Dielectronic Recombination Rate Coefficients Research Articles

The series formulas of dielectronic recombination rate coefficients for the Ne-like isoelectronic sequence

By fitting the directly computed dielectronic recombination rate coefficients on the basis of the relativistic intermediate-coupling MCDF model by M. H. Chen, we present a set of series formulas of dielectronic recombination rate coefficients for Ne-like ions from Ar8+ to Xe44+ with the electron temperature range from 0.2keV to 6.0keV. The reproduced dielectronic recombination rate coefficients are in close agreement with the orginal results of Chen. The errors are generally less than 5%. Our formulas may be used easily to obtain dielectronic recombination rate coefficients in calculations of ionization balance in hot plasmas. The detailed results are tabled and discussed.

Unified formulas of dielectronic recombination rate coefficients for the Li-like isoelectronic sequence

By fitting the directly computed dielectronic recombination rate coefficients on the basis of relativistic intermediate-coupling MCDF model by M. H. Chen, we present a set of concise formulas of dielectronic recombination rate coefficients for Li-like ions from C3+ to Mo39+, which may be used conveniently in the calculations of ionization balance in hot plasmas. The detailed results are tabled.

Dielectronic recombination coefficients for Ni-like tantalum.

Dielectronic-recombination (DR) rate coefficients for the ground state of Ni-like ${\mathrm{Ta}}^{45+}$ have been calculated for the electron temperatures in the range 0.02T10 keV. The calculations were carried out in the isolated resonance approximation using the multiconfiguration Dirac-Fock model in intermediate coupling with configuration interaction. The total DR rate coefficients were obtained by including the contributions from the 3s, 3p, and 3d excitations. The rate coefficients are found to peak at very low temperature (\ensuremath{\sim}80 eV) with a value of 3.58\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$/sec and reduce to 1.48\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$/sec at T=1 keV.

Electric field effects on dielectronic recombination in a collisional-radiative model

We have carried out quantal calculations for the dielectronic recombination of C 3+ in an electric field. We have used these results in a collisional-radiative model for a carbon seeded hydrogen plasma. We find that the plasma microfield increases the effective dielectronic recombination rate coefficient for C 3+ by only 40% at n H =10 9 cm −3 , for example, compared to the near factor of 3 enhancement predicted by Reisenfeld et al. in 1992. The large effects predicted by Reisenfeld et al. over a wide range of densities are the result of an over-estimation of the electric field enhancement of dielectronic recombination by their approximate calculations

Dielectronic recombination into excited levels of Ne-like titanium from F-like low-iying states

The energy levels, wavelengths, oscillator strengths, Auger rates and level-to-level dielectronic recombination rate coefficients describing dielectronic recombination into excited levels of Ne-like titanium from F-like low-lying states are calculated. Our calculations are based on Dr. R. D. Cowan's semi-relativistic superposition-of-configuration Hartree-Fock (HFR) code, where the relativistic mass-velocity and Darwin corrections are included in the Hamiltonian, and the distorted-wave model is used for the calculation of free electron wavefunctions. In order to set the recombination rate coefficients on a level by level basis, in a manner compatible with detailed level population kinetics modelling of highly-stripped ions in plasma, the dielectronic recombination rate coefficients as a function of free electron temperatures are given in an analytical form, which is not only very convenient in practice, but also hopefully accurate compared with the exactly calculated numerical results.

X-ray diagnostics of tokamak plasmas

The paper describes the x-ray diagnostics of central plasma parameters of present large tokamak fusion experiments by means of Johann type curved crystal spectrometers. These spectrometers have a very high spectral resolution, λ/Δλ > 10 000, and are mainly used to determine the central ion temperature from Doppler broadening measurements of the 1s-2p resonance lines of high-Z helium-like ions. The full diagnostic potential of the spectra of helium-like ions is demonstrated by the detailed analysis of Fe XXV satellite spectra from a particular high temperature tokamak discharge with reactor-like conditions. This analysis is based on least squares fit comparisons of the experimental data with synthetic spectra, which are constructed from theoretical predictions. It is found that the satellite spectra which are associated with the helium-like resonance lines are in excellent agreement with the theoretical predictions. The satellite spectra can therefore be used for electron temperature measurements, measurements of the dielectronic recombination rate coefficients and the determination of relative ion charge-state abundances. Discrepancies between experiment and theory are, however, observed for the intensity ratios of the helium-like lines. Also discussed are atomic physics data needs and the potential of the x-ray diagnostic for future large tokamaks, such as ITER.

Iron ionization and recombination rates and ionization equilibrium

In the past few years important progress has been made on the knowledge of ionization and recombination rates of iron, an astrophysically abundant heavy element and a major impurity in laboratory fusion devices. We make a critical review of the existing data on ionization and dielectronic recombination and present new computations of radiative recombination rate coefficients of Fe(+14) through Fe(+25) using the photoionization cross sections of Clark et al. (1986). We provide analytical fits to the recommended data (direct ionization and excitation-autoionization cross sections; radiative and dielectronic recombination rate coefficients). Finally we determine the iron ionic fractions at ionization equilibrium and compare them with previous computations as well as with observational data.

Dielectronic recombination as a function of electric field strength

Dielectronic recombination (DR) is the dominant recombination mechanism at coronal temperatures and densities. We present a procedure for calculating DR rate coefficients as a function of electric field strength and apply this method to carbon ions. We focus on the competing effects of enhancement by plasma microfields and rate decrease through collisional excitation and ionization. We find that, in the case of C(3+), a significant rate enhancement results, leading to a reinterpretation of C IV emission-line intensities in the sun and late-type stars. We further consider how macroscopic electric fields, in particular motional electric fields, can affect DR rate coefficients, demonstrating dramatic rate increases for a number of the carbon ions.

Dielectronic recombination from high-lying resonance states in H-like silicon, calcium, and iron.

We have calculated dielectronic recombination (DR) rate coefficients for H-like silicon, calcium, and iron at plasma temperatures 0.1--10 keV. The calculation involves all DR processes 1s+\ensuremath{\epsilon}${\mathit{l}}_{\mathit{c}}$\ensuremath{\rightarrow}(2lnl'${)}^{\mathrm{*}}$\ensuremath{\rightarrow}1sml''+\ensuremath{\gamma} with n=2-\ensuremath{\infty}. The effects of configuration interaction and spin-orbit coupling have been included for all states with n\ensuremath{\le}8; for higher-lying resonance states, the 1/${\mathit{n}}^{3}$ scaling was employed.

Dielectronic recombination of O+

We have recalculated the dielectronic recombination rate coefficient for the special case of ${\mathrm{O}}^{+}$ using an improved atomic structure. This removes the discrepancy between the results of Terao et al. [J. Phys. B 24, L321 (1991)] and of Badnell and Pindzola [Phys. Rev. A 39, 1690 (1989)].

Dielectronic recombination for F-like and Ne-like germanium ions

Auger rates, average absorption oscillator strengths (corresponding average wavelengths) and level-to-level dielectronic recombination rate coefficients describing dielectronic recombination for F-like and Ne-like germanium ions are explicitly calculated. The calculations are based on Cowan's non-relativistic multi-configuration Hartree-Fock (HFR) code which includes relativistic mass-velocity and Darwin corrections and successive subroutines for calculating average oscillator strengths and average wavelengths and dielectronic recombination rate coefficients are developed. The dielectronic recombination rate coefficients as the function of temperature of free electrons are given in an analytical form which is very convenient in practice.

Dielectronic recombination rate coefficients for S(q+) (q = 1-5) ions

We have calculated the total dielectronic recombination rate coefficient for S q+ (q=1-5) ions, in the low-density limit. We tabulate results over the temperature range T=3×10 4 -10 6 K. At electron temperatures (∼10 5 K) and densities (≤10 4 cm −3 ) applicable to the Io plasma torus, these results differ substantially from existing data

Autoionization and radiationless electron capture in complex spectra.

The factorization-interpolation model, developed to compute collisional excitation rate coefficients efficiently in dense plasma, is applied here to autoionization and radiationless electron capture. Results using a parametric atomic central potential and factorization interpolation for autoionization rates and dielectronic recombination rate coefficients in Ne-like Fe are compared to multiconfigurational Dirac-Fock calculations. Agreement is very good. As a further application, we treat the problem of indirect ionization via collisional excitation followed by autoionization in Zn-like Mo.

Measurements of Dielectronic Recombination Rate Coefficients for He-like and H-like Metal Ions from Tokamak Plasmas

The dielectronic recombination rate coefficients associated with the Δn = 1 radiative core transitions have been determined for Ti XXI, Fe XXV, Ni XXVII, and Ti XXII as a function of the electron temperature from the analysis of x-ray satellite spectra emitted from tokamak plasmas. The results obtained are in good agreement with the recent theoretical predictions of Bely-Dubau et al., and Karim and Bhalla.

Dielectronic satellite spectra of hydrogenlike iron from the Tokamak Fusion Test Reactor.

Spectra of hydrogenlike iron Fe XXVI have been observed from Tokamak Fusion Test Reactor plasmas with a high-resolution crystal spectrometer. The experimental arrangement permits simultaneous observation of the Fe XXVI Ly-${\mathrm{\ensuremath{\alpha}}}_{1}$ and Ly-${\mathrm{\ensuremath{\alpha}}}_{2}$ lines and the associated dielectronic satellites, which are due to transitions 1snl-2pnl' with n\ensuremath{\ge}2, as well as the heliumlike 1${\mathit{s}}^{2}$${(}^{1}$${\mathit{S}}_{0}$)-1s4p${(}^{1}$${\mathit{P}}_{1}$) and both hydrogenlike Ly-${\mathrm{\ensuremath{\beta}}}_{1}$ and Ly-${\mathrm{\ensuremath{\beta}}}_{2}$ lines from chromium. Relative wavelengths and line intensities can be determined very accurately. The spectral data are in very good agreement with theoretical calculations. The observed spectra have also been used to estimate the total dielectronic recombination rate coefficient of Fe XXVI.

Dielectronic recombination rates for argon ions

The theoretical calculations of dielectronic recombination (DR) rate coefficients for Ar ions are reviewed for intrashell (δ n=0) and intershell (δ n≠0) excitation transitions. This data base, which was generated by different authors, is not complete and this fact, together with the uncertainty in the accuracy of the calculations, makes it difficult to obtain a reliable empirical rate formula. New empirical formulae for the total rate α have been obtained for the two transitions (δ n=0 and δ n≠0) separately in the case of Ar ions. The rates can be evaluated simply and directly, without any further atomic input data. The 1 s-excitation of Ar ions, with N electrons before capture, has rates given by α(1s) = [ 7.0×10 -12 (kT) 3 2 ][exp( -2.5 kT )] ×[exp[-0.25(N-2) 2]× where kT is in units of keV and α in cm 3/sec. The 2 s → 2 p transition, which is allowed for all ions with N = 3–9, leads to dielectronic recombination rates given by α(2 s, δn =0) = [ 3.7×10 -13 (kT) 3 2 ][exp( -0.05 kT )][ (N−2)(10−N) (N−1) ].

Dielectronic recombination for C VI, and O VII,VII.

Dielectronic recombination (DR) cross sections and rate coefficients for the H-like and He-like C and O ions are calculated in the zero-field, zero-density limit. The peak rates are approximately (1.2--1.6){times}10{sup {minus}12} cm{sup 3}/sec for all four ions. For the H-like ions, the contribution to total rates from high Rydberg states ({ital n}{ge}6) is found large, accounting for nearly one-half of the total rates. Agreements with earlier estimates are at a {plus minus}5% level. For the He-like ions, the high-Rydberg-state contribution is strongly suppressed because of the extra Auger channel which opens up at {ital n}=5--7. Agreement with previous calculations is again at a 5% level. The DR cross sections for the initial metastable states of the He-like ions are also estimated for a few low-lying resonance states near the DR threshold. The cross section for the 2{ital s} {sup 1}S{r arrow}1s2p {sup 1}P+nl excitation capture is found to be very large.

Dielectronic recombination of O IV.

Dielectronic recombination (DR) rate coefficients and cross sections are estimated for the O{sup 3+} ion where the 2{ital s} and 2{ital p} electrons of the initial state are excited to higher, {ital n}{ge}3 states ({Delta}{ital n}{sub {ital t}}{ne}0 transitions) during the excitation-capture part of the process. This work completes the calculations of DR parameters for the O{sup 3+} ion, where the {Delta}{ital n}{sub {ital t}}=0 part of this process had been reported recently. We found that the 2{ital p} electron excitation dominates the {Delta}{ital n}{sub {ital t}}{ne}0 process, while the 2{ital s} excitation is suppressed by the cascade corrections that strongly affect the intermediate states 1{ital s}{sup 2}2s2p3snl and 1{ital s}{sup 2}2s2p3dnl. The 2{ital s} contribution is approximately 15% of the {Delta}{ital n}{sub {ital t}}{ne}0 mode, while the total {Delta}{ital n}{sub {ital t}}{ne}0 contribution is roughly 10% of the {Delta}{ital n}{sub {ital t}}=0 cross section.

Dielectronic recombination ofP5+andCl7+in configuration-average,LS-coupling, and intermediate-coupling approximations

We have calculated dielectronic recombination cross sections and rate coefficients for the Ne-like ions ${\mathrm{P}}^{5+}$ and ${\mathrm{Cl}}^{7+}$ in configuration-average, LS-coupling, and intermediate-coupling approximations. Autoionization into excited states reduces the cross sections and rate coefficients by substantial amounts in all three methods. There is only rough agreement between the configuration-average cross-section results and the corresponding intermediate-coupling results. There is good agreement, however, between the LS-coupling cross-section results and the corresponding intermediate-coupling results. The LS-coupling and intermediate-coupling rate coefficients agree to better than 5%, while the configuration-average rate coefficients are about 30% higher than the other two coupling methods. External electric field effects, as calculated in the configuration-average approximation, are found to be relatively small for the cross sections and completely negligible for the rate coefficients. Finally, the general formula of Burgess was found to overestimate the rate coefficients by roughly a factor of 5, mainly due to the neglect of autoionization into excited states.

Dielectronic recombination rate coefficient for some selected ions in the helium isoelectronic sequence.

Dielectronic recombination (DR) rate coefficients are calculated for selected heliumlike ions with atomic number Z=10, 14, 18, 22, 24, 26, and 28 at plasma temperatures 0.1\char21{}10 keV. The total DR rate coefficient has been obtained by summing over partial DR rates of recombination processes that proceed via intermediate lithiumlike resonance states \ensuremath{\Vert}1s2lnl'LSJ〉. The effects of configuration interaction and spin-orbit coupling have been included for all states with n\ensuremath{\le}8; for higher-lying autoionizing states, the 1/${n}^{3}$ scaling was employed. The results from the present calculation are compared with available theoretical and experimental values of DR rate coefficients.