Three-dimensional free boundary calculations using a spectral Green's function method
Abstract
The plasma energy is minimized over a toroidal domain ωp using an inverse representation for the cylindrical coordinates R = ΣRmn(S) cos(mθ − nζ) and Z = ΣZmn(s) sin(mθ − nζ), where (s, θ, ζ) are radial, poloidal and toroidal flux coordinates, respectively. The radial resolution of the MHD equations is significantly improved by separating R and Z into contributions from even and odd poloidal harmonics which are individually analytic near the magnetic axis. A free boundary equilibrium results when ωp is varied to make the total pressure B2 + p continuous at the plasma surface Σp and when the vacuum magnetic field Bv satisfies the Neumann condition . The vacuum field is decomposed as , where B0 is the field arising from plasma currents and external coils and φ is an single-valued potential necessary to satisfy when p ≠ 0. A Green's function method is used to obtain an integral equation over Σp for the scalar magnetic potential φ = Σφmn sin(mθ − nζ). A linear matrix equation is solved for φmn to determine B2v on the boundary. Real experimental conditions are simulated by keeping the external and net plasma currents constant during the iteration. Applications to l = 2 stellarator equilibria are presented.
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Program Title: Biot-Savart Routines with Minimal Floating Point Error
CPC Library link to program files: https://doi.org/10.17632/zcwk7zzt9y.1
Developer's repository link: https://github.com/jonathanschilling/abscab
Licensing provisions: Apache-2.0
Programming language: C, Python, Java, Fortran
Supplementary material: Reference output data for all methods described in this article.
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