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Flux surface: Difference between revisions
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This fact lies at the basis of the design of magnetic confinement devices. | This fact lies at the basis of the design of magnetic confinement devices. | ||
If a single vector field ''B'' has several such toroidal flux surfaces, they must necessarily be ''nested'' (since they cannot intersect) or be disjoint. Ignoring the latter possibility, it then makes sense to use the function ''f'' to label the flux surfaces, so ''f'' may be used as an effective "radial" coordinate. | If a single vector field ''B'' has several such toroidal flux surfaces, they must necessarily be ''nested'' (since they cannot intersect) or be disjoint. Ignoring the latter possibility, it then makes sense to use the function ''f'' to label the flux surfaces, so ''f'' may be used as an effective "radial" coordinate. Each toroidal surface ''f'' encloses a volume ''V(f)''. | ||
The surface corresponding to an infinitesimal volume ''V'' is essentially a line that corresponds to | |||
the ''toroidal axis'' (called ''magnetic axis'' when ''B'' is a magnetic field). | |||
The flux ''F'' through an arbitrary surface ''S'' is given by | |||
:<math>F = \int_S{\vec B \cdot \vec n dS}</math> | |||
When ''B'' is a magnetic field with toroidal nested flux surfaces, two magnetic fluxes can be defined from two corresponding surfaces. | |||
The poloidal flux is defined by | |||
:<math>\psi = \int_{S_p}{\vec B \cdot \vec n dS}</math> | |||
where ''S<sub>p</sub>'' is a ring-shaped ribbon stretched between the magnetic axis and the flux surface ''f'', and the toroidal flux by | |||
:<math>\phi = \int_{S_t}{\vec B \cdot \vec n dS}</math> | |||
where ''S<sub>t</sub>'' is a poloidal section of the flux surface. | |||
It is natural to use ψ or φ to label the flux surfaces instead of the unphysical label ''f''. | |||
== References == | == References == | ||
<references /> | <references /> | ||