Toroidal Ion Temperature Gradient Turbulence Research Articles

Correlation between zonal flow shearing and entropy transfer rates in toroidal ion temperature gradient turbulence

The transfer rate of the entropy variable in the wavenumber space perpendicular to the equilibrium magnetic field is evaluated by means of the gyrokinetic simulations of the toroidal ion temperature gradient turbulence. Fluctuations of the perturbed gyrocenter distribution function of the linearly unstable mode are transferred to those with higher radial wavenumbers through interactions with zonal flows driven by turbulence. The entropy transfer rate coincides with the zonal flow shearing rate in cases with weak ion temperature gradient where the zonal flows effectively regulate the turbulent transport. The obtained result verifies a correlation between the entropy transfer and the zonal flow shearing processes.

Flux tube train model for local turbulence simulation of toroidal plasmas

A new simulation method for local turbulence in toroidal plasmas is developed by extending the conventional idea of the flux tube model. In the new approach, a train of flux tubes is employed, where flux tube simulation boxes are serially connected at each end along a field line so as to preserve a symmetry of the local gyrokinetic equations for image modes in an axisymmetric torus. Validity of the flux tube train model is confirmed against the toroidal ion temperature gradient turbulence for a case with a long parallel correlation of fluctuations, demonstrating numerical advantages over the conventional method in the time step size and the symmetry-preserving property.

Dynamics of turbulent transport dominated by the geodesic acoustic mode near the critical gradient regime

The effects of geodesic acoustic modes (GAMs) on the toroidal ion temperature gradient turbulence and associated transport near the critical gradient regime in tokamak plasma are investigated based on global Landau-fluid simulations and extended predator-prey modeling analyses. A new type of intermittent dynamics of transport accompanied with the emission and propagation of the GAMs, i.e., GAM intermittency [K. Miki et al., Phys. Rev. Lett. 99, 145003 (2007)], has been found. The intermittent bursts are triggered by the onset of spatially propagating GAMs when the turbulent energy exceeds a critical value. The GAMs suffer collisionless damping during the propagation and nonlocally transfer local turbulence energy to wide radial region. The stationary zonal flows gradually increase due to the accumulation of non-damped residual part over many periods of quasi-periodic intermittent bursts and eventually quench the turbulence, leading to a nonlinear upshift of the linear critical gradient; namely, the Dimits shift. This process is categorized as a new class of transient dynamics, referred to as growing intermittency. The Dimits shift is found to be established through this dynamical process. An extended minimal predator-prey model with collisionless damping of the GAMs is proposed, which qualitatively reproduce the main features of the growing intermittency and approximately predict its various time scales observed in the simulations.

On the dynamics of edge-core coupling

One of the nagging, unresolved questions in fusion theory is concerned with the extent of the edge. Gyrokinetic particle simulations of toroidal ion temperature gradient turbulence spreading using the gyrokinetic toroidal code [Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and R. B. White, Science 281, 1835 (1998)] and its related dynamical model have been extended to a system with radially varying ion temperature gradient, in order to study the inward spreading of edge turbulence toward the core plasma. Due to such spreading, the turbulence intensity in the core region is significantly enhanced over the value obtained from the simulations of the core region only, and the precise boundary of the edge region is blurred. Even when the core gradient is within the Dimits shift regime (i.e., dominated by self-generated zonal flows which reduce the transport to a negligible value), a significant level of turbulence can penetrate to the core due to spreading from the edge. The scaling of the turbulent front propagation speed is closer to the prediction from a nonlinear diffusion model than from the one based on linear toroidal coupling.

Transport reduction by shear flows in dynamical models

The reduction in the transport of particles and heat by a strong mean shear flow is studied, in the context of interchange and ion-temperature gradient turbulence models. Compared to passive scalar transport, a stronger reduction in the transport (scaling with the shearing rate Ω as ∝Ω−3 ln Ω) results from a severe reduction in the amplitude of turbulent velocity in both models. However, the cross phase is only modestly reduced, as in the scalar field case. These results are in qualitative agreement with the results from both gyrokinetic and gyrofluid simulations of toroidal ion-temperature gradient turbulence [Lin et al., Phys. Rev. Lett. 83, 3645 (1999); Falchetto and Ottaviani, Phys. Rev. Lett. 92, 025002 (2004)], but contradict recent claims in some literature, highlighting the importance of the detailed properties of the flow in determining the overall transport level.

Turbulence spreading and transport scaling in global gyrokinetic particle simulations

An intriguing observation in magnetically confined plasma experiments and in global gyrokinetic particle simulations of toroidal ion temperature gradient turbulence is that the fluctuations are microscopic, while the resulting turbulent transport is not gyro-Bohm [Z. Lin et al., Phys. Rev. Lett. 88, 195004 (2002)]. A possible resolution to this puzzle is identified as turbulence spreading from the linearly active (unstable) region to the linearly inactive (stable) region. Large scale gyrokinetic simulations found that transport driven by microscopic fluctuations is diffusive and local, whereas the fluctuation intensity is determined by nonlocal effects. Fluctuations are found to spread from the linearly active region to the linearly inactive region. This turbulence spreading reduces the fluctuation intensity in the unstable region, especially for a smaller device size, and thus introduces a nonlocal dependence in the fluctuation intensity. The device size dependence of the fluctuation intensity, in turn, is responsible for the observed gradual transition from Bohm to gyro-Bohm transport scaling.

Role of ion diamagnetic effects in the generation of large scale flows in toroidal ion temperature gradient mode turbulence

The secondary instability of large scale flows, such as zonal flows and streamers, in toroidal ion temperature gradient turbulence is investigated. It is shown that diamagnetic effects (finite pressure fluctuations), such as those for toroidal ion temperature gradient modes, significantly increase the total Reynolds force. In general, pressure fluctuations have a finite phase shift relative to the electrostatic potential. It is shown that both parts (in-phase and out-of-phase) contribute to the diamagnetic Reynolds stress tensor. Also, the out-of-phase component of the pressure fluctuations is responsible for anomalous energy flux. It is shown here, that a specific contribution of the out-of-phase component to the Reynolds stress tensor allows us to decouple zonal flow dynamics from slow evolution of the ion pressure profile. General equations for the zonal flow and streamer instabilities in toroidal ion temperature gradient turbulence are derived and the growth rates are determined.

Simulation of ion temperature gradient turbulence in tokamaks

Results are presented from non-linear gyrokinetic simulations of toroidal ion temperature gradient turbulence and transport. The ion thermal fluxes are found to have an offset linear dependence on the temperature gradient and are significantly lower than gyrofluid or IFS-PPPL model predictions. A new phenomenon of non-linear effective critical gradients larger than the linear instability threshold gradients is observed and is associated with undamped flux surface averaged shear flows. The non-linear gyrokinetic codes have passed extensive tests, including comparison against independent linear calculations, a series of non-linear convergence tests and a comparison between two independent non-linear gyrokinetic codes. The most realistic simulations to date used actual reconstructed equilibria from experiments and a model for dilution by impurity and beam ions. These simulations highlight the importance of both self-generated and external E × B flow shear as well as the need for still more physics to be included.