COBRA: An Optimized Code for Fast Analysis of Ideal Ballooning Stability of Three-Dimensional Magnetic Equilibria

R. Sanchez; S. P. Hirshman; J. C. Whitson; A. S. Ware

doi:10.1006/jcph.2000.6514

COBRA: An Optimized Code for Fast Analysis of Ideal Ballooning Stability of Three-Dimensional Magnetic Equilibria

R. Sanchez, S. P. Hirshman, J. C. Whitson, A. S. Ware

Physics and Astronomy

Research output: Contribution to journal › Article › peer-review

58 Scopus citations

Abstract

A new, fast, and accurate numerical algorithm to assess stability against ideal ballooning modes in general three-dimensional magnetic configurations of interest to controlled thermonuclear fusion is described. The code for ballooning rapid analysis (COBRA) performs this assessment by solving an eigenvalue problem in the form of a linear second-order ordinary differential equation along magnetic field lines in the configuration. An initial approximation for the eigenvalue is obtained from a fast second order matrix method. In COBRA, this approximate eigenvalue is further refined using a variational principle to obtain fourth-order convergence with the mesh size. Richardson's extrapolation is then applied to a sequence of eigenvalues to estimate the exact eigenvalue using the coarsest possible mesh, thus minimizing the computational time.

Original language	English
Pages (from-to)	576-588
Number of pages	13
Journal	Journal of Computational Physics
Volume	161
Issue number	2
DOIs	https://doi.org/10.1006/jcph.2000.6514
State	Published - Jul 1 2000

Funding

We are very grateful to B. A. Carreras, D. A. Spong, D. B. Batchelor, and J. F. Lyon for helpful comments and enlightening discussions, and to J. Lopez for constant encouragement. We are especially grateful to W. A. Cooper for providing us with the TERPSICHORE code, and to L. P. Ku and M. Redi for advise on its use. This research was sponsored by the U.S. Department of Energy, under Contract DE-AC05-96OR22464 with Lockheed Martin Energy Research Corp., and under Contract DE-FG0397ER54423 at the University of Montana. Research was supported in part (R.S.) by an appointment to the ORNL Postdoctoral Research Associates Program, administered jointly by Oak Ridge National Laboratory and the Oak Ridge Institute for Science and Education.

Funders	Funder number
DE-AC05-96OR22464, DE-FG0397ER54423
Oak Ridge National Laboratory

Keywords

Ballooning instabilities
Growth rate
Magnetohydrodynamics
Richardson's extrapolation
Spectrum of Stürm-Liouville operators
Stellarators

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10.1006/jcph.2000.6514

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title = "COBRA: An Optimized Code for Fast Analysis of Ideal Ballooning Stability of Three-Dimensional Magnetic Equilibria",

abstract = "A new, fast, and accurate numerical algorithm to assess stability against ideal ballooning modes in general three-dimensional magnetic configurations of interest to controlled thermonuclear fusion is described. The code for ballooning rapid analysis (COBRA) performs this assessment by solving an eigenvalue problem in the form of a linear second-order ordinary differential equation along magnetic field lines in the configuration. An initial approximation for the eigenvalue is obtained from a fast second order matrix method. In COBRA, this approximate eigenvalue is further refined using a variational principle to obtain fourth-order convergence with the mesh size. Richardson's extrapolation is then applied to a sequence of eigenvalues to estimate the exact eigenvalue using the coarsest possible mesh, thus minimizing the computational time.",

keywords = "Ballooning instabilities, Growth rate, Magnetohydrodynamics, Richardson's extrapolation, Spectrum of St{\"u}rm-Liouville operators, Stellarators",

author = "R. Sanchez and Hirshman, \{S. P.\} and Whitson, \{J. C.\} and Ware, \{A. S.\}",

note = "Funding Information: We are very grateful to B. A. Carreras, D. A. Spong, D. B. Batchelor, and J. F. Lyon for helpful comments and enlightening discussions, and to J. Lopez for constant encouragement. We are especially grateful to W. A. Cooper for providing us with the TERPSICHORE code, and to L. P. Ku and M. Redi for advise on its use. This research was sponsored by the U.S. Department of Energy, under Contract DE-AC05-96OR22464 with Lockheed Martin Energy Research Corp., and under Contract DE-FG0397ER54423 at the University of Montana. Research was supported in part (R.S.) by an appointment to the ORNL Postdoctoral Research Associates Program, administered jointly by Oak Ridge National Laboratory and the Oak Ridge Institute for Science and Education.",

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AU - Ware, A. S.

N1 - Funding Information: We are very grateful to B. A. Carreras, D. A. Spong, D. B. Batchelor, and J. F. Lyon for helpful comments and enlightening discussions, and to J. Lopez for constant encouragement. We are especially grateful to W. A. Cooper for providing us with the TERPSICHORE code, and to L. P. Ku and M. Redi for advise on its use. This research was sponsored by the U.S. Department of Energy, under Contract DE-AC05-96OR22464 with Lockheed Martin Energy Research Corp., and under Contract DE-FG0397ER54423 at the University of Montana. Research was supported in part (R.S.) by an appointment to the ORNL Postdoctoral Research Associates Program, administered jointly by Oak Ridge National Laboratory and the Oak Ridge Institute for Science and Education.

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AB - A new, fast, and accurate numerical algorithm to assess stability against ideal ballooning modes in general three-dimensional magnetic configurations of interest to controlled thermonuclear fusion is described. The code for ballooning rapid analysis (COBRA) performs this assessment by solving an eigenvalue problem in the form of a linear second-order ordinary differential equation along magnetic field lines in the configuration. An initial approximation for the eigenvalue is obtained from a fast second order matrix method. In COBRA, this approximate eigenvalue is further refined using a variational principle to obtain fourth-order convergence with the mesh size. Richardson's extrapolation is then applied to a sequence of eigenvalues to estimate the exact eigenvalue using the coarsest possible mesh, thus minimizing the computational time.

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KW - Magnetohydrodynamics

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KW - Spectrum of Stürm-Liouville operators

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COBRA: An Optimized Code for Fast Analysis of Ideal Ballooning Stability of Three-Dimensional Magnetic Equilibria

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