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| which is zero for axisymmetic systems (since ''ψ'' does not depend on ''φ''), but non-zero for stellarators. | | which is zero for axisymmetic systems (since ''ψ'' does not depend on ''φ''), but non-zero for stellarators. |
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| == Effective radius based on field lines ==
| | Tip top stuff. I'll epecxt more now. |
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| If the flux surfaces are not known, the effective radius of a surface traced out by a field line can be found by following the field line and calculating the geometric mean of the distance between points on the field line and the magnetic axis. The mean should be weighed with ''1/B'' in order to account for the variation of the field strength along the flux surface.
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| This procedure, while general in principle, still assumes that the field lines lie on flux surfaces.
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| It can be used for magnetic configurations with [[Magnetic island|magnetic islands]], although this requires applying some special treatment for points inside the islands. It may be argued that assigning an effective radius to spatial points inside a magnetic island is not very useful, since such points are topologically disconnected from the main plasma volume. Similarly, the definition of an effective radius in ergodic magnetic zones is ambiguous, since the concept of flux surface has no meaning inside an ergodic zone.
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| <ref>[http://dx.doi.org/10.1016/j.jcp.2008.02.026 B. Seiwald et al, ''Optimization of energy confinement in the 1/ν regime for stellarators'', Journal of Computational Physics '''227''', 12 (2008) 6165-6183]</ref>
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| == Hybrid definitions == | | == Hybrid definitions == |