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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. | ||
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 = 2π/ι'' is preferred (called the "safety factor"). | In tokamak research, the quantity ''q = 2π/ι'' 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 /> | ||