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N. R. Badnell

Publications and source records attributed to N. R. Badnell.

66 records · Page 4Linked to original sources

Collisional Ionization Equilibrium for Optically Thin Plasmas. I. Updated Recombination Rate Coefficients for Bare though Sodium-like Ions

Reliably interpreting spectra from electron-ionized cosmic plasmas requires accurate ionization balance calculations for the plasma in question. However, much of the atomic data needed for these calculations have not been generated using modern theoretical methods and are often highly suspect. This translates directly into the reliability of the collisional ionization equilibrium (CIE) calculations. We make use of state-of-the-art calculations of dielectronic recombination (DR) rate coefficients for the hydrogenic through Na-like ions of all elements from He up to and including Zn. We also make use of state-of-the-art radiative recombination (RR) rate coefficient calculations for the bare through Na-like ions of all elements from H through to Zn. Here we present improved CIE calculations for temperatures from $10^4$ to $10^9$ K using our data and the recommended electron impact ionization data of \citet{Mazz98a} for elements up to and including Ni and Mazzotta (private communication) for Cu and Zn. DR and RR data for ionization stages that have not been updated are also taken from these two additional sources. We compare our calculated fractional ionic abundances using these data with those presented by Mazzotta et al. for all elements from H to Ni. The differences in peak fractional abundance are up to 60%. We also compare with the fractional ionic abundances for Mg, Si, S, Ar, Ca, Fe, and Ni derived from the modern DR calculations of \citet{Gu03a,Gu04a} for the H-like through Na-like ions, and the RR calculations of \citet{Gu03b} for the bare through F-like ions. These results are in better agreement with our work, with differences in peak fractional abundance of less than 10%.

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Dielectronic recombination of Fe^{13+}: benchmarking the M-shell

We have carried-out a series of multi-configuration Breit-Pauli AUTOSTRUCTURE calculations for the dielectronic recombination of Fe^{13+}. We present a detailed comparison of the results with the high-energy resolution measurements reported recently from the Heidelberg Test Storage Ring by Schmidt et al. Many Rydberg series contribute significantly from this initial 3s^2 3p M-shell ion, resulting in a complex recombination `spectrum'. While there is much close agreement between theory and experiment, differences of typically 50% in the summed resonance strengths over 0.1-10 eV result in the experimentally based total Maxwellian recombination rate coefficient being a factor of 1.52-1.38 larger than theory over 10^4-10^5 K, which is a typical temperature range of peak abundance for Fe^{13+} in a photoionized plasma. Nevertheless, this theoretical recombination rate coefficient is an order of magnitude larger than that used by modellers to-date. This may help explain the discrepancy between the iron M-shell ionization balance predicted by photoionization modelling codes such as ION and CLOUDY and that deduced from the iron M-shell unresolved-transition-array absorption feature observed in the X-ray spectrum of many active galactic nuclei. Similar data are required for Fe^{8+} through Fe^{12+} to remove the question mark hanging over the atomic data though.

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Radiative recombination data for modelling dynamic finite-density plasmas

We have calculated partial final-state resolved radiative recombination (RR) rate coefficients from the initial ground and metastable levels of all elements up to and including Zn, plus Kr, Mo, and Xe, for all isoelectronic sequences up to Na-like forming Mg-like. The data are archived according to the Atomic Data and Analysis Structure (ADAS) data class adf48, which spans a temperature range of z^2(10^1 - 10^7)K, where z is the initial ion charge. Fits to total rate coefficients have been determined, for both the ground and metastable levels, and those for the ground are presented here. Comparison is made both with previous RR rate coefficients and with (background) R-matrix photoionization cross sections. This RR database complements a DR database already produced and both are being used to produce updated ionization balances for both (electron) collisionally ionized and photoionized plasmas.

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Ionisation state, excited populations and emission of impurities in dynamic finite density plasmas. I: The generalised collisional-radiative model for light elements

The paper presents an integrated view of the population structure and its role in establishing the ionisation state of light elements in dynamic, finite density, laboratory and astrophysical plasmas. There are four main issues, the generalised collisional-radiative picture for metastables in dynamic plasmas with Maxwellian free electrons and its particularising to light elements, the methods of bundling and projection for manipulating the population equations, the systematic production/use of state selective fundamental collision data in the metastable resolved picture to all levels for collisonal-radiative modelling and the delivery of appropriate derived coefficients for experiment analysis. The ions of carbon, oxygen and neon are used in illustration. The practical implementation of the methods described here is part of the ADAS Project.

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Up-dated opacities from the Opacity Project

Using the code AUTOSTRUCTURE, extensive calculations of inner-shell atomic data have been made for the chemical elements He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Cr, Mn, Fe and Ni. The results are used to obtain up-dated opacities from the Opacity Project, OP. A number of other improvements on earlier work have also been included. Rosseland-mean opacities from OP are compared with those from OPAL. Differences of 5 to 10% occur. OP gives the `Z-bump', at log(T)=5.2, to be shifted to slightly higher temperatures. The opacities from OP, as functions of temperature and density, are smoother than those from OPAL. Extensive tests show that the numerical accuracy of the OP opacities following integration over frequency mesh and interpolation on temperature-density mesh is better than 1%. Prior to a number of recent investigations which have indicated a need for a downward revision in the solar abundances of oxygen and other elements, there was good agreement between properties of the sun deduced from helioseismology and from stellar evolution models calculated using OPAL opacities. The revisions in abundances destroy that agreement. In a recent paper Bahcall et al argue that the agreement would be restored if opacities for the regions of the sun between 0.7 and 0.4 solar radii were larger than those given by OPAL by about 10%. In the region concerned, the present results from OP do not differ from those of OPAL by more than 2.5%.

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A comparison of Rosseland-mean opacities from OP and OPAL

Monochromatic opacities from the Opacity Project (OP) (Seaton et al.) have been augmented by hitherto missing inner-shell contributions (Badnell & Seaton). OP Rosseland-mean opacities are compared with results from OPAL (Iglesias & Rogers) for the elements H, He, C, O, S and Fe. Overall, there is good agreement between OP and OPAL Rosseland-mean opacities for the 6-elements, but there are some differences. In particular, recent work (Bahcall et al.) has shown that helioseismology measurements give a very accurate value for the depth of the solar convection zone and that solar models give agreement with that value only if opacities there are about 7% larger than OPAL values. For the 6-element mix, here, we obtain Rosseland-mean opacities to be larger than OPAL by 5%.

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On the importance of inner-shell transitions for opacity calculations

For high temperatures and densities, stellar opacities obtained from the Opacity Project (OP) were smaller than those obtained from the OPAL project. Iglesias and Rogers [Ap.J. v443, 469 (1995)] suggested that the discrepancy was due to the omission by OP of important atomic inner-shell processes, and considered in detail results for a mixture of 6 elements: H, He, C, O, S and Fe. Extensive new inner-shell data have now been computed using the code AUTOSTRUCTURE. It is shown that the inclusion of these data in the OP work gives opacities for the 6-element mix which are in much closer agreement with those from OPAL. We also discuss a number of problems relating to the calculation of opacities and of equations-of-state in dense plasmas.

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Dielectronic recombination data for dynamic finite-density plasmas I. Goals and methodology

A programme is outlined for the assembly of a comprehensive dielectronic recombination database within the generalized collisional--radiative (GCR) framework. It is valid for modelling ions of elements in dynamic finite-density plasmas such as occur in transient astrophysical plasmas such as solar flares and in the divertors and high transport regions of magnetic fusion devices. The resolution and precision of the data are tuned to spectral analysis and so are sufficient for prediction of the dielectronic recombination contributions to individual spectral line emissivities. The fundamental data are structured according to the format prescriptions of the Atomic Data and Analysis Structure (ADAS) and the production of relevant GCR derived data for application is described and implemented following ADAS. The requirements on the dielectronic recombination database are reviewed and the new data are placed in context and evaluated with respect to older and more approximate treatments. Illustrative results validate the new high-resolution zero-density dielectronic recombination data in comparison with measurements made in heavy-ion storage rings utilizing an electron cooler. We also exemplify the role of the dielectronic data on GCR coefficient behaviour for some representative light and medium weight elements.

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Assessment of the Fluorescence and Auger Data Base used in Plasma Modeling

We have investigated the accuracy of the 1s-vacancy fluorescence data base of Kaastra & Mewe (1993, A&AS, 97, 443) resulting from the initial atomic physics calculations and the subsequent scaling along isoelectronic sequences. In particular, we have focused on the relatively simple Be-like and F-like 1s-vacancy sequences. We find that the earlier atomic physics calculations for the oscillator strengths and autoionization rates of singly-charged B II and Ne II are in sufficient agreement with our present calculations. However, the substantial charge dependence of these quantities along each isoelectronic sequence, the incorrect configuration averaging used for B II, and the neglect of spin-orbit effects (which become important at high-Z) all cast doubt on the reliability of the Kaastra & Mewe data for application to plasma modeling.

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Dielectronic Recombination (via N=2 --> N'=2 Core Excitations) and Radiative Recombination of Fe XX: Laboratory Measurements and Theoretical Calculations

We have measured the resonance strengths and energies for dielectronic recombination (DR) of Fe XX forming Fe XIX via N=2 --> N'=2 (Delta_N=0) core excitations. We have also calculated the DR resonance strengths and energies using AUTOSTRUCTURE, HULLAC, MCDF, and R-matrix methods, four different state-of-the-art theoretical techniques. On average the theoretical resonance strengths agree to within <~10% with experiment. However, the 1 sigma standard deviation for the ratios of the theoretical-to-experimental resonance strengths is >~30% which is significantly larger than the estimated relative experimental uncertainty of <~10%. This suggests that similar errors exist in the calculated level populations and line emission spectrum of the recombined ion. We confirm that theoretical methods based on inverse-photoionization calculations (e.g., undamped R-matrix methods) will severely overestimate the strength of the DR process unless they include the effects of radiation damping. We also find that the coupling between the DR and radiative recombination (RR) channels is small. We have used our experimental and theoretical results to produce Maxwellian-averaged rate coefficients for Delta_N=0 DR of Fe XX. For kT>~1 eV, which includes the predicted formation temperatures for Fe XX in an optically thin, low-density photoionized plasma with cosmic abundances, our experimental and theoretical results are in good agreement. We have also used our R-matrix results, topped off using AUTOSTRUCTURE for RR into J>=25 levels, to calculate the rate coefficient for RR of Fe XX. Our RR results are in good agreement with previously published calculations.

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Dielectronic Recombination of Ground-State and Metastable Li+ Ions

Dielectronic recombination has been investigated for Delta-n = 1 resonances of ground-state Li+(1s^2) and for Delta-n = 0 resonances of metastable Li+(1s2s ^3S). The ground-state spectrum shows three prominent transitions between 53 and 64 eV, while the metastable spectrum exhibits many transitions with energies < 3.2 eV. Reasonably good agreement of R-matrix, LS coupling calculations with the measured recombination rate coefficient is obtained. The time dependence of the recombination rate yields a radiative lifetime of 52.2 +- 5.0 s for the 2 ^3S level of Li+.

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Dielectronic Recombination in Photoionized Gas. II. Laboratory Measurements for Fe XVIII and Fe XIX

In photoionized gases with cosmic abundances, dielectronic recombination (DR) proceeds primarily via nlj --> nl'j' core excitations (Dn=0 DR). We have measured the resonance strengths and energies for Fe XVIII to Fe XVII and Fe XIX to Fe XVIII Dn=0 DR. Using our measurements, we have calculated the Fe XVIII and Fe XIX Dn=0 DR DR rate coefficients. Significant discrepancies exist between our inferred rates and those of published calculations. These calculations overestimate the DR rates by factors of ~2 or underestimate it by factors of ~2 to orders of magnitude, but none are in good agreement with our results. Almost all published DR rates for modeling cosmic plasmas are computed using the same theoretical techniques as the above-mentioned calculations. Hence, our measurements call into question all theoretical Dn=0 DR rates used for ionization balance calculations of cosmic plasmas. At temperatures where the Fe XVIII and Fe XIX fractional abundances are predicted to peak in photoionized gases of cosmic abundances, the theoretical rates underestimate the Fe XVIII DR rate by a factor of ~2 and overestimate the Fe XIX DR rate by a factor of ~1.6. We have carried out new multiconfiguration Dirac-Fock and multiconfiguration Breit-Pauli calculations which agree with our measured resonance strengths and rate coefficients to within typically better than <~30%. We provide a fit to our inferred rate coefficients for use in plasma modeling. Using our DR measurements, we infer a factor of ~2 error in the Fe XX through Fe XXIV Dn=0 DR rates. We investigate the effects of this estimated error for the well-known thermal instability of photoionized gas. We find that errors in these rates cannot remove the instability, but they do dramatically affect the range in parameter space over which it forms.

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