Explicit spectrally optimized Fourier series for nested magnetic surfaces
- Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)
The nonuniqueness of the poloidal angle {theta} in the parametric representation of a space curve {bold x}({theta})=[R({theta}),Z({theta})] can be exploited to condense the Fourier spectra of R and Z. The nonlinear equation describing this spectral condensation was previously derived and solved numerically using Lagrange multipliers. Here a special case of the condensation equation is shown to be exactly solvable, leading to an explicit representation for {bold x}. A family of such representations is generated that possesses increasingly condensed spectra as a parameter is varied. Applications to a variety of curves are considered as models for three-dimensional magnetohydrodynamic (MHD) equilibria with nested flux surfaces. A substantial improvement occurs in spectral convergence compared with a polar representation, while retaining the numerical simplicity of the polar constraint. The asymptotic behavior for the R and Z spectral coefficients near a magnetic axis is analyzed. Implications for improvements of MHD equilibrium calculations are discussed. {copyright} {ital 1998 American Institute of Physics.}
- OSTI ID:
- 636158
- Journal Information:
- Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 7 Vol. 5; ISSN PHPAEN; ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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