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 &kappa;]].
The magnetic well is related to the average [[Magnetic curvature|magnetic field line curvature &kappa;]].
<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>

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