Magnetic shear: Difference between revisions

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 Thus, in 3 dimensions, the shear is a 3 x 3 tensor.
-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 (field line pitch). The latter is defined as
+== Global magnetic shear ==
-:<math>\frac{\iota}{2 \pi} = \frac{d \psi}{d \phi}</math>
+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
-where ''&psi;'' is the poloidal magnetic flux, and ''&phi;'' the toroidal magnetic flux.
+:<math>s = \frac{r}{q} \frac{dq}{dr} = -\frac{r}{\iota} \frac{d\iota}{dr}</math>
-Thus, ''&iota;/2&pi;'' is the mean number of toroidal transits (''n'') divided by the
-mean number of poloidal transits (''m'') of a field line on a flux surface.
+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 ==
+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>
-In tokamak research, the quantity ''q = 1/&iota;'' is preferred (called the "safety factor").
+:<math>s_{\rm local} = 2 \pi \vec{h} \cdot \vec{\nabla} \times \vec{h}</math>
-The magnetic shear is defined as
+where
-:<math>s = \frac{r}{q} \frac{dq}{dr} = -\frac{r}{\iota} \frac{d\iota}{dr}</math>
+:<math>\vec{h} = \frac{\vec{\nabla} \psi}{|\vec{\nabla} \psi|} \times \frac{\vec{B}}{|\vec{B}|}</math>
+== See also ==
-High values of magnetic shear provide stability, since the radial extension of helically resonant modes is reduced.
+* [[Rotational transform]]
-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.
+* [[Connection length]]
-<ref>[http://link.aip.org/link/?PHPAEN/3/2221/1 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)]</ref>
 == References ==
 <references />