Determination of non-local characteristics of density transport in 2D simulations of the SOL

Abstract: By use of Lagrangian tracers propagated on 2D simulations of Scrape-Off Layer (SOL) turbulence, we are able to determine the non-local fractional-advection, fractional-diffusion equation (FADE) coefficients for a number of equilibrium cases. Solutions of the resultant FADEs shows good agreement with the simulated mean density profiles. We detail how the FADE is derived: the stochastic flux equation is introduced, and it is shown how it is used to find general forms of Fick's first and second laws, dependent on the jump function. We show for spatially homogeneous jump functions which belong to the Levy-alpha Stable distribution that transport may be approximated by a non-local FADE with four parameters. This work demonstrates the sound basis for FADEs to act as reduced models of transport in systems dominated by coherent structures; so justifies the development of a first-principles approach to calculating FADE parameters.