# Constructing Integrable High-pressure Full-current Free-boundary Stellarator Magnetohydrodynamic Equilibrium Solutions

## Abstract

For the (non-axisymmetric) stellarator class of plasma confinement devices to be feasible candidates for fusion power stations it is essential that, to a good approximation, the magnetic field lines lie on nested flux surfaces; however, the inherent lack of a continuous symmetry implies that magnetic islands responsible for breaking the smooth topology of the flux surfaces are guaranteed to exist. Thus, the suppression of magnetic islands is a critical issue for stellarator design, particularly for small aspect ratio devices. Pfirsch-Schluter currents, diamagnetic currents, and resonant coil fields contribute to the formation of magnetic islands, and the challenge is to design the plasma and coils such that these effects cancel. Magnetic islands in free-boundary high-pressure full-current stellarator magnetohydrodynamic equilibria are suppressed using a procedure based on the Princeton Iterative Equilibrium Solver [Reiman and Greenside, Comp. Phys. Comm. 43 (1986) 157] which iterate s the equilibrium equations to obtain the plasma equilibrium. At each iteration, changes to a Fourier representation of the coil geometry are made to cancel resonant fields produced by the plasma. The changes are constrained to preserve certain measures of engineering acceptability and to preserve the stability of ideal kink modes. As the iterations continue, the coil geometry andmore »

- Authors:

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab., Princeton, NJ (US)

- Sponsoring Org.:
- USDOE Office of Science (SC) (US)

- OSTI Identifier:
- 815091

- Report Number(s):
- PPPL-3867

TRN: US0304445

- DOE Contract Number:
- AC02-76CH03073

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 15 Sep 2003

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ASPECT RATIO; DESIGN; GEOMETRY; MAGNETIC FIELDS; MAGNETIC ISLANDS; MAGNETIC SURFACES; MAGNETOHYDRODYNAMICS; PLASMA; PLASMA CONFINEMENT; STABILITY; STELLARATORS; SYMMETRY; TOPOLOGY; EQUILIBRIUM, MHD - TOROIDAL; MAGNETIC ISLANDS, STABILITY, IDEAL HYDROMAGNETIC

### Citation Formats

```
Hudson, S R, Monticello, D A, Reiman, A H, Strickler, D J, Hirshman, S P, Ku, L-P, Lazarus, E, Brooks, A, Zarnstorff, M C, Boozer, A H, Fu, G-Y, and Neilson, and G.H.
```*Constructing Integrable High-pressure Full-current Free-boundary Stellarator Magnetohydrodynamic Equilibrium Solutions*. United States: N. p., 2003.
Web. doi:10.2172/815091.

```
Hudson, S R, Monticello, D A, Reiman, A H, Strickler, D J, Hirshman, S P, Ku, L-P, Lazarus, E, Brooks, A, Zarnstorff, M C, Boozer, A H, Fu, G-Y, & Neilson, and G.H.
```*Constructing Integrable High-pressure Full-current Free-boundary Stellarator Magnetohydrodynamic Equilibrium Solutions*. United States. doi:10.2172/815091.

```
Hudson, S R, Monticello, D A, Reiman, A H, Strickler, D J, Hirshman, S P, Ku, L-P, Lazarus, E, Brooks, A, Zarnstorff, M C, Boozer, A H, Fu, G-Y, and Neilson, and G.H. Mon .
"Constructing Integrable High-pressure Full-current Free-boundary Stellarator Magnetohydrodynamic Equilibrium Solutions". United States. doi:10.2172/815091. https://www.osti.gov/servlets/purl/815091.
```

```
@article{osti_815091,
```

title = {Constructing Integrable High-pressure Full-current Free-boundary Stellarator Magnetohydrodynamic Equilibrium Solutions},

author = {Hudson, S R and Monticello, D A and Reiman, A H and Strickler, D J and Hirshman, S P and Ku, L-P and Lazarus, E and Brooks, A and Zarnstorff, M C and Boozer, A H and Fu, G-Y and Neilson, and G.H.},

abstractNote = {For the (non-axisymmetric) stellarator class of plasma confinement devices to be feasible candidates for fusion power stations it is essential that, to a good approximation, the magnetic field lines lie on nested flux surfaces; however, the inherent lack of a continuous symmetry implies that magnetic islands responsible for breaking the smooth topology of the flux surfaces are guaranteed to exist. Thus, the suppression of magnetic islands is a critical issue for stellarator design, particularly for small aspect ratio devices. Pfirsch-Schluter currents, diamagnetic currents, and resonant coil fields contribute to the formation of magnetic islands, and the challenge is to design the plasma and coils such that these effects cancel. Magnetic islands in free-boundary high-pressure full-current stellarator magnetohydrodynamic equilibria are suppressed using a procedure based on the Princeton Iterative Equilibrium Solver [Reiman and Greenside, Comp. Phys. Comm. 43 (1986) 157] which iterate s the equilibrium equations to obtain the plasma equilibrium. At each iteration, changes to a Fourier representation of the coil geometry are made to cancel resonant fields produced by the plasma. The changes are constrained to preserve certain measures of engineering acceptability and to preserve the stability of ideal kink modes. As the iterations continue, the coil geometry and the plasma simultaneously converge to an equilibrium in which the island content is negligible, the plasma is stable to ideal kink modes, and the coils satisfy engineering constraints. The method is applied to a candidate plasma and coil design for the National Compact Stellarator Experiment [Reiman, et al., Phys. Plasmas 8 (May 2001) 2083].},

doi = {10.2172/815091},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2003},

month = {9}

}