UC San Diego

This paper presents a theory for the collapse of the edge zonal shear layer, as observed at the density limit at low β. This paper investigates the scaling of the transport and mean profiles with the adiabaticity parameter α, with special emphasizes on fluxes relevant to zonal flow (ZF) generation. We show that the adiabaticity parameter characterizes the strength of production of zonal flows and so determines the state of turbulence. A 1D reduced model that self-consistently describes the spatiotemporal evolution of the mean density n¯, the azimuthal flow v¯y, and the turbulent potential enstrophy ε=⟨(ñ−∇2ϕ̃)2/2⟩—related to fluctuation intensity—is presented. Quasi-linear analysis determines how the particle flux Γn and vorticity flux Π=−χy∇2vy+Πres scale with α, in both hydrodynamic and adiabatic regimes. As the plasma response passes from adiabatic (α > 1) to hydrodynamic (α < 1), the particle flux Γn is enhanced and the turbulent viscosity χy increases. However, the residual flux Πres—which drives the flow—drops with α. As a result, the mean vorticity gradient ∇2v¯y=Πres/χy—representative of the strength of the shear—also drops. The shear layer then collapses and turbulence is enhanced. The collapse is due to a decrease in ZF production, not an increase in damping. A physical picture for the onset of collapse is presented. The findings of this paper are used to motivate an explanation of the phenomenology of low β density limit evolution. A change from adiabatic (α=kz2vth2/(|ω|νei)>1) to hydrodynamic (α < 1) electron dynamics is associated with the density limit.