Magnetic shear - Revision history

Admin: Updated reference links

2018-04-03T13:41:54Z

Updated reference links

← Older revision		Revision as of 15:41, 3 April 2018
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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>~~[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>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 ==		== Local magnetic shear ==

	The local magnetic shear is defined as		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>		<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>		:<math>s_{\rm local} = 2 \pi \vec{h} \cdot \vec{\nabla} \times \vec{h}</math>

Admin: revert vandalism

2011-05-18T17:37:23Z

revert vandalism

← Older revision		Revision as of 19:37, 18 May 2011
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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.

	~~That~~'~~s way~~ the ~~besstet answer so far!~~		== 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

			:<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 ==		== Local magnetic shear ==
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	== References ==		== References ==
			<references />
	<references/>

192.42.124.216 at 07:21, 18 May 2011

2011-05-18T07:21:51Z

← Older revision		Revision as of 09:21, 18 May 2011
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	* [[Connection length]]		* [[Connection length]]

	~~Never seen a btteer post! ICOCBW~~		== References ==

			<references/>

190.90.209.196: /* Global magnetic shear */

2011-05-18T06:29:37Z

Global magnetic shear

← Older revision		Revision as of 08:29, 18 May 2011
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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 ==~~		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 ==		== Local magnetic shear ==

202.100.206.4: /* References */

2011-05-18T04:00:28Z

References

← Older revision		Revision as of 06:00, 18 May 2011
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	* [[Connection length]]		* [[Connection length]]

	~~== References ==~~		Never seen a btteer post! ICOCBW
	~~<references />~~

Admin at 14:21, 30 July 2010

2010-07-30T14:21:32Z

← Older revision		Revision as of 16:21, 30 July 2010
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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.

	~~== Rotational transform ==~~

	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>~~

	~~where ''ψ'' is the poloidal magnetic flux, and ''φ'' the toroidal magnetic flux.~~
	~~Thus, ''ι/2π'' 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.~~
	~~In tokamak research, the quantity ''q = 2π/ι'' is preferred (called the "safety factor").~~

	== Global magnetic shear ==		== 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 global magnetic shear is defined as

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	== See also ==		== See also ==

			* [[Rotational transform]]
	* [[Connection length]]		* [[Connection length]]

	== References ==		== References ==
	<references />		<references />

Admin at 12:52, 30 July 2010

2010-07-30T12:52:12Z

← Older revision		Revision as of 14:52, 30 July 2010
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	:<math>\vec{h} = \frac{\vec{\nabla} \psi}{\|\vec{\nabla} \psi\|} \times \frac{\vec{B}}{\|\vec{B}\|}</math>		:<math>\vec{h} = \frac{\vec{\nabla} \psi}{\|\vec{\nabla} \psi\|} \times \frac{\vec{B}}{\|\vec{B}\|}</math>

			== See also ==

			* [[Connection length]]

	== References ==		== References ==
	<references />		<references />

Admin: /* Local magnetic shear */

2009-10-11T16:45:05Z

Local magnetic shear

← Older revision		Revision as of 18:45, 11 October 2009
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	where		where

	:<math>\vec{h} = \frac{\vec{\nabla} \psi}{\|\vec{\nabla} \psi\|} \times \vec{b}</math>		:<math>\vec{h} = \frac{\vec{\nabla} \psi}{\|\vec{\nabla} \psi\|} \times \frac{\vec{B}}{\|\vec{B}\|}</math>

	~~and~~

	~~:<math>\vec{b} = \frac{\vec{B}}{\|\vec{B}\|}</math>~~
	== References ==		== References ==
	<references />		<references />

Admin at 15:21, 11 October 2009

2009-10-11T15:21:14Z

← Older revision		Revision as of 17:21, 11 October 2009
Line 4:		Line 4:

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

			== Rotational transform ==

	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
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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 (global) magnetic shear is defined as		== Global magnetic shear ==

			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		== Local magnetic shear ==

			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>		<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>

Admin at 14:42, 11 October 2009

2009-10-11T14:42:32Z

← Older revision		Revision as of 16:42, 11 October 2009
Line 5:		Line 5:
	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>
Line 14:		Line 14:
	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>
Line 22:		Line 22:
	<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 />