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 | |||
The magnetic shear is defined as | |||
:<math>s = \frac{r}{q} \frac{dq}{dr} = -\frac{r}{\iota} \frac{d\iota}{dr}</math> | :<math>s = \frac{r}{q} \frac{dq}{dr} = -\frac{r}{\iota} \frac{d\iota}{dr}</math> | ||
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High values of magnetic shear provide stability, since the radial extension of helically resonant modes is reduced. | 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. | 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> | <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 == | |||
The local magnetic shear is defined as | |||
<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> | |||
where | |||
:<math>\vec{h} = \frac{\vec{\nabla} \psi}{|\vec{\nabla} \psi|} \times \frac{\vec{B}}{|\vec{B}|}</math> | |||
== See also == | |||
* [[Rotational transform]] | |||
* [[Connection length]] | |||
== References == | == References == | ||
<references /> | <references /> | ||
Latest revision as of 14:41, 3 April 2018
The shear of a vector field F is
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 surfaces, the only relevant variation of the direction of the magnetic field is the radial gradient of the rotational transform. The global magnetic shear is defined as
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. [1]
Local magnetic shear
The local magnetic shear is defined as [2]
where
See also
References
- ↑ 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, Phys. Plasmas 3, 2221 (1996)
- ↑ M. Nadeem et al, Local magnetic shear and drift waves in stellarators, Phys. Plasmas 8 (2001) 4375