity.

Measurement and Modeling of OH, NO, and CO Infrared Radiation at 3400 K

The infrared emission spectrum of an air plasma containing small quantities of CO 2 and H 2 O was measured and modeled in absolute intensity in the spectral range 2.4-5.6 μm. A 50-kW radio-frequency inductively coupled plasma torch was used to produce the air plasma in local thermodynamic equilibrium. The temperature profile measured by emission spectroscopy peaks at 3400 K. The absolute intensity emission spectrum was measured and compared with numerical simulations obtained with the line-by-line radiation code SPECAIR. Spectroscopic models incorporated into the SPECAIR code include the infrared rovibrational bands of OH, NO, and CO. Absorption of the plasma emission by room-air CO 2 and H 2 O in the optical path between the plasma and the detector is taken into account. Plasma emission from CO 2 (v 1 + v 3 ) and (v 3 ) bands is also modeled, using a correlated-k model

Curves of growth of spectral lines emitted by a laser-induced plasma: influence of the temporal evolution and spatial inhomogeneity of the plasma

The curves of growth (COG) of five Fe I lines emitted from a laser-induced plasma, generated with Fe–Ni alloys in air at atmospheric pressure, have been investigated. Spectral lines with different energy levels and line widths, emitted with a broad range of optical depths, have been included in the study in order to check the validity of theoretical models proposed for COG generation, based in the radiative transfer within a plasma in local thermodynamic equilibrium. The COGs have been measured at time windows of 4–5 μs and 15–18 μs. The Stark widths of the Fe I lines have been obtained, and the line widths have been determined by measuring the plasma electron density at the time windows selected. It is shown that at a time window of 4–5 μs, the inhomogeneity of the plasma magnitudes has an important influence on the COGs of intense lines. For this time window, a two-region model of the plasma has been used to generate theoretical COGs that describe satisfactorily the experimental curves of all the lines using a single set of plasma parameters. The results reveal the existence of considerable gradients between the inner and the outer plasma regions in the temperature (9400–7800 K) and in the density of Fe atoms (4×10 16–0.02×10 16 cm −3 for a sample with 100% Fe). On the contrary, at the time window 15–18 μs, at which the plasma has suffered most of its expansion and cooling process, the COGs of all the lines may be described by a single-region model, corresponding to a plasma with uniform temperature (6700 K) and density of Fe atoms (0.06×10 16 cm −3 for a sample with 100% Fe). It is also shown that at initial times, the plasma inhomogeneity has an important effect in the line profiles of intense spectral lines, which are described by using the two-region model of the laser-induced plasma.

The reactive thermal conductivity for a two-temperature plasma

Reliable plasma thermodynamic and transport properties are required for the numerical simulation of thermal plasma systems. Although many databases for the thermal plasma properties at the local thermodynamic equilibrium (LTE) state have been compiled, the database for the two-temperature (2-T) plasma is still far from completeness. There exits considerable confusion in the literature concerning how to calculate the thermodynamic and transport properties, including the reactive thermal conductivity, for the 2-T plasma. In this paper, a detailed derivation for the reactive thermal conductivity of the 2-T argon plasma is presented using two different approaches. The present calculated results for the reactive thermal conductivity are identical to those due to Hsu [5] for the special case of LTE plasma, but are different when the electron temperature is higher than the heavy-particle temperature, the difference increases with increasing electron/heavy-particle temperature ratio, θ(= T e/ T h), and becomes quite significant at high θ.

Extinguishing phenomenon and critical discharge boundaries of argon and molecular-gas-seeded argon pulse-modulated induction thermal plasmas

A stable discharge region of pulse modulated induction thermal plasma at atmospheric pressure has been determined in terms of the duty factor (DF) and the shimmer current level (SCL) both experimentally and numerically. The experiment was performed with a MOSFET-employed inverter-feed pulse modulated power supply unit having a maximum power of up to 50 kW. The on-time of the pulsing signal was fixed at 10 ms while the off-time was varied to determine the critical/minimum DF up to which plasma discharge sustained, for a fixed SCL. In this way, for different SCLs, critical/minimum DFs were determined for different gas combinations. The gas flow was composed of 100 lpm argon and 2.5 lpm H2, N2 or CO2 as secondary gas through the sheath channel only. Steady state coil currents for Ar, Ar–H2, Ar–N2 and Ar–CO2 were 244 A, 263 A, 296 A and 296 A, respectively. In the numerical part, a two-dimensional local thermodynamic equilibrium (LTE) code was used to predict the discharge boundary for the same operating conditions as those of the experiment. Both experimental and simulated results reveal that injection of dissociative molecular gases greatly shrinks the stable discharge region, which is attributed to the lowering of temperature and particle density. It was found that the stable discharge region predicted numerically was smaller than that of the experimental one. This implies that a non-LTE plasma has a discharge zone wider than that of an LTE plasma.

Detailed-term-accounting-approximation calculations of the radiative opacity of laser-produced Al plasmas.

An extensive configuration interaction (CI) scheme and the R-matrix method are combined to calculate the radiative opacity for laser-produced aluminum plasma in local thermodynamic equilibrium using the detailed-term-accounting (DTA) approximation. The CI scheme is used to obtain the absorption oscillator strengths of the electric dipole allowed transitions for evaluating the bound-bound absorption cross sections, and the R-matrix method is used to obtain the bound-free absorption (photoionization) cross sections. For an aluminum plasma at a temperature of 20 eV and the density of 0.01 g/cm(3), the Rosseland and Planck mean opacities are calculated to be 4184 and 24891 cm(2)/g, respectively, by integrating the spectrally resolved opacities with Rosseland and Planck weighting functions. The two mean opacities are also obtained by using the average atom model, and they are 22520 and 30402 cm(2)/g, respectively. The optical transmission from the photon energy of 70-250 eV, which was experimentally measured by Winhart et al. [G. Winhart et al. Phys. Rev. E 53, R1332 (1996)], is also calculated. Generally good agreement is found between our DTA and experimental transmission. Our theoretical result reproduces all structures shown in the experiment, whereas some of the structures near the higher energy edge did not show up in some other opacity models. These structures are attributed to the detailed treatment of the photoionization process.

Detailed Spectral Line Effects on the Radiative Opacity ofLaser-Produced Al Plasmas

The detailed term accounting (DTA) approximation for the line absorptionand the average atom (AA) model for bound-free and free-free absorptionare used to calculate the radiative opacity of high-powerlaser-produced plasmas in local thermodynamic equilibrium (LTE).The spectral resolved opacities of Al plasmas are calculatedat the temperatures and densities of 40 eV and 0.0135 g/cm3,and 58 eV and 0.02 g/cm3. Rosseland and Planck mean opacities areobtained by integrating the spectral resolved opacities withRosseland and Planck weighting functions. The results show thatthe Rosseland mean opacity is very sensitive to the detailed profile.Radiative opacities under the same plasma conditionsare also obtained by using a completely pure AA model. Theresults from the DTA and pure AA models are then compared.

Detailed-term-accounting-approximation simulation of x-ray transmission through laser-produced Al plasmas

An extensive configuration interaction (CI) scheme and the R-matrix method are combined to calculate the x-ray transmission spectrum for high-power laser-produced Al plasmas in local thermodynamic equilibrium by using the detailed-term-accounting (DTA) approximation. All atomic parameters such as state levels and photoabsorption cross sections for different ionization stages are obtained by using the CI and R-matrix method. Special attention is given to the effects of autoionizing resonance broadening on the transmission. A large difference exists between the convergence of the results with and without taking account of autoionizing resonance broadening when the autoionization resonance broadening is the major broadening mechanism. This shows that autoionizing resonance widths of the K-shell excited states have large effects and should be considered to interpret the spectral-resolved transmission.

Laboratory measurement of opacity for stellar envelopes

We have measured the frequency dependent opacity of a low density iron plasma in Local Thermodynamic Equilibrium (LTE). The measured iron plasma conditions of 20 eV temperature and 10 −4 g/cc density, match those of stellar envelopes where iron dominates the radiative transport. Properties of the M-shell Δn = 0 transition arrays in iron are measured in this experiment, providing the first direct test of opacity models used in stellar pulsation and evolution calculations. We describe new methods to obtain LTE opacity data for plasmas at 100 times lower density than previous measurements. Experimental requirements include: high spectral resolution, large homogenous plasma sources, and Planckian radiation fields lasting tens of nanoseconds. These conditions were achieved using the 500 kJ SATURN facility at Sandia National Laboratory.

Statistical treatment of the spectral properties of LTE plasmas

A technique using both the screened-hydrogenic average-atom model and methods of classical statistical mechanics is recalled. It allows a fast evaluation of spectral opacities of local thermodynamic equilibrium plasmas. The atomic-physics description, electronic correlations and the splitting in integer charge stages are studied by comparing to more detailed calculations.

Statistical mechanics of highly charged ion plasmas in local thermodynamic equilibrium

The screened-hydrogenic average-atom model is well suited to describe multicharged ion plasmas in local thermodynamic equilibrium (LTE) for in-line plasma physics calculations. Using general principles of statistical mechanics, this model is shown to be properly defined and thermodynamically consistent. The grand canonical partition function ${Z}_{G}$ of the bound electrons is written as a multidimensional integral. Its saddle-point evaluation gives the intuitive average-atom equations. Using this formalism, a method for accounting the various ionization stages of a LTE plasma is proposed. It can be used to estimate the integer charge stage distribution in this type of medium from any average-atom model. Once the model is well established, simpler formulas, more suitable for fast computations, are derived in the framework of the classical theory of fluctuations. Numerical results are presented and discussed.

Statistical treatment of radiative transitions in local thermodynamic equilibrium plasmas

The fluctuations of the electronic configurations around the average-atom configuration are estimated using classical statistical mechanics. This method allows the spectral opacities to be rapidly calculated without explicit recourse to detailed configuration accounting. Coupled to a screened-hydrogenic average-atom model, it can be implemented into the atomic physics package of a hydrodynamic code. We compare our results to numerical spectra constructed with more detailed codes or experimental spectra. {copyright} {ital 1997} {ital The American Physical Society}

New screening coefficients for the hydrogenic ion model including l-splitting for fast calculations of atomic structure in plasmas

New screening coefficients are given for calculating the energy levels of many-electron atoms in the hydrogenic ion approximation including l-splitting. This model allows fast computation of various atomic parameters (one-electron energies, ionization potentials, etc.) for all ionization stages of any element with no restriction concerning the maximum nl subshell. Part of the screening coefficients have been obtained from numerical fits over a large data base containing ionization potentials and excitation energies of ions. The others have been extrapolated by means of regularities deduced from the adjustment procedure. The mean and root mean square errors are better than 5% and 16.2%, respectively, for the 15 636 data considered. Some properties of the new screened hydrogenic model are studied, such as the filling competitions between several subshells of the lanthanides. The meaning of one-electron energies available from the total ion energy is discussed and the status of the self-screening term in plasmas in local thermodynamic equilibrium is briefly addressed. These notions are of great importance for coherence between the statistical treatment of such media and the calculation of their spectral properties.

Shielding of dust grains at the edge of an equilibrium plasma

It is pointed out that in a bounded dusty plasma in local thermodynamic equilibrium, the sheath electric field can very effectively shield highly charged $(g~{10}^{4}e$ for typical low-temperature plasmas) dust grains from the wall region.

A mathematical model of TIG electric arcs operating in the hyperbaric range

In a recent paper Ducharme et al presented a model for a free-burning tungsten inert gas (TIG) electric arc with non-consumable electrodes using a flat anode and argon shielding gas. The model evaluates the laminar gas flow, temperature distribution and electric field in the arc column by treating the current carrying region of the arc as a partially ionized plasma in local thermodynamic equilibrium. The dependence of transport coefficients on temperature is taken into account, as is the entrained shielding gas flow entering the arc from around the cathode. This model is extended here to investigate both 5 mm long 200 A and 10 mm long 100 A electric arcs at elevated pressures in the ranges 1 - 5 and 1 - 14.8 bar respectively. The results of the electric arc model are found to be in satisfactory agreement with a range of experimental data including spectroscopic temperature maps, electric field distributions, voltage drops, arc radii and total radiative emissions. It has been shown by Allum et al that short arcs length < 4 mm) become unstable once a critical Reynolds number has been reached, signifying the onset of turbulence for the flow emerging from the arc nozzle. This analysis, however, does not explain the inherent instability of longer arcs, which may be present even in a still argon atmosphere. It is proposed here that these are caused by the onset of turbulence in the entrained shielding gas. Two seperate Reynolds numbers, therefore, come into play in the physics of the TIG arc in connection with instabilities and these are estimated in the paper.

The Opacity Project and the Iron Project

Systematic and large-scale calculation of accurate plasma opacities and atomic data by the Opacity Project and the Iron Project has applications in many areas of astrophysics. Analysis of EUVE observations using monochromatic opacities of elements calculated by the Opacity Project is described. Theoretical methods and atomic calculations are discussed briefly. Recent work related to ionization balance, photoionization and recombination, and the modeling of plasmas in local thermodynamic equilibrium (LTE) and non-LTE are discussed. New calculations for the important iron ions, under the Iron Project, are also described and their relevance to the more extensive non-LTE calculations is pointed out. The comprehensive radiative and collisional data sets from the Opacity and the Iron Projects should be applicable to a large number of sources in the EUV and other wavelength regions.

Determination of axial thermal plasma temperatures without Abel inversion

This paper presents an approximate formula for the determination of local axis temperatures of an inhomogeneous, axisymmetric, optically thin, local thermodynamic equilibrium plasma column without using the Abel inversion technique. The proposed method is straightforward and is based on recording the spatially integrated radiances of spectral lines. The formula is useful for high gradients thermal plasma columns of the type found in DC electric arcs or plasma jets of gaussian shaped temperature profile. The formulation permits a simple experimental arrangement for rapid monitoring or control of parameters in industrial plasma devices or for the determination of emissivities and line transition probabilities. We also show that the method can be applied to spatially unstable arc discharges, where traditional techniques are difficult and cumbersome to apply.

Configuration interaction in LTE spectra of heavy elements

We present a method for including the effects of configuration interaction (CI) between relativistic subconfigurations of an electron configuration in the calculation of emission and absorption spectra of plasmas in local thermodynamic equilibrium (LTE). Analytical expressions for the correction to the intensities, owing to CI, of an unresolved transition array (UTA) and of a supertransition array (STA) are obtained when the correction is small compared to the spin-orbit splitting, bypassing the need to diagonalize energy matrices. These expressions serve as working formulas in the STA model and, in addition, reveal a priori the conditions under which CI effects are significant. Examples of the effect are presented.