Computational Atomic and Molecular Physics for Transport Modeling of Fusion Plasmas

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Computational Atomic and Molecular Physics for
Transport Modeling of Fusion Plasmas
Principal Investigators M.S. Pindzola, F.J.
Robicheaux, D.C. Griffin, D.R. Schultz, J.T.
Hogan

• Post-doctoral fellows
• S.D. Loch, J. Ludlow,
• C.P. Balance, T. Minami

Graduate students M.C. Witthoeft, J. Hernandez,
T. Topcu, A.D. Whiteford
Collaborators N.R. Badnell, M.G. OMullane, H.P.
Summers, K.A. Berrington, J.P. Colgan, C.J.
Fontes, T.E. Evans, D.P. Stotler, P.G. Burke
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ITER Relevant Plasma Modeling Efforts

• Final choices for plasma-facing materials.
• Relevance of innovations in operational regimes.
• Chief experimental spectroscopic tools need
  reliable atomic data
• Be, C, and W components for the first wall.
• Study of Edge Localized Mode (ELM) transient in
  standard ITER operation

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ITER Relevant Plasma Modeling Efforts

• Two-dimensional, time dependent, multi-species
  transport code such as SOLPS (B2-Eirene) uses the
  ADAS database.
• Used for analysis at JET, ASDEX-Upgrade, DIII-D,
  JT-60, Tore-Supra, and Alcator C-Mod.

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Collisional-Radiative Modeling using ADAS

• Originally developed at JET
• Now used throughout the controlled fusion and
  astrophysics communities
• Solution to collisional-radiative equations for
  all atomic levels in all ionization stages of
  relevant elements. Thus requires
• Atomic structure for energies
• Radiative rates
• Collisional electron excitation rates
• Collisional electron ionization and recombination
  rates
• Collisional charge transfer recombination with
  hydrogen

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Collisional-Radiative Modeling using ADAS

• The problem is simplified through the assumption
  of quasi-static equilibrium for the excited
  states.
• The following data is produced, for ease of use
  in plasma transport codes
• Generalised collisional-radiative (GCR)
  coefficients
• Radiated power loss (RPL) coefficients
• Individual spectrum line emission coefficients
• We have completed the following sequences
• He, Li and Be

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AM collision calculations Time independent
R-Matrix

• Developed in the UK P.G. Burke and co-workers
• Each atom modeled as N-electron Hamiltonian
• Collision system modeled as N1 electron
  Hamiltonian
• Hamiltonian represented by bound and continuum
  basis states
• All eigenvalues and eigenvectors of 50,000 x
  50,000 matrix required. This can only be solved
  on parallel machines.
• Thousands of energies required to map out
  Feshbach resonances

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AM collision calculations Time independent
R-Matrix

• R-Matrix with pseudo states calculations
  completed for
• He, He
• Li, Li, Li2
• Be, Be, Be2, Be3
• B, B4
• C2, C3, C5
• O5
• Standard R-Matrix completed
• Ne, Ne4, Ne5
• Fe20, Fe21, Fe23, Fe24, and Fe25

Energy vs excitation cross section for neutral Be
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AM Collisions Time Dependent Close-Coupling

• Developed in the US by C. Bottcher and co-workers
• Treats the three body Coulomb breakup exactly
• Close-coupled set of 2D lattice equations
• TDCC calculations completed for
• H, He, He
• Li, Li, Li2
• Be, Be, Be2, Be3
• B2, C3, Mg, Al2, Si3
• Have now started to treat
• the four body Coulomb breakup
• the three-body two Coulomb center breakup

Ionization cross section for C2. Shows the
first agreement between theory and experiment for
a system with significant metastable fraction.
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AM Collisions Time-Dependent Semi-Classical

• Developed in the study of heavy-ion nuclear
  fusion
• Electron in the field of two moving Coulomb
  fields
• 3D lattice method solved by low-order finite
  differences or high-order Fourier-collocation
  representation.
• Applications
• pH, pLi, aH, Be4H, pH2
• Hybrid TDSC/AOCC method
• 4D lattice close-coupling for pHe

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AM Collisions Distorted wave and Classical
Trajectory

• Uses perturbation theory.
• Accurate for radiative and autoionization rates.
• Accurate for electron collisions with highly
  charged ions.
• Various levels of calculation
• Intermediate coupled distorted-wave (ICDW)
• LS coupled distorted wave (LSDW)
• Configuration-average distorted-wave (CADW)
• Classical Trajectory Monte Carlo (CTMC)

Resonance plot for Cl13 showing the first
observation of trielectronic recombination
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AM Collisions Distorted wave and Classical
Trajectory

• Dielectronic recombination project using ICDW for
  laboratory and astrophysical elements
• Li, Be, B, C and O iso-electronic sequences
  completed
• Support for ion storage ring experiments
• Cl13
• Heavy element ionization/recombination using CADW
• Ar, Kr, Xe, Mo, Hf, Ta, W, Au
• Charge transfer using CTMC
• High Z ions with H, D, and He.

Bi7 5s25p65d8 ionization cross section
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General Science Spin-offs

• TDCC for
• (?,2e) on He, Be, Li, quantum dots, H2
• (2?,2e) on He
• (?,3e) on Li
• e H
• TDSC for
• p- H
• BEC in fields
• CTMC for
• e atoms in ultracold plasmas
• ? atoms in high Rydberg states

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Collaborations with existing fusion laboratories
- I
DIII-D, California
Li generalised collisional-radiative coefficients
used in impurity transport studies
EFDA-JET, UK
He R-Matrix excitation data used in helium beam
studies, and in non-Maxwellian modeling.
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Collaborations with existing fusion laboratories
- II
ASDEX-upgrade, Germany
Tungsten ionization data to be used in heavy
species studies
RFX- Italy
Krypton ionization ionization data is being used
in plasma transport studies
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Conclusions

• Recent advances in non-perturbative methods
  allows high quality atomic data to be generated
  for electron-ion and ion-atom collisions for low
  Z systems, such as Li, Be and C.
• High quality atomic data is being processed into
  a form useful for plasma transport modeling of
  wall erosion and ELM experimental studies.
• High quality atomic data for high Z systems, such
  as W, remains a computational grand challenge.