Flux tube - Revision history

Admin at 10:29, 26 January 2023

2023-01-26T10:29:48Z

← Older revision		Revision as of 12:29, 26 January 2023
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	</math>		</math>
	This has the important consequence that a given volume of plasma contained within a flux tube ''remains'' inside the flux tube as it is advected, twisted, and stretched by the fluid flow.		This has the important consequence that a given volume of plasma contained within a flux tube ''remains'' inside the flux tube as it is advected, twisted, and stretched by the fluid flow.
	<ref>A. Dinklage, ''Plasma physics: confinement, transport and collective effects'', Vol. 670 of Lecture notes in physics, Springer (2005) ISBN 3540252746</ref>		<ref>A. Dinklage, ''Plasma physics: confinement, transport and collective effects'', Vol. 670 of Lecture notes in physics, Springer (2005) {{ISBN\|3540252746}}</ref>
	<ref>W.D. D'haeseleer et al, ''Flux coordinates and Magnetic Field Structure'', Springer-Verlag ISBN 3-540-52419-3</ref>		<ref>W.D. D'haeseleer et al, ''Flux coordinates and Magnetic Field Structure'', Springer-Verlag {{ISBN\|3-540-52419-3}}</ref>
	This implies that the topology of the flux tube cannot change due to the fluid flow.		This implies that the topology of the flux tube cannot change due to the fluid flow.
	Stated differently, the magnetic flux contained in a volume element of the plasma is carried along unchanged as the element moves.		Stated differently, the magnetic flux contained in a volume element of the plasma is carried along unchanged as the element moves.

Admin at 06:36, 24 August 2011

2011-08-24T06:36:31Z

← Older revision		Revision as of 08:36, 24 August 2011
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	</math>		</math>
	This has the important consequence that a given volume of plasma contained within a flux tube ''remains'' inside the flux tube as it is advected, twisted, and stretched by the fluid flow.		This has the important consequence that a given volume of plasma contained within a flux tube ''remains'' inside the flux tube as it is advected, twisted, and stretched by the fluid flow.
	<ref ~~name="~~Dinklage" />		<ref>A. Dinklage, ''Plasma physics: confinement, transport and collective effects'', Vol. 670 of Lecture notes in physics, Springer (2005) ISBN 3540252746</ref>
	<ref ~~name="Dhaeseleer"~~ />		<ref>W.D. D'haeseleer et al, ''Flux coordinates and Magnetic Field Structure'', Springer-Verlag ISBN 3-540-52419-3</ref>
	This implies that the topology of the flux tube cannot change due to the fluid flow.		This implies that the topology of the flux tube cannot change due to the fluid flow.
	Stated differently, the magnetic flux contained in a volume element of the plasma is carried along unchanged as the element moves.		Stated differently, the magnetic flux contained in a volume element of the plasma is carried along unchanged as the element moves.
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	== References ==		== References ==
	<references>		<references />
	~~<ref name="Dinklage">A. Dinklage, ''Plasma physics: confinement, transport and collective effects'', Vol. 670 of Lecture notes in physics, Springer (2005) ISBN 3540252746<~~/~~ref>~~
	~~<ref name="Dhaeseleer">W.D. D'haeseleer et al, ''Flux coordinates and Magnetic Field Structure'', Springer-Verlag ISBN 3-540-52419-3</ref>~~
	~~</references~~>

Admin at 06:36, 24 August 2011

2011-08-24T06:36:00Z

← Older revision		Revision as of 08:36, 24 August 2011
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	</math>		</math>
	This has the important consequence that a given volume of plasma contained within a flux tube ''remains'' inside the flux tube as it is advected, twisted, and stretched by the fluid flow.		This has the important consequence that a given volume of plasma contained within a flux tube ''remains'' inside the flux tube as it is advected, twisted, and stretched by the fluid flow.
	<ref~~>A.~~ Dinklage~~, ''Plasma physics: confinement, transport and collective effects'', Vol. 670 of Lecture notes in physics, Springer (2005) ISBN 3540252746<~~/~~ref~~>		<ref name="Dinklage" />
	<ref~~>W.D. D'haeseleer et al, ''Flux coordinates and Magnetic Field Structure'', Springer-Verlag ISBN 3-540-52419-3<~~/~~ref~~>		<ref name="Dhaeseleer" />
	This implies that the topology of the flux tube cannot change due to the fluid flow.		This implies that the topology of the flux tube cannot change due to the fluid flow.
	Stated differently, the magnetic flux contained in a volume element of the plasma is carried along unchanged as the element moves.		Stated differently, the magnetic flux contained in a volume element of the plasma is carried along unchanged as the element moves.
Line 28:		Line 28:

	== References ==		== References ==
	<references />		<references>
			<ref name="Dinklage">A. Dinklage, ''Plasma physics: confinement, transport and collective effects'', Vol. 670 of Lecture notes in physics, Springer (2005) ISBN 3540252746</ref>
			<ref name="Dhaeseleer">W.D. D'haeseleer et al, ''Flux coordinates and Magnetic Field Structure'', Springer-Verlag ISBN 3-540-52419-3</ref>
			</references>

Admin at 09:14, 22 August 2011

2011-08-22T09:14:29Z

← Older revision		Revision as of 11:14, 22 August 2011
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	== Flux conservation ==		== Flux conservation ==

	In the framework of [[Ideal Magneto-Hydrodynamics]], the MHD kinematic equation reads:		In the framework of [[Ideal Magneto-Hydrodynamics]], the MHD kinematic equation reads (in the perfectly conducting limit, <math>\sigma \to \infty</math>):
	:<math>		:<math>
	\frac{\partial \vec B}{\partial t} = \vec \nabla \times (\vec v \times \vec B)		\frac{\partial \vec B}{\partial t} = \vec \nabla \times (\vec v \times \vec B)
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	This has the important consequence that a given volume of plasma contained within a flux tube ''remains'' inside the flux tube as it is advected, twisted, and stretched by the fluid flow.		This has the important consequence that a given volume of plasma contained within a flux tube ''remains'' inside the flux tube as it is advected, twisted, and stretched by the fluid flow.
	<ref>A. Dinklage, ''Plasma physics: confinement, transport and collective effects'', Vol. 670 of Lecture notes in physics, Springer (2005) ISBN 3540252746</ref>		<ref>A. Dinklage, ''Plasma physics: confinement, transport and collective effects'', Vol. 670 of Lecture notes in physics, Springer (2005) ISBN 3540252746</ref>
			<ref>W.D. D'haeseleer et al, ''Flux coordinates and Magnetic Field Structure'', Springer-Verlag ISBN 3-540-52419-3</ref>
	This implies that the topology of the flux tube cannot change due to the fluid flow.		This implies that the topology of the flux tube cannot change due to the fluid flow.
	Stated differently, the magnetic flux contained in a volume element of the plasma is carried along unchanged as the element moves.		Stated differently, the magnetic flux contained in a volume element of the plasma is carried along unchanged as the element moves.
	Also, two plasma elements connected by a field line will always remain connected by that same field line as the plasma flows.		Also, two plasma elements connected by a field line will always remain connected by that same field line as the plasma flows.
	This is sometimes known as the ''Frozen ~~Flow~~ Hypothesis''.		This is sometimes known as the ''Frozen Flux Hypothesis''.

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

Admin: /* Flux conservation */

2011-08-10T16:35:52Z

Flux conservation

← Older revision		Revision as of 18:35, 10 August 2011
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	== Flux conservation ==		== Flux conservation ==

	In the framework of Ideal Magneto-Hydrodynamics, the MHD kinematic equation reads:		In the framework of [[Ideal Magneto-Hydrodynamics]], the MHD kinematic equation reads:
	:<math>		:<math>
	\frac{\partial \vec B}{\partial t} = \vec \nabla \times (\vec v \times \vec B)		\frac{\partial \vec B}{\partial t} = \vec \nabla \times (\vec v \times \vec B)

Admin at 16:06, 10 August 2011

2011-08-10T16:06:48Z

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 Contrary to [[Magnetic island|magnetic islands]], that are bounded by a [[Separatrix|separatrix]], there is not necessarily any essential dynamical difference between the regions inside and outside of a flux tube.
 == See also ==
 * [[:Wikipedia:Flux tube]]

Admin at 17:14, 7 August 2011

2011-08-07T17:14:17Z

← Older revision		Revision as of 19:14, 7 August 2011
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			[[File:Flux tube.png\|300px\|thumb\|right\|Sketch of a flux tube with magnetic field lines in red]]
	A flux tube is a region of space bounded by a [[Flux surface\|flux surface]], i.e., a surface such that the magnetic field is everywhere perpendicular to the surface normal.		A flux tube is a region of space bounded by a [[Flux surface\|flux surface]], i.e., a surface such that the magnetic field is everywhere perpendicular to the surface normal.

Admin at 09:55, 7 August 2011

2011-08-07T09:55:16Z

← Older revision		Revision as of 11:55, 7 August 2011
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	Contrary to [[Magnetic island\|magnetic islands]], that are bounded by a [[Separatrix\|separatrix]], there is not necessarily any essential dynamical difference between the regions inside and outside of a flux tube.		Contrary to [[Magnetic island\|magnetic islands]], that are bounded by a [[Separatrix\|separatrix]], there is not necessarily any essential dynamical difference between the regions inside and outside of a flux tube.

			== See also ==

			* [[:Wikipedia:Flux tube]]

Admin: Created page with 'A flux tube is a region of space bounded by a flux surface, i.e., a surface such that the magnetic field is everywhere perpendicular to the surface normal. In […'

2011-08-07T09:48:01Z

Created page with 'A flux tube is a region of space bounded by a flux surface, i.e., a surface such that the magnetic field is everywhere perpendicular to the surface normal. In […'

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A flux tube is a region of space bounded by a [[Flux surface|flux surface]], i.e., a surface such that the magnetic field is everywhere perpendicular to the surface normal.

In [[Flux coordinates|flux coordinates]], such a surface has cylindrical topology.
In a closed magnetic field region, the topology is toroidal.

The magnetic flux traversing any cross sectional area of a flux tube is invariant.

Contrary to [[Magnetic island|magnetic islands]], that are bounded by a [[Separatrix|separatrix]], there is not necessarily any essential dynamical difference between the regions inside and outside of a flux tube.