Dielectronic Recombination Research Articles

Simulation study of precision measurement of highly charged state heavy ion double electron recombination spectra based on high-intensity heavy-ion accelerator facility

Dielectronic recombination (DR) experiments of highly charged ions not only provide essential atomic benchmark data for astrophysical and fusion plasma research but also serve as a stringent test for strong-field quantum electrodynamics (QED) effects, relativistic effects, and electron correlation effects. High-intensity heavy-ion accelerator facility (HIAF), currently under construction at Huizhou, China, will have a high-precision spectrometer ring (SRing) equipped with a 450-kV electron-cooler and an 80-kV ultracold electron-target. This advanced setup facilitates precise measurements of the DR process for highly charged ions in a broad range of center-of-mass energy, from meV to tens of keV. In this work, we carry out the molecular dynamics simulation of the electron beam temperature distribution of the ultracold electron-target at the SRing. The simulation results indicate that after treatment by the designed adiabatic magnetic field and acceleration field, the transverse and longitudinal electron beam temperature generated by the thermionic electron gun can be reduced from 100 meV to below 5 meV and 0.1 meV, respectively. Furthermore, we analyze the influence of this ultracold electron beam temperature on the resonance peak and energy resolution in DR experiment. The resolution gain at the SRing electron-target is particularly pronounced at small electron-ion collision energy, which provides unique experimental conditions for the DR experiments. Taking lithium-like <inline-formula><tex-math id="M3">\begin{document}$ {}_{54}^{129}{{\mathrm{X}}{\mathrm{e}}}^{51+} $\end{document}</tex-math></inline-formula>and <inline-formula><tex-math id="M4">\begin{document}$ {}_{92}^{238}{{\mathrm{U}}}^{89+} $\end{document}</tex-math></inline-formula>ions for example, we simulate the DR resonance spectra at the SRing and compare them with the simulated results from the experimental cooler storage ring CSRe. The results reveal that the SRing experiments can resolve fine DR resonance structures with ultra-high energy resolution compared with those from the CSRe. This work lays a solid foundation for conducting cutting-edge experiments such as precise measurement and verification of strong field QED effect and extraction of atomic nucleus structure information using highly charged state heavy ion double electron composite spectra on SRing .

Studies of electron-ion resonant recombination of li-like Si11+ions

Abstract Theoretical investigations of L-shell △n = 0, 1, and 2 (2s → 2p, 3 l ′ , and 4 l ′ ) dielectronic recombination (DR), as well as K-shell △n = 1, 2, and 3 (1s → 2 l ′ , 3 l ′ , and 4 l ′ ) DR of Li-like Si 11+ ions are performed, using the relativistic distorted-wave approach. Detailed resonance energies, resonance strengths, and recombination rate coefficients are calculated including complex configuration mixing, Breit interaction, and QED corrections. Good agreement is achieved between the theoretical rate coefficients and the experimental results. The plasma rate coefficients are also calculated for electron temperatures ranging from 10−1 to 106 eV, and an analytical formula is presented to fit the total plasma rate coefficients for convenient modeling of astrophysical and fusion plasmas.

Benchmarking Dielectronic Recombination Rate Coefficients for Carbon-like Ca14+

Dielectronic recombination (DR) rate coefficients for C-like Ca14+ were measured by Wen et al. at the electron cooler storage ring in Lanzhou, China. The measured DR rate coefficients from 0 to 92 eV cover most of the DR resonances associated with the 2s 22p 2 → 2s 22p 2 and 2s 22p 2 → 2s2p 3 core transitions. In addition, Wen et al. reported theoretical results calculated with the Flexible Atomic Code (FAC) and AUTOSTRUCTURE (AS). However, these theoretical results show widespread and significant differences from the measured DR spectrum in both resonance energies and strengths, as well as between each other. In the present work, we uncover the reasons behind these large differences, both theoretical and experimental. The new FAC and AS results reproduce the observed spectrum in detail, especially at resonance energies below 8 eV, and they are in very close agreement with each other. The present plasma rate coefficients agree with the experimentally determined values to within 20% and 2% in the photoionized plasma (PP) and collisional ionized plasma (CP) temperature ranges, respectively. This is in contrast to the previous theoretical results, which showed differences with the experiment of up to ∼40% over the PP temperature range. The present FAC and AS results agree with each other within 5% in the PP and CP temperature ranges. Thus, the theoretical uncertainty is greatly reduced for the DR of Ca14+ and the present benchmarking with the experiment gives confidence to data users modeling non–local thermodynamic equilibrium plasma.

Breit interaction in dielectronic recombination of hydrogenlike xenon ions: storage-ring experiment and theory

Electron-ion collision spectroscopy of the KLL dielectronic recombination (DR) resonances of hydrogenlike xenon ions was performed at a heavy-ion storage ring with a resolving power that is competitive with x-ray spectroscopy of inner-shell transitions in highly charged ions. The KL1/2L1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$KL_{1/2}L_{1/2}$$\\end{document}, KL1/2L3/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$KL_{1/2}L_{3/2}$$\\end{document}, and KL3/2L3/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$KL_{3/2}L_{3/2}$$\\end{document} resonance groups and even parts of their fine structure are individually resolved. The resonance strengths were measured on an absolute scale and compared with results from multi-configuration Dirac–Fock (MCDF) calculations. These are in excellent agreement with the experimental findings when QED effects on the resonance energies and the Breit interaction are considered. As already found for DR of hydrogenlike uranium (Bernhardt et al. in Phys Rev A 83:020701(R), 2011), this interaction is particularly strong for the KL1/2L1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$KL_{1/2}L_{1/2}$$\\end{document} resonance group. For U91+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{91+}$$\\end{document}, it increases the KL1/2L1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$KL_{1/2}L_{1/2}$$\\end{document} DR resonance strength by 40%. For Xe53+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{53+}$$\\end{document}, the increase is found to amount to 25%, confirming the prediction that the influence of the Breit interaction grows with increasing nuclear charge. A comprehensive appendix treats the derivation of experimental and theoretical merged-beams recombination rate coefficients for interacting beams of relativistic electrons and ions.Graphical abstract

Laboratory Benchmark of n ≥ 4 Dielectronic Recombination Satellites of Fe xvii

We calculated cross sections for the dielectronic recombination (DR) satellite lines of Fe xvii and benchmarked our predictions with experimental cross sections of Fe xvii resonances that were monoenergetically excited in an electron-beam ion trap. We extend the benchmark to all resolved DR and direct electron-impact excitation (DE) channels in the experimental data set, specifically the n ≥ 4 DR resonances of Fe xvii, complementing earlier investigations of n = 3 channels. Our predictions for the DR and DE absolute cross sections for the higher n complexes disagree considerably with experimental results when using the same methods as in previous works. However, we achieve agreement within ∼10% of the experimental results by an approach whereby we doubly convolve the predicted cross sections with both the spread of the electron-beam energy and the photon energy resolution of our experiment. We then calculated rate coefficients from the experimental and theoretical cross sections, finding general agreement within 2σ with the rates found in the OPEN-ADAS atomic database.

Modeling Transition Region Hot Loops on the Sun: The Necessity of Rapid, Complex Spatiotemporal Heating and Nonequilibrium Ionization

The study examines the heating profile of hot solar transition region loops, particularly focusing on transient brightenings observed in IRIS 1400 Å slit-jaw images. The findings challenge the adequacy of simplistic, singular heating mechanisms, revealing that the heating is temporally impulsive and requires a spatially complex profile with multiple heating scales. A forward-modeling code is utilized to generate synthetic Interface Region Imaging Spectrograph (IRIS) emission spectra of these loops based on HYDRAD model output, confirming that emitting ions are out of equilibrium. The modeling further indicates that density-dependent dielectronic recombination rates must be included to reproduce the observed line ratios. Collectively, this evidence substantiates that the loops are subject to impulsive heating and that the components of the transiently brightened plasma are driven far from thermal equilibrium. Heating events such as these are ubiquitous in the transition region, and the analysis described above provides a robust observational diagnostic tool for characterizing the plasma.

Spectral simulation of multivalent collisional-radiative model for W25+–W28+ from EBIT to tokamak plasmas

Accurate and reliable atomic modeling of tungsten ions holds significance for both spectral data analysis and the investigation of tungsten behavior within fusion plasma. To examine the impact of various atomic processes on spectral lines, a collisional-radiative model (CRM) involving multiple charge states for tungsten ions was performed with level-to-level processes with configuration interaction, including spontaneous emission, electron collisional ionization, collisional (de)excitation, radiative recombination, charge exchange, resonant capture, and autoionization. The evolution of M1 spectral lines of W25+–W28+ in the 330–540 nm range was measured using the SH-HtscEBIT and was successfully replicated by the multivalent CRM. The photon emission coefficients (PECs) associated with these M1 transitions in fusion plasma have also been furnished, revealing their minimal sensitivity to the influence of recombination and ionization processes. The verification of these PECs’ properties holds potential for the forthcoming density diagnosis of tungsten ions in Tokamak. Subsequently, the multivalent CRM was also conducted to explore the impact of dielectronic recombination on extreme ultraviolet spectra. While resonant capture does lead to an augmentation in the population of autoionizing levels, the contribution of dielectronic recombination to spectral lines for W26+ and W27+ within the 2–8 nm range remains relatively insignificant.

Studies on the motion and radiation of interior plasmas in gas-filled hohlraums with different laser entrance hole sizes

An experiment on 100 kJ laser facility is performed to study the motive features and radiation properties of plasmas from different areas inside gas-filled cylindrical hohlraums. These hohlraums are designed to possess one open end and one laser entrance hole (LEH) with different diameters, which would or not result in the blocking of the LEH. An x-ray streak camera that is set at 16 degrees with respect to the hohlraum axis is applied to acquire the time-resolved x-ray images from the open end. Based on the images, we can study the evolutions of the wall plasma, corona bubble plasma and LEH plasma simultaneously through an equivalent view field of hohlraum interior. Multi-group flat response x-ray detectors are applied to measure the x-ray fluxes. In order to understand these characteristics, our two-dimensional radiation hydrodynamic code is used to simulate the experimental results. For the accuracy of reproduction, dielectronic recombination and two parameter corrections are applied in our code. Based on the comparison between experiments and simulations, we quantitatively understand the blocking process of LEH and the motion effects of other plasmas. The calibrated code is beneficial to design the gas-filled hohlraum in a nearby parameter space, especially the limit size of LEH.

Merits of atomic cascade computations

Atomic cascades refer—first and foremost—to the stepwise de-excitation of excited atoms owing to the emission of electrons or photons. Apart from dedicated experiments at storage rings and synchrotrons, such cascades frequently occur in astro and plasma physics, material research, surface science and at various places elsewhere. In addition, moreover, “atomic cascades” have been found a useful concept for modeling atomic behavior under different conditions, for instance, when dealing with the photoabsorption of matter, the generation of synthesized spectra, or for determining a rather wide class of (plasma) rate coefficients. We here compile and discuss several atomic cascades (schemes) that help predict cross sections, rate coefficients, electron and photon spectra, or ion distributions. We also demonstrate how readily these schemes have been implemented within JAC, the Jena Atomic Calculator. Emphasis is placed on the classification of atomic cascades and their (quite) natural breakdown into cascade computations, to deal with the electronic structure and transition amplitudes of atoms and ions, as well as the cascade simulation of those properties and spectra, that are experimentally accessible. As an example, we show and discuss the computation of dielectronic recombination plasma rate coefficients for beryllium-like gold ions. The concept of atomic cascades and its implementation into JAC can be applied for most ions across the periodic table and will facilitate the modeling and interpretation of many forthcoming observations.Graphical abstract

Collisional-radiative modeling for the EUV spectrum of W40+-W42+ions

The wavelengths and transition rates of W40+-W42+ ions within the range of 40–140 Å, have been calculated using the Flexible Atomic Code of the Dirac-Fock-Slater method with a central potential. We investigated the charge state distribution of W38+-W45+ ions at different temperatures by constructing an appropriate rate equation and demonstrate the importance of the dielectronic recombination process. Additionally, we simulated the emission spectra of W40+-W42+ ions in a Tokamak plasma environment using collisional-radiative modeling. Our findings demonstrate strong agreement with experimental results and other related theoretical investigations. Finally, we propose certain pairs of transition lines as diagnostic tools for plasma temperature and density, leveraging the correlation between line intensity ratio and electron temperature and density.

L-Mn dielectronic recombination of cerium ions in a room-temperature EBIT

We explore the dielectronic recombination structures at the electron beam ion trap at Jagiellonian University in Cracow, emited by cerium that is produced by the high-current cathode made of iridium and cerium. Small amounts of these elements evaporate from the cathode and form low-intensity admixtures within the electron-ion plasma in the EBIT. Their presence and specific ionic population can be observed by examining the spectral characteristics resulting from the DR process. Results have been compared with flexible atomic code calculations, working in unresolved transition array mode, providing identification of the charge states. Here we show that this mode provides quick calculations of very complex data with enough reliability for experimental comparison. These observations highlight which DR features and corresponding charge states that should be present in spectra obtained in EBITs with similar cathode specifications.

Dielectronic recombination experiment of Na-like Kr<sup>25+</sup> at heavy ion storage ring CSRe

The experimental study of precision spectroscopy of dielectronic recombination (DR) of highly charged ions is not only important for astronomical plasma and fusion plasma, but also can be used as a new precision spectroscopy to test the strong-field quantum electrodynamic effect, measure isotope shift, and extract the radius of atomic nuclei. An specially designed electron beam energy detuning system for electron-ion recombination precision spectroscopy experiments has been installed on the heavy ion storage ring CSRe in Lanzhou, China, where the electron-ion collision energy in the center-of-mass system can be detuned to 1 keV, and an independently-developed plastic scintillator detector and multiwire proportional chamber detector have been installed downstream of the electron cooler of the CSRe for detecting recombined ions. The multiwire proportional chamber detector has the ability to non-destructively monitor the profile of the ion beam in real-time while acquiring the recombined ion counts, providing guidance for optimizing the ion beam. On this basis, the first test experiment on dielectronic recombination of Kr<sup>25+</sup> ions is carried out at the CSRe, and the dielectronic recombination rate coefficients in a range of 0–70 eV in the frame of center-of-mass are measured. In order to fully understand the experimental results, we calculate the dielectronic recombination rate coefficient of the Kr<sup>25+</sup> ion by using the flexible atomic code (FAC) and make a detailed comparison with the experimental result, showing that they are in good agreement with each other, and only the resonance energy values of the two resonance peaks at 1.695 eV and 2.573 eV are significantly different. In addition, the DR resonance energy values and intensities are obtained by fitting the experimental results in a range of 0–35 eV, and we find that the transition 3s→4l (∆<i>n</i> = 1) contributes significantly to the experimental spectral lines. Furthermore, we compare the plasma rate coefficients derived from the DR rate coefficients with those derived from the AUTOSTRUCTURE and FAC theories, which differ by 20 percent in a temperature range less than 10<sup>6</sup> K. The experimental results show that the DR experimental platform of the CSRe has very good stability and reproducibility, and can provide support for the future DR experiments of highly charged ion, i.e. for testing strong-field quantum electrodynamics effect and measuring the properties of atomic nuclei.

KAPPA: A Package for the Synthesis of Optically Thin Spectra for the Non-Maxwellian κ-Distributions. III. Improvements to Ionization Equilibrium and Extension to κ < 2

The KAPPA package is designed for calculations of optically thin spectra for the non-Maxwellian κ-distributions. This paper presents an extension of the database to allow calculations of the spectra for extreme values of κ < 2, which are important for accurate diagnostics of the κ-distributions in the outer solar atmosphere. In addition, two improvements were made to the ionization equilibrium calculations within the database. First, the ionization equilibrium calculations now include the effects of electron impact multi-ionization (EIMI). Although relatively unimportant for Maxwellian distribution, EIMI becomes important for some elements, such as Fe and low values of κ, where it modifies the ionization equilibrium significantly. Second, the KAPPA database now includes the suppression of dielectronic recombination at high electron densities, evaluated via the suppression factors. We find that at the same temperature, the suppression of dielectronic recombination is almost independent of κ. The ionization equilibrium calculations for the κ-distributions are now provided for a range of electron densities.

Review of Rydberg Spectral Line Formation in Plasmas

The present review is dedicated to the problem of an array of transitions between highly-excited atomic levels. Hydrogen atoms and hydrogen-like ions in plasmas are considered here. The presented methods focus on calculation of spectral line shapes. Fast and simple methods of universal ionic profile calculation for the Hnα (Δn=1) and Hnβ (Δn=2) spectral lines are demonstrated. The universal dipole matrix elements formulas for the Hnα and Hnβ transitions are presented. A fast method for spectral line shape calculations in the presence of an external magnetic field using the formulas for universal dipole matrix elements is proposed. This approach accounts for the Doppler and Stark–Zeeman broadening mechanisms. Ion dynamics effects are treated via the frequency fluctuation model. The accuracy of the presented model is discussed. A comparison of this approach with experimental data and the results of molecular dynamics simulation is demonstrated. The kinetics equation for the populations of highly-excited ionic states is solved in the parabolic representation. The population source associated with dielectronic recombination is considered.

Theoretical study of dielectronic recombination and electron-impact excitation for helium-like isoelectronic sequence

Theoretical study of dielectronic recombination and electron-impact excitation for helium-like isoelectronic sequence

Theoretical study on dielectronic recombination process and X-ray line polarization of B-like Ar13+ ion

Theoretical study on dielectronic recombination process and X-ray line polarization of B-like Ar13+ ion

Interference between dielectronic and radiative recombination of Be-like highly charged ions

We perform a systematical study for the polarization of x rays emitted when a free electron is captured by Be-like highly charged ions theoretically. We focus on the dielectronic recombination of the $J=1/2\ensuremath{\rightarrow}J=1/2$ transition and its polarization is zero due to axial symmetry. Including the interference between the dielectronic and radiative recombinations, the polarization changes dramatically when the electron energy crosses the resonant energy. By comparing the simulations with or without certain interactions, we found that the Breit interaction is not important even for very high-$Z$ ions. For low-$Z$ ions, the configuration interaction of the dielectronic recombination states affects the polarization greatly, while for high-$Z$ ions the configuration interaction of the ground state of Be-like ions plays an important role.

Theoretical Investigation of Electron–Ion Recombination Process of Mg-like Gold

The L-shell dielectronic and trielectronic recombinations of highly charged Mg-like gold ions (Au67+) in the ground state 2s22p63s2 1S0 have been studied systematically. The recombination cross-sections and rate coefficients are carefully calculated for ∆n = 1 (2s/2p → 3l) transitions using a flexible atomic code based on the relativistic configuration interaction method and considering the Breit and QED corrections. Detailed resonance energies and resonance strengths are presented for the stronger resonances of the LMn (n = 3–12) series. It is found that the contributions of the trielectronic recombination to the total cross-section is about 13.75%, which cannot be neglected. For convenience of application, the plasma rate coefficients are also calculated and fitted to a semiempirical formula, and in the calculations, the contributions from the higher excited resonance groups n ≥ 13 are evaluated by an extrapolation method, which is about 2.93% of the total rate coefficient.

Support for the standard picture of thermal X-rays in the wind of ζ Puppis from dielectronic recombination of He-like ions

ABSTRACT We use the line ratios of resolved X-ray resonance and satellite line pairs from Si xiii and Mg xi ions to test the widely held assumption that the shocked plasma in the wind of hot stars is in collisional ionization equilibrium. We specifically apply this test to the prototypical O supergiant ζ Puppis, as its line ratios are well resolved in its total 813 ks Chandra observation. This satellite-to-resonance line ratio is known to be a reliable diagnostic of plasma temperature but has yet to be applied to hot stars due to needing a long exposure time to see both lines above the continuum. In testing the assumed plasma state, we also provide evidence against significant ionization and excitation from proton collisions. Since dielectronic recombination (DR) allows somewhat lower energy free electrons to excite resonance lines than by the usual collisional pathways, we also use the DR flux ratios to extend diagnostics of the ionization fraction of the parent ion to lower temperatures than any other method can achieve. Also, the DR ratio supports a concept of an average free electron temperature, for each target ion used, which can constrain heating models.

Multipole mixing effects on the angular distribution and polarization of dielectronic hypersatellite lines from highly charged helium-like ions

The angular distribution and the degree of linear polarization of the dielectronic hypersatellite lines of highly charged helium-like ions are studied by using the multiconfiguration Dirac-Fock method and density matrix theory with a focus on the multipole mixing effects. Detailed calculations have been carried out for the emission of characteristic X-rays from the (2s2p)P1,23 and P11 resonant states decay to the (1s2s)S13 state following the KLL dielectronic recombination of initial hydrogen-like ions with atomic nuclear charge from Z=22 to Z=100. It is shown that the mixing of electric dipole (E1) and magnetic quadrupole (M2) radiations significantly alters the angular distribution and the degree of linear polarization, in which the shifts are dependent on the resonant capture states and the atomic nuclear charges. The E1+M2 mixing has opposite effects for the (2s2p)P23 and (2s2p)P11 resonant states, except for the (2s2p)P11 resonance of the heavy ions with Z≳90, where the profile of angular distribution is reversed by strong mixing effects due to the contribution of the M2 term and its interference with the E1 radiative channel. The results should be of particular interest to the diagnosis of anisotropic plasmas and the test of fundamental physics in few-electron heavy ions.