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), 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. [2] 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 on 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. [3] However, some indirect evidence exists. Typically, such evidence involves the detection of long-range correlations in fluctuations. [4]