Atomic Radiative Processes Research Articles

Review of the 1st EUV Light Sources Code Comparison Workshop

We review the results of the 1st Extreme Ultraviolet (EUV) Light Sources Code Comparison Workshop. The goal of this workshop was to provide a platform for specialists in EUV light source plasma modeling to benchmark and validate their numerical codes using well-defined case studies. Detailed consideration of a plethora of atomic collisional and radiative processes is required for modeling EUV light source plasmas. Eight institutions spanning four countries contributed data to the workshop. Two topics were addressed, namely (i) the atomic kinetics and radiative properties of tin plasmas under EUV-generating conditions and (ii) laser absorption in a fully ionized, one-dimensional hydrogen plasma. In this paper, we summarize the key findings of the workshop and outline plans for future iterations of the code comparison activity.

Radiation influence on the plasma atomic kinetics and spectra in experiments on radiative shock waves

Radiative shocks waves are among of the most interesting astrophysical phenomena and due to their relevance, many laboratory experiments, using high-power lasers, have been performed to achieve a better understanding of them. The radiation emitted by the shock front can heat and ionize the pre-shock medium leading to the formation of radiative precursors, which are relevant in these phenomena since they absorb part of the radiation emitted by the shock front and becomes a strong source of radiation emission. The plasma in the precursor can be considered as a photoionized plasma in which the external radiation field plays a dominant role in the atomic kinetics behavior. A numerical study of the influence of the radiation field on the ion populations, radiative properties and atomic spectra of radiative precursors in radiative shocks generated in two laboratory experiments is presented. For the numerical simulations, three types of collisional-radiative models have been used. In the first one, the radiation induced processes are not included. In the second type, the radiative atomic processes induced by plasma self-absorption are considered. Finally, the radiative processes induced by both the external radiation field and the plasma self-absorption are included. The results obtained show the noticeable influence of the radiation field on the plasma properties analyzed.

Possible Polarization Measurements in Elastic Scattering at the Gamma Factory Utilizing a 2D Sensitive Strip Detector as Dedicated Compton Polarimeter

AbstractFor photon energies from several 10 keV up to a few MeV Compton polarimetry is an indispensable tool to gain insight into subtle details of fundamental atomic radiative processes. Within the SPARC collaboration several segmented semiconductor detectors are developed that are well suited for application as efficient Compton polarimeters. In this report, these recent developments are reviewed and it is discussed how Compton polarimetry can be employed at the upcoming Gamma Factory.

Overview of recent advances performed in the study of atomic structures and radiative processes for the lowest ionization stages of heavy elements

During the past 20 years, part of our work has been focused on the study of the atomic structure and the determination of radiative parameters in neutral and slightly ionized heavy atoms (Z ≥ 37). These elements attracted little previous interest because of the complexity of their electronic structures, the poor knowledge of their spectra, and the difficulty to perform experimental measurements. They present, however, great interest in the development of other scientific areas, such as astrophysics and plasma physics. In this paper, we give an overview of the recent progress performed by the group of Atomic Physics and Astrophysics at Mons University (Belgium) in the theoretical modelling and the experimental analysis of such heavy elements. We also discuss some applications of the atomic data obtained in our work for the interpretation of the spectra observed from astrophysical and laboratory plasmas.

BEAMDB and MolD – databases for atomic and molecular collisional and radiative processes: Belgrade nodes of VAMDC

We present two atomic and molecular (A&M) databases, MolD and BEAMDB, hosted by the SerVO – the Serbian virtual observatory ( http://servo.aob.rs ). These databases and web applications have been implemented in accordance to the standards developed by Virtual Atomic and Molecular Data Centre (VAMDC, http://www.vamdc.eu ). The MolD database contains photo-dissociation cross-sections for individual rovibrational states of the diatomic molecular ions and rate coefficients for the atom-Rydberg atom chemi-ionisation and inverse electron-ion-atom chemi-recombination processes. The Belgrade electron/atom(molecule) database (BEAMDB) provides collisional data for electron interactions with atoms and molecules. Differential cross sections (DCS) are presented for both elastic and inelastic (excitation) cross sections in tabulated data tables. These DCS data are integrated over a full range of scattering angles in order to achieve integral, momentum transfer and viscosity cross sections as functions of impact electron energy. Beside these tables, energy loss spectra are presented in the graphical form.

Liouville-space R-matrix-Floquet description of atomic radiative processes involving autoionizing states in the presence of intense electromagnetic fields

A reduced-density-operator description is developed for coherent optical phenomena in many-electron atomic systems, utilizing a Liouville-space, multiple-mode Floquet–Fourier representation. The Liouville-space formulation provides a natural generalization of the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method, which has been developed for multi-photon transitions and laser-assisted electron–atom collision processes. In these applications, the R-matrix-Floquet method has been demonstrated to be capable of providing an accurate representation of the complex, multi-level structure of many-electron atomic systems in bound, continuum, and autoionizing states. The ordinary Hilbert-space (Hamiltonian) formulation of the R-matrix-Floquet method has been implemented in highly developed computer programs, which can provide a non-perturbative treatment of the interaction of a classical, multiple-mode electromagnetic field with a quantum system. This quantum system may correspond to a many-electron, bound atomic system and a single continuum electron. However, including pseudo-states in the expansion of the many-electron atomic wave function can provide a representation of multiple continuum electrons. The ‘dressed’ many-electron atomic states thereby obtained can be used in a realistic non-perturbative evaluation of the transition probabilities for an extensive class of atomic collision and radiation processes in the presence of intense electromagnetic fields. In order to incorporate environmental relaxation and decoherence phenomena, we propose to utilize the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method as a starting-point for a Liouville-space (reduced-density-operator) formulation. To illustrate how the Liouville-space R-matrix-Floquet formulation can be implemented for coherent atomic radiative processes, we discuss applications to electromagnetically induced transparency, as well as to related pump–probe optical phenomena, and also to the unified description of radiative and dielectronic recombination in electron–ion beam interactions and high-temperature plasmas.

Investigation of atomic radiative recombination processes by the Bohmian-mechanics method

The light-emission process by the recombination of an ionized electron with its parent ion is investigated by the Bohmian trajectory scheme, and the efficiency of light emission calculated by 20 Bohmian trajectories is qualitatively identical to that obtained by numerically solving the time-dependent Schr\"odinger equation. It is found that the efficiency of light emission by recombination is determined by the oscillation amplitude of the Bohmian particle's Coulomb acceleration. Along with the decrease of the energy of the incident Bohmian particle, the deepening of the ion's potential well, and the increase of the product factor of the bound-state and continuum-state populations, the oscillation amplitude of the particle's Coulomb acceleration increases.

AJAC: Atomic data calculation tool in Python

In this work, new features and extensions of a currently used online atomic database management system are reported. A multiplatform flexible computation package is added to the present system, to allow the calculation of various atomic radiative and collisional processes, based on simplifying the use of some existing atomic codes adopted from the literature. The interaction between users and data is facilitated by a rather extensive Python graphical user interface working online and could be installed in personal computers of different classes. In particular, this study gives an overview of the use of one model of the package models (i.e., electron impact collisional excitation model). The accuracy of computing capability of the electron impact collisional excitation in the adopted model, which follows the distorted wave approximation approach, is enhanced by implementing the Dirac R-matrix approximation approach. The validity and utility of this approach are presented through a comparison of the current computed results with earlier available theoretical and experimental results. Finally, the source code is made available under the general public license and being distributed freely in the hope that it will be useful to a wide community of laboratory and astrophysical plasma diagnostics.

Spectral converters and luminescent solar concentrators

In this paper we present a comprehensive theoretical description of molecular spectral converters in the specific context of luminescent solar concentrators (LSCs). The theoretical model is an extension to a three-level system interacting with a solar radiation bath of the standard quantum theory of atomic radiative processes. We derive the equilibrium equations of the conversion process and provide specific examples of application of this principle to the development of solar concentration devices.

Atomic Charge-Changing Processes in Plasmas

Properties of various kinds of plasmas are determined by atomic radiation and collision processes occurring between plasma particles, therefore, the detailed knowledge of the effective cross sections and rate coefficients for these processes is highly required. In this work, charge-changing processes, mainly for heavy-particle collisions, including impurity ions, are considered using available computer codes, and the background physics is discussed. Besides general features, the role of metastable states of plasma atoms and ions, which are often observed in most of plasmas and play a key role in plasma formation, is considered. The non-linear effects observed for heavy particle collisions, such as the density effect and multiple-electron ionization, are also considered. In addition, the isotope effects are briefly discussed related with electron capture in collisions of alpha particles with hydrogen and its isotopes (D and T). c

Impact of atomic collisional and radiative processes on modeling and spectroscopy of highly ionized plasma

The reliability and scalability of atomic data used in the ionization calculations of K- and L-shell moderate-Z elements are of great concern. It is critical to include an adequate number of excited levels per ion to generate synthetic spectra with which to diagnose plasma conditions. Our model include all dominant processes such as collisional excitation, ionization and recombination and opacity effects by coupling photoexcitation and photoionization for non-LTE plasmas. Experimental data of complex L-shell ions provide a wealth of information about plasma conditions. Analysis of our spectra using self consistently generated data from state-of-the-art codes show excellent agreement with experiment.

Charge-state distribution in a photoionized laser-produced plasma

We present the first x-ray spectroscopic measurements of the ionization balance relevant to astrophysics with intense laser. Independent measurement of the radiation flux indicates values of the ionization parameter ξ ∼ 10 erg cm s-1 and Planckian radiation source of 80 eV to photoionize the nitrogen gas. The observed emission spectra of nitrogen of relatively low density (ni = 1.4 × 1019 cm−3) shows a good agreement with the synthetic spectra by a time-dependent DCA (Detailed Configuration Accounting) atomic model. In this model, it solves the rate equations for level population distributions by considering collisional and radiative atomic processes based on screened hydrogenic model. The jj configuration atomic states and transition probabilities are calculated with Hullac to synthesize spectrum. With this model, we can obtain a reasonable range of the electron temperatures of 20 — 30 eV. Comparisons of charge-state distribution with a non-LTE atomic model FLYCHK show reasonable agreement.

Radiative atomic processes and Galilean and gauge transformations

Radiative atomic processes, in which charged particles moving with velocities much less than the speed of light emit a photon, are normally considered by using the Schrödinger equation. By analysing the transformation properties of the radiative transition amplitudes under the change of a reference frame we establish that the total cross sections and decay rates, calculated with the Schrödinger equation, are Galilean invariant and that this invariance holds irrespective of the accuracy of wavefunctions describing the charged particles. By considering, within the scope of one reference frame, the radiative processes for two identical atomic systems which have different translational (centre-of-mass) velocities we show that the total cross sections and decay rates in general depend on this velocity if approximate wavefunctions are employed and that this is the direct consequence of the problem of gauge dependence. We also present a detailed discussion of the intimate interrelation between Galilean and gauge transformations which, if overlooked, can easily lead to the misinterpretation of the problem of gauge dependence as the ‘problem of Galilean non-invariance’.

FLYCHK: Generalized population kinetics and spectral model for rapid spectroscopic analysis for all elements

FLYCHK is a straightforward, rapid tool to provide ionization and population distributions of plasmas in zero dimension with accuracy sufficient for most initial estimates and in many cases is applicable for more sophisticated analysis. FLYCHK solves rate equations for level population distributions by considering collisional and radiative atomic processes. The code is designed to be straightforward to use and yet is general enough to apply for most laboratory plasmas. Further, it can be applied for low-to-high Z ions and in either steady-state or time-dependent situations. Plasmas with arbitrary electron energy distributions, single or multiple electron temperatures can be studied as well as radiation-driven plasmas. To achieve this versatility and accuracy in a code that provides rapid response we employ schematic atomic structures, scaled hydrogenic cross-sections and read-in tables. It also employs the jj configuration averaged atomic states and oscillator strengths calculated using the Dirac–Hartree–Slater model for spectrum synthesis. Numerous experimental and calculational comparisons performed in recent years show that FLYCHK provides meaningful estimates of ionization distributions, well within a charge state for most laboratory applications.

Laboratory Measurement and Theoretical Modeling of K‐Shell X‐Ray Lines from Inner‐Shell Excited and Ionized Ions of Oxygen

We present high resolution laboratory spectra of K-shell X-ray lines from inner-shell excited and ionized ions of oxygen, obtained with a reflection grating spectrometer on the electron beam ion trap (EBIT-I) at the Lawrence Livermore National Laboratory. Only with a multi-ion model including all major atomic collisional and radiative processes, are we able to identify the observed K-shell transitions of oxygen ions from \ion{O}{3} to \ion{O}{6}. The wavelengths and associated errors for some of the strongest transitions are given, taking into account both the experimental and modeling uncertainties. The present data should be useful in identifying the absorption features present in astrophysical sources, such as active galactic nuclei and X-ray binaries. They are also useful in providing benchmarks for the testing of theoretical atomic structure calculations.

Generation of higher-order atomic dipole squeezing in a high-Q micromaser cavity. (V). A linear superposition of states

In our preceding paper, we investigated the generation of higher-order atomic dipole squeezing (HOADS) in a nondegenerate two-photon Jaynes–Cummings model in the absence of Stark shift. In this paper, we continue to study HOADS in this model but with the inclusion of Stark shift. Based on the linear superposition principle of quantum mechanics, we discuss the cases where the atom or the two-mode fields are initially prepared in a superposition of states. We demonstrate that the essential condition for generating HOADS is that the initial state of the system should include phase information, and HOADS cannot appear in atomic spontaneous radiation processes. The Stark shift brings time-dependent phase information into emitted photons and has a significant effect (constructively and destructively) on HOADS. It is found that weakly coupling of the intermediate virtual state to the ground state of the atom would lead to much more squeezing and collapse-revival phenomena. The relation between HOADS and second-order atomic dipole squeezing is also discussed.

H ULLAC, an integrated computer package for atomic processes in plasmas

We describe H ULLAC, an integrated code for calculating atomic structure and cross sections for collisional and radiative atomic processes. This code evolved and has been used over the years, but so far, there was no coherent, comprehensive, and in-depth presentation of it. It is based on relativistic quantum mechanical calculations including configuration interaction. The collisional cross sections are calculated in the distorted wave approximation. The theory and code are presented, emphasizing the various novel methods that has been developed to obtain accurate results very efficiently. In particular we describe the parametric potential method used for both bound and free orbitals, the factorization–interpolation method applied in the derivation of collisional rates, the phase amplitude approach for calculating the continuum orbitals and the N JGRAF graphical method used in the calculation of the angular momentum part of the matrix elements. Special effort has been made to insure the simplicity of use, which is demonstrated in an example.

Influence of atomic radiative and collisional processes on the plasma modeling of Mg^{10+} at low electron densities

In this paper, we report on theoretical calculations of electron-impact excitation cross sections and radiative transition rates for ${\mathrm{Mg}}^{10+}.$ The excitation cross sections were calculated using semirelativistic close-coupling and fully relativistic distorted-wave theory and the radiative rates were determined using semirelativistic and fully relativistic atomic-structure theory. After the solution of the corresponding collisional-radiative equations, the $K{\ensuremath{\alpha}}_{2}/K{\ensuremath{\alpha}}_{1}$ $(1s2p{ }^{3}{P}_{1}\ensuremath{\rightarrow}{1s}^{2}{ }^{1}{S}_{0}$ over $1s2p{ }^{1}{P}_{1}\ensuremath{\rightarrow}{1s}^{2}{ }^{1}{S}_{0})$ emission line ratio and the $K{\ensuremath{\beta}}_{2}/K{\ensuremath{\beta}}_{1}$ $(1s3p{ }^{3}{P}_{1}\ensuremath{\rightarrow}{1s}^{2}{ }^{1}{S}_{0}$ over $1s3p{ }^{1}{P}_{1}\ensuremath{\rightarrow}{1s}^{2}{ }^{1}{S}_{0})$ emission line ratio were calculated as a function of electron temperature and density. The various scattering calculations involving different numbers of levels enabled us to study the influence of resonance structures and cascades from highly excited levels on the collisional-radiative modeling and we found that they have little effect on the level populations. However, even in this ten-times ionized species, the effects of orbital relaxation are found to be important in the determination of accurate electric-dipole radiative transition rates. Both line ratios were found to be strongly affected by whether the magnetic-dipole radiative transition from the $1s2s$ ${}^{3}{S}_{1}$ level to the ground state was included or not. At very low electron densities, the $1s2s$ ${}^{1}{S}_{0}$ two-photon transition to the ground state also has an effect on the $K{\ensuremath{\alpha}}_{2}/K{\ensuremath{\alpha}}_{1}$ line ratio. In addition, we found that the line ratios are enhanced at high temperatures by radiative and dielectronic recombination from the hydrogenic ${\mathrm{Mg}}^{11+}$ ion. However, the dielectronic satellite lines have no effect on the line ratios for the low-density astrophysical, solar, and magnetic-fusion plasmas considered in this paper.

Impact of detailed radiation transport on volume recombination

Recently both the Alcator C-Mod and DIII-D tokamaks observed significant recombination of major ion species in the divertor region during detachment. For sufficiently low temperatures the mixture of neutral atoms and ions can be optically thick to line radiation. The optical depth of the recombined region to Ly α radiation can be very large and opacity effects and radiation trapping can dramatically change the heat flux to the divertor walls. This paper presents an analysis of the effect of line radiation on volume recombination using CRETIN, a multi-dimensional, non-local thermodynamic equilibrium (NLTE) simulation code that includes the atomic kinetics and radiative transport processes necessary to model this complex environment.

RADIATIVE TRANSITION OF Rb ATOM BETWEEN INITIAL AND FINAL CHANNELS

As an extension of theoretical study of transition from an initial state to a final channel,the initial states with same angular momentum form varied initial channels. By defining anew renormalized matrix element, the atomic radiative processes from an initial channel to afinal channel can be treated in an unified manner. As an example, we present here the renor-malized matrix element of Rb atom between initial and final channels.