Physics:Piecewise omnigenity

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Short description: Property of the magnetic field of a magnetic confinement device


Variation of the magnetic field strength of an omnigenous field (left), and a piecewise omnigenous field. A darker color corresponds to a weaker field. The x and y axis are angles that label the flux surface.

Piecewise omnigeneity[1] is a property of the magnetic field of a magnetic confinement device . It constitutes a generalization of the property of omnigenity. Similarly to what happens in an omnigenous field, in a piecewise omnigenous field a charged particle takes does not drift radially (inwards or outwards) on average,[2] and is therefore confined to stay on a flux surface. As a consequence of this, a piecewise omnigenous field has tokamak-like neoclassical transport.[3]

For decades, stellarator designs have been optimized to meet this criterion. Piecewise represents an alternative optimization target that may expand the space of magnetic fields relevant for reactor applications.[4]

Theory

The drifting of particles across flux surfaces is generally only a problem for trapped particles, which are trapped in a magnetic mirror. Passing particles, which can circulate freely around the flux surface, are automatically confined to stay on a flux surface.[3] For trapped particles, omnigeneity and piecewise omnigenity relate closely to the second adiabatic invariant 𝒥.

One can show that the radial drift a particle experiences after one full bounce motion is simply related to a derivative of 𝒥,[5]∂𝒥∂α=qΔψwhere q is the charge of the particle, α is the magnetic field line label, and Δψ is the total radial drift expressed as a difference in toroidal flux.[6] In a piecewise omnigenous field, the flux surface of the stellarator is composed of several regions; within each of them, the second adiabatic invariant should be the same for all the magnetic field lines, and thus∂𝒥∂α=0inside each region. The junctures between regions can be shown not to cause neoclassical transport.

References

  1. ↑ Velasco, José L. (October 2024). "Piecewise Omnigenous Stellarators" (in en). Physical Review Letters 4 (133). doi:10.1103/PhysRevLett.133.185101. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.185101. 
  2. ↑ Cary, John R.; Shasharina, Svetlana G. (September 1997). "Omnigenity and quasihelicity in helical plasma confinement systems" (in en). Physics of Plasmas 4 (9): 3323–3333. doi:10.1063/1.872473. ISSN 1070-664X. Bibcode: 1997PhPl....4.3323C. http://aip.scitation.org/doi/10.1063/1.872473. 
  3. ↑ 3.0 3.1 Helander, Per (2014-07-21). "Theory of plasma confinement in non-axisymmetric magnetic fields" (in en). Reports on Progress in Physics 77 (8). doi:10.1088/0034-4885/77/8/087001. ISSN 0034-4885. PMID 25047050. Bibcode: 2014RPPh...77h7001H. 
  4. ↑ Fernández-Pacheco, Víctor. Piecewise omnigenous magnetohydrodynamic equilibria as fusion reactor candidates. https://arxiv.org/abs/2601.14886. 
  5. ↑ Hall, Laurence S.; McNamara, Brendan (1975). "Three-dimensional equilibrium of the anisotropic, finite-pressure guiding-center plasma: Theory of the magnetic plasma" (in en). Physics of Fluids 18 (5): 552. doi:10.1063/1.861189. Bibcode: 1975PhFl...18..552H. https://aip.scitation.org/doi/10.1063/1.861189. 
  6. ↑ D'haeseleer, William Denis. (6 December 2012). Flux Coordinates and Magnetic Field Structure: A Guide to a Fundamental Tool of Plasma Theory. Springer. ISBN 978-3-642-75595-8. OCLC 1159739471. 



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