# Ballooning Stability of the Compact Quasiaxially Symmetric Stellarator

## Abstract

The magnetohydrodynamic (MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), expected to achieve good stability and particle confinement is examined with a method that can lead to estimates of global stability. Making use of fully 3D, ideal-MHD stability codes, the QAS beta is predicted to be limited above 4% by ballooning and high-n kink modes. Here MHD stability is analyzed through the calculation and examination of the ballooning mode eigenvalue isosurfaces in the 3-space [s, alpha, theta(subscript ''k'')]; s is the edge normalized toroidal flux, alpha is the field line variable, and theta(subscript ''k'') is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, with new types of nonsymmetric, eigenvalue isosurfaces in both the stable and unstable spectrum. The isosurfaces around the most unstable points i n parameter space (well above marginal) are topologically spherical. In such cases, attempts to use ray tracing to construct global ballooning modes lead to a k-space runaway. Introduction of a reflecting cutoff in k(perpendicular) to model numerical truncation or finite Larmor radius (FLR) yields chaotic ray paths ergodically filling the allowed phase space, indicating thatmore »

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 788263

- Report Number(s):
- PPPL-3612

TRN: US0110859

- DOE Contract Number:
- AC02-76CH03073

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 19 Sep 2001

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BALLOONING INSTABILITY; AXIAL SYMMETRY; PLASMA CONFINEMENT; LARMOR RADIUS; MAGNETOHYDRODYNAMICS; PHASE SPACE; STELLARATORS; COMPUTERIZED SIMULATION

### Citation Formats

```
M.H. Redi, J. Canik, R.L. Dewar, J.L. Johnson, S. Klasky, W.A. Cooper, and W. Kerbichler.
```*Ballooning Stability of the Compact Quasiaxially Symmetric Stellarator*. United States: N. p., 2001.
Web. doi:10.2172/788263.

```
M.H. Redi, J. Canik, R.L. Dewar, J.L. Johnson, S. Klasky, W.A. Cooper, & W. Kerbichler.
```*Ballooning Stability of the Compact Quasiaxially Symmetric Stellarator*. United States. doi:10.2172/788263.

```
M.H. Redi, J. Canik, R.L. Dewar, J.L. Johnson, S. Klasky, W.A. Cooper, and W. Kerbichler. Wed .
"Ballooning Stability of the Compact Quasiaxially Symmetric Stellarator". United States. doi:10.2172/788263. https://www.osti.gov/servlets/purl/788263.
```

```
@article{osti_788263,
```

title = {Ballooning Stability of the Compact Quasiaxially Symmetric Stellarator},

author = {M.H. Redi and J. Canik and R.L. Dewar and J.L. Johnson and S. Klasky and W.A. Cooper and W. Kerbichler},

abstractNote = {The magnetohydrodynamic (MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), expected to achieve good stability and particle confinement is examined with a method that can lead to estimates of global stability. Making use of fully 3D, ideal-MHD stability codes, the QAS beta is predicted to be limited above 4% by ballooning and high-n kink modes. Here MHD stability is analyzed through the calculation and examination of the ballooning mode eigenvalue isosurfaces in the 3-space [s, alpha, theta(subscript ''k'')]; s is the edge normalized toroidal flux, alpha is the field line variable, and theta(subscript ''k'') is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, with new types of nonsymmetric, eigenvalue isosurfaces in both the stable and unstable spectrum. The isosurfaces around the most unstable points i n parameter space (well above marginal) are topologically spherical. In such cases, attempts to use ray tracing to construct global ballooning modes lead to a k-space runaway. Introduction of a reflecting cutoff in k(perpendicular) to model numerical truncation or finite Larmor radius (FLR) yields chaotic ray paths ergodically filling the allowed phase space, indicating that the global spectrum must be described using the language of quantum chaos theory. However, the isosurface for marginal stability in the cases studied are found to have a more complex topology, making estimation of FLR stabilization more difficult.},

doi = {10.2172/788263},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2001},

month = {9}

}