Self-Organised Criticality: Difference between revisions

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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 />

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