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Title: Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates

Abstract

The confinement of the guiding-centre trajectories in a stellarator is determined by the variation of the magnetic field strength$$B$$in Boozer coordinates$$(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$$, but$$B(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$$depends on the flux surface shape in a complicated way. Here we derive equations relating$$B(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$$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. FluidsB, 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$$B$$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.

Authors:
ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
New York Univ. (NYU), NY (United States); Univ. of Maryland, College Park, MD (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1610074
DOE Contract Number:  
FG02-86ER53223; FG02-93ER54197
Resource Type:
Journal Article
Journal Name:
Journal of Plasma Physics
Additional Journal Information:
Journal Volume: 84; Journal Issue: 6; Journal ID: ISSN 0022-3778
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
Physics

Citation Formats

Landreman, Matt, and Sengupta, Wrick. Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates. United States: N. p., 2018. Web. doi:10.1017/s0022377818001289.
Landreman, Matt, & Sengupta, Wrick. Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates. United States. https://doi.org/10.1017/s0022377818001289
Landreman, Matt, and Sengupta, Wrick. 2018. "Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates". United States. https://doi.org/10.1017/s0022377818001289.
@article{osti_1610074,
title = {Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates},
author = {Landreman, Matt and Sengupta, Wrick},
abstractNote = {The confinement of the guiding-centre trajectories in a stellarator is determined by the variation of the magnetic field strength$B$in Boozer coordinates$(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$, but$B(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$depends on the flux surface shape in a complicated way. Here we derive equations relating$B(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$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. FluidsB, 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$B$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.},
doi = {10.1017/s0022377818001289},
url = {https://www.osti.gov/biblio/1610074}, journal = {Journal of Plasma Physics},
issn = {0022-3778},
number = 6,
volume = 84,
place = {United States},
year = {2018},
month = {12}
}

Works referenced in this record:

Quasi-axisymmetric magnetic fields: weakly non-axisymmetric case in a vacuum
journal, April 2018


Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates
journal, December 2018


Omnigenity as generalized quasisymmetry
journal, May 2012


Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria
journal, January 1983


Three-dimensional free boundary calculations using a spectral Green's function method
journal, December 1986


Theory of plasma confinement in non-axisymmetric magnetic fields
journal, July 2014


Existence of quasihelically symmetric stellarators
journal, October 1991


Magnetic field strength of toroidal plasma equilibria
journal, October 1991


Stellarators with the magnetic symmetry of a tokamak
journal, July 1996


Omnigenity and quasihelicity in helical plasma confinement systems
journal, September 1997


Integrated physics optimization of a quasi-isodynamic stellarator with poloidally closed contours of the magnetic field strength
journal, September 2006


Bootstrap current and neoclassical transport in quasi-isodynamic stellarators
journal, February 2009


Physics of the compact advanced stellarator NCSX
journal, November 2001


Quasi-helically symmetric toroidal stellarators
journal, May 1988


Plasma equilibrium with rational magnetic surfaces
journal, January 1981