Non-planar elasticae as optimal curves for the magnetic axis of stellarators

D. Pfefferlé, L. Gunderson, S. R. Hudson, L. Noakes

Research output: Contribution to journalArticle

3 Citations (Scopus)


The problem of finding an optimal curve for the target magnetic axis of a stellarator is addressed. Euler-Lagrange equations are derived for finite length three-dimensional curves that extremise their bending energy while yielding fixed integrated torsion. The obvious translational and rotational symmetries are exploited to express solutions in a preferred cylindrical coordinate system in terms of elliptic Jacobi functions. These solution curves, which, up to similarity transformations, depend on three dimensionless parameters, do not necessarily close. Two closure conditions are obtained for the vertical and toroidal displacement (the radial coordinate being trivially periodic) to yield a countably infinite set of one-parameter families of closed non-planar curves. The behaviour of the integrated torsion (Twist of the Frenet frame), the Linking of the Frenet frame, and the Writhe of the solution curves are studied in light of the Calugareanu theorem. A refreshed interpretation of Mercier's formula for the on-axis rotational transform of stellarator magnetic field-lines is proposed.

Original languageEnglish
Article number092508
JournalPhysics of Plasmas
Issue number9
Publication statusPublished - 1 Sep 2018

Fingerprint Dive into the research topics of 'Non-planar elasticae as optimal curves for the magnetic axis of stellarators'. Together they form a unique fingerprint.

Cite this