# Presentation: 209373

## Computational Atomic and Molecular Physics for Transport Modeling of Fusion Plasmas

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

*Collaborators*
- N.R. Badnell, M.G. O’Mullane, H.P. Summers, K.A. Berrington, J.P. Colgan, C.J. Fontes, T.E. Evans, D.P. Stotler, P.G. Burke

*Principal Investigators*
- M.S. Pindzola, F.J. Robicheaux, D.C. Griffin,
- D.R. Schultz, J.T. Hogan

*Graduate students*
- M.C. Witthoeft, J. Hernandez, T. Topcu, A.D. Whiteford

## 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

## 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.

## 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

## 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

## 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 : N+1 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

## 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*

## 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 C**2+**.  Shows the first agreement between theory and experiment for a system with significant metastable fraction.*

## 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
- p+H, p+Li, α+H, Be4++H, p+H2+
- Hybrid TDSC/AOCC method
- 4D lattice close-coupling for p+He

## 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 Cl**13+** showing the first observation of trielectronic recombination*

## 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.

*Bi**7+** 5s**2**5p**6**5d**8 **    ionization cross section*

## General Science Spin-offs

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

## Collaborations with existing fusion laboratories - I

- DIII-D, California

- EFDA-JET, UK

- Li generalised collisional-radiative coefficients used in impurity transport studies

- He R-Matrix excitation data used in helium beam studies, and in non-Maxwellian modeling.

## Collaborations with existing fusion laboratories - II

- RFX- Italy

- ASDEX-upgrade, Germany

- Tungsten ionization data to be used in heavy species studies

- Krypton ionization ionization data is being used in plasma transport studies

## 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.