K. Miki

Spatio-temporal evolution of the L → I → H transition

We investigate the dynamics of the low(L) → high(H) transition using a time-dependent, one dimensional (in radius) model which self-consistently describes the time evolution of zonal flows (ZFs), mean flows (MFs), poloidal spin-up, and density and pressure profiles. The model represents the physics of ZF and MF competition, turbulence suppression via E×B shearing, and poloidal flows driven by turbulence. Numerical solutions of this model show that the L→H transition can occur via an intermediate phase (I-phase) which involves oscillations of profiles due to ZF and MF competition. The I-phase appears as a nonlinear transition wave originating at the edge boundary and propagates inward. Locally, I-phase exhibits the characteristics of a limit-cycle oscillation. All these observations are consistent with recent experimental results. We examine the trigger of the L→H transition, by defining a ratio of the rate of energy transfer from the turbulence to the zonal flow to the rate of energy input into the turbul...

Zonal flow triggers the L-H transition in the Experimental Advanced Superconducting Tokamak

The kinetic energy transfer between shear flows and the ambient turbulence is investigated in the Experimental Advanced Superconducting Tokamak during the L-H transition. As the rate of energy transfer from the turbulence into the shear flow becomes comparable to the energy input rate into the turbulence, the transition into the H-mode occurs. As the observed behavior exhibits several predicted features of zonal flows, the results show the key role that zonal flows play in mediating the transition into H-mode.

Momentum theorems and the structure of atmospheric jets and zonal flows in plasmas

The inviscid invariance of potential vorticity is used to derive momentum balance relations for zonal flows in drift wave turbulence. The relations are constructed by exploiting potential enstrophy balance and the Taylor identity, and link flow momentum to turbulence pseudomomentum, along with the driving flux, the dissipation and turbulence spreading. Applications to atmospheric jets and to zonal flows in plasmas are discussed.

Analysis of symmetry breaking mechanisms and the role of turbulence self-regulation in intrinsic rotation

We present analyses of mechanisms which convert radial inhomogeneity to broken k||-symmetry and thus produce turbulence driven intrinsic rotation in tokamak plasmas. By performing gyrokinetic simulations of ITG turbulence, we explore the many origins of broken k||-symmetry in the fluctuation spectrum and identify both E ? B shear and the radial gradient of turbulence intensity?a ubiquitous radial inhomogeneity in tokamak plasmas?as important k||-symmetry breaking mechanisms. By studying and comparing the correlations between residual stress, E ? B shearing, fluctuation intensity and its radial gradient, we investigate the dynamics of residual stress generation by various symmetry breaking mechanisms and explore the implication of the self-regulating dynamics of fluctuation intensity and E ? B shearing for intrinsic rotation generation. Several scalings for intrinsic rotation are reported and are linked to investigations of underlying local dynamics. It is found that stronger intrinsic rotation is generated for higher values of ion temperature gradient, safety factor and weaker magnetic shear. These trends are broadly consistent with the intrinsic rotation scaling found from experiment?the so-called Rice scaling.

Study of the L–I–H transition with a new dual gas puff imaging system in the EAST superconducting tokamak

The intermediate oscillatory phase during the L–H transition, termed the I-phase, is studied in the EAST superconducting tokamak using a newly developed dual gas puff imaging (GPI) system near the L–H transition power threshold. The experimental observations suggest that the oscillatory behaviour appearing at the L–H transition could be induced by the synergistic effect of the two components of the sheared m, n = 0 E × B flow, i.e. the turbulence-driven zonal flow (ZF) and the equilibrium flow. The latter arises from the equilibrium, and is, to leading order, balanced by the ion diamagnetic term in the radial force balance equation. A slow increase in the poloidal flow and its shear at the plasma edge are observed tens of milliseconds prior to the I-phase. During the I-phase, the turbulence recovery appears to originate from the vicinity of the separatrix with clear wave fronts propagating both outwards into the far scrape-off layer (SOL) and inwards into the core plasma. The turbulence Reynolds stress is directly measured using the GPI system during the I-phase, providing direct evidence of kinetic energy transfer from turbulence to ZFs at the plasma edge. The GPI observations strongly suggest that the SOL transport physics and the evolution of pressure gradient near the separatrix play an important role in the L–I–H transition dynamics. To highlight these new physics, the previous predator–prey model is extended to include a new equation for the SOL physics. The model successfully reproduces the L–I–H transition process with several features comparing favourably with GPI observations.

Role of the geodesic acoustic mode shearing feedback loop in transport bifurcations and turbulence spreading

A theory of the effect of the geodesic acoustic mode (GAM) on turbulence is presented. Two synergistic issues are elucidated: namely, the physics of the zonal flow modulation and its role in the L-H transition, and the role of the GAM wave group propagation in turbulence spreading. Using a wavekinetic modulational analysis, the response of the turbulence intensity field to the GAM is calculated. This analysis differs from previous studies of zero-frequency zonal flows since it accounts for resonance between the drift wave group speed and the GAM strain field, which induces secularity. This mechanism is referred to as secular stochastic shearing. Finite real frequency and radial group velocity are intrinsic to the GAM, so its propagation can induce nonlocal phenomena at the edge and pedestal regions. To understand the effect of the GAM on turbulence and transition dynamics, a predator-prey model incorporating the dynamics of both turbulence and the GAMs is constructed and analyzed for stability around fixed points. Three possible states are identified, namely, an L-modelike stationary state, a reduced turbulence state, and a GAM limit-cycle state. The system is attracted to the state with the minimum turbulence level.

Novel states of pre-transition edge turbulence emerging from shearing mode competition

Recent experiments have noted the coexistence of multiple shearing fields in edge turbulence, and have observed that the shearing population ratios evolve as the L–H transition is approached. A novel model including zonal flows (ZFs), geodesic acoustic modes (GAMs) and turbulence as a zero-dimensional self-consistent two predator–one prey system with multiple frequency shearings is proposed. ZF with finite frequency (i.e. GAM) can have different shearing dynamics from that with zero frequency, because of the finite shearing field autocorrelation times. Decomposing the broadband ZF spectrum into the two populations enables us to assign different shearing weights to the components of the shearing field. We define states with no ZF and GAM as an L-mode-like state, that with ZF and without GAM as an ZF-only state, with GAM and without ZF as a GAM-only state and both with ZF and GAM as the coexistence state. To resolve the origins of multiple shear coexistence, mode-competition effects are introduced. These originate from higher order perturbation of wave populations. The model exhibits a sequence of transitions between various states as the net driving flux increases. For some parameters, bistability of ZF and GAM is evident, which predicts hysteretic behaviour in the turbulence intensity field during power ramp up/down studies. The presence of noise due to ambient turbulence offers a mechanism to explain the bursts and pulsations observed in the turbulence field prior to the L–H transition.

Spatio-temporal evolution of the H → L back transition

Since ITER will operate close to threshold and with limited control, the H → L back transition is a topic important for machine operations as well as physics. Using a reduced mesoscale model [Miki et al., Phys. Plasmas 19, 092306 (2012)], we investigate ELM-free H → L back transition dynamics in order to isolate transport physics effects. Model studies indicate that turbulence spreading is the key process which triggers the back transition. The transition involves a feedback loop linking turbulence and profiles. The I-phase appears during the back transition following a slow power ramp down, while fast ramp-downs reveal a single burst of zonal flow during the back transition. The I-phase nucleates at the pedestal shoulder, as this is the site of the residual turbulence in H-mode. Hysteresis in the profile gradient scale length is characterized by the Nusselt number, where Nu=χi,turb/χi,neo. Relative hysteresis of temperature gradient vs density gradient is sensitive to the pedestal Prandtl number, where P...

Dynamics of stimulated L → H transitions

We report on model studies of stimulated L → H transitions [K. Miki et al., Phys. Rev. Lett. 110, 195002 (2013)]. These studies use a reduced mesoscale model. Model studies reveal that L → H transition can be triggered by particle injection into a subcritical state (i.e., P<PThresh). Particle injection changes edge mean flow shear via changes of density and temperature gradients. The change of edge mean flow shear is critical to turbulence collapse and the subsequent stimulated transition. For low ambient heating, strong injection is predicted to trigger a transient turbulence collapse. Repetitive injection at a period less than the lifetime of the collapsed state can thus maintain the turbulence collapse and so sustain a driven H-mode-like state. The total number of particles required to induce a transition by either injection or gas puffing is estimated. Results indicate that the total number of injected particles required is much smaller than that required for a transition by gas puffing. We thus show ...