An Exact Turbulence Law For the Fluid Description of Fusion Edge Plasmas

TL;DR

This paper introduces a new exact turbulence law for the edge of fusion plasmas, derived within the Braginskii fluid model, validated by simulations, and useful for measuring turbulence cascade rates in tokamak edge regions.

Contribution

It presents a novel high-order turbulence law based on the Yaglom-Monin approach, specifically for the Scrape-off Layer in fusion plasmas, extending turbulence analysis tools.

Findings

Derivation of a third-order von Kármán-Howarth equation for plasma turbulence.

Validation of the new law through direct numerical simulations.

Identification of a well-defined inertial range in plasma turbulence.

Abstract

Understanding turbulence via simplified fluid models is crucial for optimizing magnetic confinement in tokamak devices. In this work, we propose a novel high-order turbulence law that describes the turbulent cascade at the edges of fusion plasmas, namely valid within the Scrape-off Layer (SOL), in the framework of the Braginskii fluid model. Using the Yaglom-Monin approach, we derive an exact relation characterizing density fluctuations in these strongly magnetized systems. We obtain a third-order von K\'arm\'an-Howarth equation in increment form for the case of electrostatic Braginskii model, applied to a decaying turbulence regime. The new Yaglom-Braginskii law is validated through direct numerical simulations within a reduced (two-dimensional) model. Our analysis reveals that the plasma dynamics obey the cross-scale balance, exhibiting a well-defined inertial range of turbulence. This third-order law can provide an accurate measure of the cascade rate of density fluctuations in the scrape-off layer of laboratory plasmas.