Self-Organised Criticality
Self-Organised Criticality (SOC) is a generic concept, applicable to a host of complex systems [1]. 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).
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) [2], 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. [3] Power degradation shows up in global transport 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 turbulence. [4] 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.
Indeed, there is direct evidence for avalanching behaviour in numerical simulations [5], but experimental evidence is scarce. [6] However, some indirect evidence exists. Typically, such evidence involves the detection of long-range correlations in fluctuations. [7]
Evidence for critical gradients is much more abundant. [8] [9] However, the existence of a critical gradient by itself does not prove the system is in a SOC state.
References
- ↑ Self-Organised Ciriticality in the Wikipedia
- ↑ B.A. Carreras, IEEE Trans. Plasma Science 25, 1281 (1997)
- ↑ F. Ryter et al., Plasma Phys. Control. Fusion 43, A323 (2001)
- ↑ D.E. Newman et al., Phys. Plasmas 3, 1858 (1996)
- ↑ L. García and B.A. Carreras, Phys. Plasmas 12, 092305 (2005)
- ↑ P.A. Politzer, Phys. Rev. Lett. 84, 1192 (2000)
- ↑ B.A. Carreras et al., Phys. Plasmas 6, 1885 (1999)
- ↑ D.R. Baker et al., Phys. Plasmas 8, 4128 (2001)
- ↑ F. Ryter et al., Plasma Phys. Control. Fusion 43, A323 (2001)