Connection length - Revision history

Admin at 10:36, 26 January 2023

2023-01-26T10:36:03Z

← Older revision		Revision as of 12:36, 26 January 2023
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	Assuming <math>B_\phi \gg B_\theta</math>,		Assuming <math>B_\phi \gg B_\theta</math>,
	one has <math>\sin(\alpha) \simeq \tan(\alpha)</math>, so that		one has <math>\sin(\alpha) \simeq \tan(\alpha)</math>, so that
	<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>L = 2 \pi r \frac{B_\phi}{B_\theta} = 2 \pi R q</math>		:<math>L = 2 \pi r \frac{B_\phi}{B_\theta} = 2 \pi R q</math>

Admin at 12:14, 17 April 2015

2015-04-17T12:14:42Z

← Older revision		Revision as of 14:14, 17 April 2015
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	In a circular [[tokamak]], the [[Toroidal coordinates\|poloidal circumference]] is ''2πr''.		In a circular [[tokamak]], the [[Toroidal coordinates\|poloidal circumference]] is ''2πr''.
	The connection length is ''L = 2πr/sin(α)'',		The connection length is <math>L = 2\pi r/\sin(\alpha)</math>,
	where ~~''&~~alpha~~;''~~ is the pitch angle of the field line, namely		where <math>\alpha</math> is the pitch angle of the field line, namely
	''tan(α) = ~~B<sub>&~~theta;</~~sub>/B<sub>&~~phi;</~~sub~~>''.		<math>\tan(\alpha) = B_\theta/B_\phi</math>.
	Assuming ~~''B~~<~~sub~~>&phi~~;</sub> >> B<sub>&~~theta;</~~sub~~>'',		Assuming <math>B_\phi \gg B_\theta</math>,
	one has ''sin(α) ~~&sim;~~ tan(α)'', so that		one has <math>\sin(\alpha) \simeq \tan(\alpha)</math>, so that
	<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>L = 2 \pi r \frac{B_\phi}{B_\theta} = 2 \pi R q</math>		:<math>L = 2 \pi r \frac{B_\phi}{B_\theta} = 2 \pi R q</math>

	where q is the [[Rotational transform\|safety factor]], approximated by		where ''q'' is the [[Rotational transform\|safety factor]], approximated by
	''q = r ~~B<sub>&~~phi~~;</sub>~~ / R ~~B<sub>&~~theta;</~~sub~~>''.		<math>q = r B_\phi / R B_\theta</math>.

	== Open field lines ==		== Open field lines ==

Admin at 15:17, 10 August 2012

2012-08-10T15:17:06Z

← Older revision		Revision as of 17:17, 10 August 2012
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	== Closed field lines ==		== Closed field lines ==

	In a toroidally confined plasma, inside the [[~~Last Closed~~ Flux surface\|Flux Surface]], the connection length		In a toroidally confined plasma, inside the [[Flux surface\|Last Closed Flux Surface]], the connection length
	is commonly defined as the length, measured along the magnetic field,		is commonly defined as the length, measured along the magnetic field,
	to complete a poloidal turn.		to complete a poloidal turn.

	In a circular [[~~Tokamak\|~~tokamak]], the [[Toroidal coordinates\|poloidal circumference]] is ''2πr''.		In a circular [[tokamak]], the [[Toroidal coordinates\|poloidal circumference]] is ''2πr''.
	The connection length is ''L = 2πr/sin(α)'',		The connection length is ''L = 2πr/sin(α)'',
	where ''α'' is the pitch angle of the field line, namely		where ''α'' is the pitch angle of the field line, namely

Admin at 15:16, 10 August 2012

2012-08-10T15:16:18Z

← Older revision		Revision as of 17:16, 10 August 2012
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	== Closed field lines ==		== Closed field lines ==

	In a toroidally confined plasma, inside the Last Closed [[Flux surface\|Flux Surface]], the connection length		In a toroidally confined plasma, inside the [[Last Closed Flux surface\|Flux Surface]], the connection length
	is commonly defined as the length, measured along the magnetic field,		is commonly defined as the length, measured along the magnetic field,
	to complete a poloidal turn.		to complete a poloidal turn.

Admin: /* Closed field lines */

2012-08-10T10:28:22Z

Closed field lines

← Older revision		Revision as of 12:28, 10 August 2012
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	== Closed field lines ==		== Closed field lines ==

	~~Inside~~ the Last Closed Flux Surface, the connection length		In a toroidally confined plasma, inside the Last Closed [[Flux surface\|Flux Surface]], the connection length
	is commonly defined as the length, measured along the magnetic field,		is commonly defined as the length, measured along the magnetic field,
	to complete a poloidal turn.		to complete a poloidal turn.

Admin: /* Closed field lines */

2010-07-30T14:23:14Z

Closed field lines

← Older revision		Revision as of 16:23, 30 July 2010
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	:<math>L = 2 \pi r \frac{B_\phi}{B_\theta} = 2 \pi R q</math>		:<math>L = 2 \pi r \frac{B_\phi}{B_\theta} = 2 \pi R q</math>

	where q is the [[~~Magnetic shear~~\|safety factor]], approximated by		where q is the [[Rotational transform\|safety factor]], approximated by
	''q = r B<sub>φ</sub> / R B<sub>θ</sub>''.		''q = r B<sub>φ</sub> / R B<sub>θ</sub>''.

Admin at 12:39, 30 July 2010

2010-07-30T12:39:23Z

← Older revision		Revision as of 14:39, 30 July 2010
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	to complete a poloidal turn.		to complete a poloidal turn.

	In a circular tokamak, the poloidal circumference is ''2πr''.		In a circular [[Tokamak\|tokamak]], the [[Toroidal coordinates\|poloidal circumference]] is ''2πr''.
	The connection length is ''L = 2πr/sin(α)'',		The connection length is ''L = 2πr/sin(α)'',
	where ''α'' is the pitch angle of the field line, namely		where ''α'' is the pitch angle of the field line, namely

Admin: Created page with 'The connection length is understood to be the distance between two points, measured along a magnetic field line passing through these points. In the fusion context, a distincti…'

2010-07-30T12:35:01Z

Created page with 'The connection length is understood to be the distance between two points, measured along a magnetic field line passing through these points. In the fusion context, a distincti…'

New page

The connection length is understood to be the distance between two points,
measured along a magnetic field line passing through these points.

In the fusion context, a distinction is made between closed field lines
(inside the [[Flux surface|Last Closed Flux Surface]]) and open field lines (outside).

== Closed field lines ==

Inside the Last Closed Flux Surface, the connection length
is commonly defined as the length, measured along the magnetic field,
to complete a poloidal turn.

In a circular tokamak, the poloidal circumference is ''2πr''.
The connection length is ''L = 2πr/sin(α)'',
where ''α'' is the pitch angle of the field line, namely
''tan(α) = Bθ/Bφ''.
Assuming ''Bφ >> Bθ'',
one has ''sin(α) &sim; tan(α)'', so that
<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref>

:<math>L = 2 \pi r \frac{B_\phi}{B_\theta} = 2 \pi R q</math>

where q is the [[Magnetic shear|safety factor]], approximated by
''q = r Bφ / R Bθ''.

== Open field lines ==

Outside Last Closed Flux Surface, the connection length associated with a given point is defined as
the shortest distance from that point to any material surface measured along the field line
through that point.

== References ==
<references />