Ion Temperature Gradient Mode Turbulence Research Articles

Prediction of temperature profiles in helical plasmas by integrated code coupled with gyrokinetic transport models

Transport simulation is performed by integrated code using reduced transport models (Toda S et al 2019 Phys. Plasmas 26 012510) in a kinetic electron condition for turbulent heat transport including the effect of zonal flows in helical plasmas. A reduced model can be formulated for the heat diffusivity using only the linear properties, or can be constructed by considering the expression of the quasilinear flux. These reduced models reproduce nonlinear gyrokinetic simulation results for ion temperature gradient mode turbulence by a linear growth rate and zonal flow decay time. Temperature profiles can be obtained when the turbulent heat transport is evaluated by reduced models at each time step in the evolution of integrated simulation. Computational cost using the reduced models where linear gyrokinetic simulation is performed at each time step in the integrated simulation is about two orders of magnitude lower than that using nonlinear gyrokinetic simulation. Stationary temperature profiles are predicted by simulation, in which, the linear simulation is performed at each time step in the integrated simulation for steady heating power. The density profile and the edge temperature are needed in this simulation.

Inverse Compton scattering of the ITG turbulence by energetic ions

Linearly stable toroidal Alfvén eigenmodes (TAEs) can be non-linearly excited by the ion temperature gradient mode turbulence having frequencies an order of magnitude lower than TAE. An excitation mechanism is the inverse Compton scattering by energetic ions, i.e., the inverse non-linear Landau damping accompanied by a frequency increase in the scattered waves. This effect can be responsible for excitation of the stable TAE by turbulence observed in numerical simulations [Di Siena et al., Nucl. Fusion 59, 124001 (2019)]. Such non-linear coupling to stable TAE via energetic ions provides an efficient energy sink for turbulence and can explain strong reduction of the thermal ion heat flux in the presence of fast ions observed in gyro-kinetic modeling [Citrin et al., Phys. Rev. Lett. 111, 155001 (2013)].

Magnetic shear effect on zonal flow generation in ion-temperature-gradient mode turbulence

By decoupling the nonlinear fluid equations of ion-temperature-gradient (ITG) mode, the zonal flow-drift wave nonlinear dynamical equation including magnetic shear is derived. The role of magnetic shear for zonal flow generation by ITG mode turbulence is studied using a four-wave interaction model of modulational instability. Finally we can draw the conclusion that within a smaller range of k//, as |k//| increases, the growth rate of zonal flow is also increased.

Zonal flow dynamics in background of ion-temperature-gradient mode turbulence based on minimal freedom model

In the ITG (ion-temperature-gradient) mode turbulence background, the dynamics of zonal flow generation is studied based on the minimal freedom model. We study the dynamical instability and present detailed numerical results. The energy cascade process in the ITG mode turbulence and the relationship between Reynolds stress and zonal flow are also discussed. The mechanism of turbulence suppression by zonal flow is clearly explored and displayed.

Zonal flow in toroidal ion temperature gradient mode turbulence

AbstractThe properties of zonal flows in the toroidal ion temperature gradient mode turbulence are investigated taking into account the polarization drift effects. The stability criterion and the characteristic oscillation frequency of the zonal flow are determined in terms of the spectra of turbulent fluctuations. The nonlinear evolution of zonal flows may lead to the formation of stationary long-lived coherent structures supporting stationary shear layers. These results indicate the existence of regions with reduced levels of anomalous transport attributed to zonal flows generalizing previous findings regarding zonal flows in electron drift turbulence.

Gyrokinetic turbulence simulation of profile shear stabilization and broken gyroBohm scaling

A newly developed continuum gyrokinetic code GYRO has been formulated on a radial grid to operate at finite relative gyroradius in a noncyclic radial annulus with profile variation. The code is used to simulate ion temperature gradient mode turbulence and to demonstrate that gyroBohm scaling can be obtained well above the instability threshold but sufficiently strong profile shear stabilization can break gyroBohm scaling down to Bohm scaling (or worse) near threshold. An adaptive source technique is used to maintain profiles. Clear evidence for nonlocal transport is also found in which the local diffusivity depends on the plasma gradients at some considerable radial distance.

Gas puff fueled H-mode discharges with good energy confinement above the Greenwald density limit on DIII-D

ELMing (edge-localized) H-mode discharges with densities as high as 40% above the Greenwald density and good energy confinement, HITER-89P=2, were obtained with D2 gas puffing on DIII-D [Chan et al., Proceedings of the 16th IAEA Conference, Montreal (International Atomic Energy Agency, Vienna, 1996), Vol. 1, p. 95]. These discharges have performance comparable to the best pellet fueled DIII-D discharges. Spontaneous peaking of the density profile was an important factor in obtaining high energy confinement. Without density profile peaking, the energy confinement at high density degraded with reduction in the H-mode pedestal pressure under the stiff temperature profile conditions observed at high density on DIII-D. Reduction in the pedestal pressure was associated with loss of access to the second stable regime for ideal ballooning modes at the edge, and change in the edge-localized mode (ELM) instability from a low to high toroidal mode number. Gyrokinetic stability calculations indicate that the core of the high-density discharges is dominated by ion temperature gradient mode turbulence. A turbulent transport simulation with the GLF23 [Waltz et al., Phys. Plasmas 4, 2482 (1997)] code produced stiff temperature profiles in agreement with the experiment and did not indicate the formation of an internal transport barrier. Helium transport studies showed an anomalous inward particle pinch at high density. The highest density discharges were terminated by onset of a magnetohydromagnetic instability, which is consistent with destabilization of neoclassical tearing modes through peaking of the pressure profile.

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.

Nonlocal simulation of the transition from ballooning to ion temperature gradient mode turbulence in the tokamak edge

The transition from resistive ballooning to ion temperature gradient (ITG) mode turbulence in the tokamak edge is studied in three dimensions using the electrostatic reduced Braginskii equations with ion temperature dynamics. In contrast to most previous simulations of plasma edge turbulence, which assume the parameters (density, temperature, collisionality, etc.) to be constant in space and time (local approximation), a realistic spatial variation and the nonlinear dependence of the parameters on the fluctuating quantities is taken into account. The influence of nonlocal effects is studied by a scan in the ratio of profile to turbulence scale length. For a large ratio, good agreement between local and nonlocal results on the ITG mode and ballooning turbulence is found. With increasing nonlocality, however, the anomalous transport is more and more suppressed. For the ITG mode, the turbulence quench is due to a decrease of the linear growth rate, while for the ballooning mode a novel, inherently nonlocal saturation mechanism is identified.

Impurity effects on drift wave stability and impurity transport

A numerical linear stability analysis of electrostatic ion temperature gradient (ITG) and dissipative trapped electron (DTE) modes in a three-component plasma (electrons, primary ions and impurity ions) is performed using a fully kinetic, sheared slab model. The quasi-linear particle and energy fluxes for each species are also computed. For the ITG mode, it is found that increasing plasma dilution (increasing Zeff) as well as increasing peakedness of the Zeff profile are strongly stabilizing. The quasi-linear calculations of the total anomalous energy flow driven by ITG mode turbulence shows that for Zeff profiles that are nearly flat and of moderately low value (Zeff ≲ 2), an energy 'pinch' is possible. A possible connection of this result with recent DIII-D off-axis heating experiments is discussed. A concomitant feature of this inward energy flow is an inward flow of primary ion particles, and an outward flow of impurity ion particles that greatly exceeds the neoclassical level. The impurity effects on the DTE mode are opposite, i.e. increasing dilution and Zeff profile peakedness are strongly destabilizing. As a result, quasi-linear theory predicts a large increase in the anomalous electron energy flux and much smaller effects on the anomalous fluxes of the ion species

Isotope scaling in the drift wave model

Impurity ion dynamics are incorporated into a numerical stability analysis of electrostatic drift waves in a sheared slab model. Using a simple iδ model for the electron branch, it is shown that a significant increase in growth rate, proportional to the primary ion mass at moderate Zeff, results for Te ≫ Ti. For the ion branch, the ion temperature gradient (ITG) mode, it is found that in hydrogen and deuterium plasmas the growth rates are inversely proportional to the primary ion mass when Zeff < 2; for Zeff ≥ 2, the ITG mode is generally stable. Using quasilinear theory, it is also shown that for ITG mode turbulence in hydrogen and deuterium plasmas in the low Zeff range (typical of high density Ohmic plasmas) the energy confinement time scaling with atomic mass number A of the primary ion species is τE ∝ Aβ, with β ≃ 0.6. Conversely, the present analysis indicates that confinement in helium plasmas is similar to that obtained for hydrogen. It is suggested that a similar result obtains for electron drift wave turbulence in low density Ohmic plasmas where Tc ≫ Ti when Zeff ≫ 1.

Ion temperature gradient mode and H-mode confinement

The stability properties of the toroidal ion temperature gradient (ITG) mode change dramatically for plasmas with flat density profiles, as found in H-mode plasmas. Even though ηi ≫ 1, the relevant stability parameter is is the ion temperature gradient scale length and R is the major radius). It is proposed that a significant element in the improved confinement observed in the L- to H-mode transient is the diminution of ITG mode turbulence, mediated by broader H-mode ion temperature profiles. Confinement results of L- and H-mode simulations of DIII-D, based on a simplified energy transport equation, are presented to support this hypothesis.

Three-dimensional global numerical simulation of ion temperature gradient mode turbulence

Three-dimensional global numerical simulations of ion temperature gradient mode turbulence in a sheared and curved magnetic field corresponding to tokamak geometry is obtained. The key result demonstrates that there is no significant dependence of the bulk heat transport on the edge safety factor q in agreement with analytic theories. The motivation for this question in relation to tokamak experiments is discussed.