Magnetic shear: Difference between revisions

Revision as of 08:29, 18 May 2011

The shear of a vector field F is

{\vec {\nabla }}{\vec {F}}

Thus, in 3 dimensions, the shear is a 3 x 3 tensor.

That's way the besstet answer so far!

The local magnetic shear is defined as ^[1]

s_{\rm {local}}=2\pi {\vec {h}}\cdot {\vec {\nabla }}\times {\vec {h}}

where

{\vec {h}}={\frac {{\vec {\nabla }}\psi }{|{\vec {\nabla }}\psi |}}\times {\frac {\vec {B}}{|{\vec {B}}|}}

@@ Line 5: / Line 5: @@
 Thus, in 3 dimensions, the shear is a 3 x 3 tensor.
-== Global magnetic shear ==
+That's way the besstet answer so far!
-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>[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>
 == Local magnetic shear ==