Self-consistent model of the plasma staircase and nonlinear Schrödinger equation with subquadratic power nonlinearity

A new basis has been found for the theory of self-organization transport avalanches and jet zonal flows in L-mode tokamak plasma, so-called "plasma staircase." The are considered as a wave packet coupled nonlinear oscillators characterized by complex time- wave-number dependent function; mean-field approximation this function is argued to obey discrete Schr\"odinger equation with subquadratic power nonlinearity. It shown that leads directly white L\'evy noise, L\'evy-fractional Fokker-Planck radial test particles (via wave-particle interactions). In self-consistent description avalanches, which driven interact flows, form system semi-permeable barriers transport. We argue plasma staircase saturates at state marginal stability, whose vicinity undergo an ever-pursuing localization-delocalization transition. At transition point, event-size distribution be power-law $w_\tau (\Delta n) \sim \Delta n^{-\tau}$, drop-off exponent $\tau = ({\sqrt{17}} + 1)/{2} \simeq 2.56$. This value exact result model. edge behavior bears signatures enabling associate it dynamics self-organized critical (SOC) state. same time exponents, pertaining state, inconsistent classic models avalanche based on sand-piles their generalizations, suggesting avalanche-jet flow operates different organizing principles. results obtained have validated numerical simulation using flux-driven gyrokinetic code Tore-Supra plasma.