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.


To calculate the well, this condition must be averaged over a flux surface. The final definition is:
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 &kappa;.
The magnetic well is related to the average 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>
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 ==
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