Frequently used second-order spectral line width formulae from the projector operator and kinetic theory methods have not been formally compared previously. It is shown that a systematic second-order expansion of the projection operator expression including initial correlations agrees with the second-order kinetic theory result. The agreement assumes a common approximation in the projector operator method that introduces a screened radiator–perturber interaction to account for neglected electron–electron correlations. On the other hand, it is shown that the usual width expression from the projection operator approach neglecting initial correlations differs from kinetic theory. The differences, however, are at least third order in the radiator–perturber interaction. The comparisons suggest using the more compact width expression from kinetic theory, which includes initial correlations and a systematic screening of the radiator–perturber interactions, as the starting point for second-order width calculations.

The second-order spectral line width formulae from the projection operator and kinetic theory methods were recently compared. It was shown that a systematic expansion of the projection operator width expression including initial correlations formally agrees with the second-order kinetic theory result. It is now shown that the second-order dynamic shifts are also formally the same. The static shifts, however, differ due to an ad hoc treatment of electron-electron correlations in the projection operator method. The approximation is necessary in order to screen the radiator-electron interactions. The differences, however, are expected to be small. The results suggest using the rigorous and more compact second-order width and shift expressions from the kinetic theory method as the starting point for spectral line shape calculations. At line center, however, the projection operator second-order expression for the width and shift simplifies and reduces to the kinetic theory result.

The photon scattering cross-section was previously written as a sum over irreducible tensors [Delserieys et al., Phys. Rev. A 78, 055404(2008)]. The expression can be further simplified using angular momentum algebra. This reduces the number of terms and explicitly displays direct and interference terms in the scattering cross-section.@font-face{font-family:"Cambria Math";panose-1:2 4 5 3 5 4 6 3 2 4;mso-font-charset:0;mso-generic-font-family:roman;mso-font-pitch:variable;mso-font-signature:-536870145 1107305727 0 0 415 0;}@font-face{font-family:Calibri;panose-1:2 15 5 2 2 2 4 3 2 4;mso-font-charset:0;mso-generic-font-family:swiss;mso-font-pitch:variable;mso-font-signature:-536859905 -1073732485 9 0 511 0;}@font-face{font-family:"Palatino Linotype";panose-1:2 4 5 2 5 5 5 3 3 4;mso-font-charset:0;mso-generic-font-family:roman;mso-font-pitch:variable;mso-font-signature:-536870265 1073741843 0 0 415 0;}p.MsoNormal, li.MsoNormal, div.MsoNormal{mso-style-unhide:no;mso-style-qformat:yes;mso-style-parent:"";margin:0in;mso-pagination:widow-orphan;font-size:12.0pt;font-family:"Calibri",sans-serif;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;}p.MDPI17abstract, li.MDPI17abstract, div.MDPI17abstract{mso-style-name:"MDPI_1\.7_abstract";mso-style-unhide:no;mso-style-qformat:yes;mso-style-parent:"";mso-style-next:Normal;margin-top:12.0pt;margin-right:0in;margin-bottom:0in;margin-left:130.4pt;text-align:justify;line-height:13.0pt;mso-pagination:widow-orphan;layout-grid-mode:char;mso-layout-grid-align:none;font-size:9.0pt;mso-bidi-font-size:11.0pt;font-family:"Palatino Linotype",serif;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";color:black;mso-fareast-language:DE;mso-bidi-language:EN-US;}.MsoChpDefault{mso-style-type:export-only;mso-default-props:yes;font-family:"Calibri",sans-serif;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;}div.WordSection1{page:WordSection1;}

Significant discrepancies relevant to helioseismology between experimental and theoretical photon absorption by plasmas remain unresolved. Interestingly, a new process called transient spatial localization (TSL), where the plasma perturbs the final states in photon ionization processes, ostensibly enhances cross-sections resolving the extant discrepancies. The TSL model, however, is shown to involve ad hoc formulas not derived from fundamental principles and systematic approximations. In addition, a variant of the TSL model, which claimed to enhance electron collisional ionization, is inconsistent with the Schrodinger equation and fails to reproduce known results.

A long-standing ambiguity in spectral line broadening theory related to the electric field divergence in the quadrupole term of the screened Coulomb radiator-plasma interaction is examined. This is accomplished with multipole expansions from a Taylor series as well as a partial wave analysis of the screened Coulomb interaction. It is explicitly shown that the two approaches agree up to the octupole term for an effective radiator size small compared to the plasma screening length. Furthermore, the ambigous corrections are confirmed appearing naturally in both methods. For higher multipoles the agreement is demonstrated numerically with a computer program using exact arithmetic.

Radiation opacity is a key property of material systems which describes the absorption and scattering of photons. Such processes are an important part of energy transport, diagnostics, and astrophysical phenomena. Recent experiments in iron opacity and continuum lowering have sparked renewed interest in and careful vetting of opacity models. Even within the local thermodynamic equilibrium approximation, opacity varies over a large parameter space: material, temperature, density, and energy. Opacity tables that span wide regimes of this parameter space are of prime importance to radiation-hydrodynamics codes. Accurate opacity calculations cannot be achieved inline during a radiation hydrodynamics simulation since they involve accounting for all possible electron transitions of all important atomic states of a thermal ensemble. Livermore’s current framework utilizes precalculated tables at many densities, temperatures, and energies. Last year, the opacity theory team completed an L2 milestone concerning the development of a new code, Opus, which served the dual purpose of creating a modern code infrastructure and version control as well as the basis for training new members of that team, a critical need as key members near or are passed retirement. For the current L2 milestone, we exercised and validated Opus on three elements: boron, carbon, and nitrogen, which have few enough electrons to allow a careful convergence study over many input parameters. Here, we report on the production of new tables, show their convergence with respect to important parameters, state some of their limitations, and document a mostly automated production process. In this section, we address the milestone completion criteria, found on the title page and the subsection headings. In section 2, we validate Opus against Tycho and compare with TabOp and Atomic. Section 3 details some of the physics implemented in Opus and relevant to this report. We then cover details of the density-temperature grid in section 4 and do a spectral comparison between different parameter settings and different codes in section 5. After summarizing these results in section 6, we give instructions how to run the opacity table scripts in appendix A and document the scripts and input/output files in appendix B.

The discrepancies between theoretical and experimental opacities reported by experiments performed at the Sandia National Laboratory Z-pinch relevant to the solar interior remain unexplained. The suggestion that two photon ionization could help resolve the discrepancies was recently examined and found not to account for the higher than predicted measured opacities. That test, however, was limited in scope and is now extended to include excited configurations and different charge states of several elements. Comparisons of one-and two photon ionization cross-sections show that the latter fail to resolve the aforementioned discrepancies.

The implosion efficiency in inertial confinement fusion depends on the degree of stagnated fuel compression, density uniformity, sphericity, and minimum residual kinetic energy achieved. Compton scattering-mediated 50-200 keV x-ray radiographs of indirect-drive cryogenic implosions at the National Ignition Facility capture the dynamic evolution of the fuel as it goes through peak compression, revealing low-mode 3D nonuniformities and thicker fuel with lower peak density than simulated. By differencing two radiographs taken at different times during the same implosion, we also measure the residual kinetic energy not transferred to the hot spot and quantify its impact on the implosion performance.

This report describes the development of our new radiative opacity code Opus, submitted as part of a 2020 Level 2 milestone requirement. This code aims to incorporate the capabilities in existing but separate opacity codes previously developed at LLNL (Opal, Topaz, and Tycho). The first phase in the development, which was to implement the super-transition (STA) method of Bar-Shalom and co-workers is now completed. In this work, we describe the underlying physics, implementation, usage, and regression testing as well as providing numerical examples for the opacity tables of boron, chromium, iron, and nickel. The latter are benchmarked against the LLNL legacy STA code Tycho, with an average absolute relative difference of ~1.5 and 0.5% for Planck and Rosseland opacity means, respectively. The cases where differences are larger are well understood in terms of numerical instabilities near discontinuities of the average degree of ionization inherent to the assumed opacity/equation-of-state model.

Existing discrepancies between helioseismic data and solar models have questioned the accuracy of theoretical opacities for the solar interior. The opacities were further challenged by recent estimates claiming significant retardation effects, often neglected in opacity calculations, for radiative transitions relevant to the solar problem. Contrary to these claims, it is shown that the retardation effects, in agreement with past results, are negligible in radiative transitions relevant to solar opacities.

Spectral line Stark broadening calculations in the "standard theory" typically retain only the long-ranged dipole term in the interaction between the perturbing plasma and emitting or absorbing atom. Thus, penetrating collisions as well as higher multipoles are neglected. The full Coulomb interaction is applied to hydrogen lines using a quantum mechanical treatment. It is found that the line widths from the quantum mechanical approach moderately disagree with earlier semi-classical treatment of penetrating collisions.

The opacities of iron and other mid-Z elements help to regulate the transport of energy in the sun. Recent experiments on the Sandia National Laboratories Z machine have shown large discrepancies between the measured and calculated opacities of iron at certain solar conditions. To replicate these opacity measurements a platform is being developed on the National Ignition Facility to measure the opacities of iron and other elements at the same conditions as in the Z experiments. The NIF platform consists of a hohlraum to heat the opacity sample to the desired conditions, a separate backlighter to radiograph the sample, and a spectrometer to give the spectrally resolved opacity. Not only must the opacity be measured but the temperature and density of the sample must also be accurately determined. This platform has now produced its first iron transmission measurements. These measurements will be presented along with plans for future measurements and details on how the measurements will be improved.

A recent paper [1] reported an enhancement of the boron K-shell photon ionization cross-section per electron at high photon energies along the principal Hugoniot. It is shown that the enhancement is due to known properties of isolated ions rather than subtle plasma effects. In addition, approximations and corrections to the photon absorption cross-section are examined.

A simplification of a fit to the free electron potential in ion-sphere models to obtain an analytic formula for level shifts (Li and Rosmej, 2012 [5]) is shown to be inconsistent with the fundamental premise of a neutral ion-cell. On the other hand, the original fit (Rosmej et al., 2011 [4]) avoids the problem and also leads to analytic formulas.

The first systematic study of opacity dependence on atomic number at stellar interior temperatures is used to evaluate discrepancies between measured and modeled iron opacity [J. E. Bailey et al., Nature (London) 517, 56 (2015)NATUAS0028-083610.1038/nature14048]. High-temperature (>180  eV) chromium and nickel opacities are measured with ±6%-10% uncertainty, using the same methods employed in the previous iron experiments. The 10%-20% experiment reproducibility demonstrates experiment reliability. The overall model-data disagreements are smaller than for iron. However, the systematic study reveals shortcomings in models for density effects, excited states, and open L-shell configurations. The 30%-45% underestimate in the modeled quasicontinuum opacity at short wavelengths was observed only from iron and only at temperature above 180 eV. Thus, either opacity theories are missing physics that has nonmonotonic dependence on the number of bound electrons or there is an experimental flaw unique to the iron measurement at temperatures above 180 eV.