Flux surface: Difference between revisions

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:<math>\vec B \cdot \vec n = 0</math>
:<math>\vec B \cdot \vec n = 0</math>


everywhere on ''S''. It is then possible to define a scalar ''flux function'' (''f'') such that its value is constant on the surface ''S'', and
everywhere on ''S''.  
In other words, the magnetic field does not ''cross'' the surface ''S'' anywhere, i.e., the magnetic flux traversing ''S'' is zero.
It is then possible to define a scalar ''flux function'' (''f'') such that its value is constant on the surface ''S'', and


:<math>\vec B \cdot \vec \nabla f = 0</math>
:<math>\vec B \cdot \vec \nabla f = 0</math>
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[[File:Flux_definition.png|250px|thumb|right|Diagram showing the surfaces defining the poloidal (red) and toroidal (blue) flux]]
[[File:Flux_definition.png|250px|thumb|right|Diagram showing the surfaces defining the poloidal (red) and toroidal (blue) flux]]
When ''B'' is a magnetic field with toroidal nested flux surfaces, two magnetic fluxes can be defined from two corresponding surfaces.
When ''B'' is a magnetic field with toroidal nested flux surfaces, two magnetic fluxes can be defined from two corresponding surfaces.
<ref>R.D. Hazeltine, J.D. Meiss, ''Plasma Confinement'', Courier Dover Publications (2003) ISBN 0486432424</ref>
<ref>R.D. Hazeltine, J.D. Meiss, ''Plasma Confinement'', Courier Dover Publications (2003) {{ISBN|0486432424}}</ref>
The poloidal flux is defined by
The poloidal flux is defined by


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where ''S<sub>p</sub>'' is a ring-shaped ribbon stretched between the magnetic axis and the flux surface ''f''.
where ''S<sub>p</sub>'' is a ring-shaped ribbon stretched between the magnetic axis and the flux surface ''f''.
(Alternatively, ''S<sub>p</sub>'' can be taken to be a horizontal surface spanning the central hole of the torus.<ref>[http://link.aps.org/doi/10.1103/RevModPhys.76.1071 A.H. Boozer, ''Physics of magnetically confined plasmas'', Rev. Mod. Phys. '''76''' (2005) 1071 - 1141]</ref>)
(Complementarily, ''S<sub>p</sub>'' can be taken to be a surface spanning the central hole of the torus.<ref>[http://link.aps.org/doi/10.1103/RevModPhys.76.1071 A.H. Boozer, ''Physics of magnetically confined plasmas'', Rev. Mod. Phys. '''76''' (2005) 1071 - 1141]</ref>)
Likewise, the toroidal flux is defined by
Likewise, the toroidal flux is defined by


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* [[MHD equilibrium]]
* [[MHD equilibrium]]
* [[Toroidal coordinates]]
* [[Toroidal coordinates]]
* [[Flux coordinates]]
* [[Rotational transform]]
* [[Magnetic shear]]
* [[Magnetic shear]]
* [[Effective plasma radius]]
* [[Effective plasma radius]]
* [[Separatrix]]
* [[Flux tube]]


== References ==
== References ==
<references />
<references />

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