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Magnetic shear: Difference between revisions
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Thus, in 3 dimensions, the shear is a 3 x 3 tensor. | Thus, in 3 dimensions, the shear is a 3 x 3 tensor. | ||
== Global magnetic shear == | |||
In the context of magnetic confinement, and assuming the existence of toroidally nested magnetic [[Flux surface|flux surfaces]], the only relevant variation of the direction of the magnetic field is the radial gradient of the [[Rotational transform|rotational transform]]. | |||
The global magnetic shear is defined as | |||
:<math>s = \frac{r}{q} \frac{dq}{dr} = -\frac{r}{\iota} \frac{d\iota}{dr}</math> | |||
High values of magnetic shear provide stability, since the radial extension of helically resonant modes is reduced. | |||
Negative shear also provides stability, possibly because convective cells, generated by curvature-driven instabilities, are sheared apart as the field lines twist around the torus. | |||
<ref>T.M. Antonsen, Jr., et al, ''Physical mechanism of enhanced stability from negative shear in tokamaks: Implications for edge transport and the L-H transition'', [[doi:10.1063/1.871928|Phys. Plasmas '''3''', 2221 (1996)]]</ref> | |||
== Local magnetic shear == | == Local magnetic shear == | ||
The local magnetic shear is defined as | The local magnetic shear is defined as | ||
<ref> | <ref>M. Nadeem et al, ''Local magnetic shear and drift waves in stellarators'', [[doi:10.1063/1.1396842|Phys. Plasmas '''8''' (2001) 4375]]</ref> | ||
:<math>s_{\rm local} = 2 \pi \vec{h} \cdot \vec{\nabla} \times \vec{h}</math> | :<math>s_{\rm local} = 2 \pi \vec{h} \cdot \vec{\nabla} \times \vec{h}</math> | ||
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* [[Connection length]] | * [[Connection length]] | ||
== References == | |||
<references /> | |||