Session DI2: L/H, Zonal

Rethinking wave-kinetic theory applied to zonal flows

Over the past two decades, a number of studies have employed a wave-kinetic theory to describe fluctuations interacting with zonal flows. Recent work has uncovered a defect in this wave-kinetic formulation: the system is dominated by the growth of (arbitrarily) small-scale zonal structures. Theoretical calculations of linear growth rates suggest, and nonlinear simulations confirm, that this system leads to the concentration of zonal flow energy in the smallest resolved scales, irrespective of the numerical resolution [1,2]. This behavior results from the assumption that zonal flows are extremely long wavelength, leading to the neglect of key terms responsible for conservation of enstrophy. A corrected theory, CE2-GO, is presented; it is free of these errors yet preserves the intuitive phase-space mathematical structure [1,2]. CE2-GO properly conserves enstrophy as well as energy, and yields accurate growth rates of zonal flow. Numerical simulations are shown to be well-behaved and not dependent on box size. The steady-state limit simplifies into an exact wave-kinetic form which offers the promise of deeper insight into the behavior of wavepackets. The CE2-GO theory takes its place in a hierarchy of models as the geometrical-optics reduction of the more complete cumulant-expansion statistical theory CE2 [3,4]. The new theory represents the minimal statistical description, enabling an intuitive phase-space formulation and an accurate description of turbulence–-zonal flow dynamics. \\{} [1] J. B. Parker, J. Plasma. Phys. (2016), 82, 595820602. \\{} [2] D. E. Ruiz, J. B. Parker, E. L. Shi, and I. Y. Dodin, Phys. Plasmas 23, 122304 (2016). \\{} [3] J. B. Parker and J. A. Krommes, New J. Phys. 16 (2014) 035006.\\{} [4] J. B. Parker and J. A. Krommes, Phys. Plasmas, 20, 100703 (2013).   

Cascades, "Blobby" Turbulence, and Target Pattern Formation in Elastic Systems: A New Take on Classic Themes in Plasma Turbulence

Concerns central to understanding turbulence and transport include: 1) Dynamics of dual cascades in EM turbulence; 2) Understanding ‘negative viscosity phenomena’ in drift-ZF systems; 3) The physics of blobby turbulence (re: SOL). Here, we present a study of a simple model – that of Cahn-Hilliard Navier-Stokes (CHNS) Turbulence – which sheds important new light on these issues. The CHNS equations describe the motion of binary fluid undergoing a second order phase transition and separation called spinodal decomposition. The CHNS system and 2D MHD are analogous [1], as they both contain a vorticity equation and a “diffusion” equation. The CHNS system differs from 2D MHD by the appearance of negative diffusivity, and a nonlinear dissipative flux. An analogue of the Alfven wave exists in the 2D CHNS system. DNS shows that mean square concentration spectrum $H^ψ_k$ scales as $k^{−7/3}$ in the elastic range. This suggests an inverse cascade of $H^ψ$. However, the kinetic energy spectrum $E^K_k$ scales as $k^{−3}$, as in the direct enstrophy cascade range for a 2D fluid (not MHD!). The resolution is that the feedback of capillarity acts only at blob interfaces. Thus, as blob merger progresses, the packing fraction of interfaces decreases, thus explaining the weakened surface tension feedback and the outcome for $E^K_k$. We also examine the evolution of scalar concentration in a single eddy in the Cahn-Hilliard system. This extends the classic problem of flux expulsion in 2D MHD. The simulation results show that a target pattern is formed. Target pattern is a meta stable state, since the band merger process continues on a time scale exponentially long relative to the eddy turnover time. Band merger resembles step merger in drift-ZF staircases. [1] Phys. Rev. Fluids 1, 054403.\\ \\Collaborators: P H Diamond, and Luis Chacon.   

Energy Exchange Dynamics across L-H transitions in NSTX

H-mode is planned for future devices such as ITER, and is preceded by a low (L) to high (H) transition. A key question remains. What is the mechanism behind the L-H transition? Most theoretical descriptions of the L--H transition are based on the shear of the radial electric field and coincident ExB poloidal flow shear, which is thought to be responsible for the onset of the anomalous transport suppression that leads to the L-H transition. This talk will focus on the analysis of the flow dynamics across the L-H transition in NSTX. We analyze the L-H transition dynamics using the velocimetry of 2D edge turbulence data from gas-puff imaging (GPI). We determine the velocity components at the edge across the L--H transition for 17 discharges with three types of heating power (NBI, ohmic, and RF). Using a reduced model equation of edge flows and turbulence, the energy transfer dynamics is compared with the turbulence depletion hypothesis of the predator--prey model. In order for Reynolds work to suppress the turbulence, it must deplete the total turbulent free energy, including the thermal free-energy term. For this to occur, the increase in kinetic energy in the mean flow over the L--H transition must be comparable to the pre-transition thermal free energy. However, this ratio was found to be of order 10$^{\mathrm{-2}}$. Although there are significant simplifications in the theoretical model, they are unlikely to cause inaccuracy by two orders of magnitude, suggesting that direct turbulence depletion by the Reynolds work may not be large enough to explain the L--H transition on NSTX, contrary to the predator--prey model.   

Gyrokinetic simulation of fast L-H bifurcation dynamics in a realistic diverted tokamak edge geometry

We report the first observation of an edge transport barrier formation event in an electrostatic gyrokinetic simulation carried out in a low beta C-Mod like plasma in realistic diverted tokamak edge geometry [1]. The results show that the synergistic action between two multiscale dynamical phenomena, 1) the turbulent Reynolds-stress driven and 2) the neoclassical X-point orbit-loss driven sheared $E \times B$ flows, work together to quench turbulent transport and form a transport barrier just inside the last closed flux surface. The bifurcation occurs when the $E \times B$ shearing rate becomes greater than the strongest dissipative mode growth rate, which results from the dissipative trapped-electron mode in this plasma. The synergism helps reconcile experimental reports of the key role of turbulent stress in the bifurcation with other experimental observations that ascribe the bifurcation to X-point orbit loss/neoclassical effects. The synergism is consistent with the general experimental observation that the L-H bifurcation requires more power with the ion $\nabla B$-drift away from the single-null X-point, in which the X-point orbit-loss effect is weaker. When the ion $\nabla B$-drift is backward, the bifurcation occurs at the same critical $E \times B$ shearing rate, but is accompanied by persistent GAM oscillations in the bifurcation layer. The effect of isotope mass on the L-H bifurcation will also be validated against DIII-D results. \newline [1] C.S. Chang, S. Ku et al., Phys. Rev. Lett. 118, 175001 (2017)