An Explanation From First-Principle Equations For The Universality of Non-Gaussian Distributions in Edge Plasma Fluctuations

TL;DR

This paper derives the universal non-Gaussian distribution shapes of edge plasma fluctuations from first-principle Langevin equations, explaining their independence from specific plasma conditions.

Contribution

It presents a theoretical derivation linking plasma fluctuation PDFs to fundamental Langevin equations with quadratic nonlinearities, providing a first-principles explanation for their universality.

Findings

PDFs of plasma edge fluctuations are skewed and non-Gaussian.

Universality of PDFs is explained by properties of Langevin equations.

Analytical solutions for fluctuation distributions are obtained from minimal fluid models.

Abstract

Probability Distributions Functions (PDFs) of fluctuations of plasma edge parameters are skewed curves fairly different from normal distributions, whose shape appears almost independent of the plasma conditions and devices. We start from a minimal fluid model of edge turbulence and reformulate it in terms of uncoupled Langevin equations, admiting analytical solution for the PDFs of all the fields involved. We show that the supposed peculiarities of PDFs, and their universal character, are related to the generic properties of Langevin equations involving quadratic nonlinearities.