Self-Organised Criticality

Self-Organised Criticality (SOC) is a generic concept, applicable to a host of complex systems . 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) , 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. 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 this phenomenon is self-regulation of the profiles by turbulence. 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 , but experimental evidence is scarce. However, some indirect evidence exists. Typically, such evidence involves the detection of long-range correlations in fluctuations.

Evidence for critical gradients is much more abundant. However, the existence of a critical gradient by itself does not prove the system is in a SOC state.