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 Kármán–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 SOL of laboratory plasmas.
This paper proposes a novel turbulence law that describes the turbulent cascade in the edge of fusion plasmas, using the Braginskii fluid model. The authors derive an exact third-order equation that can accurately measure the rate of density fluctuations in the scrape-off layer (SOL) of fusion devices.