The author calculates dielectronic recombination rate coefficients for the Be-like and B-like ions Fe22+ and Fe21+ using a multiconfiguration LS-coupling expansion and allowing for Delta nc=0 and Delta nc=1 autoionising transition into the continuum of excited states. The effect of intermediate coupling is also investigated and found to be less than 10%. They use autostructure-a general program for the calculation of multiconfiguration LS-coupling or intermediate-coupling autoionisation transition rates (incorporating superstructure)-to calculate the dielectronic recombination rate coefficient for the 1-2 and 2-3 core transitions. Together with the Burgess general formula for the 2-2 transition, they obtain about 95% of the total dielectronic recombination rate coefficient for ground state and look at its effect on the ionisation balance for a steady-state plasma. They confirm the recent findings of Smith et al. (1985) that the effect of Delta nc=0 secondary autoionisation is much less significant for highly charged ions than was suggested by Jacobs et al.

https://iopscience.iop.org/article/10.1088/0022-3700/19/22/023/pdf

Dielectronic recombination of Fe22+ and Fe21+

Aims. The interpretation of astrophysical spectra depends directly on a knowledge of the ionization state of the emitting plasma. This is determined, in part, from collisional ionization rate coefficients. The most recent assessments of these were performed by Arnaud & Rothenflug (1985, A&AS, 60, 425) and Arnaud & Raymond (1992, ApJ, 398, 394). Since their work, new laboratory measurements of ionization cross sections have become available as well as the Flexible Atomic Code (FAC) which enables theoretical calculations of these rates. Our goal is to provide a complete set of ionization rate coefficients for the elements hydrogen through zinc. Methods. A scaling law, which assists the analysis of ionization cross sections and rate coefficients, has been developed following the approach of Burgess & Tully (1992, A&A, 254, 436). Essentially all available measured cross sections along each isoelectronic sequence have been examined and compared to cross sections calculated with the Flexible Atomic Code (FAC) and with other calculations. Two approaches has been taken to provide a complete set of ionization cross sections. In the first, fits to scaled measured ionization cross sections, particularly for neutral and singly ionized species, are performed. In the second, fits to scaled calculated direct ionization and excitation-autoionization cross sections are performed to provide the remainder of the set. The fits to the cross sections are then integrated over a Maxwellian velocity distribution to derive ionization rate coefficients. Results. A complete set of ground level ionization cross sections and rate coefficients has been developed through the combination of these two approaches. A tabulation of parameter fits to ground level ionization rate coefficients for all atoms and ions of the elements of H through Zn is provided.

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Ionization rate coefficients for the elements hydrogen through zinc

Impurities continue to be a concern for future fusion devices, and ongoing efforts are made to study their generation, confinement, and control. Techniques for analysis of concentrations, power losses, and confinement of impurities are surveyed, and experimental examples illustrating typical observations in tokamak plasmas are presented. The use of impurities for diagnosing plasma properties is outlined briefly.

https://iopscience.iop.org/article/10.1088/0029-5515/24/12/008/pdf

Impurities in tokamaks

Electron–ion collisions are among the most important atomic processes in ionized gases. They comprise elastic scattering, excitation, ionization, and recombination. Theoretical approaches are numerous but calculating reliable results for applications is a task that has not generally been solved, although theory has progressed considerably in the last decade and can now provide reference data for electron collisions with few-electron systems. Experimental data on electron–ion collisions can be inferred from plasma observations, from ion trap measurements, from careful preparation and analysis of ion–atom collisions, and from colliding-beams experiments. The spectrum of equipment employed in the measurements ranges from table top size to large accelerator and storage-ring facilities. This article provides an overview of the processes involved in electron–ion collisions, their cross sections, the experimental approaches and typical results. The present status of the field is discussed and characterized by numerous examples illuminating the accomplishments as well as the limitations of experimental access to accurate detailed cross sections and rate coefficients, as they are required for understanding and modelling laboratory or astrophysical plasmas.

Electron–ion collisions: Fundamental processes in the focus of applied research

Extensive theoretical and experimental studies have been carried out for the past 20 years on electron - ion recombination processes, as they are applied to the analysis of astrophysical and laboratory plasmas. We review the basic understanding gained through these efforts, with emphasis on some of the more recent progress made in recombination theory as the recombining system is affected by time-dependent electric fields and plasma particles at low temperature. Together with collisional ionization and excitation processes, recombination is important in determining ionization balance and excited-state population in non-equilibrium plasmas. The radiation emitted by plasmas is usually the principal medium with which to study the plasma condition, as it is produced mainly during the recombination and decay of excited states of ions inside the plasma. This is especially true when the plasma under study is not readily accessible by direct probes, as in astrophysical plasmas. Moreover, external probes may sometimes cause undesirable disturbances of the plasma. Electron-ion recombination proceeds in several different modes. The direct modes include three-body recombination (TBR) and one-step radiative recombination (RR), all to the ground- and singly-excited states of the target ions. By contrast, the indirect resonant mode is a two-step dielectronic recombination (DR), which proceeds first with the formation of doubly-excited states by radiationless excitation/capture. The resonant states thus formed may relax by autoionization and/or radiative cascades. For more exotic modes of recombination, we consider off-shell dielectronic recombination (radiative DR = RDR), in which an electron capture is accompanied by simultaneous radiative emission and excitation of the target ion. Some discussion on attachment of electrons to neutral atoms, resulting in the formation of negative ions, is also given. When resonance states involve one or more electrons in high Rydberg states, presence of an external or intrinsic electric field in the vicinity of the target ions can seriously affect the ionic states involved and the resulting reaction rates. Such perturbative fields can be intrinsic, as in the case of the plasma ion field, or externally imposed. A proper theoretical treatment of this difficult problem is crucial in understanding the recombination process which takes place in a field contaminated environment. The simple off-shell dressing procedure of high Rydberg states by a time-dependent field is reviewed, and the possibility of an anomalously large enhancement in the rates, due to the momentum coherence effect (MCE), is discussed. The presently available data on recombination rates are summarized, and several important deficiencies and future directions for further research are pointed out. Based on the detailed calculations for a number of cases, several empirical rate formulae for RR and DR processes have been generated to summarize the data for ready applications. As the collection of atoms is cooled to very low temperatures, , and the bound electrons are ionized by laser irradiation to states of very precisely controlled energies, the prospect for accurate experimental measurements of very-low-energy recombination rates is considered, where the electron temperature can be very low. Therefore, it is of interest to reconsider theoretically some new phenomena which may occur at such cold environments, in which the electron de Broglie wavelength can be very large, and both the density and coherent effects, as well as possible field effects, must be properly taken into account. Finally, a broader understanding of the various recombination processes may be achieved by studying their relationships to other reactions initiated by electron, ion and photon impact.

https://iopscience.iop.org/article/10.1088/0034-4885/60/7/001/pdf

Electron - ion recombination processes - an overview

An electron-impact-ionization mechanism for ions is considered in which the projectile is first captured by the target to form a doubly excited resonant intermediate state. Subsequently, this state decays in two steps by double Auger emission. The effect upon the ionization cross section is large near the excitation threshold and effectively extends the apparent threshold for scattering excitation single Auger ionization to lower energies. A detailed calculation of the ionization cross section and rate coefficient is presented for ${\mathrm{Fe}}^{15+}$ targets.

Electron impact ionization of Fe 1 5 + by resonant excitation double Auger ionization

Dielectronic recombination and related resonance processes

The effect on the dielectronic recombination cross section of electric-field-induced mixing of high Rydberg-state (HRS) levels is determined, for both ${\mathrm{Mg}}^{1+}$ and ${\mathrm{Ca}}^{1+}$ target ions. After diagonalizing the energy matrix, ${\ensuremath{\sigma}}_{n}^{\mathrm{DR}}$ is calculated in the isolated resonance approximation as a function of n, the principal quantum number of the HRS electron. From this result, both the total cross section, ${\ensuremath{\sigma}}^{\mathrm{DR}\mathrm{\ensuremath{\equiv}}{\mathcal{J}}_{{n}_{\mathrm{}}{\ensuremath{\sigma}}_{n}^{\mathrm{DR}}}}$, and the total cross section integrated over energy, ${\ensuremath{\Omega}}^{\mathrm{DR}}$\ensuremath{\equiv}F ${\mathrm{de}}_{c}$ ${\ensuremath{\sigma}}^{\mathrm{DR}}$, are obtained. The agreement between theory and experiment for ${\ensuremath{\Omega}}^{\mathrm{DR}}$ is very good in the case of ${\mathrm{Mg}}^{1+}$, while roughly a factor of 2 discrepancy still exists for ${\mathrm{Ca}}^{1+}$.

Electric-field-induced mixing of high Rydberg-state levels in dielectronic recombination: Mg 1 + and Ca 1 + target ions

The dielectronic recombination (DR) rate coefficient ${\ensuremath{\alpha}}^{\mathrm{DR}}$ is explicitly calculated for Mo, Fe, and Ar target ions of the Na isoelectronic sequence (11 electrons). This work is an extension of a previous study of DR for ${\mathrm{Mo}}^{31+}$ ions. Both $\ensuremath{\Delta}n\ensuremath{\ne}0$ and $\ensuremath{\Delta}n=0$ transitions are considered in detail, with full $\mathrm{LS}$ coupling. The radiative and Auger cascade effects are found to be important, especially for high Rydberg states, and are included in the final rate-coefficient estimate. Scaling of ${\ensuremath{\alpha}}^{\mathrm{DR}}$ with ionic charge and free-electron temperature is discussed.

Dielectronic recombination rates for ions of the sodium sequence

A theoretical method for determining the effects of static applied electric fields F on the dielectronic recombination (DR) cross section sigma is described. Distorted-wave theory and the isolated resonance approximation are invoked, in an angular momentum average formalism. First, the intermediate-state Hamiltonian is diagonalised in a basis of high Rydberg state functions of fixed principal n and orbital magnetic m quantum numbers. Fine structure is included, and provision is made for the effects of field ionisation. Then, the explicitly F-dependent DR cross section, integrated over continuum electron energy ec, is obtained as Sigma n,m integral dec sigma nm (ec) identical to Sigma n,m Omega nm identical to Omega tot. Results are displayed for ground-state sodium sequence ions of net charge Z1<or=6, undergoing intrashell ( Delta ns=0) dipole excitations.

K. LaGattuta

Papers

Electron impact ionization of Fe 1 5 + by resonant excitation double Auger ionization

Dielectronic recombination and related resonance processes

Electric-field-induced mixing of high Rydberg-state levels in dielectronic recombination: Mg 1 + and Ca 1 + target ions

Dielectronic recombination rates for ions of the sodium sequence

The effect of static electric fields on dielectronic recombination. I. Basic theory