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Equilibrium 𝛽-limits in classical stellarators

  • J. Loizu (a1), S. R. Hudson (a2), C. Nührenberg (a1), J. Geiger (a1) and P. Helander (a1)...

Abstract

A numerical investigation is carried out to understand the equilibrium $\unicode[STIX]{x1D6FD}$ -limit in a classical stellarator. The stepped-pressure equilibrium code (Hudson et al., Phys. Plasmas, vol. 19 (11), 2012) is used in order to assess whether or not magnetic islands and stochastic field-lines can emerge at high $\unicode[STIX]{x1D6FD}$ . Two modes of operation are considered: a zero-net-current stellarator and a fixed-iota stellarator. Despite the fact that relaxation is allowed (Taylor, Rev. Mod. Phys., vol. 58 (3), 1986, pp. 741–763), the former is shown to maintain good flux surfaces up to the equilibrium $\unicode[STIX]{x1D6FD}$ -limit predicted by ideal-magnetohydrodynamics (MHD), above which a separatrix forms. The latter, which has no ideal equilibrium $\unicode[STIX]{x1D6FD}$ -limit, is shown to develop regions of magnetic islands and chaos at sufficiently high $\unicode[STIX]{x1D6FD}$ , thereby providing a ‘non-ideal $\unicode[STIX]{x1D6FD}$ -limit’. Perhaps surprisingly, however, the value of $\unicode[STIX]{x1D6FD}$ at which the Shafranov shift of the axis reaches a fraction of the minor radius follows in all cases the scaling laws predicted by ideal-MHD. We compare our results to the High-Beta-Stellarator theory of Freidberg (Ideal MHD, 2014, Cambridge University Press) and derive a new prediction for the non-ideal equilibrium $\unicode[STIX]{x1D6FD}$ -limit above which chaos emerges.

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Copyright

Corresponding author

Email address for correspondence: joaquim.loizu@ipp.mpg.de

References

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Keywords

Equilibrium 𝛽-limits in classical stellarators

  • J. Loizu (a1), S. R. Hudson (a2), C. Nührenberg (a1), J. Geiger (a1) and P. Helander (a1)...

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