Recombination Rate Coefficients Research Articles

Electron energetics in the Martian dayside ionosphere: Model comparisons with MAVEN data

AbstractThis paper presents a study of the energetics of the dayside ionosphere of Mars using models and data from several instruments on board the Mars Atmosphere and Volatile EvolutioN spacecraft. In particular, calculated photoelectron fluxes are compared with suprathermal electron fluxes measured by the Solar Wind Electron Analyzer, and calculated electron temperatures are compared with temperatures measured by the Langmuir Probe and Waves experiment. The major heat source for the thermal electrons is Coulomb heating from the suprathermal electron population, and cooling due to collisional rotational and vibrational CO2 dominates the energy loss. The models used in this study were largely able to reproduce the observed high topside ionosphere electron temperatures (e.g., 3000 K at 300 km altitude) without using a topside heat flux when magnetic field topologies consistent with the measured magnetic field were adopted. Magnetic topology affects both suprathermal electron transport and thermal electron heat conduction. The effects of using two different solar irradiance models were also investigated. In particular, photoelectron fluxes and electron temperatures found using the Heliospheric Environment Solar Spectrum Radiation irradiance were higher than those with the Flare Irradiance Spectrum Model‐Mars. The electron temperature is shown to affect the O2+ dissociative recombination rate coefficient, which in turn affects photochemical escape of oxygen from Mars.

Free electron degeneracy effects on collisional excitation, ionization, de-excitation and three-body recombination

Collisional-radiative models enable average ionization and ionization populations, plus the rates of absorption and emission of radiation to be calculated for plasmas not in thermal equilbrium. At high densities and low temperatures, electrons may have a high occupancy of the free electron quantum states and evaluations of rate coefficients need to take into account the free electron degeneracy. We demonstrate that electron degeneracy can reduce collisional rate coefficients by orders-of-magnitude from values calculated neglecting degeneracy. We show that assumptions regarding the collisional differential cross-section can alter collisional ionization and recombination rate coefficients by a further factor two under conditions relevant to inertial fusion.

On stabilization of scattering resonances in recombination reaction that forms ozone.

Calculations of energy transfer in the recombination reaction that forms ozone are carried out within the framework of the mixed quantum/classical theory and using the dimensionally reduced 2D-model of ozone molecule, with bending motion neglected. Recombination rate coefficients are obtained at room temperature for symmetric and asymmetric isotopomers of singly and doubly substituted isotopologues. The processes of resonance formation, spontaneous decay, collisional dissociation, and stabilization by bath gas (Ar) are all characterized and taken into account within the steady-state approximation for kinetics. The focus is on stabilization step, where the mysterious isotopic η-effect was thought to originate from. Our results indicate no difference in cross sections for stabilization of scatteringresonances in symmetric and asymmetric isotopomers. As practical results, the general and simple analytic models for stabilization and dissociation cross sections are presented, which can be applied to resonances in any ozone molecule, symmetric or asymmetric, singly or doubly substituted. Present calculations show some isotope effect that looks similar to the experimentally observed η-effect, and the origin of this phenomenon is in the rates of formation/decay of scatteringresonances, determined by their widths, that are somewhat larger in asymmetric isotopomers than in their symmetric analogues. However, the approximate two-dimensional model used here is insufficient for consistent and reliable description of all features of the isotopic effect in ozone. Calculations using an accurate 3D model are still needed.

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.

Partial and total dielectronic recombination rate coefficients forW73+toW56+

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.

Parameterization of the level-resolved radiative recombination rate coefficients for the SPEX code

The level-resolved radiative recombination (RR) rate coefficients for H-like to Na-like ions from H (Z = 1) up to and including Zn (Z = 30) are studied here. For H-like ions, the quantum-mechanical exact photoionization cross sections for nonrelativistic hydrogenic systems are used to calculate the RR rate coefficients under the principle of detailed balance, while for He-like to Na-like ions, the archival data on ADAS are adopted. Parameterizations are made for the direct capture rates in a wide temperature range. The fitting accuracies are better than 5% for about 99% of the 30, 000 levels considered here. The 1% exceptions include levels from low- charged many-electron ions, and/or high-shell (n>=4) levels are less important in terms of interpreting X-ray emitting astrophysical plasmas. The RR data will be incorporated into the high-resolution spectral analysis package SPEX.

Theoretical studies of dielectronic recombination for Au34+ ions

Dielectronic recombination (DR) rate coefficients of complex structure ions are very important for spectral simulation in some application researches, such as nuclear fusion and extreme ultraviolet lithography. Theoretical calculations are made for dielectronic recombination rate coefficients of Au34+ ions by using a flexible relativistic atomic code. Influences of excitation and radiation channels, configuration interactions, and decays to autoionizing levels possibly followed by radiative cascades (DAC) on DR rate coefficient are analyzed. The contribution of DAC is evident. The total DR rate coefficient is greater than either the radiation recombination coefficient or three-body recombination coefficient for electron temperature greater than 1 eV. In order to facilitate simple applications, the total DR rate coefficients for the ground state and the first excited state are fitted to an empirical formula. These results should be useful for further analyzing the DR process of complex structures ions.

A full-dimensional model of ozone forming reaction: the absolute value of the recombination rate coefficient, its pressure and temperature dependencies.

Rigorous calculations of scattering resonances in ozone are carried out for a broad range of rotational excitations. The accurate potential energy surface of Dawes is adopted, and a new efficient method for calculations of ro-vibrational energies, wave functions and resonance lifetimes is employed (which uses hyper-spherical coordinates, the sequential diagonalization/truncation approach, grid optimization and complex absorbing potential). A detailed analysis is carried out to characterize distributions of resonance energies and lifetimes, their rotational/vibrational content and their positions with respect to the centrifugal barrier. Emphasis is on the contribution of these resonances to the recombination process that forms ozone. It is found that major contributions come from localized resonances at energies near the top of the barrier. Delocalized resonances at higher energies should also be taken into account, while very narrow resonances at low energies (trapped far behind the centrifugal barrier) should be treated as bound states. The absolute value of the recombination rate coefficient, its pressure and temperature dependencies are obtained using the energy-transfer model developed in the earlier work. Good agreement with experimental data is obtained if one follows the suggestion of Troe, who argued that the energy transfer mechanism of recombination is responsible only for 55% of the recombination rate (with the remaining 45% coming from the competing chaperon mechanism).

Photoionization and electron-ion recombination of Ti I

Study of the inverse processes of photoionization and electron-ion recombination of (Ti I + hν⇋ Ti II + e) using the unified method is reported. The method, based on close coupling (CC) approximation and R-matrix method, subsumes both the radiative recombination (RR) and dielectronic recombination (DR) in a unified manner and provides state-specific and total electron-ion recombination rate coefficients which are self-consistent with the state-specific photoionization cross sections. The present results include state-specific electron-ion recombination rates (αRC(i))and partial photoionization cross sections (σPI(i)) leaving the ion in the ground state of 813 bound states with n ≤ 10 and l ≤ 9 of Ti I. Various features of state-specific and total electron-ion recombination with temperature, and the corresponding photoionization cross sections with energies are discussed with illustrations. Due to closely lying excited states near the ground state of the core, photoionization cross sections show presence of narrow Rydberg resonances in low energy region near the ionization threshold. Many excited states also show broad and enhanced Seaton resonances due to PEC (photo-excitation-of-core) which contribute to the high temperature recombination. The total recombination rate coefficient is found to show a low hump around temperature 280 K and a high dielectronic recombination peak at temperature 25,000 K. Total spectrum of recombination cross sections and rates with photoelectron energy are also presented for experimental observation. Calculations were carried out using a CC wave function expansion of 36 states of the core ion Ti II. The large set of data for recombination rates and partial photoionization cross sections with resonances should provide a complete and accurate modelings of plasmas.

Recombination of H+3 ions with electrons in He/H2 ambient gas at temperatures from 240 K to 340 K

We have studied the recombination of ions with electrons in a stationary afterglow experiment either in pure hydrogen or in mixtures of helium, hydrogen, and argon. The decay of the ion density during the afterglow was monitored using near-infrared cavity ring-down absorption spectroscopy. The gas temperatures ranged from 240 K to 340 K. We find that three-body recombination, where molecular hydrogen acts as a third body, increases the recombination rate significantly. However, assisted three-body recombination saturates at hydrogen densities above and the recombination rate then becomes nearly independent of the neutral gas density. The saturation can lead to the erroneous conclusion that the recombination is purely binary and this appears to be the cause of some inconsistencies between previously reported recombination rate coefficients. At temperatures 240–340 K the obtained three-body recombination rate coefficient is independent on temperature () and it is larger by five orders of magnitude than those expected from the classical theory for atomic ions of Bates and Khare (). The observed dependences on density suggest that a substantial fraction of neutral complexes formed in capture of electrons by ions do not rapidly predissociate but can be stabilized by interactions with third bodies. Saturation occurs if the capture step is rate limiting rather than stabilization.

Reactive collisions of very low-energy electrons with H$_2^{+}$: rotational transitions and dissociative recombination

A new series of computations has been performed to obtain cross-sections and rate coefficients for state-to-state rotational transitions in the H|$_{2}^{+}$| ion, induced by collisions with very low-energy electrons. Following our recent work on the HD+ ion (Motapon et al. 2014), and using the same molecular structure data sets, excitations |$N_{i}^{+} \rightarrow$||$N_{i}^{+}+2$| for |$N_{i}^{+}=0$| to 10, and de-excitations |$N_{i}^{+}$| → |$N_{i}^{+}-2$|⁠, for |$N_{i}^{+}=2$| to 10, in the energy range 0.01 meV–0.3 eV, have been explored. The calculated cross-sections have been convolved in order to obtain Maxwell rate coefficients for electronic temperatures up to a few hundred of Kelvin. Moreover, Maxwell rate coefficients for dissociative recombination have been calculated for the same initial rotational levels.

Quantitative analysis of electrically detected Ramsey fringes in P-doped Si

This work describes detection of the laser preparation and subsequent coherent manipulation of the quantum states of orbital levels of donors in doped Si, by measuring the voltage drop across an irradiated Si sample. This electrical signal, which arises from thermal ionization of excited orbital states, and which is detected on a millisecond time scale by a voltmeter, leads to much more sensitive detection than can be had using optical methods, but has not before been quantitatively described from first principles. We present here a unified theory which relates the voltage drop across the sample to the wave function of the excited donors, and compare its predictions to experiments in which pairs of picosecond pulses from the Dutch free-electron laser FELIX are used to resonantly and coherently excite P donors in Si. Although the voltage drop varies on a millisecond time scale we are able to measure Ramsey oscillation of the excitation on a picosecond time scale, thus confirming that the donor wave function, and not just its excited state population, is crucial in determining the electrical signal. We are also able to extract the recombination rate coefficient to the ground state of the donor as well as the photoionization cross section of the excited state and phonon induced thermal ionization rate from the excited state. These quantities, which were previously of limited interest, are here shown to be important in the description of electrical detection, which, in our unoptimized configuration, is sensitive enough to enable us to detect the excitation of $\ensuremath{\sim}{10}^{7}$ donors.

Subshell-selective x-ray studies of radiative recombination ofU92+ions with electrons for very low relative energies

Radiative recombination (RR) into the K shell and L subshells of U92+ ions interacting with cooling electrons has been studied in an x-ray RR experiment at the electron cooler of the Experimental Storage Ring at GSI. The measured radiative recombination rate coefficients for electron-ion relative energies in the range 0–1000 meV demonstrate the importance of relativistic effects. The observed asymmetry of the measured K-RR x-ray emission with respect to the cooling energy, i.e., zero average relative velocity (〈vrel〉=0), are explained by fully relativistic RR calculations. With our new approach, we show that the study of the angular distribution of RR photons for different relative energies opens new perspectives for detailed understanding of the RR of ions with cooling electrons in cold magnetized plasma.7 MoreReceived 13 July 2015DOI:https://doi.org/10.1103/PhysRevA.92.032710©2015 American Physical Society

Recombination of H2D+ and HD2+ ions with electrons at 80 K

SynopsisStationary afterglow with Cavity Ring Down Spectrometer was utilized to probe the number densities of H3+, H2D+, HD2+ and D3+ ions in discharge and afterglow plasma. The recombination rate coefficients for recombination of H2D+ and HD2+ ions with electrons were obtained from the time decays of overall ion number density at different fractions of [H2]/[D2].

Near-Threshold Dielectronic Recombination Studies of Si-Like Ions

SynopsisDielectronic recombination rate coefficients are computed for the Si-like isoelectronic sequence, focusing on the near-threshold resonances of S2+.

The dielectronic recombination of Ar+–Ar4+

We present new, level-resolved rate coefficients for the dielectronic recombination of low charge states of argon (Ar+–Ar4+). The existing literature consists of either configuration-averaged distorted-wave or semi-empirical data. Level-resolved rate coefficients are necessary for accurate modeling and diagnostics in plasmas containing argon. We present our level-resolved results and compare with existing datasets, finding significant differences. We also present equilibrium ionization balance calculations using the new data, finding large differences in the predicted fractional abundances, particularly for Ar3+.

Electron-ion recombination of the open-4f-shell ion W19+

SynopsisElectron-ion recombination of W19+ forming W18+ has been studied both experimentally and theoretically. An exceptionally large recombination rate coefficient was observed by the storage-ring experiment at zero electron-ion collision energy. It exceeds the expectation for nonresonant radiative recombination (RR) by more than two orders of magnitude. This follows the pattern seen previously for the neighboring charge states of tungsten. The results of our present theoretical calculations, which were carried-out within the Breit-Wigner partitioned framework for resonant electron-ion recombination of complex ions, agree with this observation.

Dielectronic recombination of Zn-likeW44+from Cu-likeW45+

Energy levels, radiative transition probabilities, and autoionization rates for $\text{[Ar]}3{d}^{10}4{l}^{\ensuremath{'}}nl (n=4--12, l\ensuremath{\le}n\ensuremath{-}1), \text{[Ar]}3{d}^{10}5{l}^{\ensuremath{'}}nl (n=5--8, l\ensuremath{\le}n\ensuremath{-}1)$, and $\text{[Ar]}3{d}^{9}4{l}^{\ensuremath{'}}4{l}^{\ensuremath{'}\ensuremath{'}}nl (n=4--5, l\ensuremath{\le}n\ensuremath{-}1$) states in Zn-like tungsten (${\mathrm{W}}^{44+}$) are calculated using the relativistic Hartree-Fock method (cowan code), the multiconfiiguration relativistic Hebrew University Lawrence Livermore Atomic Code (hullac code), and the relativistic many-body perturbation theory method (rmbpt code). Autoionizing levels above the thresholds $\text{[Ar]}3{d}^{10}4s$ are considered. It is found that configuration mixing $[4sns+4pnp+4dnd+4fnf], [4snp+4pns+4pnd+4dnp+4fns+4fnd]$ plays an important role for all atomic characteristics. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the first excited odd- and even-parity states. It is shown that the contribution of the highly excited states is very important for the calculation of total DR rates. Contributions to DR rate coefficients from the excited $\text{[Ar]}3{d}^{10}4{l}^{\ensuremath{'}}nl$ states with $ng12$ and $\text{[Ar]}3{d}^{10}5{l}^{\ensuremath{'}}nl$ states with $ng8$, and additionally from core-excited $\text{[Ar]}3{d}^{9}4{l}^{\ensuremath{'}}4{l}^{\ensuremath{'}\ensuremath{'}}nl$ states with $ng5$, are estimated by extrapolation of all atomic parameters. The orbital angular momentum quantum number $l$ distribution of the rate coefficients shows two peaks at $l=2$ and $l=5$. The total DR rate coefficient is derived as a function of electron temperature. The dielectronic satellite spectra of ${\mathrm{W}}^{44+}$ are important for $M$-shell diagnostic of very high-temperature laboratory plasmas such as those found in future tokamaks.

Tungsten Data for Current and Future Uses in Fusion and Plasma Science

We give a brief overview of our recent experimental and theoretical work involving highly charged tungsten ions in high-temperature magnetically confined plasmas. Our work includes X-ray and extreme ultraviolet spectroscopy, state-of-the-art structure calculations, the generation of dielectronic recombination rate coefficients, collisional-radiative spectral modeling and assessments of the atomic data need for X-ray diagnostics monitoring of the parameters of the core plasma of future tokamaks, such as ITER. We give examples of our recent results in these areas.

THE ABUNDANCES OF LIGHT NEUTRON-CAPTURE ELEMENTS IN PLANETARY NEBULAE. III. THE IMPACT OF NEW ATOMIC DATA ON NEBULAR SELENIUM AND KRYPTON ABUNDANCE DETERMINATIONS

The detection of neutron(n)-capture elements in several planetary nebulae (PNe) has provided a new means of investigating s-process nucleosynthesis in low-mass stars. However, a lack of atomic data has inhibited accurate trans-iron element abundance determinations in astrophysical nebulae. Recently, photoionization and recombination data were determined for Se and Kr, the two most widely detected n-capture elements in nebular spectra. We have incorporated these new data into the photoionization code Cloudy. To test the atomic data, numerical models were computed for 15 PNe that exhibit emission lines from multiple Kr ions. We found systematic discrepancies between the predicted and observed emission lines that are most likely caused by inaccurate photoionization and recombination data. These discrepancies were removed by adjusting the Kr$^+$--Kr$^{3+}$ photoionization cross sections within their cited uncertainties and the dielectronic recombination rate coefficients by slightly larger amounts. From grids of models spanning the physical conditions encountered in PNe, we derive new, broadly applicable ionization correction factor (ICF) formulae for calculating Se and Kr elemental abundances. The ICFs were applied to our previous survey of near-infrared [Kr III] and [Se IV] emission lines in 120 PNe. The revised Se and Kr abundances are 0.1-0.3 dex lower than former estimates, with average values of [Se/(O, Ar)]=0.12$\pm$0.27 and [Kr/(O, Ar)]=0.82$\pm$0.29, but correlations previously found between their abundances and other nebular and stellar properties are unaffected. We also find a tendency for high-velocity PNe that can be associated with the Galactic thick disk to exhibit larger s-process enrichments than low-velocity PNe belonging to the thin disk population.