Transport hysteresis in electromagnetic microturbulence caused by mesoscale zonal flow pattern-induced mitigation of high β turbulence runaways

Abstract

Electromagnetic microturbulence at finite normalized plasma pressure β=n0T0/(B02/2μ0) (n0 is the equilibrium density, T0 the equilibrium temperature, B0 the equilibrium magnetic field, and μ0 the permeability of free space) is investigated within a local gradient-driven gyrokinetic framework. The focus lies on the well-known high β turbulence runaways [R. E. Waltz, Phys. Plasmas 17, 072501 (2010)] that have been proposed to set a nonlinear upper threshold βc, also known as the nonzonal transition [M. J. Pueschel, Phys. Rev. Lett. 110, 155005 (2013)]. In this paper, it is shown that persistent mesoscale zonal flow patterns, developing self-consistently on long time scales, mitigate high β turbulence runaways. The application of such mesoscale zonal flow states as initial conditions allows for the access of an improved β-regime, that is, β>βc, in which no turbulence runaway occurs. Various aspects of those mesoscale zonal flow-dominated improved states are investigated, such as (i) the stability constraints with respect to the mesoscale zonal flow level for the triggering of turbulence runaways, (ii) the influence of mesoscale zonal flows on magnetic stochasticity [W. M. Nevins, Phys. Rev. Lett. 106, 065003 (2010)], and (iii) the transfer processes connected to the drive and damping of mesoscale zonal flows. This work implies that βc does not set the upper limit in the normalized plasma pressure for stationary operation, provided persistent mesoscale zonal flow patterns can develop. Since variations of β occur on the energy confinement time, which is large compared to the time required for mesoscale zonal flows to develop, the reported mesoscale zonal flow-dominated improved β-regime is expected to be the experimentally relevant branch. Furthermore, this work highlights the need for sufficiently long simulation time traces of at least a few ∼103 R0/vth,i (R0 is the major radius, and vth,i is the ion thermal velocity), also within kinetic electron frameworks, to capture non-negligible long-term dynamics.