# Presentation: 223363

## Theory and Modeling

- Allan Reiman

- NCSX Research Forum
- Dec. 7, 2006

## Equilibrium
Stability
Transport
Edge Modeling

- Stability
- Transport
- Edge Modeling

- 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.

- Theory projects being pursued, and some plans for the future.

## 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 ****. *

## 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.

## 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).*

## 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.*

## 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).*

## 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).*

## 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)*

## 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.