Rotational transform - Revision history

Admin at 10:31, 26 January 2023

2023-01-26T10:31:24Z

← Older revision		Revision as of 12:31, 26 January 2023
Line 14:		Line 14:
	In a circular tokamak,		In a circular tokamak,
	the equations of a field line on the flux surface are, approximately:		the equations of a field line on the flux surface are, approximately:
	<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref>		<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) {{ISBN\|3540242171}}</ref>

	:<math>\frac{r d\theta}{B_\theta} = \frac{Rd\varphi}{B_\varphi}</math>		:<math>\frac{r d\theta}{B_\theta} = \frac{Rd\varphi}{B_\varphi}</math>
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	:<math>q \simeq \frac{r B_\varphi}{R B_\theta}</math>		:<math>q \simeq \frac{r B_\varphi}{R B_\theta}</math>

	Where the poloidal magnetic field <math>{B_\theta}</math> is mostly produced by a toroidal plasma current. The principal significance of the safety factor ''q'' is that if <math>q \leq 2</math> at the last closed flux surface (the edge), the plasma is [[:Wikipedia:Magnetohydrodynamics\|magnetohydrodynamically]] unstable.<ref>Wesson J 1997 Tokamaks 2nd edn (Oxford: Oxford University Press) p280 ISBN 0198509227</ref>		Where the poloidal magnetic field <math>{B_\theta}</math> is mostly produced by a toroidal plasma current. The principal significance of the safety factor ''q'' is that if <math>q \leq 2</math> at the last closed flux surface (the edge), the plasma is [[:Wikipedia:Magnetohydrodynamics\|magnetohydrodynamically]] unstable.<ref>Wesson J 1997 Tokamaks 2nd edn (Oxford: Oxford University Press) p280 {{ISBN\|0198509227}}</ref>

	In [[Tokamak\|tokamaks]] with a [[divertor]], ''q'' approaches infinity at the [[separatrix]], so it is more useful to consider ''q'' just inside the separatrix. It is customary to use ''q'' at the 95% flux surface (the flux surface that encloses 95% of the poloidal flux), ''q<sub>95</sub>''.		In [[Tokamak\|tokamaks]] with a [[divertor]], ''q'' approaches infinity at the [[separatrix]], so it is more useful to consider ''q'' just inside the separatrix. It is customary to use ''q'' at the 95% flux surface (the flux surface that encloses 95% of the poloidal flux), ''q<sub>95</sub>''.

Odstrcilt: Wrong definition of q95, it is 95% of poloidal flux (J. Wesson, Tokamaks pg. 411)

2022-03-03T20:31:34Z

Wrong definition of q95, it is 95% of poloidal flux (J. Wesson, Tokamaks pg. 411)

← Older revision		Revision as of 22:31, 3 March 2022
Line 25:		Line 25:
	Where the poloidal magnetic field <math>{B_\theta}</math> is mostly produced by a toroidal plasma current. The principal significance of the safety factor ''q'' is that if <math>q \leq 2</math> at the last closed flux surface (the edge), the plasma is [[:Wikipedia:Magnetohydrodynamics\|magnetohydrodynamically]] unstable.<ref>Wesson J 1997 Tokamaks 2nd edn (Oxford: Oxford University Press) p280 ISBN 0198509227</ref>		Where the poloidal magnetic field <math>{B_\theta}</math> is mostly produced by a toroidal plasma current. The principal significance of the safety factor ''q'' is that if <math>q \leq 2</math> at the last closed flux surface (the edge), the plasma is [[:Wikipedia:Magnetohydrodynamics\|magnetohydrodynamically]] unstable.<ref>Wesson J 1997 Tokamaks 2nd edn (Oxford: Oxford University Press) p280 ISBN 0198509227</ref>

	In [[Tokamak\|tokamaks]] with a [[divertor]], ''q'' approaches infinity at the [[separatrix]], so it is more useful to consider ''q'' just inside the separatrix. It is customary to use ''q'' at the 95% flux surface (the flux surface that encloses 95% of the ~~toroidal~~ flux), ''q<sub>95</sub>''.		In [[Tokamak\|tokamaks]] with a [[divertor]], ''q'' approaches infinity at the [[separatrix]], so it is more useful to consider ''q'' just inside the separatrix. It is customary to use ''q'' at the 95% flux surface (the flux surface that encloses 95% of the poloidal flux), ''q<sub>95</sub>''.

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

JuanMGomez at 18:35, 13 April 2015

2015-04-13T18:35:50Z

← Older revision		Revision as of 20:35, 13 April 2015
Line 1:		Line 1:
	The rotational transform (or field line pitch) ''ι/2π'' is defined as the ~~mean number of toroidal transits (''n'') divided by the mean~~ number of poloidal transits ~~(''m'')~~ of a field line on a toroidal flux surface.		The rotational transform (or field line pitch) ''ι/2π'' is defined as the number of poloidal transits per single toroidal transit of a field line on a toroidal flux surface.
	The definition can be relaxed somewhat to include field lines moving in a spatial volume between two nested toroidal surfaces (e.g., a stochastic field region).		The definition can be relaxed somewhat to include field lines moving in a spatial volume between two nested toroidal surfaces (e.g., a stochastic field region).

Admin: /* Safety factor */

2014-06-11T07:25:07Z

Safety factor

← Older revision		Revision as of 09:25, 11 June 2014
Line 12:		Line 12:

	In [[Tokamak\|tokamak]] research, the quantity ''q = 2π/ι'' is preferred (called the "safety factor").		In [[Tokamak\|tokamak]] research, the quantity ''q = 2π/ι'' is preferred (called the "safety factor").
	In a circular ~~[[Tokamak\|~~tokamak]],		In a circular tokamak,
	the equations of a field line on the flux surface are, approximately:		the equations of a field line on the flux surface are, approximately:
	<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref>		<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref>
Line 25:		Line 25:
	Where the poloidal magnetic field <math>{B_\theta}</math> is mostly produced by a toroidal plasma current. The principal significance of the safety factor ''q'' is that if <math>q \leq 2</math> at the last closed flux surface (the edge), the plasma is [[:Wikipedia:Magnetohydrodynamics\|magnetohydrodynamically]] unstable.<ref>Wesson J 1997 Tokamaks 2nd edn (Oxford: Oxford University Press) p280 ISBN 0198509227</ref>		Where the poloidal magnetic field <math>{B_\theta}</math> is mostly produced by a toroidal plasma current. The principal significance of the safety factor ''q'' is that if <math>q \leq 2</math> at the last closed flux surface (the edge), the plasma is [[:Wikipedia:Magnetohydrodynamics\|magnetohydrodynamically]] unstable.<ref>Wesson J 1997 Tokamaks 2nd edn (Oxford: Oxford University Press) p280 ISBN 0198509227</ref>

	In [[Tokamak\|tokamaks]] with a [[divertor]], ''q'' approaches infinity at the [[separatrix]], so it is more useful to consider ''q'' just inside the separatrix. It is customary to use ''q'' at the 95% flux surface (''q<sub>95</sub>'').		In [[Tokamak\|tokamaks]] with a [[divertor]], ''q'' approaches infinity at the [[separatrix]], so it is more useful to consider ''q'' just inside the separatrix. It is customary to use ''q'' at the 95% flux surface (the flux surface that encloses 95% of the toroidal flux), ''q<sub>95</sub>''.

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

Admin: /* Safety factor */

2013-05-07T14:55:53Z

Safety factor

← Older revision		Revision as of 16:55, 7 May 2013
Line 25:		Line 25:
	Where the poloidal magnetic field <math>{B_\theta}</math> is mostly produced by a toroidal plasma current. The principal significance of the safety factor ''q'' is that if <math>q \leq 2</math> at the last closed flux surface (the edge), the plasma is [[:Wikipedia:Magnetohydrodynamics\|magnetohydrodynamically]] unstable.<ref>Wesson J 1997 Tokamaks 2nd edn (Oxford: Oxford University Press) p280 ISBN 0198509227</ref>		Where the poloidal magnetic field <math>{B_\theta}</math> is mostly produced by a toroidal plasma current. The principal significance of the safety factor ''q'' is that if <math>q \leq 2</math> at the last closed flux surface (the edge), the plasma is [[:Wikipedia:Magnetohydrodynamics\|magnetohydrodynamically]] unstable.<ref>Wesson J 1997 Tokamaks 2nd edn (Oxford: Oxford University Press) p280 ISBN 0198509227</ref>

	In [[Tokamak\|tokamaks]] with a [[divertor]], ''q'' approaches infinity at the [[separatrix]], so it is more useful to consider ''q'' just inside the separatrix. Is is customary to use ''q'' at the 95% flux surface (''q<sub>95</sub>'').		In [[Tokamak\|tokamaks]] with a [[divertor]], ''q'' approaches infinity at the [[separatrix]], so it is more useful to consider ''q'' just inside the separatrix. It is customary to use ''q'' at the 95% flux surface (''q<sub>95</sub>'').

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

Admin: revert vandalism

2011-07-02T10:51:41Z

revert vandalism

← Older revision		Revision as of 12:51, 2 July 2011
Line 1:		Line 1:
	~~Wow~~, ~~thats~~ a ~~really cleevr way~~ of ~~thinking about~~ it!		The rotational transform (or field line pitch) ''ι/2π'' is defined as the mean number of toroidal transits (''n'') divided by the mean number of poloidal transits (''m'') of a field line on a toroidal flux surface.
			The definition can be relaxed somewhat to include field lines moving in a spatial volume between two nested toroidal surfaces (e.g., a stochastic field region).

			Assuming the existence of toroidally nested magnetic [[Flux surface\|flux surfaces]], the rotational transform on such a surface may also be defined as
			<ref>[http://link.aps.org/doi/10.1103/RevModPhys.76.1071 A.H. Boozer, ''Physics of magnetically confined plasmas'', Rev. Mod. Phys. '''76''' (2004) 1071]</ref>

			:<math>\frac{\iota}{2 \pi} = \frac{d \psi}{d \Phi}</math>

			where ''ψ'' is the poloidal magnetic flux, and Φ the toroidal magnetic flux.

			== Safety factor ==

			In [[Tokamak\|tokamak]] research, the quantity ''q = 2π/ι'' is preferred (called the "safety factor").
			In a circular [[Tokamak\|tokamak]],
			the equations of a field line on the flux surface are, approximately:
			<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref>

			:<math>\frac{r d\theta}{B_\theta} = \frac{Rd\varphi}{B_\varphi}</math>

			where <math>\phi</math> and ''θ'' are the [[Toroidal coordinates\|toroidal and poloidal angles]], respectively.
			Thus <math>q = m/n = \left \langle d\varphi /d\theta \right \rangle </math> can be approximated by

			:<math>q \simeq \frac{r B_\varphi}{R B_\theta}</math>

			Where the poloidal magnetic field <math>{B_\theta}</math> is mostly produced by a toroidal plasma current. The principal significance of the safety factor ''q'' is that if <math>q \leq 2</math> at the last closed flux surface (the edge), the plasma is [[:Wikipedia:Magnetohydrodynamics\|magnetohydrodynamically]] unstable.<ref>Wesson J 1997 Tokamaks 2nd edn (Oxford: Oxford University Press) p280 ISBN 0198509227</ref>

			In [[Tokamak\|tokamaks]] with a [[divertor]], ''q'' approaches infinity at the [[separatrix]], so it is more useful to consider ''q'' just inside the separatrix. Is is customary to use ''q'' at the 95% flux surface (''q<sub>95</sub>'').

			== See also ==

			* [[Magnetic island]]
			* [[Magnetic shear]]

			== References ==
			<references />

Admin: Reverted edits by 77.91.158.34 (Talk) to last revision by 113.28.121.29

2011-07-02T10:46:52Z

Reverted edits by 77.91.158.34 (Talk) to last revision by 113.28.121.29

← Older revision		Revision as of 12:46, 2 July 2011
Line 1:		Line 1:
	~~I suppsoe that sounds and smells just~~ about ~~right.~~		Wow, thats a really cleevr way of thinking about it!

77.91.158.34: mXQmkMeRNKXK

2011-07-02T10:20:01Z

mXQmkMeRNKXK

← Older revision		Revision as of 12:20, 2 July 2011
Line 1:		Line 1:
	~~Wow, thats a really cleevr way of thinking~~ about ~~it!~~		I suppsoe that sounds and smells just about right.

113.28.121.29: ZjARcMwjq

2011-07-02T08:49:46Z

ZjARcMwjq

← Older revision		Revision as of 10:49, 2 July 2011
Line 1:		Line 1:
	~~A mliolin thanks for posting this information.~~		Wow, thats a really cleevr way of thinking about it!

200.101.82.216: gVBrguGWNKGWsgkftpN

2011-07-02T08:48:59Z

gVBrguGWNKGWsgkftpN

← Older revision		Revision as of 10:48, 2 July 2011
Line 1:		Line 1:
	The rotational transform (or field line pitch) ''ι/2π'' is defined as the mean number of toroidal transits (''n'') divided by the mean number of poloidal transits (''m'') of a field line on a toroidal flux surface.		A mliolin thanks for posting this information.
	~~The definition can be relaxed somewhat to include field lines moving in a spatial volume between two nested toroidal surfaces (e.g., a stochastic field region).~~

	~~Assuming the existence of toroidally nested magnetic [[Flux surface\|flux surfaces]], the rotational transform on such a surface may also be defined as~~
	~~<ref>[http://link.aps.org/doi/10.1103/RevModPhys.76.1071~~ A.~~H. Boozer, ''Physics of magnetically confined plasmas'', Rev. Mod. Phys. '''76''' (2004) 1071]</ref>~~

	~~:<math>\frac{\iota}{2 \pi} = \frac{d \psi}{d \Phi}</math>~~

	~~where ''ψ'' is the poloidal magnetic flux, and Φ the toroidal magnetic flux.~~

	~~== Safety factor ==~~

	~~In [[Tokamak\|tokamak]] research, the quantity ''q = 2π/ι'' is preferred (called the "safety factor").~~
	~~In a circular [[Tokamak\|tokamak]],~~
	~~the equations of a field line on the flux surface are, approximately:~~
	~~<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref>~~

	~~:<math>\frac{r d\theta}{B_\theta} = \frac{Rd\varphi}{B_\varphi}</math>~~

	~~where <math>\phi</math> and ''θ'' are the [[Toroidal coordinates\|toroidal and poloidal angles]], respectively.~~
	~~Thus <math>q = m/n = \left \langle d\varphi /d\theta \right \rangle </math> can be approximated by~~

	~~:<math>q \simeq \frac{r B_\varphi}{R B_\theta}</math>~~

	Where the poloidal magnetic field <math>{B_\theta}</math> is mostly produced by a toroidal plasma current. The principal significance of the safety factor ''q'' is that if <math>q \leq 2</math> at the last closed flux surface (the edge), the plasma is [[:Wikipedia:Magnetohydrodynamics\|magnetohydrodynamically]] unstable.<ref>Wesson J 1997 Tokamaks 2nd edn (Oxford: Oxford University Press) p280 ISBN 0198509227</ref>

	In [[Tokamak\|tokamaks]] with a [[divertor]], ''q'' approaches infinity at the [[separatrix]], so it is more useful to consider ''q'' just inside the separatrix. Is is customary to use ''q'' at the 95% flux surface (''q<sub>95</sub>'').

	~~== See also ==~~

	* [[Magnetic island]]
	* [[Magnetic shear]]

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