arXiv subjects

N. R. Badnell

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

At least 37 records · Page 2Linked to original sources

arXiv2019

Uncertainties on atomic data. A case study: N IV

We consider three recent large-scale calculations for the radiative and electron-impact excitation data of N IV, carried out with different methods and codes. The scattering calculations employed the relativistic Dirac $R$-matrix (DARC) method, the intermediate coupling frame transformation (ICFT) $R$-matrix method, and the B-spline $R$-matrix (BSR) method. These are all large-scale scattering calculations with well-tested and sophisticated codes, which use the same set of target states. One concern raised in previous literature is related to the increasingly large discrepancies in the effective collision strengths between the three sets of calculations for increasingly weak and/or high-lying transitions. We have built three model ions and calculated the intensities of all the main spectral lines in this ion. We have found that, despite such large differences, excellent agreement (to within $\pm$~20\%) exists between all the spectroscopically-relevant line intensities. This provides confidence in the reliability of the calculations for plasma diagnostics. We have used the differences in the radiative and excitation rates amongst the three sets of calculations to obtain a measure of the uncertainty in each rate. Using a Monte Carlo approach, we have shown how these uncertainties affect the main theoretical ratios which are used to measure electron densities and temperatures.

astro-ph.SR↗

arXiv2018

Dielectronic recombination of the open $4d$-shell of Tungsten: W$^{37+}$ - W$^{28+}$

Tungsten is an important element for magnetically confined fusion plasmas but has the potential to cool, or even quench the plasma due to it being an efficient radiator. Total and level-resolved dielectronic recombination (DR) rate coefficients, for all ionization stages, are essential to model tungsten. We describe a set calculations performed using the distorted wave code AUTOSTRUCTURE for the tungsten ions W$^{37+}$ to W$^{28+}$. We demonstrate the importance of relativistic configuration mixing in such calculations. In particular, we show that the partial DR rate coefficients calculated in level and configuration resolution can differ by as little as 5%, and up to as much as 75%. Using the new data, we calculate a revised steady-state ionization fraction for tungsten. We find that, relative to the ionization fraction calculated using the recombination rate coefficients of Putterich et al. (Plasma Phys. Control. Fusion, 50, 085016), the peak temperatures of W$^{37+}$ to W$^{28+}$ ionization states are shifted to lower temperatures spanning 0.9-1.6keV. This temperature range is important for understanding the performance of large tokamaks, such as ITER, because the temperatures in the pedestal, edge, scrape-off-layer and divertor region fall in this range.

physics.atom-ph↗

arXiv2018

Dielectronic recombination of lanthanide and low ionization state tungsten ions: W$^{13+}$ - W$^{1+}$

The experimental thermonuclear reactor, ITER, is currently being constructed in Cadarache, France. The reactor vessel will be constructred with a beryllium coated wall, and a tungsten coated divertor. As a plasma-facing component, the divertor will be under conditions of extreme temperature, resulting in the sputtering of tungsten impurities into the main body plasma. Modelling and understanding the potential cooling effects of these impurities requires detailed collisional-radiative modelling. These models require a wealth of atomic data for the various atomic species in the plasma. In particular, partial, final-state resolved dielectronic/radiative recombination (DR/RR) rate coefficients for tungsten are required. In this manuscript, we present our calculations of detailed DR/RR rate coefficients for the lanthanide-like, and low ionization stages of tungsten, spanning charge states W$^{13+}$ to W$^{1+}$. The calculations presented here constitutes the first detailed exploration of such low ionization state tungsten ions. We are able to reproduce the general trend of calculations performed by other authors, but find significant differences between ours and their DR rate coefficients, especially at the lowest temperatures considered.

physics.atom-ph↗

arXiv2018

Suppression of Dielectronic Recombination Due to Finite Density Effects II: Analytical Refinement and Application to Density-dependent Ionization Balances and AGN Broad-line Emission

We present improved fits to our treatment of suppression of dielectronic recombination at intermediate densities. At low densities, most recombined excited states eventually decay to the ground state, and therefore the total dielectronic recombination rate to all levels is preserved. At intermediate densities, on the other hand, collisions can lead to ionization of higher-lying excited states, thereby suppressing the dielectronic recombination rate. The improved suppression factors presented here, although highly approximate, allow summed recombination rate coefficients to be used to intermediate densities. There have been several technical improvements to our previously presented fits. For H- through B-like ions the activation log densities have been adjusted to better reproduce existing data. For B-, C-, Al-, and Si-like ions secondary autoionization is now included. The treatment of density discontinuity in electron excitations out of ground state H-, He-, and Ne-like ions has been improved. These refined dielectronic recombination suppression factors are used in the most recent version of the plasma simulation code Cloudy. We show how the ionization and emission spectrum change when this physics is included. Although these suppression factors improve the treatment of intermediate densities, they are highly approximate and are not a substitution for a complete collisional-radiative model of the ionization balance.

physics.atom-ph↗

arXiv2018

A Quantitative Comparison of Opacities Calculated Using the Distorted- Wave and $\boldsymbol{R}$-Matrix Methods

The present debate on the reliability of astrophysical opacities has reached a new climax with the recent measurements of Fe opacities on the Z-machine at the Sandia National Laboratory \citep{Bailey2015}. To understand the differences between theoretical results, on the one hand, and experiments on the other, as well as the differences among the various theoretical results, detailed comparisons are needed. Many ingredients are involved in the calculation of opacities; deconstructing the whole process and comparing the differences at each step are necessary to quantify their importance and impact on the final results. We present here such a comparison using the two main approaches to calculate the required atomic data, the $R$-Matrix and distorted-wave methods, as well as sets of configurations and coupling schemes to quantify the effects on the opacities for the $Fe\ XVII$ and $Ni\ XIV$ ions.

astro-ph.SR↗

arXiv2018

Dielectronic recombination data for dynamic finite-density plasmas XV. The silicon isoelectronic sequence

We aim to present a comprehensive theoretical investigation of dielectronic recombination (DR) of the silicon-like isoelectronic sequence and provide DR and radiative recombination (RR) data that can be used within a generalized collisional-radiative modelling framework. Total and final-state level-resolved DR and RR rate coefficients for the ground and metastable initial levels of 16 ions between $\rm{P^{+}}$ and $\rm{Zn^{16+}}$ are determined. We carried out multi-configurational Breit-Pauli (MCBP) DR calculations for silicon-like ions in the independent processes, isolated resonance, distorted wave (IPIRDW) approximation. Both $Δn_c =0$ and $Δn_c =1$ core excitations are included using $LS$ and intermediate coupling schemes. Results are presented for a selected number of ions and compared to all other existing theoretical and experimental data. The total dielectronic and radiative recombination rate coefficients for the ground state are presented in tabulated form for easy implementation into spectral modelling codes. These data can also be accessed from the Atomic Data and Analysis Structure (ADAS) OPEN-ADAS database. This work is a part of an assembly of a dielectronic recombination database for the modelling of dynamic finite-density plasmas.

physics.atom-ph↗

arXiv2017

Thermodynamically-consistent semi-classical $\ell$-changing rates

We compare the results of the semi-classical (SC) and quantum-mechanical (QM) formalisms for angular-momentum changing transitions in Rydberg atom collisions given by Vrinceanu & Flannery, J. Phys. B 34, L1 (2001), and Vrinceanu, Onofrio & Sadeghpour, ApJ 747, 56 (2012), with those of the SC formalism using a modified Monte Carlo realization. We find that this revised SC formalism agrees well with the QM results. This provides further evidence that the rates derived from the QM treatment are appropriate to be used when modelling recombination through Rydberg cascades, an important process in understanding the state of material in the early universe. The rates for $Δ\ell=\pm1$ derived from the QM formalism diverge when integrated to sufficiently large impact parameter, $b$. Further to the empirical limits to the $b$ integration suggested by Pengelly & Seaton, MNRAS 127, 165 (1964), we suggest that the fundamental issue causing this divergence in the theory is that it does not fully cater for the finite time taken for such distant collisions to complete.

physics.atom-ph↗

arXiv2017

Partial and Total Dielectronic Recombination Rate Coefficients for W$^{55+}$ to W$^{38+}$

Dielectronic recombination (DR) is the dominant mode of recombination in magnetically confined fusion plasmas for intermediate to low-charged ions of W. Complete, final-state resolved partial isonuclear W DR rate coefficient data is required for detailed collisional-radiative modelling for such plasmas in preparation for the upcoming fusion experiment ITER. To realize this requirement, we continue {\it The Tungsten Project} by presenting our calculations for tungsten ions W$^{55+}$ to W$^{38+}$. As per our prior calculations for W$^{73+}$ to W$^{56+}$, we use the collision package {\sc autostructure} to calculate partial and total DR rate coefficients for all relevant core-excitations in intermediate coupling (IC) and configuration average (CA) using $κ$-averaged relativistic wavefunctions. Radiative recombination (RR) rate coefficients are also calculated for the purpose of evaluating ionization fractions. Comparison of our DR rate coefficients for W$^{46+}$ with other authors yields agreement to within 7-19\% at peak abundance verifying the reliability of our method. Comparison of partial DR rate coefficients calculated in IC and CA yield differences of a factor $\sim{2}$ at peak abundance temperature, highlighting the importance of relativistic configuration mixing. Large differences are observed between ionization fractions calculated using our recombination rate coefficient data and that of Pütterich~\etal [Plasma Phys. and Control. Fusion 50 085016, (2008)]. These differences are attributed to deficiencies in the average-atom method used by the former to calculate their data.

physics.atom-ph↗

arXiv2017

Testing atomic collision theory with the two-photon continuum of astrophysical nebulae

Accurate rates for energy-degenerate l-changing collisions are needed to determine cosmological abundances and recombination. There are now several competing theories for the treatment of this process, and it is not possible to test these experimentally. We show that the H I two-photon continuum produced by astrophysical nebulae is strongly affected by l-changing collisions. We perform an analysis of the different underlying atomic processes and simulate the recombination and two-photon spectrum of a nebula containing H and He. We provide an extended set of effective recombination coefficients and updated l-changing 2s-2p transition rates using several competing theories. In principle, accurate astronomical observations could determine which theory is correct.

astro-ph.CO↗

arXiv2016

The electron energy-loss rate due to radiative recombination

For photoionized plasmas, electron energy-loss rates due to radiative recombination (RR) are required for thermal equilib- rium calculations, which assume a local balance between the energy gain and loss. While many calculations of total and/or partial RR rates are available from literature, specific calculations of associated RR electron energy-loss rates are lacking. Here we focus on electron energy-loss rates due to radiative recombination of H-like to Ne-like ions for all the elements up to and including zinc (Z = 30), over a wide temperature range. We use the AUTOSTRUCTURE code to calculate the level-resolved photoionization cross section and modify the ADASRR code so that we can simultaneously obtain level-resolved RR rate coefficients and associated RR electron energy-loss rate coefficients. The total RR rates and electron energy-loss rates of H i and He i are compared with those found in literature. Furthermore, we utilize and parameterize the weighted electron energy-loss factors (dimensionless) to characterize total electron energy-loss rates due to RR. The RR electron energy-loss data are archived according to the Atomic Data and Analysis Structure (ADAS) data class adf48. The RR electron energy-loss data are also incorporated into the SPEX code for detailed modelling of photoionized plamsas.

astro-ph.HE↗

arXiv2016

Hot DA white dwarf model atmosphere calculations: Including improved Ni PI cross sections

To calculate realistic models of objects with Ni in their atmospheres, accurate atomic data for the relevant ionization stages needs to be included in model atmosphere calculations. In the context of white dwarf stars, we investigate the effect of changing the Ni {\sc iv}-{\sc vi} bound-bound and bound-free atomic data has on model atmosphere calculations. Models including PICS calculated with {\sc autostructure} show significant flux attenuation of up to $\sim 80$\% shortward of 180Å\, in the EUV region compared to a model using hydrogenic PICS. Comparatively, models including a larger set of Ni transitions left the EUV, UV, and optical continua unaffected. We use models calculated with permutations of this atomic data to test for potential changes to measured metal abundances of the hot DA white dwarf G191-B2B. Models including {\sc autostructure} PICS were found to change the abundances of N and O by as much as $\sim 22$\% compared to models using hydrogenic PICS, but heavier species were relatively unaffected. Models including {\sc autostructure} PICS caused the abundances of N/O {\sc iv} and {\sc v} to diverge. This is because the increased opacity in the {\sc autostructure} PICS model causes these charge states to form higher in the atmosphere, moreso for N/O {\sc v}. Models using an extended line list caused significant changes to the Ni {\sc iv}-{\sc v} abundances. While both PICS and an extended line list cause changes in both synthetic spectra and measured abundances, the biggest changes are caused by using {\sc autostructure} PICS for Ni.

astro-ph.SR↗

arXiv2016

The Tungsten Project: Dielectronic Recombination Data For Collisional-Radiative Modelling In ITER

Tungsten is an important metal in nuclear fusion reactors. It will be used in the divertor component of ITER (Latin for 'the way'). The Tungsten Project aims to calculate partial and total DR rate coefficients for the isonuclear sequence of Tungsten. The calculated data will be made available as and when they are produced via the open access database OPEN- ADAS in the standard adf09 and adf48 file formats. We present our progress thus far, detailing calculational methods, and showing comparisons with other available data. We conclude with plans for the future.

physics.atom-ph↗

arXiv2016

H, He-like recombination spectra II: $l$-changing collisions for He Rydberg states

Cosmological models can be constrained by determining primordial abundances. Accurate predictions of the He I spectrum are needed to determine the primordial helium abundance to a precision of $< 1$% in order to constrain Big Bang Nucleosynthesis models. Theoretical line emissivities at least this accurate are needed if this precision is to be achieved. In the first paper of this series, which focused on H I, we showed that differences in $l$-changing collisional rate coefficients predicted by three different theories can translate into 10% changes in predictions for H I spectra. Here we consider the more complicated case of He atoms, where low-$l$ subshells are not energy degenerate. A criterion for deciding when the energy separation between $l$ subshells is small enough to apply energy-degenerate collisional theories is given. Moreover, for certain conditions, the Bethe approximation originally proposed by Pengelly & Seaton (1964) is not sufficiently accurate. We introduce a simple modification of this theory which leads to rate coefficients which agree well with those obtained from pure quantal calculations using the approach of Vrinceanu et al. (2012). We show that the $l$-changing rate coefficients from the different theoretical approaches lead to differences of $\sim 10$% in He I emissivities in simulations of H II regions using spectral code Cloudy.

astro-ph.CO↗

arXiv2016

Scaling of collision strengths for highly-excited states of ions of the H- and He-like sequences

Emission lines from highly-excited states (n >= 5) of H- and He-like ions have been detected in astrophysical sources and fusion plasmas. For such excited states, R-matrix or distorted wave calculations for electron-impact excitation are very limited, due to the large size of the atomic basis set needed to describe them. Calculations for n >= 6 are also not generally available. We study the behaviour of the electron-impact excitation collision strengths and effective collision strengths for the most important transitions used to model electron collision dominated astrophysical plasmas, solar, for example. We investigate the dependence on the relevant parameters: the principal quantum number n or the nuclear charge Z. We also estimate the importance of coupling to highly-excited states and the continuum by comparing the results of different sized calculations. We provide analytic formulae to calculate the electron-impact excitation collision strengths and effective collision strengths to highly-excited states (n >= 8) of H- and He-like ions. These extrapolated effective collision strengths can be used to interpret astrophysical and fusion plasma via collisional-radiative modelling.

astro-ph.IM↗

arXiv2016

H, He-like recombination spectra I: $l$-changing collisions for hydrogen

Hydrogen and helium emission lines in nebulae form by radiative recombination. This is a simple process which, in principle, can be described to very high precision. Ratios of He I and H I emission lines can be used to measure the He$^+$/H$^+$ abundance ratio to the same precision as the recombination rate coefficients. This paper investigates the controversy over the correct theory to describe dipole $l$-changing collisions ($nl\rightarrow nl'=l\pm 1$) between energy-degenerate states within an $n$-shell. The work of Pengelly & Seaton (1964) has, for half-a-century, been considered the definitive study which "solved" the problem. Recent work by Vrinceanu et al.(2012) recommended the use of rate coefficients from a semi-classical approximation which are nearly an order of magnitude smaller than those of Pengelly & Seaton (1964), with the result that significantly higher densities are needed for the $nl$ populations to come into local thermodynamic equilibrium. Here, we compare predicted H~I emissivities from the two works and find widespread differences, of up to $\approx 10$%. This far exceeds the 1% precision required to obtain the primordial He/H abundance ratio from observations so as to constrain Big Bang cosmologies. We recommend using the rate coefficients of Pengelly & Seaton (1964) for $l$-changing collisions, to describe the H recombination spectrum, based-on their quantum mechanical representation of the long-range dipole interaction.

astro-ph.GA↗

arXiv2016

Partial and Total Dielectronic Recombination rate coefficients for W73+ to W56+

Dielectronic recombination (DR) is a key atomic process which affects the spectroscopic diagnostic modelling of tungsten, most of whose ionization stages will be found somewhere in the ITER fusion reactor: in the edge, divertor, or core plasma. Accurate DR data is sparse while complete DR coverage is unsophisticated (e.g. average-atom or Burgess General Formula) as illustrated by the large uncertainties which currently exist in the tungsten ionization balance. To this end, we present a series of partial final state-resolved and total DR rate coefficients for W73+ to W56+ Tungsten ions. This is part of a wider effort within The Tungsten Project to calculate accurate dielectronic recombination rate coefficients for the tungsten isonuclear sequence for use in collisional-radiative modelling of finite-density tokamak plasmas. The recombination rate coefficients have been calculated with autostructure using kappa-averaged relativistic wavefunctions in level resolution (intermediate coupling) and configuration resolution (configuration average). The results are available from OPEN-ADAS according to the adf09 and adf48 standard formats. Comparison with previous calculations of total DR rate coefficients for W63+ and W56+ yield agreement to within 20% and 10%, respectively, at peak temperature. It is also seen that the Juttner correction to the Maxwell distribution has a significant effect on the ionization balance of tungsten at the highest charge states, changing both the peak abundance temperatures and the ionization fractions of several ions.

physics.atom-ph↗

arXiv2015

Dirac $R$-matrix and Breit-Pauli distorted wave calculations of the electron-impact excitation of W$^{44+}$

With construction of ITER progressing and existing tokamaks carrying out ITER-relevant experiments, accurate fundamental and derived atomic data for numerous ionization stages of tungsten (W) is required to assess the potential effect of this species upon fusion plasmas. The results of fully relativistic, partially radiation damped, Dirac $R$-matrix electron-impact excitation calculations for the W$^{44+}$ ion are presented. These calculations use a configuration interaction and close-coupling expansion that opens-up the 3d-subshell, which does not appear to have been considered before in a collision calculation. As a result, it is possible to investigate the arrays, [3d$^{10}$4s$^2-$3d$^9$4s$^2$4f] and [3d$^{10}$4s$^2-$3d$^9$4s4p4d], which are predicted to contain transitions of diagnostic importance for the soft x-ray region. Our $R$-matrix collision data are compared with previous $R$-matrix results by Ballance and Griffin as well as our own relativistically corrected, Breit-Pauli distorted wave and plane-wave Born calculations. All relevant data are applied to the collisional-radiative modelling of atomic populations, for further comparison. This reveals the paramount nature of the 3d-subshell transitions from the perspectives of radiated power loss and detailed spectroscopy.

physics.atom-ph↗

arXiv2015

Validity of the ICFT R-matrix method: Be-like Al$^{9+}$ a case study

We have carried-out 98-level configuration-interaction / close-coupling (CI/CC) intermediate coupling frame transformation (ICFT) and Breit-Pauli R-matrix calculations for the electron-impact excitation of Be-like Al$^{9+}$. The close agreement that we find between the two sets of effective collision strengths demonstrates the continued robustness of the ICFT method. On the other hand, a comparison of this data with previous 238-level CI/CC ICFT effective collision strengths shows that the results for excitation up to n=4 levels are systematically and increasingly underestimated over a wide range of temperatures by R-matrix calculations whose close-coupling expansion extends only to n=4 (98-levels). Thus, we find to be false a recent conjecture that the ICFT approach may not be completely robust. The conjecture was based upon a comparison of 98-level CI/CC Dirac R-matrix effective collision strengths for Al$^{9+}$ with those from the 238-level CI/CC ICFT R-matrix calculations. The disagreement found recently is due to a lack of convergence of the close-coupling expansion in the 98-level CI/CC Dirac work. The earlier 238-level CI/CC ICFT work has a superior target to the 98-level CI/CC Dirac one and provides more accurate atomic data. Similar considerations need to be made for other Be-like ions and for other sequences.

astro-ph.IM↗