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Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates
Landreman, Matt; Sengupta, Wrick
AA(Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742, USA), AB(Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA)
Journal of Plasma Physics, Volume 84, Issue 6, article id. 905840616, 22 pp.
Publication Date:
fusion plasma, plasma confinement
Abstract Copyright:
(c) 2018: © Cambridge University Press 2018
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The confinement of the guiding-centre trajectories in a stellarator is determined by the variation of the magnetic field strength in Boozer coordinates , but depends on the flux surface shape in a complicated way. Here we derive equations relating in Boozer coordinates and the rotational transform to the shape of flux surfaces in cylindrical coordinates, using an expansion in distance from the magnetic axis. A related expansion was done by Garren and Boozer (Phys. Fluids B, vol. 3, 1991a, 2805) based on the Frenet-Serret frame, which can be discontinuous anywhere the magnetic axis is straight, a situation that occurs in the interesting case of omnigenity with poloidally closed
contours. Our calculation in contrast does not use the Frenet-Serret frame. The transformation between the Garren-Boozer approach and cylindrical coordinates is derived, and the two approaches are shown to be equivalent if the axis curvature does not vanish. The expressions derived here help enable optimized plasma shapes to be constructed that can be provided as input to VMEC and other stellarator codes, or to generate initial configurations for conventional stellarator optimization.
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