The Brunt–Väisälä frequency of rotating tokamak plasmas

The continuous spectrum of analytical toroidally rotating magnetically confined plasma equilibria is investigated analytically and numerically. In the presence of purely toroidal flow, the ideal magnetohydrodynamic equations leave the freedom to specify which thermodynamic quantity is constant on th...

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Bibliographic Details
Published in:Journal of computational physics 2012-02, Vol.231 (3), p.981-1001
Main Authors: Haverkort, J.W., de Blank, H.J., Koren, B.
Format: Article
Language:English
Subjects:
Analytical solutions
Buoyancy
Continuous spectrum
Convective effect
Density
Entropy
Grad–Shafranov equation
Ideal magnetohydrodynamics
Mathematical analysis
Plasma flow
Plasmas
Rotating
Spectra
Tokamak devices
Toroidal rotation
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Summary:The continuous spectrum of analytical toroidally rotating magnetically confined plasma equilibria is investigated analytically and numerically. In the presence of purely toroidal flow, the ideal magnetohydrodynamic equations leave the freedom to specify which thermodynamic quantity is constant on the magnetic surfaces. Introducing a general parametrization of this quantity, analytical equilibrium solutions are derived that still posses this freedom. These equilibria and their spectral properties are shown to be ideally suited for testing numerical equilibrium and stability codes including toroidal rotation. Analytical expressions are derived for the low-frequency continuous Alfvén spectrum. These expressions still allow one to choose which quantity is constant on the magnetic surfaces of the equilibrium, thereby generalizing previous results. The centrifugal convective effect is shown to modify the lowest Alfvén continuum branch to a buoyancy frequency, or Brunt–Väisälä frequency. A comparison with numerical results for the case that the specific entropy, the temperature, or the density is constant on the magnetic surfaces yields excellent agreement, showing the usefulness of the derived expressions for the validation of numerical codes.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2011.03.016