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Theory and Modeling

Theory and Modeling. Allan Reiman. NCSX Research Forum Dec. 7, 2006. Theory projects being pursued, and some plans for the future. Introduction. Most theoretical work supported by broader contracts rather than by projects (unlike experimental work). Not well represented here.

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Theory and Modeling

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  1. Theory and Modeling Allan Reiman NCSX Research Forum Dec. 7, 2006

  2. Theory projects being pursued, and some plans for the future. Introduction • Most theoretical work supported by broader contracts rather than by projects (unlike experimental work). Not well represented here. • Long term plans to be discussed in more detail at follow-up national stellarator theory teleconference on Dec. 14. • Equilibrium • Stability • Transport • Edge Modeling AHR 12/7/06

  3. Calculation of equilibrium is a necessary first step before doing further analysis. • STELLOPT optimizer for stellarator design (Hirshman et al, ORNL) adapted for equilibrium reconstruction (Zarnstorff, PPPL) • V3FIT collaboration on equilibrium reconstruction uses VMEC equilibrium code. Jim Hanson (Auburn), Hirshman & Lazarus (ORNL), Lao (GA) • HINT2 code (Suzuki & Hayashi, NIFS, Japan) and PIES code (PPPL) can handle equilibria with magnetic islands and/or stochastic regions. Fraction of good flux surfaces versuscalculated by PIES for two values of control coil current for W7AS. The circles indicate PIES calculations done for experimentally achieved . AHR 12/7/06

  4. Improvement of 3D equilibrium codes is continuing. • PIES (Monticello, Reiman, Raburn - PPPL). • Comparing predictions with W7AS data, improving physics model in response to observations (e.g. pressure in stochastic region). • Speed up via algorithm improvement, parallelization, development of PIES-Lite for rapid evaluation. • Plan to incorporate neoclassical effects, flow-shielding. • Development of new codes • Hirshman et al (ORNL): VMEC with islands. • Hegna et al (Univ. Wisconsin), initiating new project, to address stochastic regions. • Over long run will also want to incorporate flow and kinetic effects. AHR 12/7/06

  5. Instability: Under what circumstances does it limit  or restrict desirable operating space? • Linear, global MHD stability codes: Terpsichore (Cooper, Lausanne), CAS3D (C. Nűhrenberg, Germany). • Terpsichore optimized to be very fast. • CAS3D generalized to handle conducting walls with arbitrary holes (Merkel). Kinetic effects being introduced. • Ideal ballooning • New suites of codes developed by Sanchez and Hirshman (Spain and ORNL), Ware (Univ. Montana), Hegna, Hudson et al (Univ. Wisconsin, PPPL). Marginal stability diagram for NCSX VMEC surface s = 0.6, β = 4.2%(——), β = 9.5%(· · · · · ·) and β = 14.0%(- - - -) (Hudson, Hegna, Nakajima). AHR 12/7/06

  6. Instability: Effects of nonlinearity, additional physics being studied. • Ballooning • Ray tracing to make connection to global modes. (Ware, Hudson, Hegna). • Work on kinetic effects also in initial stage. • Nonlinear 3D MHD • DNS code, H. Miura et al (NIFS, Japan). • Extended-MHD: M3D. Strauss (NYU), Sugiyama (MIT), Hudson (PPPL) • Energetic particle driven modes • Spong (ORNL): STELLGAP global eigenmode calculation. • High mode number kinetic, Gorelenkov (PPPL). In development. • Nonlinear: Fu, M3D (PPPL) Saturated pressure in LHD at =1.5%. Ichiguchi et al, NORM 3D reduced MHD code. AHR 12/7/06

  7. Transport: How is it affected by interaction between 3D neoclassical effects and turbulence? • Mynick, Boozer et al using simplified models to study physics of neoclassical-turbulence interaction. • Gyrokinetic flux tube codes have been extended to stellarators (US, IPP, NIFS). • Jenko (IPP, Germany) collaborating with Mynick & Boozer on physics studies • Collaborative computational gyrokinetic studies planned (IPP, NIFS, U. MD., U. Wisc., PPPL) Diffusion coefficient vs. amplitude of turbulence. Monte-Carlo calculations with model turbulent spectrum. (Mynick and Boozer). AHR 12/7/06

  8. Development of Transport Codes Continuing • Global gyrokinetic GTC code to be extended to stellarators, first for neoclassical calculations, later for turbulent transport (PPPL). • Global gyrokinetic TORB in development at Greifswald (SORGE et al) • DKES/PENTA codes (Spong et al, ORNL): calculate Er, bootstrap current, plasma flow • Longer term will also need computation of transport with magnetic islands. Ion flow velocity streamlines on a flux surface for NCSX (Spong et al). AHR 12/7/06

  9. Edge Modeling • Livermore field line tracing code. Kaiser et al. • Uses either MFBE/VMEC or PIES with Drevlak postprocessor for field. • Tool for generating DEGAS 2 geometries from VMEC equilibria under development. • EMC/EIRENE code to be imported from Germany. • E3D code under development at Greifswald (Schneider et al). Calculated heat deposition on a proposed NCSX divertor plate. (Kaiser et al) AHR 12/7/06

  10. Solid theoretical understanding will be necessary if we are to impact design of Demo reactor following ITER. • Three-dimensionality complicates calculation of equilibrium, stability, transport, and edge modeling. • New computational tools under development will address needs of NCSX project. • New physics issues arise in 3D: equilibrium islands; effect of 3D shaping on linear & nonlinear stability; interaction between turbulent & neoclassical transport effects; stochastic field lines at edge; etc. • Issues are being addressed, and NCSX experiments will help us develop an understanding of them. • Computational tools and physics understanding will also be applicable to 3D issues in tokamaks. AHR 12/7/06

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