When can Fokker-Planck Equation describe anomalous or chaotic transport?

TL;DR

This paper discusses the conditions under which the Fokker-Planck Equation can effectively model anomalous and chaotic transport phenomena in fusion plasmas, emphasizing the role of randomness and system complexity.

Contribution

It clarifies when the Fokker-Planck Equation is applicable to particle transport in complex systems, highlighting the importance of randomness and system degrees of freedom.

Findings

Fokker-Planck can model uphill transport and confinement scaling.

Transport coefficients are largely independent in systems with sufficient randomness.

Dynamical systems may exhibit diffusive or Levy flight behavior depending on statistics.

Abstract

The Fokker-Planck Equation, applied to transport processes in fusion plasmas, can model several anomalous features, including uphill transport, scaling of confinement time with system size, and convective propagation of externally induced perturbations. It can be justified for generic particle transport provided that there is enough randomness in the Hamiltonian describing the dynamics. Then, except for 1 degree-of-freedom, the two transport coefficients are largely independent. Depending on the statistics of interest, the same dynamical system may be found diffusive or dominated by its L\'{e}vy flights.