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

TL;DR

This paper introduces a hybrid model combining SOC and turbulence concepts to explain nonlocal transport in plasma, deriving a space-fractional Fokker-Planck equation from stochastic processes.

Contribution

It presents a novel mixed SOC-turbulence model and derives a space-fractional Fokker-Planck equation from Markovian stochastic processes.

Findings

Nonlocal transport modeled by a space-fractional Fokker-Planck equation.

Amplification mechanisms are essential for nonlocal dynamics.

The model links turbulence, SOC behavior, and nonlocal transport phenomena.

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 Markovian process with the transition probabilities defined in reciprocal space.