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Near-axis expansion of stellarator equilibrium at arbitrary order in the distance to the axis

Part of: Focus on Fusion

Published online by Cambridge University Press:  28 January 2020

R. Jorge Open the ORCID record for R. Jorge [Opens in a new window] ,
W. Sengupta Open the ORCID record for W. Sengupta [Opens in a new window]  and
M. Landreman Open the ORCID record for M. Landreman [Opens in a new window]
R. Jorge*
Affiliation:
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742, USA
W. Sengupta
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
M. Landreman
Affiliation:
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742, USA
*
†Email address for correspondence: [email protected]
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Abstract

A direct construction of equilibrium magnetic fields with toroidal topology at arbitrary order in the distance from the magnetic axis is carried out, yielding an analytical framework able to explore the landscape of possible magnetic flux surfaces in the vicinity of the axis. This framework can provide meaningful analytical insight into the character of high-aspect-ratio stellarator shapes, such as the dependence of the rotational transform and the plasma beta limit on geometrical properties of the resulting flux surfaces. The approach developed here is based on an asymptotic expansion on the inverse aspect ratio of the ideal magnetohydrodynamics equation. The analysis is simplified by using an orthogonal coordinate system relative to the Frenet–Serret frame at the magnetic axis. The magnetic field vector, the toroidal magnetic flux, the current density, the field line label and the rotational transform are derived at arbitrary order in the expansion parameter. Moreover, a comparison with a near-axis expansion formalism employing an inverse coordinate method based on Boozer coordinates (the so-called Garren–Boozer construction) is made, where both methods are shown to agree at lowest order. Finally, as a practical example, a numerical solution using a W7-X equilibrium is presented, and a comparison between the lowest-order solution and the W7-X magnetic field is performed.

Keywords

fusion plasmaplasma confinement
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 1 , February 2020 , 905860106
Copyright
© Cambridge University Press 2020

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