Physics:Omnigeneity
Omnigeneity (sometimes also called omnigenity) is a property of a magnetic field inside a magnetic confinement fusion reactor. Such a magnetic field is called omnigenous if the path a single particle takes does not drift radially inwards or outwards on average.[1] A particle is then confined to stay on a flux surface. All tokamaks are exactly omnigenous by virtue of their axisymmetry,[2] and conversely an unoptimized stellarator is generally not omnigenous.
Because an exactly omnigenous reactor has no neoclassical transport (in the collisionless limit),[3] stellarators are usually optimized in a way such that this criterion is met. One way to achieve this is by making the magnetic field quasi-symmetric,[4] and the Helically Symmetric eXperiment takes this approach. One can also achieve this property without quasi-symmetry, and Wendelstein 7-X is an example of a device which is close to omnigeneity without being quasi-symmetric.[5]
Theory
The drifting of particles across flux surfaces is generally only a problem for trapped particles, which are trapped in a magnetic mirror. Untrapped (or passing) particles, which can circulate freely around the flux surface, are automatically confined to stay on a flux surface.[6] For trapped particles, omnigeneity relates closely to the second adiabatic invariant [math]\displaystyle{ \cal{J} }[/math] (often called the parallel or longitudinal invariant).
One can show that the radial drift a particle experiences after one full bounce motion is simply related to a derivative of [math]\displaystyle{ \cal{J} }[/math],[7][math]\displaystyle{ \frac{\partial \cal{J}}{\partial \alpha} = q \Delta \psi }[/math]where [math]\displaystyle{ q }[/math] is the charge of the particle, [math]\displaystyle{ \alpha }[/math] is the magnetic field line label, and [math]\displaystyle{ \Delta \psi }[/math] is the total radial drift expressed as a difference in toroidal flux.[8] With this relation, omnigeneity can be expressed as the criterion that the second adiabatic invariant should be the same for all the magnetic field lines on a flux surface,[math]\displaystyle{ \frac{\partial \cal{J}}{\partial \alpha} = 0 }[/math]This criterion is exactly met in axisymmetric systems, as the derivative with respect to [math]\displaystyle{ \alpha }[/math] can be expressed as a derivative with respect to the toroidal angle (under which the system is invariant).
References
- ↑ 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.
- ↑ Landreman, Matt (2019). "Quasisymmetry: A hidden symmetry of magnetic fields". https://hiddensymmetries.princeton.edu/sites/g/files/toruqf1546/files/landreman_-_introduction_to_quasisymmetry.pdf.
- ↑ Beidler, C.D.; Allmaier, K.; Isaev, M.Yu.; Kasilov, S.V.; Kernbichler, W.; Leitold, G.O.; Maaßberg, H.; Mikkelsen, D.R. et al. (2011-07-01). "Benchmarking of the mono-energetic transport coefficients—results from the International Collaboration on Neoclassical Transport in Stellarators (ICNTS)". Nuclear Fusion 51 (7): 076001. doi:10.1088/0029-5515/51/7/076001. ISSN 0029-5515. Bibcode: 2011NucFu..51g6001B. https://iopscience.iop.org/article/10.1088/0029-5515/51/7/076001.
- ↑ Rodríguez, E.; Helander, P.; Bhattacharjee, A. (June 2020). "Necessary and sufficient conditions for quasisymmetry" (in en). Physics of Plasmas 27 (6): 062501. doi:10.1063/5.0008551. ISSN 1070-664X. Bibcode: 2020PhPl...27f2501R. http://aip.scitation.org/doi/10.1063/5.0008551.
- ↑ Nührenberg, Jürgen (2010-12-01). "Development of quasi-isodynamic stellarators". Plasma Physics and Controlled Fusion 52 (12): 124003. doi:10.1088/0741-3335/52/12/124003. ISSN 0741-3335. Bibcode: 2010PPCF...52l4003N. https://iopscience.iop.org/article/10.1088/0741-3335/52/12/124003.
- ↑ Helander, Per (2014-07-21). "Theory of plasma confinement in non-axisymmetric magnetic fields" (in en). Reports on Progress in Physics 77 (8): 087001. doi:10.1088/0034-4885/77/8/087001. ISSN 0034-4885. PMID 25047050. Bibcode: 2014RPPh...77h7001H. https://doi.org/10.1088/0034-4885/77/8/087001.
- ↑ 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.
- ↑ 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. http://worldcat.org/oclc/1159739471.
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