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Magnetic well: Difference between revisions
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(Created page with 'The magnetic well, along with the magnetic shear, is a fundamental concept for the stability of magnetically confined plasmas. A toroidally confined plasma with given pressure ha…') |
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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: | |||
:<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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where ''dl'' is an arc segment along the field line. | where ''dl'' is an arc segment along the field line. | ||
The magnetic well is related to the average field line curvature κ. | The magnetic well is related to the average 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> | ||
The relative magnetic well depth is defined as: | |||
:<math>w(\bar r) = \frac{(dV(0)/d\Phi - dV(\bar r)/d\Phi)}{dV(0)/d\Phi }</math> | |||
where <math>\bar r</math> is the average radius of a flux surface. | |||
A positive gradient of ''w'' corresponds to a magnetic well, and a negative gradient to a magnetic hill. | |||
== References == | == References == | ||
<references /> | <references /> | ||