4,378
edits
Magnetic well: Difference between revisions
no edit summary
No edit summary |
No edit summary |
||
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
The magnetic well, along with the [[Magnetic shear|magnetic shear]], is a fundamental concept for the stability of magnetically confined plasmas. <ref>[https://fusion.gat.com/pubs-ext/ComPlasmaPhys/A22135.pdf J.M. Greene, ''A brief review of magnetic wells', General Atomics Report GA-A22135 (1998)]</ref> | The magnetic well, along with the [[Magnetic shear|magnetic shear]], is a fundamental concept for the stability of magnetically confined plasmas. <ref>[https://fusion.gat.com/pubs-ext/ComPlasmaPhys/A22135.pdf J.M. Greene, ''A brief review of magnetic wells'', General Atomics Report GA-A22135 (1998)]</ref> | ||
A toroidally confined plasma with given pressure has a tendency to expand. | A toroidally confined plasma with given pressure has a tendency to expand. | ||
However, an ideal, collisionless plasma is bound to the magnetic field lines, and the flux in a magnetic [[Flux tube|flux tube]] is conserved. | However, an ideal, collisionless plasma is bound to the magnetic field lines, and the flux in a magnetic [[Flux tube|flux tube]] is conserved. | ||
The plasma will therefore prefer to move to a location where the volume to flux ratio (the ''specific volume'') is maximum. | The plasma will therefore prefer to move to a location where the volume to flux ratio (the ''specific volume'') is maximum. | ||
Assuming the existence of nested (toroidal) flux surfaces, labelled by | Assuming the existence of nested (toroidal) flux surfaces, labelled by <math>\psi</math>, and with volume <math>V(\psi)</math> and toroidal flux <math>\Phi(\psi)</math>, this specific volume is | ||
:<math>U = \frac{dV}{d\Phi}</math> | :<math>U = \frac{dV}{d\Phi}</math> | ||
| Line 24: | Line 24: | ||
where ''dl'' is an [[:Wikipedia:Arc_(geometry)|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> | ||
The relative magnetic well depth is defined as: | The relative magnetic well depth is defined as: | ||