Ion-temperature-gradient-driven Research Articles

Enhanced Transport at High Plasma Pressure and Subthreshold Kinetic Ballooning Modes in Wendelstein 7-X.

High-performance fusion plasmas, requiring high pressure β, are not well understood in stellarator-type experiments. Here, the effect of β on ion-temperature-gradient-driven (ITG) turbulence is studied in Wendelstein 7-X (W7-X), showing that subdominant kinetic ballooning modes (KBMs) are unstable well below the ideal MHD threshold and get strongly excited in the turbulence. By zonal-flow erosion, these subthreshold KBMs (stKBMs) affect ITG saturation and enable higher heat fluxes. Controlling stKBMs will be essential to allow W7-X and future stellarators to achieve maximum performance.

Gyrokinetic Particle-in-Cell simulation of the effect of compressional magnetic perturbations on the microscopic instabilities in Tokamak

The compressional magnetic component δB|| has been implemented in the gyrokinetic Particle-in-Cell (PIC) code GEM for the fully electromagnetic simulation of microscopic instabilities in high-β tokamak plasmas. The simulation model is formulated for the split-weight scheme that is based on the canonical momentum formulation of the gyrokinetic equation. A pseudo-spectral method is used to solve the coupled gyrokinetic field equations while preserving all finite-Larmor-radius (FLR) effects. The algorithm is verified by the method of manufactured solutions. Simulations of the ion-temperature-gradient-driven (ITG) mode, the kinetic balloon mode (KBM) and the trapped electron mode (TEM) are presented.

Phase synchronization versus modulational instability for zonal flow generation and pattern formation

From global gyrokinetic simulations of toroidal ion temperature gradient-driven (ITG) turbulence, we identify two distinguished regimes where zonal flow generation and its radial pattern formation is governed by either phases or amplitudes of the turbulence spectrum. When the unstable region is wider than the correlation length of ITG modes, the zonal flow structure changes in a turbulence time scale. We newly uncover that the radial phases of ITG modes determine the evolution of the zonal flow structure. Synchronization of mode phases induced by the global zonal flow drives a fine-scale zonal flow pattern. With a narrow unstable region comparable to the mode correlation length, the phase effect almost vanishes. In this regime, we recover that the modulational instability promptly amplifies a coherent zonal flow, leading to a lower turbulence saturation level. This finding explains the reduction of turbulent transport at a narrow width of the strong gradient region, which has been attributed to the system size effects in ion-scale gyrokinetic turbulence.

Dynamics of enhanced neoclassical particle transport of tracer impurity ions in ion temperature gradient driven turbulence

Tracer impurity transport in ion temperature gradient-driven (ITG) turbulence is investigated using a global full-f gyrokinetic simulation including kinetic electrons, bulk ions, and low to medium Z tracer impurities, where Z is the charge number. It is found that in addition to turbulent particle transport, enhanced neoclassical particle transport due to a new synergy effect between turbulent and neoclassical transports makes a significant contribution to tracer impurity transport. Bursty excitation of the ITG mode generates non-ambipolar turbulent particle fluxes of electrons and bulk ions, leading to a fast growth of the radial electric field following the ambipolar condition. The divergence of E × B flows compresses up-down asymmetric density perturbations, which are subject to transport induced by the magnetic drift. The enhanced neoclassical particle transport depends on the ion mass because the magnitude of up-down asymmetric density perturbation is determined by a competition between the E × B compression effect and the return current given by the parallel streaming motion. This mechanism does not work for the temperature and, thus, selectively enhances only particle transport.

A comparison of turbulent transport in a quasi-helical and a quasi-axisymmetric stellarator

Ion-temperature-gradient-driven (ITG) turbulence is compared for two quasi-symmetric (QS) stellarator configurations to determine the relationship between linear growth rates and nonlinear heat fluxes. We focus on the quasi-helically symmetric (QHS) stellarator HSX and the quasi-axisymmetric (QAS) stellarator NCSX. In normalized units, HSX exhibits higher growth rates than NCSX, while heat fluxes in gyro-Bohm units are lower in HSX. These results hold for simulations made with both adiabatic and kinetic electrons. The results show that HSX has a larger number of subdominant modes than NCSX and that eigenmodes are more spatially extended in HSX. We conclude that the consideration of nonlinear physics is necessary to accurately assess the heat flux due to ITG turbulence when comparing QS stellarator equilibria.

Saturation and nonlinear electromagnetic stabilization of ITG turbulence

Energy transfer in ion-temperature-gradient-driven (ITG) turbulence and its role in modeling transport are examined for finite normalized plasma pressure β for a number of test cases and experimental discharges. The analysis shows that like the zero-β case, finite-β ITG turbulence saturates by nonlinear energy transfer to stable modes mediated by a zonal flow. Electromagnetic effects reliably increase stable mode amplitudes but affect heat fluxes only at the ≈5% level. The most important change with increased β is an increase in the correlation time of the triplet interaction of the unstable mode, stable mode, and zonal flow, thus providing a heightened nonlinear energy transfer efficiency, which allows the instability to saturate at lower amplitude. The heat flux is examined in connection with nonlinear electromagnetic stabilization, the phenomenon where the flux falloff with β is more pronounced than the falloff predicted by quasilinear transport models. The inclusion of the triplet correlation time in the quasilinear model captures most of the nonlinearly enhanced stabilization for the configurations studied here.

Chaos in toroidal ion-temperature-gradient-driven modes in dust-contaminated magnetoplasma

A new set of nonlinear equations for toroidal ion-temperature-gradient-driven (ITGD) drift-dissipative waves is derived by using Braginskii's transport model of the ion dynamics and the Boltzmann distribution of electrons in the presence of negatively charged dust grains. The temporal behaviour of the nonlinear ITGD mode is found to be governed by three nonlinear equations for the amplitudes, which is a generalization of Lorenz- and Stenflo-type equations admitting chaotic trajectories. The linear stability analysis has been presented and stationary points for our generalized mode coupling equations are also derived.

Simulations of turbulent transport with kinetic electrons and electromagnetic effects

A new electromagnetic kinetic electron simulation model that uses a generalized split-weight scheme, where the adiabatic part is adjustable, along with a parallel canonical momentum formulation has been developed in three-dimensional toroidal flux-tube geometry. This model includes electron–ion collisional effects and has been linearly benchmarked. It is found that for H-mode parameters, the nonadiabatic effects of kinetic electrons increase linear growth rates of the ion-temperature-gradient-driven (ITG) modes, mainly due to trapped-electron drive. The ion heat transport is also increased from that obtained with adiabatic electrons. The linear behaviour of the zonal flow is not significantly affected by kinetic electrons. The ion heat transport decreases to below the adiabatic electron level when finite plasma β is included due to finite-β stabilization of the ITG modes. This work is being carried out using the ‘Summit Framework’.

Effects of current density on ion-temperature-gradient modes

A model for the ion-temperature-gradient-driven (ITG) instability is derived from the Braginskii magnetohydrodynamic equations of ions. The heat flow of electrons carried by the current density J|| in collision-dominant plasmas is introduced into the model. It is found that, in contrast to the finite Larmor radius effect, the current density suppresses the ITG instabilities with small wavenumber k⊥ as well as large wavenumber k||. In addition, the effects of J|| on the critical stability thresholds for the ITG mode are studied, and two critical values, ηic1 ⩽ ηic2, for the temperature gradient parameter ηi = d ln Ti/d ln n are identified. For typical tokamak parameters the stability condition ηi ⩽ ηic1 may be realized when the parameter εn = −(d ln n/dr)−1/R is large. However, the other stable regime ηi ⩾ ηic2 can only be reached when the safety factor is large enough. Similarly, there are two critical values for the safety factor, qc1 and qc2. It is shown that, under specific conditions, qc1 = qc2 so that the ITG modes are stable for any q value.

Electron temperature gradient driven turbulence

Collisionless electron-temperature-gradient-driven (ETG) turbulence in toroidal geometry is studied via nonlinear numerical simulations. To this aim, two massively parallel, fully gyrokinetic Vlasov codes are used, both including electromagnetic effects. Somewhat surprisingly, and unlike in the analogous case of ion-temperature-gradient-driven (ITG) turbulence, we find that the turbulent electron heat flux is significantly underpredicted by simple mixing length estimates in a certain parameter regime (ŝ∼1, low α). This observation is directly linked to the presence of radially highly elongated vortices (“streamers”) which lead to very effective cross-field transport. The simulations therefore indicate that ETG turbulence is likely to be relevant to magnetic confinement fusion experiments.

The gyro-radius scaling of ion thermal transport from global numerical simulations of ion temperature gradient driven turbulence

A three-dimensional, fluid code is used to study the scaling of ion thermal transport caused by ion-temperature-gradient-driven (ITG) turbulence. The code includes toroidal effects and is capable of simulating the whole torus. It is found that both close to the ITG threshold and well above threshold, the thermal transport and the turbulence structures exhibit a gyro-Bohm scaling, at least for plasmas with moderate poloidal flow.

Second stable regime of nonlocal mixed slab-toroidal anisotropic ion-temperature-gradient-driven mode

Nonlocal effects on the mixed slab-toroidal ion-temperature-gradient-driven (ITG) instability are investigated with analytical and numerical approaches. Although it is more complex than the local analysis, the nonlocal analysis also leads to the same conclusion that a second stable regime exists at large values of the perpendicular temperature gradient. From a strictly theoretical point of view, this result provides a possible stabilization scheme for the ITG instability.

Scalings of Ion-Temperature-Gradient-Driven Anomalous Transport in Tokamaks.

Results are presented from the first systematic nonlinear gyrokinetic simulation study of the scalings and parameter dependences of toroidal ion-temperature-gradient-driven (ITG) turbulence and transport in large magnetic-fusion-relevant tokamaks. Such simulations are made possible by significant advances in computational physics algorithms which are summarized. The simulated ion-thermal transport rates have clear ``gyroreduced Bohm'' scaling and are too low to account for the anomalous transport seen in the outer half of some TFTR $L$-mode discharges, indicating that additional mechanisms, such as nonadiabatic-electron effects, are operative.

Quantitative predictions of tokamak energy confinement from first-principles simulations with kinetic effects

A first-principles model of anomalous thermal transport based on numerical simulations is presented, with stringent comparisons to experimental data from the Tokamak Fusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)]. This model is based on nonlinear gyrofluid simulations, which predict the fluctuation and thermal transport characteristics of toroidal ion-temperature-gradient-driven (ITG) turbulence, and on comprehensive linear gyrokinetic ballooning calculations, which provide very accurate growth rates, critical temperature gradients, and a quasilinear estimate of χe/χi. The model is derived solely from the simulation results. More than 70 TFTR low confinement (L-mode) discharges have been simulated with quantitative success. Typically, the ion and electron temperature profiles are predicted within the error bars, and the global energy confinement time within ±10%. The measured temperatures at r/a≂0.8 are used as a boundary condition to predict the temperature profiles in the main confinement zone. The dramatic transition to the improved confinement in the supershot regime is also qualitatively explained. Further work is needed to extend this model of core heat transport to include particle and momentum transport, the edge region, and other operating regimes besides the ITG-dominated L mode. Nevertheless, the present model is very successful in predicting thermal transport in the main plasma over a wide range of parameters.

Effects of anisotropic ηi and collisions on the mixed slab and toroidal ITG mode

The effects of collisions and anisotropy in the ion temperature gradient on the ion-temperature-gradient-driven (ITG) mode are investigated with dissipative trapped electrons and fully kinetic ions, in the presence of both transit and magnetic drift resonances. For the slab and toroidal modes, electron collisions stabilize the ion branch but destabilize the electron branch. For the mixed slab and toroidal mode, a coupling effect is found that causes a split of the stability region in the ηi∥-ηi⊥ plane. A second stability region at large ηi⊥ with electron collisions may provide a possible stabilization scheme for ITG instabilities.

Fluctuation measurements in the DIII-D and TEXT tokamaks via collective scattering and reflectometry

Anomalous transport in fusion plasmas remains an enigma requiring explanation. A predictive capability is highly desirable if confinement enhancement regimes such as H mode or super shots are to be extrapolated to the next phase in development of the International Fusion program, epitomized, for example in ITER. Therefore, identification of the role that electrostatic turbulence plays in confinement is a critical issue requiring detailed experimental data capable of testing and challenging existing theoretical models. This article presents microturbulence measurements obtained on the DIII-D and TEXT tokamaks utilizing heterodyne, far-infrared collective scattering, and reflectometry techniques. The experimental systems are described on both machines and emphasis placed on results obtained during the L-H transition, ELM activity, and saturated ohmic operation where ion temperature gradient driven (ITGD) turbulence is theoretically predicted to exist.