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Computational Atomic Physics for Controlled Fusion

US Principal Investigators:
M S Pindzola, F J Robicheaux, E Oks, J P Colgan, and S D Loch,
Auburn University
D R Schultz and T Minami, ORNL
D C Griffin and C P Ballance, Rollins College

UK Collaborators:
N R Badnell and H P Summers, University of Strathclyde
B M McLaughlin and P G Burke, Queen's University of Belfast
K Berrington, Sheffield Hallam University

Other Collaborators:
C J Fontes, Los Alamos National Laboratory
T W Gorczyca, Western Michigan University
D M Mitnik, University of Buenos Aires

Summary

A DoE Scientific Discovery through Advanced Computing (SciDAC) program has brought together a US-UK collaboration to implement state-of-the-art atomic collision codes on the next generation of terascale computing facilities. Studies are proceeding on a wide range of atomic collision processes present in controlled fusion plasmas. Computational research advances have already been applied to other general science areas, including laser interactions with atoms and molecules, x-ray spectra from astrophysical objects, and the dynamics of cold atom gases.

Controlled Fusion Applications
We have completed a series of large-scale computer calculations to provide a complete atomic data base for Li beam diagnostics on tokamaks, with specific application to Li impurity transport at DIII-D. The time-dependent close-coupling and the R-matrix with pseudo-states methods were used to calculate electron-impact excitation and ionization cross sections for Li, Li⁺, and Li²⁺. A letter in the Physical Review highlighted differences in theory and experiment for the electron ionization of Li and suggested that the results from the new large-scale atomic collision calculations were more accurate than the older atomic experiments. Time-dependent semi-classical calculations for the proton excitation of and charge-transfer with neutral Li have also been recently completed. The R-matrix with pseudo-states method was employed to make a very large calculation for the electron-impact excitation of C²⁺. This will provide much improved atomic data on this ion, in support of edge impurity inflow measurements at JET. The campaign for this year includes:

• Large-scale time-dependent and R-matrix calculations to revise the atomic data base for He and He⁺, in support of He beam diagnostics
  
• Collisional-radiative modeling of Li plasmas using the ADAS and the LANL/CATS suites of codes to ascertain the sensitivity of emissivities and generalized rate coefficients to the underlying atomic data base,
  
• Large-scale R-matrix calculations for neutral Ne, in support of gas puff diagnostics of edge transport barriers in tokamaks,
  
• Large-scale time-dependent and R-matrix calculations to construct complete atomic data bases for the Be and B isonuclear sequences, in support of divertor design studies at UCSD and impurity suppression studies on TEXTOR,
  
• Time-dependent semi-classical calculations for He²⁺ and Be⁴⁺ collisions with H, in support of diagnostics on beam penetrated plasma,
  
• Time-independent distorted-wave calculations to construct atomic data bases for the Xe, W, and Au isonuclear sequences, in support of wall erosion studies at JET and hohlraum design studies at NIF.

General Science Applications
The time-dependent close-coupling method was used to calculate double photoionization of He and Be to compare with ongoing synchrotron experiments worldwide.

A letter in the Physical Review highlighted unusual resonance enhancements in the double ionization cross section following two-photon absorption. We reported the results of simulations that explained many properties of ultracold neutral plasmas in a letter in the Physical Review. The ultra-cold plasmas start with ion temperatures less than 1 mK and electron temperatures between 1-100 K. We performed classical and the first quantal simulations of the ionization of hydrogen in a strong microwave field. The problem is similar to atomic state dissolution in plasma micro-fields. The campaign for this year includes time-dependent and time-independent calculations for:

• Double and triple photoionization of Li,
  
• Multiphoton ionization of H²⁺,
  
• Proton charge transfer with H and Li in static and varying electric fields,
  
• Flow of Bose-Einstein condensates in optical traps.

Advances in Computational Methods
The time-dependent close-coupling, R-matrix pseudo-states, and time-dependent semi-classical codes are now fully operational on the IBM-SP machines at NERSC and ORNL, a non-trivial task indeed. Specific help on memory access and buffers was given by Dr. Jodi Lamoureux at LBNL and the entire US group attended a special two-day workshop on the IBM-SP4 machine at ORNL in July 2002. The campaign for this year includes:

• Comparing the parallel R-matrix I and the parallel R-matrix II suites of codes for an identical collision problem on the IBM-SP machines at NERSC/ORNL and Daresbury/QUB,
  
• Extending the three-body time-dependent close-coupling codes from six to nine dimensions to handle important four-body problems,
  
• Comparing a rotating coordinate system with our standard Cartesian coordinate system for solving the time-dependent semi-classical equations, with the eventual goal of treating two-moving centers three-body problems,
  
• Continuing work with the NERSC staff, in particular Dr. David Turner, to improve the performance of all of our massively parallel codes.

Appendix A for PAC Recommendations

The time-dependent close-coupling method was used to study electronic capture in He. As reported in a letter in the Physical Review this study is the first step in an attempt to include resonances in a wavepacket approach. The time-independent distorted-wave method was used to calculate dielectronic recombination cross sections for O⁵⁺ in the presence of crossed electric and magnetic fields, in support of experimental measurements at the Stockholm heavy ion storage ring. Distorted-wave methods were used to study electronic capture with radiative decay in Cl¹³⁺, in support of heavy ion storage ring experiments at Heidelberg which, for the first time, observed both dielectronic and trielectronic recombination resonances. A letter to the Physical Review will be submitted shortly. Work continues on a dielectronic recombination project to calculate LSJ level resolved rate coefficients for all ionization stages of the elements of interest in astrophysical and controlled fusion research. Dielectronic recombination data for the Li-like, Be-like, and B-like ions was generated in the last year.

Recombination spectrum for Be-like Cl ions. The black points show the experimental results from the TSR storage ring in Heidelberg, Germany. The green curve shows the theoretical results for recombination into 2s2pnl resonance states, and the red curve recombination into 2p²nl resonance states.

Appendix B for SciDAC Questions

What has your SciDAC project accomplished that has enabled scientists to better realize the potential of terascale computing?
Through example to other scientists, we have shown that the boundaries of accuracy for atomic collision cross sections can be extended using terascale computing platforms.

What science can be done now that was not previously possible?
The three-body long-range Coulomb problem can now be addressed routinely using time-dependent close-coupling and time-independent R-matrix with pseudostates methods. Thus, for example, the electron ionization of simple atomic ions can be calculated to arbitrary precision.

How is the SciDAC team approach to science changing the way you conduct your research?
The team approach for us means an integration of basic atomic collision research through to a plasma diagnostic on a specific fusion experiment. Thus, for example, the atomic species needs of an erosion test for ITER design motivate the application of terascale computing resources.

How have you advanced the state-of-the-art or the state-of-the-science?
The difficulty in atomic collision physics has always been the sheer number of quantum paths available for any structural or dynamical process. We have advanced basic time-dependent and time-independent scattering theory through the use of terascale computing platforms.

What algorithms or software are you using from other SciDAC projects that are helping to advance your research?
When it is appropriate to use "black box" routines, we have found that the ScaLAPACK linear algebra routines to be very useful. On the other hand, our implementation of wavepacket transforms, non-linear lattice meshes, and multi-dimensional domain partitioning has occurred by interaction with fellow scientists through APS meetings and the science research literature.

What are your plans for the next year or two in accomplishing your project's goals in the SciDAC context?
As put forward in our annual report, we plan to further solidify interactions with ongoing magnetic fusion experiments, especially as to their design efforts for ITER.

What resource needs do you anticipate, both for high-end computing and for associated infrastructure, to accomplish your goals?
It would be interesting to explore the application of massively parallel vector computing machines to atomic collision physics.

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