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.


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 (field line pitch). The latter is defined as
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''' (field line pitch). The latter is defined as


:<math>\frac{\iota}{2 \pi} = \frac{d \psi}{d \phi}</math>
:<math>\frac{\iota}{2 \pi} = \frac{d \psi}{d \phi}</math>
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In tokamak research, the quantity ''q = 2&pi;/&iota;'' is preferred (called the "safety factor").
In tokamak research, the quantity ''q = 2&pi;/&iota;'' is preferred (called the "safety factor").


The magnetic shear is defined as
The (global) 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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<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>
<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>


The (local) magnetic shear is defined as
<ref>[http://link.aip.org/link/?PHPAEN/8/4375/1 M. Nadeem et al, ''Local magnetic shear and drift waves in stellarators'', 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 \vec{b}</math>
and
:<math>\vec{b} = \frac{\vec{B}}{|\vec{B}|}</math>
== References ==
== References ==
<references />
<references />

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