Atomic data for heavy elements relevant to magnetic fusion and astrophysics using the Los Alamos atomic physics codes James Colgan, Honglin Zhang, and Christopher Fontes, Los Alamos National Laboratory, NM, USA

Overview In the last 5 years we have used the LANL codes to compute various sets of atomic data. In this talk I give some highlights of these calculations and comparisons with other methods and experiment, if available. I first discuss, very briefly, the methods used to generate the atomic data. Then some comparisons of our results with experiment are made for a selection of transitions. I also discuss a recent study of radiative losses from the solar corona, in which significant amounts of atomic data were generated and used. End with some conclusions and future outlooks.

The LANL Suite of Atomic Modeling Codes 20+ years of development, created by Joe Abdallah & Bob Clark, updated for fully relativistic calculations by Chris Fontes & Honglin Zhang Atomic Physics CodesAtomic Models fine-structureLTE or NLTE config-averagelow or high-Z populations energy levels spectral modeling gf-values emission e - excitation absorption e - ionizationtransmission photoionizationpower loss autoionization CATS: Cowan Code RATS: relativistic ACE: e - excitation GIPPER: ionization ATOMIC

Method Atomic collisional data may be computed in a variety of approximations in the LANL codes: Excitation cross sections: –Plane-wave Born (PWB) approach. –Distorted-wave/First-order many-body perturbation theory (DW/FOMBT). Ionization cross sections: –Scaled hydrogenic method. –Distorted-wave (DW) approach. We use FOMBT for excitation and the DW approach for ionization in the data discussed here. Once the atomic data for all relevant ion stages have been calculated, the Los Alamos plasma kinetics modeling code, ATOMIC, can be used to compute the radiative losses.

Los Alamos Atomic Physics Codes: Strengths/Weaknesses Consistent treatment of all states and ion stages; accurate and fast calculations for highly ionized species. Storage of atomic data in a compact binary format (IPCRESS files) which allows very large amounts of data to be stored in a manageable form. Codes are now in a mature state, are portable, and well tested on a variety of platforms. Accuracy of PWB and/or DW approach may be poorer in collisional calculations including neutral or near- neutral systems (less of a problem for hot plasmas where ions are likely to be more stripped). No current ability to insert (more accurate) other calculations instead of PWB/DW if required. This is due to problems of consistently treating the resonance contribution of autoionizing states when combining different types of calculations.

Data generated for the CRP Electron-impact excitation cross sections for all ion stages of Si, Cl, and Ar.  n=0 and  n=1 (and selected  n=2) excitation cross sections calculated from the fine-structure levels of the ground complex. FOMBT method used to generate all excitation cross sections. Photoionization cross sections from all fine-structure levels. Autoionization rates from all fine- structure levels. Electron-impact ionization cross sections for all ion stages of Si, Cl, and Ar. Scaled-hydrogenic cross sections from all fine-structure levels. Distorted-wave ionization cross sections from all levels associated with the ground configuration. Selected close-coupling (TDCC) ionization cross sections from the ground and first excited configurations of a few Si ions. DW inner-shell ionization cross sections for selected neutral heavy atoms.

Excitation: Comparison with RDW results Comparison with the published RDW data for Be- through Na-like Si, Cl, and Ar is generally good. One example is shown in the figure for B-like Si, Cl, and Ar ; the RDW results are from Zhang & Sampson, ADNDT, 56, 41 (1994). The discrepancy for higher energies is not due to the relativistic effects, but to configuration-interaction. The red curves represent another calculation from CATS/ACE with only three n=2 configurations, as in the RDW calculation, which almost overlap with the RDW curves. The present collision strength data thus appear to be quite accurate. Colgan et al, Phys. Rev. A 77, (2008).

Electron-impact ionization calculations Electron-impact ionization of Si 2+ (3s 2 ). DW calculations compared with measurements of Djuric et al [PRA 47, 4786 (1993)]. Non-perturbative time-dependent close- coupling (TDCC) method used to check the accuracy of the DW calculations. TDCC calculations somewhat lower than DW, and in better agreement with experiment. At around 125 eV, excitation- autoionization makes a significant contribution. We choose to only present direct ionization cross sections, since the data we submit will include DW ionization from all configurations, including autoionizing configurations. Since we have calculated excitation and autoionization data, the excitation- autoionization contribution can be included. Si 2+ Colgan et al, Phys. Rev. A 77, (2008).

Electron-impact ionization calculations Electron-impact ionization of Si 3+ (3s). DW calculations compared with measurements of Crandall et al [PRA 25, 143 (1982)]. TDCC calculations are only slightly lower than DW; both are in good agreement with experiment for the direct ionization component. For the more highly charged Si ions, this good agreement allows us to use only the DW method to compute ionization cross sections. At above 100 eV, excitation- autoionization again dominates the cross section. Si 3+ Colgan et al, Phys. Rev. A 77, (2008).

Electron-impact ionization calculations Electron-impact ionization of Si 7+ (2s 2 2p 3 ). DW calculations compared with measurements of Zeijlmans et al [PRA 47, 2888 (1993)]. Good agreement with experiment is found. For the more highly charged ions, the DW results appear to be in good agreement with available experiment, and should be of sufficient accuracy for modeling purposes. Si 7+ Colgan et al, Phys. Rev. A 77, (2008).

Electron-impact ionization calculations Electron-impact ionization of Si-like Cl 3+ and Ar 4+ (3s 2 3p 2 ). For Ar 4+ DW calculations compared with measurements of Müller et al [JPB 13, 1877 (1980)]. Again, good agreement with experiment is found. For the more highly charged ions, the DW results appear to be in good agreement with available experiment, and should be of sufficient accuracy for modeling purposes. Colgan et al, Phys. Rev. A 77, (2008). Ar 4+ Cl 3+

Electron-impact ionization – K-shell We also have been able to use a fully relativistic DW approach (RDW) to calculate K-shell ionization of heavy neutral targets, to compare with the experimental measurements of Professor Luo’s group. Even though the ionization measurements are from a solid target, DW (isolated atom) calculations appear to work well. Agreement with experiment is excellent. Further semi-relativistic DW (SRDW) calculations show that a fully relativistic approach is necessary for these tightly bound electrons to obtain good agreement with experiment. Mn: K-shell Colgan et al, Phys. Rev. A 73, (2006).

Electron-impact ionization – K-shell Similar conclusions can be drawn from the other targets in our study, for example Fe. K-shell ionization cross sections were calculated for Mn, Fe, Ni, and Cu. We can investigate the K-shell ionization of other heavy targets of interest to this working group, if necessary. Fe: K-shell Colgan et al, Phys. Rev. A 73, (2006).

Electron-impact ionization – L-shell The Luo group has also been able to study ionization from the L-shell of W. We again use our RDW method to compute ionization from the 2s 1/2 and 2p 1/2 & 2p 3/2 sub-shells. The inset shows the individual shell contributions. The agreement with experiment is still quite good, although not as spectacular as for the K-shell studies. Differences here may be due to interactions of the ejected electron with bound electrons, which are only approximately taken into account in the RDW calculations. W: L-shell Colgan et al, Phys. Rev. A 73, (2006).

Solar coronal plasmas The radiative cooling, or radiative loss, of the solar corona is an important quantity in solar physics. –Crucial in evaluating the plasma’s energy balance –Provides an understanding of the corresponding energy source of the Sun But… –Observational data are scarce –Calculations are difficult, since the contributions from all elements present in the solar corona must be taken into account. –One must consider atomic processes in all ion stages of all the (15) elements which contribute –Implies a model spanning almost 200 ion stages!

Method A recent addition to ATOMIC also allows us to consider all elements under the influence of a single electron density. This density may be determined using an iterative procedure, under the constraints of a user-input electron temperature and user-input set of elemental abundances. We also must satisfy global charge conservation. Radiative losses (bound-bound) are computed using: We also include bound-free (from radiative recombination) and free-free (from bremsstrahlung) contributions to the radiative losses. Electron temperature & density Spontaneous emission rate Transition energy Ion level population Total ion number density Sherrill et al, Phys. Rev. E 76, (2007).

Atomic structure and data were computed for all ion stages of the 15 most abundant solar coronal elements: Collisional data was computed using PWB and FOMBT/DW approaches, to test the sensitivity of the radiative losses to the quality of the excitation data. The Calculation

Results – comparisons to previous work We compare the ATOMIC calculations to previous work of Landi & Landini (1999) and from the CHIANTI database. Substantial differences are found with Landi & Landini (1999) over most of the temperature range. Significant differences with the latest CHIANTI calculations persist at low temperatures below 10 6 K (~ 100 eV). Landi & Landini, A & A, 347, 401 (1999).

Radiative losses from the individual elements We present the contribution of the radiative losses from the individual 15 elements included in our calculation. At low temperatures H, He, C, and O are the dominant contributors. At high temperatures, Si and Fe contribute most to the radiative loss, although at the highest temperatures, continuum radiation from H also contributes strongly. Colgan et al, Astrophysical Journal 689, 585 (2008).

Results – comparisons to previous work Currently generating a fine- structure model for all 15 coronal elements with which to compute the radiative losses. Differences between LANL calculations and CHIANTI results may be partly due to FS vs CA differences, and partly due to the LANL inclusion of many more excited and autoionizing states.

Assessing the sensitivity to the atomic data If we replace the DW excitation cross sections with PWB, we find that the DW data makes a significant difference only at low temperatures, less than ~ 2 X 10 5 K. Nonperturbative cross sections for neutral H are known to be ~ factor of two lower than DW cross sections. We can also then scale the H cross sections by a factor of two to gauge the sensitivity. This only makes a difference at the very lowest temperatures of 2 X 10 4 K (~ 1-2 eV).

Ion fractions of C, O, Si, and Fe It is also instructive to know which ion stages contribute most to the radiative losses. For C, at the temperatures at which it is the strongest contributor, we find that most of the emission arises from C IV and C V ions. For O, O V, O VI, and O VII contribute most at the temperatures for which O dominates. We also see that many ion stages of Si and Fe are present for a wide temperature range and so must be included.

Sensitivity to elemental abundances The previous radiative losses were computed using “quiet region” elemental abundances. Some regions of the corona have different abundances of elements with low (< 10 eV) first-ionization-potentials (FIPs). These include the elements Na, Mg, Al. Si, Ca, Fe, and Ni. Thus we present the radiative losses for a variety of FIP bias values (relative to the photospheric abundances). Colgan et al, Astrophysical Journal 689, 585 (2008).

In the last 5 years we have generated significant amounts of atomic data for use in the plasma modeling communities. We are in the process of converting these data to the ALADDIN format for inclusion in the IAEA database. We note that the LANL atomic physics codes can be run through our webpage, where limited datasets may also be created. We hope to add to the data generated to the fusion modeling community, particularly for tungsten (W). Preliminary radiative power loss calculations for W have been generated and appear to compare well with other calculations. Conclusions/Future Work

Our published data are already starting to be used by the atomic physics and plasma modeling communities: –We have had requests from M. Reinke (MIT) for Ar ionization data so that ionization balance for Ar may be generated for use in plasma transport codes. –We have had requests from M. Ali (NIST) for comparison of our ionization data for selected near-neutral ions as tests of new BEB calculations. We are willing to generate data to meet future data needs – if the time & funding are there! Conclusions/Future Work