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arXiv · 2404.17531

Application of Lagrangian techniques for calculating the on-axis rotational transform

S. Guinchard·W. Sengupta·S. R. Hudson
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Abstract

The Floquet exponents of periodic field lines are studied through the variations of the magnetic action on the magnetic axis, which is assumed to be elliptical. The near-axis formalism developed by Mercier, Solov'ev and Shafranov is combined with a Lagrangian approach. The on-axis Floquet exponent is shown to coincide with the on-axis rotational transform, and this is a coordinate-independent result. A discrete solution suitable for numerical implementation is introduced, which gives the Floquet exponents as solutions to an eigenvalue problem. This discrete formalism expresses the exponents as the eigenvalues of a $6\times 6$ matrix.

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S. Guinchard, W. Sengupta, S. R. Hudson. 2024-04-26. Application of Lagrangian techniques for calculating the on-axis rotational transform. https://doi.org/10.1017/s0022377824001648

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