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

Landreman, Matt; Sengupta, Wrick

doi:10.1017/s0022377818001289

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

Journal Article · Fri Nov 30 23:00:00 EST 2018 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/s0022377818001289· OSTI ID:1610074

^[1];

DOE/OSTI

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.

Research Organization:: New York Univ. (NYU), NY (United States); Univ. of Maryland, College Park, MD (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: FG02-86ER53223; FG02-93ER54197

OSTI ID:: 1610074

Journal Information:: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 6 Vol. 84; ISSN 0022-3778

Publisher:: Cambridge University Press

Country of Publication:: United States

Language:: English

References (16)

Stellarators with the magnetic symmetry of a tokamak Garabedian, P. R. Physics of Plasmas, Vol. 3, Issue 7 https://doi.org/10.1063/1.871965	journal	July 1996
Three-dimensional free boundary calculations using a spectral Green's function method Hirshman, S. P.; van RIJ, W. I.; Merkel, P. Computer Physics Communications, Vol. 43, Issue 1 https://doi.org/10.1016/0010-4655(86)90058-5	journal	December 1986
Plasma equilibrium with rational magnetic surfaces Boozer, Allen H. Physics of Fluids, Vol. 24, Issue 11 https://doi.org/10.1063/1.863297	journal	January 1981
Omnigenity and quasihelicity in helical plasma confinement systems Cary, John R.; Shasharina, Svetlana G. Physics of Plasmas, Vol. 4, Issue 9 https://doi.org/10.1063/1.872473	journal	September 1997
Magnetic field strength of toroidal plasma equilibria Garren, D. A.; Boozer, A. H. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 10 https://doi.org/10.1063/1.859915	journal	October 1991
Existence of quasihelically symmetric stellarators Garren, D. A.; Boozer, A. H. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 10 https://doi.org/10.1063/1.859916	journal	October 1991
Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria Hirshman, S. P. Physics of Fluids, Vol. 26, Issue 12 https://doi.org/10.1063/1.864116	journal	January 1983
Integrated physics optimization of a quasi-isodynamic stellarator with poloidally closed contours of the magnetic field strength Subbotin, A. A.; Mikhailov, M. I.; Shafranov, V. D. Nuclear Fusion, Vol. 46, Issue 11 https://doi.org/10.1088/0029-5515/46/11/006	journal	September 2006
Equilibrium and stability of a toroidal magnetohydrodynamic system in the neighbourhood of a magnetic axis Mercier, Claude Nuclear Fusion, Vol. 4, Issue 3 https://doi.org/10.1088/0029-5515/4/3/008	journal	September 1964
Omnigenity as generalized quasisymmetry Landreman, Matt; Catto, Peter J. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.3693187	journal	May 2012
Quasi-axisymmetric magnetic fields: weakly non-axisymmetric case in a vacuum Plunk, G. G.; Helander, Per Journal of Plasma Physics, Vol. 84, Issue 2 https://doi.org/10.1017/S0022377818000259	journal	April 2018
Physics of the compact advanced stellarator NCSX Zarnstorff, M. C.; Berry, L. A.; Brooks, A. Plasma Physics and Controlled Fusion, Vol. 43, Issue 12A https://doi.org/10.1088/0741-3335/43/12A/318	journal	November 2001
Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates Landreman, Matt; Sengupta, Wrick Journal of Plasma Physics, Vol. 84, Issue 6 https://doi.org/10.1017/S0022377818001289	journal	December 2018
Theory of plasma confinement in non-axisymmetric magnetic fields Helander, Per Reports on Progress in Physics, Vol. 77, Issue 8 https://doi.org/10.1088/0034-4885/77/8/087001	journal	July 2014
Quasi-helically symmetric toroidal stellarators Nührenberg, J.; Zille, R. Physics Letters A, Vol. 129, Issue 2 https://doi.org/10.1016/0375-9601(88)90080-1	journal	May 1988
Bootstrap current and neoclassical transport in quasi-isodynamic stellarators Helander, P.; Nührenberg, J. Plasma Physics and Controlled Fusion, Vol. 51, Issue 5 https://doi.org/10.1088/0741-3335/51/5/055004	journal	February 2009

Similar Records

Simulation study of particle clouds in oscillating shear flow

Journal Article · Tue Aug 07 00:00:00 EDT 2018 · Journal of Fluid Mechanics · OSTI ID:1538916

Inclined porous medium convection at large Rayleigh number

Journal Article · Thu Jan 04 23:00:00 EST 2018 · Journal of Fluid Mechanics · OSTI ID:1538909

Related Subjects

Physics

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

Citation Formats

References (16)

Similar Records

Related Subjects