Self-Organised Criticality - Revision history

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	In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of:		In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of:
	* [[profile consistency]], which is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.<ref>[~~http~~:~~//dx.doi.org/~~10.1088/0741-3335/43/12A/325 ~~F. Ryter et al.,~~ Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>		* [[profile consistency]], which is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.<ref>F. Ryter et al., [[doi:10.1088/0741-3335/43/12A/325\|Plasma Phys. Control. Fusion '''43''', A323 (2001)]]</ref>
	* the [[Scaling law\|Bohm scaling]] of confinement in L-mode (scaling of transport with system size) <ref>[~~http~~:~~//dx.doi.org/~~10.1109/27.650902 ~~B.A. Carreras,~~ IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>, and		* the [[Scaling law\|Bohm scaling]] of confinement in L-mode (scaling of transport with system size) <ref>B.A. Carreras, [[doi:10.1109/27.650902\|IEEE Trans. Plasma Science '''25''', 1281 (1997)]]</ref>, and
	* power degradation, as reflected in global transport [[Scaling law\|scaling laws]]. The scaling of the plasma energy content with injected power is generally found to be sub-linear, i.e., considerably worse than expected from simple diffusion.		* power degradation, as reflected in global transport [[Scaling law\|scaling laws]]. The scaling of the plasma energy content with injected power is generally found to be sub-linear, i.e., considerably worse than expected from simple diffusion.

	The basic explanation for these phenomena is self-regulation of the profiles by turbulence (see [[Anomalous transport]]).		The basic explanation for these phenomena is self-regulation of the profiles by turbulence (see [[Anomalous transport]]).
	<ref>~~[http://link.aip.org/link/?PHPAEN/3/1858/1~~ D.E. Newman et al., Phys. Plasmas '''3''', 1858 (1996)]</ref>		<ref>D.E. Newman et al., [[doi:10.1063/1.871681\|Phys. Plasmas '''3''', 1858 (1996)]]</ref>
	The strong temperature and density gradients in fusion-grade plasmas provide free energy that may drive turbulence. The turbulence then enhances transport locally, leading to a local reduction of gradients and a consequential damping of the turbulence amplitude. This feedback could be responsible for keeping the gradients below a critical value. Considered locally, the former is a description of a simple marginal state.		The strong temperature and density gradients in fusion-grade plasmas provide free energy that may drive turbulence. The turbulence then enhances transport locally, leading to a local reduction of gradients and a consequential damping of the turbulence amplitude. This feedback could be responsible for keeping the gradients below a critical value. Considered locally, the former is a description of a simple marginal state.
	But the interaction of such feedback mechanisms at various radial locations would lead to ''avalanche'' behaviour and a true (scale-free) self-organised state.		But the interaction of such feedback mechanisms at various radial locations would lead to ''avalanche'' behaviour and a true (scale-free) self-organised state.

	Indeed, there is direct evidence for avalanching behaviour in numerical simulations		Indeed, there is direct evidence for avalanching behaviour in numerical simulations
	<ref>~~[http://link.aip.org/link/?PHPAEN/12/092305/1~~ L. García and B.A. Carreras, Phys. Plasmas '''12''', 092305 (2005)]</ref>,		<ref>L. García and B.A. Carreras, [[doi:10.1063/1.2041614\|Phys. Plasmas '''12''', 092305 (2005)]]</ref>,
	but experimental evidence is scarce.		but experimental evidence is scarce.
	<ref>~~[http://link~~.~~aps~~.~~org/~~doi/10.1103/PhysRevLett.84.1192 ~~P.A. Politzer,~~ Phys. Rev. Lett. '''84''', 1192 (2000)]</ref>		<ref>P.A. Politzer, [[doi:10.1103/PhysRevLett.84.1192\|Phys. Rev. Lett. '''84''', 1192 (2000)]]</ref>
	However, some indirect evidence exists. Typically, such evidence involves the detection of [[Long-range correlation\|long-range correlations]] in fluctuations.		However, some indirect evidence exists. Typically, such evidence involves the detection of [[Long-range correlation\|long-range correlations]] in fluctuations.
	<ref>~~[http://link.aip.org/link/?PHPAEN/6/1885/1~~ B.A. Carreras et al., Phys. Plasmas '''6''', 1885 (1999)]</ref>		<ref>B.A. Carreras et al., [[doi:10.1063/1.873490\|Phys. Plasmas '''6''', 1885 (1999)]]</ref>

	Evidence for critical gradients is much more abundant.		Evidence for critical gradients is much more abundant.
	<ref>~~[http://link.aip.org/link/?PHPAEN/8/4128/1~~ D.R. Baker et al., Phys. Plasmas '''8''', 4128 (2001)]</ref>		<ref>D.R. Baker et al., [[doi:10.1063/1.1395567\|Phys. Plasmas '''8''', 4128 (2001)]]</ref>
	<ref>[~~http~~:~~//dx.doi.org/~~10.1088/0741-3335/43/12A/325 ~~F. Ryter et al.,~~ Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>		<ref>F. Ryter et al., [[doi:10.1088/0741-3335/43/12A/325\|Plasma Phys. Control. Fusion '''43''', A323 (2001)]]</ref>
	However, the existence of a critical gradient by itself does not prove the system is in a SOC state.		However, the existence of a critical gradient by itself does not prove the system is in a SOC state.

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

Admin at 14:46, 4 April 2012

2012-04-04T14:46:36Z

← Older revision		Revision as of 16:46, 4 April 2012
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	but experimental evidence is scarce.		but experimental evidence is scarce.
	<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.84.1192 P.A. Politzer, Phys. Rev. Lett. '''84''', 1192 (2000)]</ref>		<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.84.1192 P.A. Politzer, Phys. Rev. Lett. '''84''', 1192 (2000)]</ref>
	However, some indirect evidence exists. Typically, such evidence involves the detection of long-range correlations in fluctuations.		However, some indirect evidence exists. Typically, such evidence involves the detection of [[Long-range correlation\|long-range correlations]] in fluctuations.
	<ref>[http://link.aip.org/link/?PHPAEN/6/1885/1 B.A. Carreras et al., Phys. Plasmas '''6''', 1885 (1999)]</ref>		<ref>[http://link.aip.org/link/?PHPAEN/6/1885/1 B.A. Carreras et al., Phys. Plasmas '''6''', 1885 (1999)]</ref>

Admin at 14:16, 17 September 2011

2011-09-17T14:16:53Z

← Older revision		Revision as of 16:16, 17 September 2011
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	Self-Organised Criticality (SOC) is a generic concept, applicable to a host of complex systems		Self-Organised Criticality (SOC) is a generic concept, applicable to a host of complex systems
	<ref>[http://en.wikipedia.org/wiki/Self-organised_criticality Self-Organised ~~Ciriticality~~ in the Wikipedia]</ref>.		<ref>[http://en.wikipedia.org/wiki/Self-organised_criticality Self-Organised Criticality in the Wikipedia]</ref>.
	A system is said to be in this state when it is at an ''attractive'' critical point at which it behaves as in a phase transition (i.e., the spatial and temporal scales are scale-invariant, or nearly so).		A system is said to be in this state when it is at an ''attractive'' critical point at which it behaves as in a phase transition (i.e., the spatial and temporal scales are scale-invariant, or nearly so).
	Note that ordinary phase transitions are not attractive, and maintaining the system near such a phase transition point requires fine-tuning some system parameters.		Note that ordinary phase transitions are not attractive, and maintaining the system near such a phase transition point requires fine-tuning some system parameters.
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	This situation can only occur in systems that are ''not in equilibrium'', in which fluctuations provide a mechanism for regulating the system and keeping it close to criticality.		This situation can only occur in systems that are ''not in equilibrium'', in which fluctuations provide a mechanism for regulating the system and keeping it close to criticality.

	In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of ~~profile consistency, the [[Scaling law\|Bohm scaling]] of confinement (in L-mode)~~		In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of:
	~~<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>, and power degradation.~~ [[~~Profile~~ consistency]] is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.		* [[profile consistency]], which is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>
	<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>		* the [[Scaling law\|Bohm scaling]] of confinement in L-mode (scaling of transport with system size) <ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>, and
	~~Power~~ degradation ~~shows up~~ in global transport [[Scaling law\|scaling laws]]~~, and implies a sub-linear~~ scaling of the plasma energy content with ~~the~~ injected power.		* power degradation, as reflected in global transport [[Scaling law\|scaling laws]]. The scaling of the plasma energy content with injected power is generally found to be sub-linear, i.e., considerably worse than expected from simple diffusion.

	The basic explanation for these phenomena is self-regulation of the profiles by turbulence (see [[Anomalous transport]]).		The basic explanation for these phenomena is self-regulation of the profiles by turbulence (see [[Anomalous transport]]).

Admin at 09:05, 17 September 2009

2009-09-17T09:05:57Z

← Older revision		Revision as of 11:05, 17 September 2009
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	Power degradation shows up in global transport [[Scaling law\|scaling laws]], and implies a sub-linear scaling of the plasma energy content with the injected power.		Power degradation shows up in global transport [[Scaling law\|scaling laws]], and implies a sub-linear scaling of the plasma energy content with the injected power.

	The basic explanation for these phenomena is self-regulation of the profiles by [[~~TJ-II:Turbulence\|turbulence~~]].		The basic explanation for these phenomena is self-regulation of the profiles by turbulence (see [[Anomalous transport]]).
	<ref>[http://link.aip.org/link/?PHPAEN/3/1858/1 D.E. Newman et al., Phys. Plasmas '''3''', 1858 (1996)]</ref>		<ref>[http://link.aip.org/link/?PHPAEN/3/1858/1 D.E. Newman et al., Phys. Plasmas '''3''', 1858 (1996)]</ref>
	The strong temperature and density gradients in fusion-grade plasmas provide free energy that may drive turbulence. The turbulence then enhances transport locally, leading to a local reduction of gradients and a consequential damping of the turbulence amplitude. This feedback could be responsible for keeping the gradients below a critical value. Considered locally, the former is a description of a simple marginal state.		The strong temperature and density gradients in fusion-grade plasmas provide free energy that may drive turbulence. The turbulence then enhances transport locally, leading to a local reduction of gradients and a consequential damping of the turbulence amplitude. This feedback could be responsible for keeping the gradients below a critical value. Considered locally, the former is a description of a simple marginal state.

Admin at 07:25, 13 September 2009

2009-09-13T07:25:05Z

← Older revision		Revision as of 09:25, 13 September 2009
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	This situation can only occur in systems that are ''not in equilibrium'', in which fluctuations provide a mechanism for regulating the system and keeping it close to criticality.		This situation can only occur in systems that are ''not in equilibrium'', in which fluctuations provide a mechanism for regulating the system and keeping it close to criticality.

	In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of profile consistency, the Bohm scaling of confinement (in L-mode)		In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of profile consistency, the [[Scaling law\|Bohm scaling]] of confinement (in L-mode)
	<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>, and ''power degradation''. [[Profile consistency]] is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.		<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>, and power degradation. [[Profile consistency]] is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.
	<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>		<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>
	Power degradation shows up in global transport [[Scaling law\|scaling laws]], and implies a sub-linear scaling of the plasma energy content with the injected power.		Power degradation shows up in global transport [[Scaling law\|scaling laws]], and implies a sub-linear scaling of the plasma energy content with the injected power.

Admin at 07:23, 13 September 2009

2009-09-13T07:23:39Z

← Older revision		Revision as of 09:23, 13 September 2009
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	This situation can only occur in systems that are ''not in equilibrium'', in which fluctuations provide a mechanism for regulating the system and keeping it close to criticality.		This situation can only occur in systems that are ''not in equilibrium'', in which fluctuations provide a mechanism for regulating the system and keeping it close to criticality.

	In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of ''profile consistency'', the ''Bohm scaling'' of confinement (in L-mode)		In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of profile consistency, the Bohm scaling of confinement (in L-mode)
	<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>, and ''power degradation''. Profile consistency is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.		<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>, and ''power degradation''. [[Profile consistency]] is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.
	<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>		<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>
	Power degradation shows up in global transport [[Scaling law\|scaling laws]], and implies a sub-linear scaling of the plasma energy content with the injected power.		Power degradation shows up in global transport [[Scaling law\|scaling laws]], and implies a sub-linear scaling of the plasma energy content with the injected power.

Admin at 15:12, 11 September 2009

2009-09-11T15:12:06Z

← Older revision		Revision as of 17:12, 11 September 2009
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	<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>, and ''power degradation''. Profile consistency is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.		<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>, and ''power degradation''. Profile consistency is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.
	<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>		<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>
	Power degradation shows up in global transport [[Scaling ~~laws~~\|scaling laws]], and implies a sub-linear scaling of the plasma energy content with the injected power.		Power degradation shows up in global transport [[Scaling law\|scaling laws]], and implies a sub-linear scaling of the plasma energy content with the injected power.

	The basic explanation for these phenomena is self-regulation of the profiles by [[TJ-II:Turbulence\|turbulence]].		The basic explanation for these phenomena is self-regulation of the profiles by [[TJ-II:Turbulence\|turbulence]].

Admin at 15:10, 11 September 2009

2009-09-11T15:10:02Z

← Older revision		Revision as of 17:10, 11 September 2009
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	In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of ''profile consistency'', the ''Bohm scaling'' of confinement (in L-mode)		In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of ''profile consistency'', the ''Bohm scaling'' of confinement (in L-mode)
	<ref>B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)</ref>, and ''power degradation''. Profile consistency is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.		<ref>[http://dx.doi.org/10.1109/27.650902 B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)]</ref>, and ''power degradation''. Profile consistency is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.
	<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>		<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>
	Power degradation shows up in global transport [[Scaling laws\|scaling laws]], and implies a sub-linear scaling of the plasma energy content with the injected power.		Power degradation shows up in global transport [[Scaling laws\|scaling laws]], and implies a sub-linear scaling of the plasma energy content with the injected power.

Admin at 09:18, 11 September 2009

2009-09-11T09:18:47Z

← Older revision		Revision as of 11:18, 11 September 2009
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	<ref>B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)</ref>, and ''power degradation''. Profile consistency is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.		<ref>B.A. Carreras, IEEE Trans. Plasma Science '''25''', 1281 (1997)</ref>, and ''power degradation''. Profile consistency is the observation that profiles tend to have roughly the same shape, regardless of the power and location of the applied heating.
	<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>		<ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter et al., Plasma Phys. Control. Fusion '''43''', A323 (2001)]</ref>
	Power degradation shows up in global transport scaling laws, and implies a sub-linear scaling of the plasma energy content with the injected power.		Power degradation shows up in global transport [[Scaling laws\|scaling laws]], and implies a sub-linear scaling of the plasma energy content with the injected power.

	The basic explanation for these phenomena is self-regulation of the profiles by [[TJ-II:Turbulence\|turbulence]].		The basic explanation for these phenomena is self-regulation of the profiles by [[TJ-II:Turbulence\|turbulence]].

Admin at 18:49, 10 August 2009

2009-08-10T18:49:06Z

← Older revision		Revision as of 20:49, 10 August 2009
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	Self-Organised Criticality (SOC) is a generic concept, applicable to a host of complex systems		Self-Organised Criticality (SOC) is a generic concept, applicable to a host of complex systems
	<ref>[http://en.wikipedia.org/wiki/Self-organised_criticality Self-Organised Ciriticality in the Wikipedia]</ref>.		<ref>[http://en.wikipedia.org/wiki/Self-organised_criticality Self-Organised Ciriticality in the Wikipedia]</ref>.
	A system is said to be in this state when it is at an attractive critical point at which it behaves as in a phase transition (i.e., the spatial and temporal scales are scale-invariant, or nearly so).		A system is said to be in this state when it is at an ''attractive'' critical point at which it behaves as in a phase transition (i.e., the spatial and temporal scales are scale-invariant, or nearly so).
			Note that ordinary phase transitions are not attractive, and maintaining the system near such a phase transition point requires fine-tuning some system parameters.
			SOC is different in that the system is attracted to the critical point.
			This situation can only occur in systems that are ''not in equilibrium'', in which fluctuations provide a mechanism for regulating the system and keeping it close to criticality.

	In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of ''profile consistency'', the ''Bohm scaling'' of confinement (in L-mode)		In magnetically confined plasmas, this state is thought to be responsible for the global transport phenomena of ''profile consistency'', the ''Bohm scaling'' of confinement (in L-mode)