Rotational Transform

Some work carried on the rotational transform.

The rotational transform, \(\iota\), has been shown to be an important parameter in Stellarator design. We propose a novel approach to recover the on-axis rotational transform from variational principles, carrying the appropriate near-axis expansion of the magnetic action.

\(\iota = \oint \frac{\frac{J_0(s)/2}{B_0(s)}- \tau(s) +\delta'(s)}{2 \cosh{\eta(s)}} ds\), where \(\tau\) denotes the torsion of the magnetic axis, \(J_0\) and \(B_0\) the lowest order current density and magnetic field resepctively, \(\delta\) characterizes the ellipticity of flux surfaces and \(\eta\) the rotation. \(s\) is an parameter describing the axis and the integral is performed along the latter.

A paper is currently being written and should be submitted or at least posted on arXiv soon.

Elliptical flux surface rotating around the magnetic axis, generating according to Mercier's formula, some rotational transform. The image is taken from [BaA2023].
  • BaA2023: Baillod, A. (2023). Equilibrium pressure limits in stellarators. page 221.
  • Hel2014: Helander, P. (2014), Theory of plasma confinement in non-axisymmetric magnetic fields.
  • CaLij83: Cary, J. and Littlejohn, R. Noncanonical Hamiltonian mechanics and its application to magnetic field line flow.