Theory of Zonal Flow Generation by Coherent Structures

Coherent structures are ubiquitous at the plasma edge. Recent experimental results from MAST [1] show that poloidal flows—including low frequency zonal flow and GAM—arise right after bursts in density fluctuation. This is strong evidence that coherent structures (holes) can drive zonal flows. No existing theory can explain this phenomenon. In this work, a model is proposed to unearth the mechanism of structure-driven zonal flows. We mainly focus on the case of a single coherent structure moving in a background plasma. Just as a moving charged particle can radiate electromagnetic waves, the coherent structure, which can be viewed as a macro particle, will leave a wake flow behind it. Thus the space of concern could be divided into two regions: the near field region surrounding the structure and the far field region where the wake is located. Starting from the Hasegawa-Wakatani equation, equations for the near field and the far field are derived by taking hydrodynamic and adiabatic limits, respectively. Hence the wake is composed of drift waves, which is consistent with experimental observations [2]. By using Green’s function, the far field is analytically calculated. As a result of the twist of the structure by mean shear flow, the Reynolds stress of the wake flow is found to be non-trivial, indicating the generation of zonal flow.

[1]. Sladkomedova, A., et al., 2023. J. Plasma Phys., 89(6), p.905890614.

[2]. Zweben, et al., 2019. Phys. Plasmas., 26(7).