Anomalous transport - Revision history

Admin at 10:37, 26 January 2023

2023-01-26T10:37:14Z

Admin: Reverted edits by Otihizuv (Talk) to last revision by Admin

2010-11-24T11:20:50Z

Reverted edits by Otihizuv (Talk) to last revision by Admin

Otihizuv at 00:22, 24 November 2010

2010-11-24T00:22:24Z

Admin at 17:09, 25 July 2010

2010-07-25T17:09:23Z

← Older revision		Revision as of 19:09, 25 July 2010
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	<ref name="Freidberg" />		<ref name="Freidberg" />
	the cited [[Scaling law\|scaling laws]] can be rewritten in terms of the temperature dependence (eliminating the heating power dependence).		the cited [[Scaling law\|scaling laws]] can be rewritten in terms of the temperature dependence (eliminating the heating power dependence).
	Then, classical and neoclassical estimates would predict that the confinement increases with ''T'' (namely: ''τ<sub>E</sub>'' &prop; ''T<sup>0.5</sup>'', associated with collisionality).		Then, classical and neoclassical estimates would predict that the confinement increases with ''T'' (namely: ''τ<sub>E</sub>'' &prop; ''T<sup>0.5</sup>'', associated with [[Collisionality\|collisionality]]).
	However, the experimental scalings give a ''decrease'' with ''T''		However, the experimental scalings give a ''decrease'' with ''T''
	(namely: ''τ<sub>E</sub>'' &prop; ''T<sup>α</sup>'' with '' α'' < -1).		(namely: ''τ<sub>E</sub>'' &prop; ''T<sup>α</sup>'' with '' α'' < -1).

87.220.93.209: /* Physical mechanism */

2009-09-28T10:15:23Z

Physical mechanism

← Older revision		Revision as of 12:15, 28 September 2009
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	* Ion Temperature Gradient (ITG) instabilities		* Ion Temperature Gradient (ITG) instabilities
	* Electron Temperature Gradient (ETG) instabilities		* Electron Temperature Gradient (ETG) instabilities
	* Collisionless Trapped Electron Modes (TEM) <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.95.085001 F. Ryter et al, ''Experimental Study of Trapped-Electron-Mode Properties in Tokamaks: Threshold and Stabilization by Collisions'', Phys. Rev. Lett. '''95''' (2005) 085001]</ref>		* Collisionless Trapped Electron Modes (TEM) <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.33.1329 B. Coppi and G. Rewoldt, ''New Trapped-Electron Instability'', Phys. Rev. Lett. '''33''' (1974) 1329 - 1332]</ref> <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.95.085001 F. Ryter et al, ''Experimental Study of Trapped-Electron-Mode Properties in Tokamaks: Threshold and Stabilization by Collisions'', Phys. Rev. Lett. '''95''' (2005) 085001]</ref>
	* Dissipative Trapped Electron Modes (DTEM)		* Dissipative Trapped Electron Modes (DTEM)
	''(to be completed; references needed)''		''(to be completed; references needed)''

Admin: /* Physical mechanism */

2009-09-27T16:58:29Z

Physical mechanism

← Older revision		Revision as of 18:58, 27 September 2009
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	The plasma potentially produces a plethora of such instabilities, due to the fact that it is in a state far from thermodynamic equilibrium, with steep density, temperature, and pressure gradients.		The plasma potentially produces a plethora of such instabilities, due to the fact that it is in a state far from thermodynamic equilibrium, with steep density, temperature, and pressure gradients.
	The most likely candidates involved in generating the observed anomalous transport are:		The most likely candidates involved in generating the observed anomalous transport are:
			<ref>J. Weiland, ''Collective modes in inhomogeneous plasma: kinetic and advanced fluid theory'', Plasma physics series, CRC Press (2000) ISBN 0750305894</ref>
	* Ion Temperature Gradient (ITG) instabilities		* Ion Temperature Gradient (ITG) instabilities
	* Electron Temperature Gradient (ETG) instabilities		* Electron Temperature Gradient (ETG) instabilities

Admin: /* Physical mechanism */

2009-09-27T15:22:50Z

Physical mechanism

← Older revision		Revision as of 17:22, 27 September 2009
Line 45:		Line 45:
	* Ion Temperature Gradient (ITG) instabilities		* Ion Temperature Gradient (ITG) instabilities
	* Electron Temperature Gradient (ETG) instabilities		* Electron Temperature Gradient (ETG) instabilities
	* Trapped Electron Modes (TEM) <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.95.085001 F. Ryter et al, ''Experimental Study of Trapped-Electron-Mode Properties in Tokamaks: Threshold and Stabilization by Collisions'', Phys. Rev. Lett. '''95''' (2005) 085001]</ref>		* Collisionless Trapped Electron Modes (TEM) <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.95.085001 F. Ryter et al, ''Experimental Study of Trapped-Electron-Mode Properties in Tokamaks: Threshold and Stabilization by Collisions'', Phys. Rev. Lett. '''95''' (2005) 085001]</ref>
	* Dissipative Trapped Electron Modes (DTEM)		* Dissipative Trapped Electron Modes (DTEM)
	''(to be completed; references needed)''		''(to be completed; references needed)''

87.220.93.218: /* Physical mechanism */

2009-09-27T15:16:32Z

Physical mechanism

← Older revision		Revision as of 17:16, 27 September 2009
Line 45:		Line 45:
	* Ion Temperature Gradient (ITG) instabilities		* Ion Temperature Gradient (ITG) instabilities
	* Electron Temperature Gradient (ETG) instabilities		* Electron Temperature Gradient (ETG) instabilities
			* Trapped Electron Modes (TEM) <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.95.085001 F. Ryter et al, ''Experimental Study of Trapped-Electron-Mode Properties in Tokamaks: Threshold and Stabilization by Collisions'', Phys. Rev. Lett. '''95''' (2005) 085001]</ref>
	* Dissipative Trapped Electron Modes (DTEM)		* Dissipative Trapped Electron Modes (DTEM)
	''(to be completed; references needed)''		''(to be completed; references needed)''

Admin: /* Physical mechanism */

2009-09-26T14:53:55Z

Physical mechanism

← Older revision		Revision as of 16:53, 26 September 2009
Line 45:		Line 45:
	* Ion Temperature Gradient (ITG) instabilities		* Ion Temperature Gradient (ITG) instabilities
	* Electron Temperature Gradient (ETG) instabilities		* Electron Temperature Gradient (ETG) instabilities
	* ~~Drift~~ Trapped Electron Modes (DTEM)		* Dissipative Trapped Electron Modes (DTEM)
	''(to be completed; references needed)''		''(to be completed; references needed)''

Admin: /* Arguments in favour */

2009-09-21T16:55:32Z

Arguments in favour

← Older revision		Revision as of 18:55, 21 September 2009
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	<ref>[http://dx.doi.org/10.1088/0741-3335/36/5/002 J.W. Conner and H.R. Wilson, ''Survey of theories of anomalous transport'', Plasma Phys. Control. Fusion '''36''' (1994) 719-795]</ref>		<ref>[http://dx.doi.org/10.1088/0741-3335/36/5/002 J.W. Conner and H.R. Wilson, ''Survey of theories of anomalous transport'', Plasma Phys. Control. Fusion '''36''' (1994) 719-795]</ref>

	=== Arguments ~~in favour~~ ===		=== Arguments for ===

	An important argument suggesting that anomalous transport is important to the degree that it often dominates the total transport is the [[Scaling law\|scaling]] of transport with heating power and machine size.		An important argument suggesting that anomalous transport is important to the degree that it often dominates the total transport is the [[Scaling law\|scaling]] of transport with heating power and machine size.

← Older revision		Revision as of 12:37, 26 January 2023
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	The difference between actual transport and the Neoclassical expectation is called "[[:Wiktionary:anomaly\|anomalous]]" transport.		The difference between actual transport and the Neoclassical expectation is called "[[:Wiktionary:anomaly\|anomalous]]" transport.
	It is generally assumed that the anomalous component of transport is generated by turbulence driven by micro-instabilities.		It is generally assumed that the anomalous component of transport is generated by turbulence driven by micro-instabilities.
	<ref name="Freidberg">J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) ISBN 0521851076</ref>		<ref name="Freidberg">J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) {{ISBN\|0521851076}}</ref>

	== How important is turbulence? ==		== How important is turbulence? ==
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	It has been argued that turbulence cannot be responsible for a significant fraction of the anomalous component of transport, since that would lead to high resistivity (due to collisions), which contradicts experimental observation.		It has been argued that turbulence cannot be responsible for a significant fraction of the anomalous component of transport, since that would lead to high resistivity (due to collisions), which contradicts experimental observation.
	<ref>L.C. Woods, ''Theory of tokamak transport: new aspects for nuclear fusion reactor design'', John Wiley and Sons (2006) ISBN 3527406255</ref>		<ref>L.C. Woods, ''Theory of tokamak transport: new aspects for nuclear fusion reactor design'', John Wiley and Sons (2006) {{ISBN\|3527406255}}</ref>
	However, this argument fails to note that anomalous transport may consist of collective events (e.g., ''streamers''), which does not require an enhanced collisionality.		However, this argument fails to note that anomalous transport may consist of collective events (e.g., ''streamers''), which does not require an enhanced collisionality.
	As a side remark, this argument does show that the contribution of turbulence to transport is likely ''not'' of the diffusive type (see [[Non-diffusive transport]]).		As a side remark, this argument does show that the contribution of turbulence to transport is likely ''not'' of the diffusive type (see [[Non-diffusive transport]]).
Line 43:		Line 43:
	The plasma potentially produces a plethora of such instabilities, due to the fact that it is in a state far from thermodynamic equilibrium, with steep density, temperature, and pressure gradients.		The plasma potentially produces a plethora of such instabilities, due to the fact that it is in a state far from thermodynamic equilibrium, with steep density, temperature, and pressure gradients.
	The most likely candidates involved in generating the observed anomalous transport are:		The most likely candidates involved in generating the observed anomalous transport are:
	<ref>J. Weiland, ''Collective modes in inhomogeneous plasma: kinetic and advanced fluid theory'', Plasma physics series, CRC Press (2000) ISBN 0750305894</ref>		<ref>J. Weiland, ''Collective modes in inhomogeneous plasma: kinetic and advanced fluid theory'', Plasma physics series, CRC Press (2000) {{ISBN\|0750305894}}</ref>
	* Ion Temperature Gradient (ITG) instabilities		* Ion Temperature Gradient (ITG) instabilities
	* Electron Temperature Gradient (ETG) instabilities		* Electron Temperature Gradient (ETG) instabilities

← Older revision		Revision as of 13:20, 24 November 2010
Line 1:		Line 1:
	~~=[http://axuzexy.co.cc Page Is Unavailable Due To Site Maintenance, Please Visit Reserve Copy Page]=~~
	The best and most complete theory of transport in magnetically confined systems is the [[Neoclassical transport\|Neoclassical]] theory.		The best and most complete theory of transport in magnetically confined systems is the [[Neoclassical transport\|Neoclassical]] theory.
	However, it is found that transport often exceeds Neoclassical expectations by an order of magnitude or more (also see [[Non-diffusive transport]]).		However, it is found that transport often exceeds Neoclassical expectations by an order of magnitude or more (also see [[Non-diffusive transport]]).
	~~<~~ref~~>~~[http://dx.doi.org/10.1063/1.859358 A.J.Wootton et al, ''Fluctuations and anomalous transport in tokamaks'', Phys. Fluids B ''2'' (1990) 2879]~~<~~/ref~~>~~		<ref>[http://dx.doi.org/10.1063/1.859358 A.J.Wootton et al, ''Fluctuations and anomalous transport in tokamaks'', Phys. Fluids B ''2'' (1990) 2879]</ref>
	The difference between actual transport and the Neoclassical expectation is called ~~"~~[[:Wiktionary:anomaly\|anomalous]]~~"~~ transport.		The difference between actual transport and the Neoclassical expectation is called "[[:Wiktionary:anomaly\|anomalous]]" transport.
	It is generally assumed that the anomalous component of transport is generated by turbulence driven by micro-instabilities.		It is generally assumed that the anomalous component of transport is generated by turbulence driven by micro-instabilities.
	~~<~~ref name=~~"~~Freidberg~~">~~J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) ISBN 0521851076~~<~~/ref~~>~~		<ref name="Freidberg">J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) ISBN 0521851076</ref>

	== How important is turbulence? ==		== How important is turbulence? ==
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	In part, this may be because turbulent transport gives a variable contribution to transport (depending on local and global parameters), whereas Neoclassical transport is always present.		In part, this may be because turbulent transport gives a variable contribution to transport (depending on local and global parameters), whereas Neoclassical transport is always present.
	And in part, because no complete theory for anomalous transport is available.		And in part, because no complete theory for anomalous transport is available.
	~~<~~ref~~>~~[http://dx.doi.org/10.1088/0741-3335/36/5/002 J.W. Conner and H.R. Wilson, ''Survey of theories of anomalous transport'', Plasma Phys. Control. Fusion '''36''' (1994) 719-795]~~<~~/ref~~>~~		<ref>[http://dx.doi.org/10.1088/0741-3335/36/5/002 J.W. Conner and H.R. Wilson, ''Survey of theories of anomalous transport'', Plasma Phys. Control. Fusion '''36''' (1994) 719-795]</ref>

	=== Arguments for ===		=== Arguments for ===

	An important argument suggesting that anomalous transport is important to the degree that it often dominates the total transport is the [[Scaling law\|scaling]] of transport with heating power and machine size.		An important argument suggesting that anomalous transport is important to the degree that it often dominates the total transport is the [[Scaling law\|scaling]] of transport with heating power and machine size.
	~~<~~ref~~>~~[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, ''Progress in anomalous transport research in toroidal magnetic confinement devices'', IEEE Trans. Plasma Science '''25''', 1281 (1997)]~~<~~/ref~~>~~		<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, ''Progress in anomalous transport research in toroidal magnetic confinement devices'', IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>
	The phenomenon of [[Scaling law\|power degradation]], universally observed in all devices, is an indication that standard transport theories are inadequate to explain all transport, since these would not predict power degradation.		The phenomenon of [[Scaling law\|power degradation]], universally observed in all devices, is an indication that standard transport theories are inadequate to explain all transport, since these would not predict power degradation.
	Following Freidberg,		Following Freidberg,
	~~<~~ref name=~~"~~Freidberg~~"~~ /~~>~~		<ref name="Freidberg" />
	the cited [[Scaling law\|scaling laws]] can be rewritten in terms of the temperature dependence (eliminating the heating power dependence).		the cited [[Scaling law\|scaling laws]] can be rewritten in terms of the temperature dependence (eliminating the heating power dependence).
	Then, classical and neoclassical estimates would predict that the confinement increases with ''T'' (namely: ''&~~amp;~~tau;~~<~~sub~~>~~E~~<~~/sub~~>~~'' &~~amp;~~prop; ''T~~<~~sup~~>~~0.5~~<~~/sup~~>~~'', associated with [[Collisionality\|collisionality]]).		Then, classical and neoclassical estimates would predict that the confinement increases with ''T'' (namely: ''τ<sub>E</sub>'' &prop; ''T<sup>0.5</sup>'', associated with [[Collisionality\|collisionality]]).
	However, the experimental scalings give a ''decrease'' with ''T''		However, the experimental scalings give a ''decrease'' with ''T''
	(namely: ''&~~amp;~~tau;~~<~~sub~~>~~E~~<~~/sub~~>~~'' &~~amp;~~prop; ''T~~<~~sup&~~gt;&~~alpha;~~<~~/sup~~>~~'' with '' &~~amp;~~alpha;'' &~~amp;~~lt; -1).		(namely: ''τ<sub>E</sub>'' &prop; ''T<sup>α</sup>'' with '' α'' < -1).
	This unexpected behaviour is explained from increased turbulence levels (and enhanced transport) at higher values of (the gradients of) ''T''.		This unexpected behaviour is explained from increased turbulence levels (and enhanced transport) at higher values of (the gradients of) ''T''.

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	It has been argued that turbulence cannot be responsible for a significant fraction of the anomalous component of transport, since that would lead to high resistivity (due to collisions), which contradicts experimental observation.		It has been argued that turbulence cannot be responsible for a significant fraction of the anomalous component of transport, since that would lead to high resistivity (due to collisions), which contradicts experimental observation.
	~~<~~ref~~>~~L.C. Woods, ''Theory of tokamak transport: new aspects for nuclear fusion reactor design'', John Wiley and Sons (2006) ISBN 3527406255~~<~~/ref~~>~~		<ref>L.C. Woods, ''Theory of tokamak transport: new aspects for nuclear fusion reactor design'', John Wiley and Sons (2006) ISBN 3527406255</ref>
	However, this argument fails to note that anomalous transport may consist of collective events (e.g., ''streamers''), which does not require an enhanced collisionality.		However, this argument fails to note that anomalous transport may consist of collective events (e.g., ''streamers''), which does not require an enhanced collisionality.
	As a side remark, this argument does show that the contribution of turbulence to transport is likely ''not'' of the diffusive type (see [[Non-diffusive transport]]).		As a side remark, this argument does show that the contribution of turbulence to transport is likely ''not'' of the diffusive type (see [[Non-diffusive transport]]).
Line 44:		Line 43:
	The plasma potentially produces a plethora of such instabilities, due to the fact that it is in a state far from thermodynamic equilibrium, with steep density, temperature, and pressure gradients.		The plasma potentially produces a plethora of such instabilities, due to the fact that it is in a state far from thermodynamic equilibrium, with steep density, temperature, and pressure gradients.
	The most likely candidates involved in generating the observed anomalous transport are:		The most likely candidates involved in generating the observed anomalous transport are:
	~~<~~ref~~>~~J. Weiland, ''Collective modes in inhomogeneous plasma: kinetic and advanced fluid theory'', Plasma physics series, CRC Press (2000) ISBN 0750305894~~<~~/ref~~>~~		<ref>J. Weiland, ''Collective modes in inhomogeneous plasma: kinetic and advanced fluid theory'', Plasma physics series, CRC Press (2000) ISBN 0750305894</ref>
	* Ion Temperature Gradient (ITG) instabilities		* Ion Temperature Gradient (ITG) instabilities
	* Electron Temperature Gradient (ETG) instabilities		* Electron Temperature Gradient (ETG) instabilities
	* Collisionless Trapped Electron Modes (TEM) ~~<~~ref~~>~~[http://link.aps.org/doi/10.1103/PhysRevLett.33.1329 B. Coppi and G. Rewoldt, ''New Trapped-Electron Instability'', Phys. Rev. Lett. '''33''' (1974) 1329 - 1332]~~<~~/ref~~> <~~ref~~>~~[http://link.aps.org/doi/10.1103/PhysRevLett.95.085001 F. Ryter et al, ''Experimental Study of Trapped-Electron-Mode Properties in Tokamaks: Threshold and Stabilization by Collisions'', Phys. Rev. Lett. '''95''' (2005) 085001]~~<~~/ref~~>~~		* Collisionless Trapped Electron Modes (TEM) <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.33.1329 B. Coppi and G. Rewoldt, ''New Trapped-Electron Instability'', Phys. Rev. Lett. '''33''' (1974) 1329 - 1332]</ref> <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.95.085001 F. Ryter et al, ''Experimental Study of Trapped-Electron-Mode Properties in Tokamaks: Threshold and Stabilization by Collisions'', Phys. Rev. Lett. '''95''' (2005) 085001]</ref>
	* Dissipative Trapped Electron Modes (DTEM)		* Dissipative Trapped Electron Modes (DTEM)
	''(to be completed; references needed)''		''(to be completed; references needed)''
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	There are several answers to this question. Since all equations describing the motion of charged particles in fields are known, as well as the effects of collisions, detailed numerical (gyrokinetic) [[Plasma simulation\|simulations]] are possible.		There are several answers to this question. Since all equations describing the motion of charged particles in fields are known, as well as the effects of collisions, detailed numerical (gyrokinetic) [[Plasma simulation\|simulations]] are possible.
	~~<~~ref~~>~~[http://link.aps.org/doi/10.1103/PhysRevLett.77.71 A.M. Dimits et al, ''Scalings of Ion-Temperature-Gradient-Driven Anomalous Transport in Tokamaks'', Phys. Rev. Lett. '''77''' (1996) 71 - 74]~~<~~/ref~~>~~		<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.77.71 A.M. Dimits et al, ''Scalings of Ion-Temperature-Gradient-Driven Anomalous Transport in Tokamaks'', Phys. Rev. Lett. '''77''' (1996) 71 - 74]</ref>
	However, due to the enormous disparity between the minimum and maximum scales involved (gyration times vs. transport times, and the gyroradius vs. the machine size), this is a major challenge.		However, due to the enormous disparity between the minimum and maximum scales involved (gyration times vs. transport times, and the gyroradius vs. the machine size), this is a major challenge.

	An alternative approach is to model the net effect of turbulence without simulating the fine detail.		An alternative approach is to model the net effect of turbulence without simulating the fine detail.
	In doing so, it is not sufficient to introduce a simple additional ~~"~~turbulent diffusivity~~"~~, as this cannot possibly reproduce the observed global transport scaling behaviour.		In doing so, it is not sufficient to introduce a simple additional "turbulent diffusivity", as this cannot possibly reproduce the observed global transport scaling behaviour.
	It is probably necessary to use a [[Non-diffusive transport\|non-diffusive]] description,		It is probably necessary to use a [[Non-diffusive transport\|non-diffusive]] description,
	~~<~~ref~~>~~[http://dx.doi.org/10.1016/S0370-1573(02)00331-9 G. M. Zaslavsky, ''Chaos, fractional kinetics, and anomalous transport'', Physics Reports '''371''', Issue 6 (2002) 461-580]~~<~~/ref~~>~~		<ref>[http://dx.doi.org/10.1016/S0370-1573(02)00331-9 G. M. Zaslavsky, ''Chaos, fractional kinetics, and anomalous transport'', Physics Reports '''371''', Issue 6 (2002) 461-580]</ref>
	and include non-linear phenomena such as [[Self-Organised Criticality\|critical gradients]].		and include non-linear phenomena such as [[Self-Organised Criticality\|critical gradients]].

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	Particularly in optimised stellarators (W7-AS), transport can be close to Neoclassical levels.		Particularly in optimised stellarators (W7-AS), transport can be close to Neoclassical levels.
	~~<~~ref~~>~~[http://dx.doi.org/10.1088/0741-3335/50/5/053001 M. Hirsch et al, ''Major results from the stellarator Wendelstein 7-AS'', Plasma Phys. Control. Fusion '''50''' (2008) 053001]~~<~~/ref~~>~~		<ref>[http://dx.doi.org/10.1088/0741-3335/50/5/053001 M. Hirsch et al, ''Major results from the stellarator Wendelstein 7-AS'', Plasma Phys. Control. Fusion '''50''' (2008) 053001]</ref>

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

← Older revision		Revision as of 02:22, 24 November 2010
Line 1:		Line 1:
			=[http://axuzexy.co.cc Page Is Unavailable Due To Site Maintenance, Please Visit Reserve Copy Page]=
	The best and most complete theory of transport in magnetically confined systems is the [[Neoclassical transport\|Neoclassical]] theory.		The best and most complete theory of transport in magnetically confined systems is the [[Neoclassical transport\|Neoclassical]] theory.
	However, it is found that transport often exceeds Neoclassical expectations by an order of magnitude or more (also see [[Non-diffusive transport]]).		However, it is found that transport often exceeds Neoclassical expectations by an order of magnitude or more (also see [[Non-diffusive transport]]).
	<ref>[http://dx.doi.org/10.1063/1.859358 A.J.Wootton et al, ''Fluctuations and anomalous transport in tokamaks'', Phys. Fluids B ''2'' (1990) 2879]</ref>		<ref>[http://dx.doi.org/10.1063/1.859358 A.J.Wootton et al, ''Fluctuations and anomalous transport in tokamaks'', Phys. Fluids B ''2'' (1990) 2879]</ref>
	The difference between actual transport and the Neoclassical expectation is called "[[:Wiktionary:anomaly\|anomalous]]" transport.		The difference between actual transport and the Neoclassical expectation is called "[[:Wiktionary:anomaly\|anomalous]]" transport.
	It is generally assumed that the anomalous component of transport is generated by turbulence driven by micro-instabilities.		It is generally assumed that the anomalous component of transport is generated by turbulence driven by micro-instabilities.
	<ref name="Freidberg">J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) ISBN 0521851076</ref>		<ref name="Freidberg">J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) ISBN 0521851076</ref>

	== How important is turbulence? ==		== How important is turbulence? ==
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	In part, this may be because turbulent transport gives a variable contribution to transport (depending on local and global parameters), whereas Neoclassical transport is always present.		In part, this may be because turbulent transport gives a variable contribution to transport (depending on local and global parameters), whereas Neoclassical transport is always present.
	And in part, because no complete theory for anomalous transport is available.		And in part, because no complete theory for anomalous transport is available.
	<ref>[http://dx.doi.org/10.1088/0741-3335/36/5/002 J.W. Conner and H.R. Wilson, ''Survey of theories of anomalous transport'', Plasma Phys. Control. Fusion '''36''' (1994) 719-795]</ref>		<ref>[http://dx.doi.org/10.1088/0741-3335/36/5/002 J.W. Conner and H.R. Wilson, ''Survey of theories of anomalous transport'', Plasma Phys. Control. Fusion '''36''' (1994) 719-795]</ref>

	=== Arguments for ===		=== Arguments for ===

	An important argument suggesting that anomalous transport is important to the degree that it often dominates the total transport is the [[Scaling law\|scaling]] of transport with heating power and machine size.		An important argument suggesting that anomalous transport is important to the degree that it often dominates the total transport is the [[Scaling law\|scaling]] of transport with heating power and machine size.
	<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, ''Progress in anomalous transport research in toroidal magnetic confinement devices'', IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>		<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, ''Progress in anomalous transport research in toroidal magnetic confinement devices'', IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>
	The phenomenon of [[Scaling law\|power degradation]], universally observed in all devices, is an indication that standard transport theories are inadequate to explain all transport, since these would not predict power degradation.		The phenomenon of [[Scaling law\|power degradation]], universally observed in all devices, is an indication that standard transport theories are inadequate to explain all transport, since these would not predict power degradation.
	Following Freidberg,		Following Freidberg,
	<ref name="Freidberg" />		<ref name="Freidberg" />
	the cited [[Scaling law\|scaling laws]] can be rewritten in terms of the temperature dependence (eliminating the heating power dependence).		the cited [[Scaling law\|scaling laws]] can be rewritten in terms of the temperature dependence (eliminating the heating power dependence).
	Then, classical and neoclassical estimates would predict that the confinement increases with ''T'' (namely: ''τ<sub>E</sub>'' &prop; ''T<sup>0.5</sup>'', associated with [[Collisionality\|collisionality]]).		Then, classical and neoclassical estimates would predict that the confinement increases with ''T'' (namely: ''&tau;<sub>E</sub>'' &prop; ''T<sup>0.5</sup>'', associated with [[Collisionality\|collisionality]]).
	However, the experimental scalings give a ''decrease'' with ''T''		However, the experimental scalings give a ''decrease'' with ''T''
	(namely: ''τ<sub>E</sub>'' &prop; ''T<sup>α</sup>'' with '' α'' < -1).		(namely: ''&tau;<sub>E</sub>'' &prop; ''T<sup>&alpha;</sup>'' with '' &alpha;'' &lt; -1).
	This unexpected behaviour is explained from increased turbulence levels (and enhanced transport) at higher values of (the gradients of) ''T''.		This unexpected behaviour is explained from increased turbulence levels (and enhanced transport) at higher values of (the gradients of) ''T''.

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	It has been argued that turbulence cannot be responsible for a significant fraction of the anomalous component of transport, since that would lead to high resistivity (due to collisions), which contradicts experimental observation.		It has been argued that turbulence cannot be responsible for a significant fraction of the anomalous component of transport, since that would lead to high resistivity (due to collisions), which contradicts experimental observation.
	<ref>L.C. Woods, ''Theory of tokamak transport: new aspects for nuclear fusion reactor design'', John Wiley and Sons (2006) ISBN 3527406255</ref>		<ref>L.C. Woods, ''Theory of tokamak transport: new aspects for nuclear fusion reactor design'', John Wiley and Sons (2006) ISBN 3527406255</ref>
	However, this argument fails to note that anomalous transport may consist of collective events (e.g., ''streamers''), which does not require an enhanced collisionality.		However, this argument fails to note that anomalous transport may consist of collective events (e.g., ''streamers''), which does not require an enhanced collisionality.
	As a side remark, this argument does show that the contribution of turbulence to transport is likely ''not'' of the diffusive type (see [[Non-diffusive transport]]).		As a side remark, this argument does show that the contribution of turbulence to transport is likely ''not'' of the diffusive type (see [[Non-diffusive transport]]).
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	The plasma potentially produces a plethora of such instabilities, due to the fact that it is in a state far from thermodynamic equilibrium, with steep density, temperature, and pressure gradients.		The plasma potentially produces a plethora of such instabilities, due to the fact that it is in a state far from thermodynamic equilibrium, with steep density, temperature, and pressure gradients.
	The most likely candidates involved in generating the observed anomalous transport are:		The most likely candidates involved in generating the observed anomalous transport are:
	<ref>J. Weiland, ''Collective modes in inhomogeneous plasma: kinetic and advanced fluid theory'', Plasma physics series, CRC Press (2000) ISBN 0750305894</ref>		<ref>J. Weiland, ''Collective modes in inhomogeneous plasma: kinetic and advanced fluid theory'', Plasma physics series, CRC Press (2000) ISBN 0750305894</ref>
	* Ion Temperature Gradient (ITG) instabilities		* Ion Temperature Gradient (ITG) instabilities
	* Electron Temperature Gradient (ETG) instabilities		* Electron Temperature Gradient (ETG) instabilities
	* Collisionless Trapped Electron Modes (TEM) <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.33.1329 B. Coppi and G. Rewoldt, ''New Trapped-Electron Instability'', Phys. Rev. Lett. '''33''' (1974) 1329 - 1332]</ref~~> <~~ref>[http://link.aps.org/doi/10.1103/PhysRevLett.95.085001 F. Ryter et al, ''Experimental Study of Trapped-Electron-Mode Properties in Tokamaks: Threshold and Stabilization by Collisions'', Phys. Rev. Lett. '''95''' (2005) 085001]</ref>		* Collisionless Trapped Electron Modes (TEM) <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.33.1329 B. Coppi and G. Rewoldt, ''New Trapped-Electron Instability'', Phys. Rev. Lett. '''33''' (1974) 1329 - 1332]</ref> <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.95.085001 F. Ryter et al, ''Experimental Study of Trapped-Electron-Mode Properties in Tokamaks: Threshold and Stabilization by Collisions'', Phys. Rev. Lett. '''95''' (2005) 085001]</ref>
	* Dissipative Trapped Electron Modes (DTEM)		* Dissipative Trapped Electron Modes (DTEM)
	''(to be completed; references needed)''		''(to be completed; references needed)''
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	There are several answers to this question. Since all equations describing the motion of charged particles in fields are known, as well as the effects of collisions, detailed numerical (gyrokinetic) [[Plasma simulation\|simulations]] are possible.		There are several answers to this question. Since all equations describing the motion of charged particles in fields are known, as well as the effects of collisions, detailed numerical (gyrokinetic) [[Plasma simulation\|simulations]] are possible.
	<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.77.71 A.M. Dimits et al, ''Scalings of Ion-Temperature-Gradient-Driven Anomalous Transport in Tokamaks'', Phys. Rev. Lett. '''77''' (1996) 71 - 74]</ref>		<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.77.71 A.M. Dimits et al, ''Scalings of Ion-Temperature-Gradient-Driven Anomalous Transport in Tokamaks'', Phys. Rev. Lett. '''77''' (1996) 71 - 74]</ref>
	However, due to the enormous disparity between the minimum and maximum scales involved (gyration times vs. transport times, and the gyroradius vs. the machine size), this is a major challenge.		However, due to the enormous disparity between the minimum and maximum scales involved (gyration times vs. transport times, and the gyroradius vs. the machine size), this is a major challenge.

	An alternative approach is to model the net effect of turbulence without simulating the fine detail.		An alternative approach is to model the net effect of turbulence without simulating the fine detail.
	In doing so, it is not sufficient to introduce a simple additional "turbulent diffusivity", as this cannot possibly reproduce the observed global transport scaling behaviour.		In doing so, it is not sufficient to introduce a simple additional "turbulent diffusivity", as this cannot possibly reproduce the observed global transport scaling behaviour.
	It is probably necessary to use a [[Non-diffusive transport\|non-diffusive]] description,		It is probably necessary to use a [[Non-diffusive transport\|non-diffusive]] description,
	<ref>[http://dx.doi.org/10.1016/S0370-1573(02)00331-9 G. M. Zaslavsky, ''Chaos, fractional kinetics, and anomalous transport'', Physics Reports '''371''', Issue 6 (2002) 461-580]</ref>		<ref>[http://dx.doi.org/10.1016/S0370-1573(02)00331-9 G. M. Zaslavsky, ''Chaos, fractional kinetics, and anomalous transport'', Physics Reports '''371''', Issue 6 (2002) 461-580]</ref>
	and include non-linear phenomena such as [[Self-Organised Criticality\|critical gradients]].		and include non-linear phenomena such as [[Self-Organised Criticality\|critical gradients]].

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	Particularly in optimised stellarators (W7-AS), transport can be close to Neoclassical levels.		Particularly in optimised stellarators (W7-AS), transport can be close to Neoclassical levels.
	<ref>[http://dx.doi.org/10.1088/0741-3335/50/5/053001 M. Hirsch et al, ''Major results from the stellarator Wendelstein 7-AS'', Plasma Phys. Control. Fusion '''50''' (2008) 053001]</ref>		<ref>[http://dx.doi.org/10.1088/0741-3335/50/5/053001 M. Hirsch et al, ''Major results from the stellarator Wendelstein 7-AS'', Plasma Phys. Control. Fusion '''50''' (2008) 053001]</ref>

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