Self-Organised Criticality: Difference between revisions

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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]]).