Flux surface: Difference between revisions
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(Created page with 'A given surface ''S'' with normal ''n'' is a flux surface of a vector field ''B'' when :<math>\vec B \cdot \vec n = 0</math> everywhere. Defining a scalar ''flux function'' (''…') |
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A given surface ''S'' with normal ''n'' is a flux surface of a vector field ''B'' when | A given smooth surface ''S'' with normal ''n'' is a flux surface of a smooth vector field ''B'' when | ||
:<math>\vec B \cdot \vec n = 0</math> | :<math>\vec B \cdot \vec n = 0</math> | ||
Revision as of 15:53, 19 August 2009
A given smooth surface S with normal n is a flux surface of a smooth vector field B when
everywhere. Defining a scalar flux function (f) such that its value is constant on the surface S, this can be rewritten
In three dimensions, the only closed flux surface corresponding to a non-vanishing vector field is a topological toroid. [1] This fact lies at the basis of the design of magnetic confinement devices.
References
- ↑ The Poincaré-Hopf Theorem.