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PreprintCC BY 4.0arXiv

Macroscopic Stability of a Rapidly Rotating Isothermal Magnetic Mirror

  • Richard Fitzpatrick
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Abstract

The macroscopic ideal-MHD stability of an axisymmetric mirror device with sonic levels of plasma rotation is analyzed by approximating the plasma equilibrium as a rotating isothermal theta pinch possessing an artificial gravity. Starting from a set of single-fluid, ideal-MHD, isothermal fluid equations, a linear, second-order, eigenmode equation for the radial component of the Lagrangian fluid displacement is derived which governs the stability of the equilibrium to small perturbations in the case of an arbitrary plasma angular velocity profile. The stability of the m=1 and m=2 modes is investigated. For the case of rigid plasma rotation, the plasma is found to be stable to these two modes provided that it is sufficiently short in the axial direction. For the case of sheared plasma rotation, the m=2 mode is found to be difficult to stabilize. This is the case for both monotonically decreasing rotation profiles, and profiles that peak off the magnetic axis.

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Cite

BibTeXRIS
BibTeX
@misc{fitzpatrick2026macroscopic,
  title = {{Macroscopic Stability of a Rapidly Rotating Isothermal Magnetic Mirror}},
  author = {Richard Fitzpatrick},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.13485},
  eprint = {2608.13485},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.13485},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Macroscopic Stability of a Rapidly Rotating Isothermal Magnetic Mirror
AU  - Richard Fitzpatrick
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2608.13485
UR  - https://arxiv.org/abs/2608.13485
AB  - The macroscopic ideal-MHD stability of an axisymmetric mirror device with sonic levels of plasma rotation is analyzed by approximating the plasma equilibrium as a rotating isothermal theta pinch possessing an artificial gravity. Starting from a set of single-fluid, ideal-MHD, isothermal fluid equations, a linear, second-order, eigenmode equation for the radial component of the Lagrangian fluid displacement is derived which governs the stability of the equilibrium to small perturbations in the case of an arbitrary plasma angular velocity profile. The stability of the m=1 and m=2 modes is investigated. For the case of rigid plasma rotation, the plasma is found to be stable to these two modes provided that it is sufficiently short in the axial direction. For the case of sheared plasma rotation, the m=2 mode is found to be difficult to stabilize. This is the case for both monotonically decreasing rotation profiles, and profiles that peak off the magnetic axis.
ER  -