A mixed SOC-turbulence model for nonlocal transport and Levy-fractional Fokker-Planck equation

Abstract

The phenomena of nonlocal transport in magnetically confined plasma are theoretically analyzed. A hybrid model is proposed, which brings together the notion of inverse energy cascade, typical of drift-wave- and two-dimensional fluid turbulence, and the ideas of avalanching behavior, associable with self-organized critical (SOC) behavior. Using statistical arguments, it is shown that an amplification mechanism is needed to introduce nonlocality into dynamics. We obtain a consistent derivation of nonlocal Fokker-Planck equation with space-fractional derivatives from a stochastic Markov process with the transition probabilities defined in reciprocal space. The hybrid model observes the Sparre Andersen universality and defines a new universality class of SOC.

11 pages, 2 figures; submitted to Physics Letters A. arXiv admin note: substantial text overlap with arXiv:1307.0387

References in corpus (6)

• Fractional Fokker-Planck equation for Lévy flights in nonhomogeneous environments
• Stretched-exponential decay functions from a self-consistent model of dielectric relaxation
• Stretched exponential relaxation and ac universality in disordered dielectrics
• Pseudochaos and low-frequency percolation scaling for turbulent diffusion in magnetized plasma
• Criticality and self-organization in branching processes: application to natural hazards
• Percolation Models of Self-Organized Critical Phenomena

Cited by in corpus (6)

• 25 Years of Self-Organized Criticality: Solar and Astrophysics
• A topological approximation of the nonlinear Anderson model
• A self-consistent model of the plasma staircase and nonlinear Schrödinger equation with subquadratic power nonlinearity
• A data-driven dynamic nonlocal subgrid-scale model for turbulent flows
• Subdiffusive Lévy flights in quantum nonlinear Schrödinger lattices with algebraic power nonlinearity
• Dynamic Nonlocal Passive Scalar Subgrid-Scale Turbulence Modeling