Omnigeneity

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A flux surface of Wendelstein 7-X (yellow), a magnetic field line on that flux surface (green), and the coils needed to generate the magnetic field (blue). Wendelstein 7-X is designed to be nearly omnigenous. W7X-Spulen Plasma blau gelb.jpg
A flux surface of Wendelstein 7-X (yellow), a magnetic field line on that flux surface (green), and the coils needed to generate the magnetic field (blue). Wendelstein 7-X is designed to be nearly omnigenous.

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 (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 , [7]

where is the charge of the particle, is the magnetic field line label, and 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,

This criterion is exactly met in axisymmetric systems, as the derivative with respect to can be expressed as a derivative with respect to the toroidal angle (under which the system is invariant).

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References

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  2. Landreman, Matt (2019). "Quasisymmetry: A hidden symmetry of magnetic fields" (PDF).
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  5. 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. S2CID   54572939.
  6. Helander, Per (2014-07-21). "Theory of plasma confinement in non-axisymmetric magnetic fields". Reports on Progress in Physics. 77 (8): 087001. doi:10.1088/0034-4885/77/8/087001. hdl: 11858/00-001M-0000-0023-C75B-7 . ISSN   0034-4885. PMID   25047050. S2CID   33909405.
  7. Hall, Laurence S.; McNamara, Brendan (1975). "Three-dimensional equilibrium of the anisotropic, finite-pressure guiding-center plasma: Theory of the magnetic plasma". Physics of Fluids. 18 (5): 552. doi:10.1063/1.861189.
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