Ion Temperature Gradient Turbulence Research Articles

Excited ion-scale turbulence by a magnetic island in fusion plasmas

The characteristics of ion-scale turbulence in the presence of a magnetic island are numerically investigated using a gyrokinetic model in fusion plasma. We observe that in the absence of the usual ion temperature gradient (ITG) drive gradient, a magnetic island and its flatten effect could drive ITG instability. The magnetic island (MI) not only drives high-n modes of ITG instability but also induces low-n modes of vortex flow. Moreover, as the magnetic island width increases, the width of the vortex flow also increases. This implies that wider islands may more easily induce vortex flows. The study further indicates that the saturated amplitude and transport level of MI-induced ITG turbulence vary with different magnetic island widths. In general, larger magnetic islands enhance both particle and heat transport. When the magnetic island width reaches to 21ρi, the turbulence-driven transport becomes the same level with the cases that ITG is driven by pressure gradients. Our findings indicate the presence of intricate nonlinear effects in the modulation of plasma turbulence by MIs. These effects are of significant importance for comprehending the phenomenon of nonlinear coupling in forthcoming tokamaks such as ITER.

Limit cycle oscillations in the zonal-flow-catalyzed interactions of ion-temperature-gradient turbulence

Limit-cycle oscillations are studied for ion temperature gradient turbulence, which, in the absence of large diamagnetic (mean) shear flows, saturates through energy transfer from unstable modes to large-scale stable modes via zonal-flow intermediary modes. Oscillations of zonal flow and turbulence levels are strongly constrained by the reactive, largely non-dissipative character of the zonal flows. Since existing predator–prey models for observed oscillations in experiments do not include energy transfer through zonal flows to stable modes, low-order fluid models with this physics are constructed and investigated. A simple three-wave truncation produces low-amplitude zonal flows that slowly oscillate around a zero mean, with turbulence oscillations between coupled wavenumbers that exceed linear frequencies by orders of magnitude. This inconsistency with experimental observations is caused by the weak non-linear drive of zonal flows in three-wave systems and the lack of multiple-wavenumber turbulent interactions. A more comprehensive model that preserves multiple wavenumber interactions within the context of conservative zonal-flow-mediated energy transfer to stable modes accurately reflects observed dynamics when the phase between stable and unstable modes is occasionally randomized.

Turbulence Transition in Magnetically Confined Hydrogen and Deuterium Plasmas.

In this study, we discovered a turbulence transition in a large helical device. The turbulence level and turbulence-driven energy transport decrease to a specific transition density and increase above it. The ruling turbulences below and above the transition density were ion-temperature gradient (ITG) and resistive-interchange (RI) turbulences, consistent with the predictions of gyrokinetic theory and two-fluid MHD model, respectively. Isotope experiments on hydrogen (H) and deuterium (D)clarified the role of transitions. In the ITG regime, turbulence levels and energy transport were comparable in the H and D plasmas. In contrast, in the RI regime, they were clearly suppressed in the D plasma. The results provide crucial knowledge for understanding isotope effects and future optimization of stellarator and heliotron devices.

Energy exchange between electrons and ions in ion temperature gradient turbulence

Microturbulence in magnetic confined plasmas contributes to energy exchange between particles of different species as well as the particle and heat fluxes. Although the effect of turbulent energy exchange has not been considered significant in previous studies, it is anticipated to have a greater impact than collisional energy exchange in low collisional plasmas such as those in future fusion reactors. In this study, gyrokinetic simulations are performed to evaluate the energy exchange due to ion temperature gradient (ITG) turbulence in a tokamak configuration. The energy exchange due to the ITG turbulence mainly consists of the cooling of ions in the ∇B-curvature drift motion and the heating of electrons streaming along a field line. It is found that the ITG turbulence transfers energy from ions to electrons regardless of whether the ions or electrons are hotter, which is in marked contrast to the energy transfer by Coulomb collisions. This implies that the ITG turbulence should be suppressed from the viewpoint of sustaining the high ion temperature required for fusion reactions since it prevents energy transfer from alpha-heated electrons to ions as well as enhancing ion heat transport toward the outside of the reactor. Furthermore, linear and nonlinear simulation analyses confirm the feasibility of quasilinear modeling for predicting the turbulent energy exchange in addition to the particle and heat fluxes.

Safety factor influence on the edge E × B velocity establishment in tokamak plasmas

This study is motivated by experiments on Tore Supra and WEST tokamaks where a deepening of the E × B velocity—governed by the radial electric field Er —near the edge is observed when the safety factor decreases in L-mode plasmas. Flux-driven global simulations of ion temperature gradient turbulence recover qualitatively the trend observed in the experiments, i.e. the E × B velocity increases when decreasing the safety factor. From these simulations, multiple clues point out the role of turbulence in the establishment of the radial electric field even though the turbulent intensity increases with the safety factor. The proposed mechanism to elucidate this phenomenon, backed up by a reduced model, is that the damping of the poloidal flow, governed by the neoclassical friction, increases more strongly with the safety factor than the turbulent drive for Er , due to the (r,θ) component of the Reynolds stress.

Global gyrokinetic simulations of electrostatic microturbulent transport in LHD stellarator with boron impurity

Global gyrokinetic simulations of electrostatic microturbulent transport for discharge # 166256 of the Large Helical Device stellarator in the presence of boron impurity show the co-existence of the ion temperature gradient (ITG) turbulence and trapped electron mode (TEM) turbulence before and during boron powder injection. ITG turbulence dominates in the core, whereas TEM dominates near the edge, consistent with the experimental observations. Linear TEM frequency increases from ∼80 kHz to ∼100 kHz during boron injection, and ITG frequency decreases from ∼20 kHz to ∼13 kHz, consistent with the experiments. The poloidal wave number spectrum is broad for both ITG (0–0.5 mm−1) and TEM (0–0.25 mm−1). The nonlinear simulations with boron impurity show a reduction in the heat conductivity compared to the case without boron. The comparison of the nonlinear transport before and during boron injection shows that the ion heat transport is substantially reduced in the region where the TEM is dominant. However, the average electron heat transport throughout the radial domain and the average ion heat transport in the region where the ITG is dominant are similar. The simulations with boron show the effective heat conductivity values qualitatively agree with the estimate obtained from the experiment.

Impact of fast ions on microturbulence and zonal flow dynamics in HL-2A internal transport barriers

The turbulent transport properties and dynamics of zonal flows (ZFs) in the presence of fast ions (FIs) are investigated for a typical internal transport barrier (ITB) plasma based on the gyrokinetic approach, focusing on the role of FI temperature and the effects of the toroidal rotation, including the E× B rotational shear, parallel velocity gradient (PVG) as well as the rotation velocity itself. Linear GENE simulations have shown that the core ITB plasma on HL-2A is dominated by ion temperature gradient (ITG) modes and trapped electron modes (TEMs), where the former is stabilized by FIs whereas destabilized by the PVG. Neither of the FIs or the PVG has observable effect on TEMs. The ion heat transport generally decreases at large FI temperature due to the nonlinear electromagnetic stabilization of turbulence with increased total plasma β until electromagnetic modes are excited. The transport fluxes peak around a certain FI temperature and the ZF shearing rate is significantly higher at such value compared with that in the absence of FIs, and the heat flux reduction is a result of the synergistic interaction between turbulence, ZFs and the external rotational shear. The E× B shear stabilizing and PVG destabilizing is not obvious at low normalized ITG R/L Ti, indicating they are less important in determining the stiffness level in the relatively low density and rotation scenarios regarding the HL-2A ITB discharges. The turbulence suppression is predominated by the nonlinear stabilization of ITG turbulence as well as enhanced ZFs simultaneously in the presence of FIs. These results have also provided the possible way to reduce the turbulence transport through increasing the FI temperature in the off-axis neutral beam heated plasmas such as in HL-2A.

Cross phases of temperature-gradient-driven turbulence as a model basis for I-mode particle transport

As a model for understanding the type of transport behavior characteristic of the tokamak I mode, cross-phase physics for particle-transport is studied analytically for turbulence dominated by either ion-temperature-gradient (ITG) or electron-temperature-gradient (ETG) instability. I mode is a transport-barrier regime of reduced thermal transport but essentially unaffected particle transport. It is assumed that ITG turbulence applies to the baseline L mode, ETG to I mode, and that E × B flow shear is stronger in I mode, lowering all fluxes. In ITG turbulence, particle transport is governed by trapped electrons. Sensitivity to collisions produces the well-known temperature-gradient-driven pinch that offsets density-gradient-driven outward diffusion, weakening particle transport in L mode. In ETG turbulence, nonadiabatic ions are collisionless. Nonzero transport requires an ion spectrum feature whose magnetic-drift resonance supplies the necessary cross phase. If frequencies of order the ion diamagnetic drift frequency dominate the ion part of the spectrum, as would occur with weakly unstable ITG turbulence, all components of the particle transport are outward and can offset flow-shear-induced flux reductions to produce a flux that is similar to the ITG L-mode particle flux. Nonlinear frequencies are potentially relevant and discussed in relation to I mode.

On the effect of negative triangularity on ion temperature gradient turbulence in tokamaks

Considering the same magnetic equilibrium and plasma conditions as in Duff et al. [Phys. Plasmas 29, 012303 (2022)], we perform linear and nonlinear simulations of electrostatic ion temperature gradient turbulence investigating the role of triangularity δ. Differently from what was previously reported, we find that triangularity increases the transport level regardless of its sign, but more strongly when δ is positive. For the case analyzed, we identify the shear of triangularity as the critical parameter determining the transport level, indicating that even in the local limit negative triangularity can reduce the transport efficiently, suggesting that confinement improvement can also be expected for larger devices.

Isotope effects on energy transport in the core of ASDEX-Upgrade tokamak plasmas: Turbulence measurements and model validation

Design and operation of future tokamak fusion reactors using a deuterium–tritium 50:50 mix requires a solid understanding of how energy confinement properties change with ion mass. This study looks at how turbulence and energy transport change in L-mode plasmas in the ASDEX Upgrade tokamak when changing ion species between hydrogen and deuterium. For this purpose, both experimental turbulence measurements and modeling are employed. Local measurements of ion-scale (with wavevector of fluctuations perpendicular to the B-field k⊥< 2 cm−1, k⊥ρs< 0.2, where ρs is the ion sound Larmor radius using the deuterium ion mass) electron temperature fluctuations have been performed in the outer core (normalized toroidal flux ρTor=0.65−0.8) using a multi-channel correlation electron cyclotron emission diagnostic. Lower root mean square perpendicular fluctuation amplitudes and radial correlation lengths have been measured in hydrogen vs deuterium. Measurements of the cross-phase angle between a normal-incidence reflectometer and an ECE signal were made to infer the cross-phase angle between density and temperature fluctuations. The magnitude of the cross-phase angle was found larger (more out-of-phase) in hydrogen than in deuterium. TRANSP power balance simulations show a larger ion heat flux in hydrogen where the electron-ion heat exchange term is found to play an important role. These experimental observations were used as the basis of a validation study of both quasilinear gyrofluid trapped gyro-Landau fluid-SAT2 and nonlinear gyrokinetic GENE codes. Linear solvers indicate that, at long wavelengths (k⊥ρs<1), energy transport in the deuterium discharge is dominated by a mixed ion-temperature-gradient (ITG) and trapped-electron mode turbulence while in hydrogen transport is exclusively and more strongly driven by ITG turbulence. The Ricci validation metric has been used to quantify the agreement between experiments and simulations taking into account both experimental and simulation uncertainties as well as four different observables across different levels of the primacy hierarchy.

Self-consistent gyrokinetic modeling of turbulent and neoclassical tungsten transport in toroidally rotating plasmas

The effect of toroidal rotation on both turbulent and neoclassical transport of tungsten (W) in tokamaks is investigated using the flux-driven, global, nonlinear 5D gyrokinetic code GYSELA. Nonlinear simulations are carried out with different levels of momentum injection that drive W into the supersonic regime, while the toroidal velocity of the main ions remains in the subsonic regime. The numerical simulations demonstrate that toroidal rotation induces centrifugal forces that cause W to accumulate in the outboard region, generating an in–out poloidal asymmetry. This asymmetry enhances neoclassical inward convection, which can lead to central accumulation of W in cases of strong plasma rotation. The core accumulation of W is mainly driven by inward neoclassical convection. However, as momentum injection continues, roto-diffusion, proportional to the radial gradient of the toroidal velocity, becomes significant and generates outward turbulent flux in the case of ion temperature gradient turbulence. Overall, the numerical results from nonlinear GYSELA simulations are in qualitative agreement with the theoretical predictions for impurity transport.

Global gyrokinetic simulations of the impact of magnetic island on ion temperature gradient driven turbulence

The effect of island width on the multi-scale interactions between magnetic island (MI) and ion temperature gradient (ITG) turbulence has been investigated based on the global gyrokinetic approach. It is found that the coupling between the island and turbulence is enhanced when the MI width (w) becomes larger. A vortex flow that is highly sensitive to the width of the MI can be triggered, ultimately resulting in a potent shear flow and a consequent reduction in turbulent transport. The shearing rate induced by the vortex flow is minimum at the O-point while it is maximum at both of the two reconnection points of the island, i.e. the X-points, regardless of the island width. There exists a nonmonotonic relationship between zonal flow (ZF) amplitude and island width, showing that the ZF is partially suppressed by medium-sized MIs whereas enhanced in the case of large island. A larger MI can tremendously damage the ITG mode structure, resulting in higher turbulent transport at the X-point whereas a lower one at the O-point, respectively. Such phenomenon will be less distinct at very small island widths below w/a ∼ 8% ≈ 12 (a is the minor radius and the ion gyroradius), where it shows that turbulence near the X-point is hardly affected although it is still suppressed inside the island. Furthermore, the influence of different island sizes on turbulence transport level is also discussed.

Full-flux-surface effects on electrostatic turbulence in Wendelstein 7-X-like plasmas

We present the first nonlinear, gyrokinetic, surface-global simulations of a Wendelstein 7-X-like stellarator with kinetic electrons. As a first application, we investigate the interplay between Ion Temperature Gradient (ITG) and Trapped Electron Mode (TEM) driven turbulence in a Full-Flux-Surface (FFS) approach, as well as the effect of a neoclassical radial electric field, something that escapes the capabilities of flux-tube simulations. We find that even in this more complex setup, ITG turbulence is stabilised through a finite density gradient while TEM turbulence remains relatively weak. Furthermore, we show that the effect of the radial electric field itself is small in comparison with the variation of the gradients. Nevertheless, we observe that for some of the cases shown here, there is not only quantitative but also qualitative disagreement between flux-tube and FFS simulations, in contrast to earlier studies with an adiabatic electron model. These results emphasise the potential importance of retaining geometrical variations on the flux-surface when describing stellarator turbulence under realistic conditions.

Development of an unstructured mesh gyrokinetic particle-in-cell code for exascale fusion plasma simulations on GPUs

This paper presents XGCm, a new unstructured mesh gyrokinetic Particle-in-Cell (PIC) code for modeling fusion plasma. The physical models and aspects of the numerical methods employed are the same as those used in the X-point gyrokinetic code, XGC. The core difference is that XGCm builds on an unstructured mesh-centric infrastructure that supports a distributed mesh, making it scalable in both the number of mesh elements and number of particles. A second advantage of an unstructured mesh infrastructure is its performance is not degraded when generally graded or anisotropic meshes are used. The switch from a particle-centric data infrastructure to a distributed mesh-centric infrastructure required the introduction of new methods to execute core PIC operations and substantial modifications to a number of key algorithms from those used in XGC. First, we present the methods and algorithms used in the development of XGCm, which performs all key computing steps on the GPU accelerators. GPU accelerators are providing the main computational power of current generation U.S. Department of Energy supercomputers. Secondly, we perform code validation and test using the circular geometry cyclone base case and realistic DIII-D geometry case, respectively. The turbulence growth rate shows excellent agreement with existing XGC result in the first case, while ion temperature gradient turbulence growth is further demonstrated in the second case. Finally, we present weak scaling results, using up to full system (27,648 GPUs) of the Oak Ridge National Laboratory's Summit supercomputer.

The performance of equilibrium radial electric field shear on microturbulence with different magnetic shears in tokamak plasmas

Global gyrokinetic particle simulations show that equilibrium radial electric field (E r ) shear reduces the linear growth rate, ion heat conductivity, and nonlinear turbulence amplitude for both the ion temperature gradient (ITG) and kinetic ballooning mode (KBM) microturbulence by tilting the poloidal mode structure. The increase in the magnetic shear enhances the stabilizing performance of the E r shear on linear growth rate for the ITG case but has no effect on that for the KBM case. The radial correlation length of the ITG turbulence is decreased by increasing the magnetic shear in a weak ion diamagnetic flow shear condition with low β, leading to a reduction in the effective E × B shearing rate, which weakens the suppression performance of the E r shear on the ITG turbulence amplitude. In contrast, under a larger ion diamagnetic shear flow for higher β, an increase in magnetic shear strengthens the suppression performance of the E r shear on the KBM turbulence amplitude due to an increase in the effective shearing rate by increasing the radial correlation length of the turbulence.

ITB formation in gyrokinetic flux-driven ITG/TEM turbulence

The formation mechanism of internal transport barriers (ITBs) in flux-driven turbulence is studied by means of the full-f gyrokinetic code GKNET. In the adiabatic electron case with a weak magnetic shear configuration, toroidal momentum injection can change the radial mean electric field through radial force balance, leading to a kind of driven ITB formation in which the ion thermal diffusivity by ion temperature gradient (ITG) turbulence decreases to the neoclassical transport level. Only cocurrent toroidal rotation in the outer core region can benefit the ITB formation, and this mechanism is identified to originate from a positive feedback loop between the radial shear and resultant momentum flux. On the other hand, in the kinetic electron case with a reversed magnetic shear configuration, robust co-intrinsic rotation is driven near the surface in ITG turbulence and sustains the shear through the radial force balance, leading to the spontaneous reduction of ion turbulent thermal diffusivity, while this is not observed in the adiabatic electron case. In the presence of electron heating, counter-intrinsic rotation by trapped electron mode turbulence is selectively driven in the negative magnetic shear region, which provides steeper shear formation and a resultant larger reduction of ion turbulent thermal diffusivity. This indicates that the co-existence of different modes can trigger the ‘discontinuity’ of mode structure, intrinsic rotation, and resultant mean near , leading to spontaneous ITB formation.

Effects of alpha particles on the transport of helium ash driven by collisionless trapped electron mode turbulence

The effects of alpha (α) particles on the transport of helium ash driven by collisionless trapped electron mode (CTEM) turbulence are analytically studied using quasi-linear theory in tokamak deuterium (D) and tritium (T) plasmas. Under the parameters used in this work, the transport of helium ash is mainly determined by the diffusion due to very weak convection. It is found that the ratio between helium ash diffusivity and effective electron thermal conductivity (D He/χ eff) driven by CTEM turbulence, which is a proper normalized parameter for quantifying the efficiency of helium ash removal, is smaller than unity. This indicates the less efficient removal of helium ash through CTEM turbulence as compared with ion temperature gradient (ITG) turbulence in [Angioni et al 2009 Nucl. Fusion 49 055013]. However, the efficiency of helium ash removal is increased 55% by the presence of 3% α particles with their density gradient being equivalent to that of electrons, and this enhancement can be further strengthened by steeper profile of α particles. This is mainly because the enhancement of helium ash diffusivity by α particles is stronger than that of the effective electron thermal conductivity. Moreover, the higher fraction of T ions, higher temperature ratio between electrons and thermal ions as well as flatter electron density profile, the stronger enhancement of D He/χ eff, and α particles further strengthen the favorable effects of these parameters on the removal of helium ash.

Global gyrokinetic simulations of electrostatic microturbulent transport using kinetic electrons in LHD stellarator

Global gyrokinetic simulations of ion temperature gradient (ITG) and trapped electron mode (TEM) in the LHD stellarator are carried out using the gyrokinetic toroidal code (GTC) with kinetic electrons. ITG simulations show that kinetic electron effects increase the growth rate by more than 50% and more than double the turbulent transport levels compared with simulations using adiabatic electrons. Zonal flow dominates the saturation mechanism in the ITG turbulence. Nonlinear simulations of the TEM turbulence show that the main saturation mechanism is not the zonal flow but the inverse cascade of high to low toroidal harmonics. Further nonlinear simulations with various pressure profiles indicate that the ITG turbulence is more effective in driving heat conductivity whereas the TEM turbulence is more effective for particle diffusivity.

Seeking turbulence optimized configurations for the Wendelstein 7-X stellarator: ion temperature gradient and electron temperature gradient turbulence

We examine the turbulence driven by the ion and electron temperature gradients in selected magnetic configurations of the Wendelstein 7-X (W7-X) stellarator. The inherent flexibility in the configuration space of W7-X enables us to find candidate configurations manifesting low turbulent transport. We follow insights gained by stellarator optimization techniques, in order to identify key geometric features, which are directly related to the ion and electron heat fluxes produced by plasma turbulence. One such a feature is the flux expansion at locations where the curvature is particularly unfavourable. Starting from a configuration routinely used in the W7-X experiment, we end up with an optimized configuration. Based on this equilibrium, we select a configuration from W7-X configuration database with a similar feature as the optimized one. With the help of nonlinear gyrokinetic simulations, we show that the heat flux in this configuration is less stiff than in the initial configuration, both for ion temperature gradient and electron temperature gradient turbulence.

Transport events and $$E \times B$$ staircase in flux-driven gyrokinetic simulation of ion temperature gradient turbulence

Transport events and $$E \times B$$ staircase in flux-driven gyrokinetic simulation of ion temperature gradient turbulence