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Magnetic well: Difference between revisions
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where <math>\bar L</math> is the length of the (toroidal) magnetic axis, one sees that the condition of maximum specific volume is equivalent to minimum B. | where <math>\bar L</math> is the length of the (toroidal) magnetic axis, one sees that the condition of maximum specific volume is equivalent to minimum B. | ||
The vacuum magnetic well is defined via an average of the magnetic pressure over a flux surface: | The vacuum magnetic well is defined via an average of the magnetic pressure over a [[flux surface]]: | ||
:<math>W = 2 \frac{V}{ \left \langle B^2 \right \rangle } \frac{d}{dV} \left \langle \frac{B^2}{2} \right \rangle </math> | :<math>W = 2 \frac{V}{ \left \langle B^2 \right \rangle } \frac{d}{dV} \left \langle \frac{B^2}{2} \right \rangle </math> | ||
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:<math>\left \langle f \right \rangle = \int{\frac{f dl}{B}} \bigg / \int{\frac{dl}{B}}</math> | :<math>\left \langle f \right \rangle = \int{\frac{f dl}{B}} \bigg / \int{\frac{dl}{B}}</math> | ||
where ''dl'' is an arc segment along the field line. | where ''dl'' is an [[:Wikipedia:Arc_(geometry)|arc segment]] along the field line. | ||
The magnetic well is related to the average [[Magnetic curvature|magnetic field line curvature κ]]. | The magnetic well is related to the average [[Magnetic curvature|magnetic field line curvature κ]]. | ||
<ref>M. Wakatani, ''Stellarator and Heliotron devices'', Oxford University Press, New York and Oxford (1998) ISBN 0-19-507831-4</ref> | <ref>M. Wakatani, ''Stellarator and Heliotron devices'', Oxford University Press, New York and Oxford (1998) ISBN 0-19-507831-4</ref> | ||