ITG Modes Research Articles

Progress in the development of the ITER baseline scenario in TCV

Under the auspices of EUROfusion, the ITER baseline (IBL) scenario has been jointly investigated on AUG and TCV in the past years and this paper reports on the developments on TCV. Three ITER shapes, namely the JET, AUG and ITER IBL have been reproduced in TCV, illustrating that the higher the triangularity the larger the ELM perturbation and the more difficult it is to reach stationary states with q 95< 3.6. It is found that the performance of TCV IBL is mainly limited by (neoclassical) tearing modes, in particular 2/1 modes which are triggered after a large ELM. It is demonstrated that the shorter the ELM period the larger β N at the NTM onset. We show that these modes can be avoided with central X3 EC heating at relatively high q 95 and moderate β N . However, the lack of significant ECH at the high central densities obtained in TCV IBL scenario limits the duration of low q 95 cases to about four confinement times. During this time, density usually keeps peaking until (neoclassical) tearing modes are triggered. Nevertheless, the TCV IBL database covers the ITER target values ( H98y2∼ 1, βN∼ 1.8 at q95∼ 3) and a slightly better confinement than requested for ITER is reported. Integrated modelling results show that ITG modes are the dominant instabilities, and show that, in TCV, fuelling also plays a role to sustain peaked density profiles. The role of profiles, sawteeth and ELMs regarding MHD stability are also discussed.

Gyrokinetic simulation of short wavelength ion temperature gradient instabilities in the ADITYA-U tokamak

In this work, linear and nonlinear collisionless electrostatic simulation studies of the standard and short wavelength ion temperature gradient mode (SWITG) for experimental profiles and parameters of ADITYA-U tokamak are performed using the linear global eigenvalue gyrokinetic code GLOGYSTO and the nonlinear global gyrokinetic particle-in-cell code ORB5. All simulations are carried out with non-adiabatic ions and adiabatic electrons. The ADITYA-U tokamak which has recently been upgraded to divertor configuration, is small in size and well suited for investigation of micro-instabilities in the presence of density and temperature gradients. Due to steep density and temperature gradients, simulation shows that the SWITG mode naturally exists along with the standard ion temperature gradient (ITG) mode in ADITYA-U. In this work, the experimental shot# 33536 of the ADITYA-U tokamak is considered as a reference. There is good agreement in the growth rate and the real frequency values between GLOGYSTO and ORB5 with variations of less than . Two maxima of growth rate versus mode number are obtained, the first around is the standard ITG, the second around is the SWITG. Additionally, using linear stability analysis, it is observed that the SWITGs are suppressed for low values of i.e. only the standard ITG mode remains unstable. For the ADITYA-U tokamak, nonlinear global simulations with ORB5 are also carried out. Nonlinearly, SWITG dominating case results are compared with the conventional ITG case, where SWITG is relatively suppressed. The nonlinear contribution of the SWITG mode to the total thermal ion heat transport is found to be minimal due to an increased zonal flow shearing effect on the SWITG mode suppression, even though it may be linearly more unstable than the conventional long wavelength () ITG mode.

Neon seeding effects on two high-performance baseline plasmas on the Joint European Torus

We present the JETTO-QuaLiKiz-SANCO fully predictive modelling of two JET-ILW high-performance baseline plasmas, a Ne seeded shot and an equivalent unseeded one. The motivation of the work lies in the experimental observation of a slightly higher confinement and performance of the Ne seeded shot with respect to the unseeded one, despite sharing the same main plasma parameters and heating powers. Moreover, the neon seeded shot shows a lower pedestal electron density and a higher core ion temperature with respect to the unseeded one. Integrated modelling is performed in order to understand if the cause of the improved confinement has to be ascribed to the improved pedestal parameters with neon seeding or if an impurity-induced turbulence stabilization is at play. The QuaLiKiz transport model is used for predicting the electron density, electron and ion temperatures and rotation in the core up to the pedestal top, while the pedestal is empirically modelled to reproduce the experimental kinetic profiles. The thermal diffusivities of the two shots, computed by QuaLiKiz, are compared, as well as the turbulence spectra, suggesting that the reduced transport found in the neon seeded shot is due in part to the stabilization of ion temperature gradient and electron temperature gradient modes. Further modelling is performed in order to disentangle the neon seeding effects, which are a direct effect on the turbulence stabilization and an indirect effect on the pedestal parameters. The results suggest that the improved performance with neon is due to a combination of turbulence stabilization and improved pedestal parameters.

Kinematic viscosity estimates in reversed-field pinch fusion plasmas

This paper concerns the kinematic viscosity in reversed-field pinch fusion plasmas, including both the study of numerical magneto-hydrodynamics (MHD) simulations and the analysis of RFX-mod experimental data.In the first part, we study the role of non-uniform time-constant radial viscosity profiles in 3D non-linear visco-resistive MHD simulations. The new profiles induce a moderate damp (for the velocity field) and a correspondent enhancement (for the magnetic field) of the spectral components resonating in the regions where the viscosity is higher.In the second part, we evaluate the kinematic viscosity coefficient on a wide database of RFX-mod shots according to the transport theories of Braginskii (considering parallel, perpendicular and gyro viscosity coefficients), considering the action on viscosity of ITG modes (ion temperature gradient) and according to the transport theory of Finn. We then exploit the comparison with the visco-resistive MHD simulations (where the visco-resistive dissipation rules the MHD activity) to show that the classical Braginskii perpendicular viscosity produces the best agreement between simulations and data, followed by the Braginskii gyro-viscosity.

On the role of density fluctuations in the core turbulent transport of Wendelstein 7-X

A recent characterization of core turbulence carried out with a Doppler reflectometer in the optimized stellarator Wendelstein 7-X (W7-X) found that discharges achieving high ion temperatures at the core featured an ITG-like suppression of density fluctuations driven by a reduction of the gradient ratio (Carralero et al 2021 Nucl. Fusion 61 096015). In order to confirm the role of ITG turbulence in this process, we set out to establish experimentally the relation between core density fluctuations, turbulent heat flux and global confinement. With this aim, we consider the scenarios found in the previous work and carry out power balance analysis for a number of representative ones, including some featuring high ion temperature. We also evaluate the global energy confinement time and discuss it in the context of the ISS04 inter-stellarator scaling. We find that when turbulence is suppressed as a result of a reduction of η i , there is a reduction of ion turbulent transport, and global performance is improved as a result. This is consistent with ITG turbulence limiting the ion temperature at the core of W7-X. In contrast, when turbulence is reduced following a decrease in collisionality, no changes are observed in transport or confinement. This could be explained by ITG modes being combined with TEM turbulence when the latter is destabilized at low collisionalities.

The role of ion and electron-scale turbulence in setting heat and particle transport in the DIII-D ITER baseline scenario

The heat and particle transport in a DIII-D ITER baseline scenario discharge has been investigated using both linear and nonlinear gyrokinetic simulations performed with the CGYRO code [Candy et al J. Comput. Phys. 2016]. These simulations were used to investigate the role that ion-scale (k θ ρ s < 1.0) and electron-scale (k θ ρ s > 1.0) turbulence play in determining heat and particle transport in the core of conditions believed to directly extrapolate to ITER operation. This investigation spans over nearly half of the plasma minor radius, from ρ = 0.45–0.85. To probe the nature of the transport and turbulence in these conditions and to validate the model against experimental fluxes, scans of , , and a/L n were performed at all radial locations. Long wavelength turbulence is found to be dominated by ITG modes with strong non-adiabatic electron effects and appears unable to reproduce ion and electron heat fluxes and electron particle fluxes simultaneously at most radial positions when single parameter scans are performed. To investigate the potential role of short wavelength turbulence, a series of electron-scale simulations are performed that indicate that experimentally relevant levels of electron heat flux could arise at sub-ion scales. Quantitative comparison of the simulated fluxes obtained from ion and electron-scale simulations with experimental levels along with the sensitivity of simulations results to changes in inputs is presented. Through extensive sensitivity scans and comparison with multiple transport channels, this work demonstrates a clear need for self-consistent modification of multiple inputs and suggests multi-scale interactions play a significant role at many of the radial locations studied. The results of this analysis help shape our understanding of the model fidelity needed to predict turbulence and transport reactor-relevant conditions and have important implications for the prediction of future fusion devices.

An experimental characterization of core turbulence regimes in Wendelstein 7-X

First results from the optimized helias Wendelstein 7-X stellarator (W7-X) have shown that core transport is no longer mostly neoclassical, as is the case in previous kinds of stellarators. Instead, power balance analysis has shown that turbulent transport poses a serious limitation to the global performance of the machine. Several studies have found this particularly relevant for ion transport, with core ion temperatures becoming clamped at relatively low values of T i ≃ 1.7 keV, except in the few scenarios in which turbulence can be suppressed. In order to understand the precise turbulent mechanisms at play and thus design improved performance scenarios, it is important to have a clear understanding of the parametric dependencies of turbulent fluctuations, and the relation between them and turbulent transport. As a first step in this direction, in this work we use Doppler reflectometry measurements carried out during a number of relevant operational scenarios to provide a systematic characterization of ion-scale (k ⊥ ρ i ≃ 1) density fluctuations in the core of W7-X. Then, we study the relation between fluctuation amplitude and plasma profiles and show how distinct regimes can be defined for the former, depending on normalized gradients and . Furthermore, we discuss the importance of other potentially relevant parameters such as T e/T i, E r or collisionality. Comparing the different regimes, we find that turbulence amplitude depends generally on the gradient ratio η i = , as would be expected for ITG modes, with the exception of a range of discharges, for which turbulence suppression may be better explained by an ITG to TEM transition triggered by a drop in collisionality. Finally, we show a number of scenarios under which T i,core > 1.7 keV is achieved and how core fluctuations are suppressed in all of them, thus providing experimental evidence of microturbulence being the main responsible for the limited ion confinement in W7-X.

Recent results of fusion triple product on EAST tokamak

High fusion triple product has been obtained in the advanced scenarios with high normalized beta (β N) on the Experimental Advanced Superconducting Tokamak (EAST). A record value of n i0 T i0 τ E ∼ 1.0 × 1019 m−3 keV s for EAST deuterium plasma has been achieved, which is due to the formation of strong and broad internal transport barriers (ITBs) in n e, T e and T i profiles. Analysis shows that the strong ITB formation could be attributed to the reduction of transport from ITG modes. Based on the analysis, the physical mechanisms and methods to further improve the plasma performance are discussed.

Calculating the linear critical gradient for the ion-temperature-gradient mode in magnetically confined plasmas

A first-principles method to calculate the critical temperature gradient for the onset of the ion-temperature-gradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions of the connection length previously invoked in tokamak research should be revised and replaced by a generalized correlation length to explain this onset in stellarators. Simple numerical experiments and gyrokinetic theory show that localized ‘spikes’ in shear, a hallmark of stellarator geometry, are generally insufficient to constrain the parallel correlation length of the mode. ITG modes that localize within bad drift curvature wells that have a critical gradient set by peak drift curvature are also observed. A case study of near-helical stellarators of increasing field period demonstrates that the critical gradient can indeed be controlled by manipulating the magnetic geometry, but underscores the need for a general framework to evaluate the critical gradient. We conclude that average curvature and global shear set the correlation length of resonant ITG modes near the absolute critical gradient, the physics of which is included through direct solution of the gyrokinetic equation. Our method, which handles the general geometry and is more efficient than conventional gyrokinetic solvers, could be applied to future studies of stellarator ITG turbulence optimization.

Fast-ion pressure dominating the mass dependence of the core heat transport in ASDEX Upgrade H-modes

H-mode plasmas in ASDEX Upgrade (AUG) using different hydrogen isotopes are analysed with respect to their core transport properties. The experimental results are discussed and we present gyrokinetic simulations which are able to reproduce the experimental observations. A novel strategy allows us to disentangle core and pedestal physics by mitigating the isotopic dependence of pedestal properties while keeping the heat and particle sources the same. Matched pedestal profiles are obtained between hydrogen (H) and deuterium (D) plasmas when increasing the triangularity in H plasmas with respect to D plasmas. In the core of these plasmas little isotopic dependence is observed when the fast-ion content is low W fast/W th < 1/3. Quasi-linear modelling with TGLF reproduces the experimental trends under these conditions. For larger fast-ion fractions an isotope dependence is observed in the core heat transport. This is related to a difference in fast-ion stabilization of turbulent transport. The fast-ion pressure in H and D plasmas is different due to the mass dependence in the fast-ion slowing down time as well as to operational restrictions when heating with H neutral beam injection (H-NBI) or D-NBI. Typically, W fast,H < 1/2W fast,D for comparable NBI heating powers in AUG. The gyrokinetic analysis shows that linear growth rates of ITG modes do not show a pure gyro-Bohm mass dependence, but follow the experimentally observed mass dependence when taking collisions, EM-effects and fast ions into account. Non-linear gyrokinetic simulations reproduce the experimental heat fluxes for different isotopes when fast ions are included. This highlights the role of the fast-ion pressure as a key element to explain the observed differences in the core of H and D plasmas.

Understanding LOC/SOC phenomenology in tokamaks

Phenomenology of Ohmic energy confinement saturation in tokamaks is reviewed. Characteristics of the linear Ohmic confinement (LOC) and saturated Ohmic confinement (SOC) regimes are documented and transformations in all transport channels across the LOC/SOC transition are described, including rotation reversals, ‘non-local’ cut-off and density peaking, in addition to dramatic changes in fluctuation intensity. Unification of results from nearly 20 devices indicates that the LOC/SOC transition occurs at a critical value of the product of the density, edge safety factor and device major radius, and that this product increases with toroidal magnetic field. Comparison with gyro-kinetic simulations suggests that the effects of sub-dominant TEMs are important in the LOC regime while ITG mode turbulence dominates with SOC.

Nonlinear dynamics of ion temperature gradient driven modes in non-Maxwellian magnetoplasmas

In this paper, low frequency () two dimensional wave propagating in an electron-ion magnetoplasma is analytically studied in the presence of background density and ion temperature gradient using two fluid theory. Electrons are assumed to follow non-Maxwellian distribution, namely, kappa and Cairns distribution. In the linear regime, real and imaginary parts of dispersion relation are plotted for different distributions and the comparison is also drawn. In the nonlinear case, nonlinear partial differential equations (NLPDEs) are derived both for dispersive and dissipative cases for the ITG mode. The solutions of these NLPDEs are obtained using the functional variable method. The propagation characteristics of these nonlinear structures are observed by plotting them with different electron distributions for Tokamak parameters. It is found that the non-Maxwellian electrons alter the behavior of nonlinear structures for the ITG mode. The differences in the behavior of dispersive and dissipative solutions for different physical parameters of interest are also explored in detail. This work may be helpful to understand low frequency electrostatic modes in space and Tokamak plasmas where both background density inhomogeneity and nonthermal electron distributions have been observed.

Generalized curvature modified plasma dispersion functions and Dupree renormalization of toroidal ITG

A new generalization of curvature modified plasma dispersion functions is introduced in order to express Dupree renormalized dispersion relations used in quasi-linear theory. For instance the Dupree renormalized dispersion relation for gyrokinetic, toroidal ion temperature gradient driven (ITG) modes, where the Dupree’s diffusion coefficient is assumed to be a low order polynomial of the velocity, can be written entirely using generalized curvature modified plasma dispersion functions: Knm's. Using those, Dupree’s formulation of renormalized quasi-linear theory is revisited for the toroidal ITG mode. The Dupree diffusion coefficient has been obtained as a function of velocity using an iteration scheme, first by assuming that the diffusion coefficient is constant at each v (i.e. applicable for slow dependence), and then substituting the resulting v dependence in the form of complex polynomial coefficients into the Knm's for verification. The algorithm generally converges rapidly after only a few iterations. Since the quasi-linear calculation relies on an assumed form for the wave-number spectrum, especially around its peak, practical usefulness of the method is to be determined in actual applications. A parameter scan of ηi shows that the form of the diffusion coefficient is better represented by the polynomial form as ηi is increased.

Scaling study for positive magnetic shear ELMy H-mode plasmas in JT-60U

Scaling of the density peaking for positive magnetic shear ELMy H-mode plasmas in JT-60U has been developed. Although the density peaking generally depends on collisionality, a variation of the density peaking factor for the same collisionality exists, and the variation is different between plasmas with co-directed and ctr-directed toroidal rotation(co-VT plasmas and ctr-VT plasmas). The variation of the co-VT plasmas can be explained by particle source profile. As a result of scaling, the peaking factor of the co-VT plasmas depends on the particle source rate profile from neutral beams (NBs) as much as collisionality. The dataset of the ctr-VT plasmas has a larger variation of the peaking factor compared to that of the co-VT plasmas. The larger variation stems from that the peaking factor of the ctr-VT plasmas also depends on the normalized ion temperature gradient at the edge region. As a result of scaling, the normalized ion temperature gradient influences the peaking factor as much as or a little larger than collisionality. The parameter regime of the ctr-VT plasmas ranges from the trapped electron mode (TEM) to the ion temperature gradient mode (ITG mode). The plasmas with the positive correlation between the normalized density gradient and the normalized ion temperature gradient are dominated by the TEM. On the other hand, the plasmas with the negative correlation are dominated by the ITG mode.

Gyrokinetic simulation of ITG turbulence with toroidal geometry including the magnetic axis by using field-aligned coordinates

Simulation domain in field-aligned coordinates of the electrostatic gyrokinetic nonlinear turbulence global code, NLT, is extended to include the magnetic axis. The artificial boundary near the magnetic axis is replaced by the natural boundary. The singularity at the magnetic axis in Vlasov solver is treated by considering the spatial relation of fixed grid points in field-aligned coordinates. A new Poisson’s equation solver is developed, the coefficient matrix of algebraic equations is derived by using Gauss’s theorem. Linear ITG modes test, Rosenbluth–Hinton test and nonlinear relaxation test of the ITG turbulence with adiabatic electrons are performed. The gyrocenter conservation is much improved by including the magnetic axis in the simulation domain.

Growth rates of ITG modes in the presence of flow shear

Plasma microinstabilities in toroidal magnetic confinement devices can be driven unstable by a radial ion temperature gradient and stabilized by rotational flow shear. In this study, we argue that these nonlinear dynamics can be captured by the linear stabilization of Floquet modes. To that end, we propose a novel method (the τAC method) to calculate growth rates by averaging over linear Floquet modes. The τAC method is compared to nonlinear and other linear approaches and is shown to work well at low parallel velocity gradient drive. As such, the method provides a promising approach to explore the parameter dependencies of flow shear stabilization.

Stable and unstable roots of ion temperature gradient driven mode using curvature modified plasma dispersion functions

Basic, local kinetic theory of ion temperature gradient driven (ITG) mode, with adiabatic electrons is reconsidered. Standard unstable, purely oscillating as well as damped solutions of the local dispersion relation are obtained using a bracketing technique that uses the argument principle. This method requires computing the plasma dielectric function and its derivatives, which are implemented here using modified plasma dispersion functions with curvature and their derivatives, and allows bracketing/following the zeros of the plasma dielectric function which corresponds to different roots of the ITG dispersion relation. We provide an open source implementation of the derivatives of modified plasma dispersion functions with curvature, which are used in this formulation. Studying the local ITG dispersion, we find that near the threshold of instability the unstable branch is rather asymmetric with oscillating solutions towards lower wave numbers (i.e. drift waves), and damped solutions toward higher wave numbers. This suggests a process akin to inverse cascade by coupling to the oscillating branch towards lower wave numbers may play a role in the nonlinear evolution of the ITG, near the instability threshold. Also, using the algorithm, the linear wave diffusion is estimated for the marginally stable ITG mode.

Role of impurities in modifying isotope scaling law of ion temperature gradient turbulence driven transport in tokamak

Tokamak experiments show that the plasma empirical energy confinement scaling law varies with plasma ion mass (Ai) in a certain range under conditions of different plasma parameters or different devices. In order to understand such a modification of the empirical energy confinement scaling law, the isotope mass dependence of ion temperature gradient (ITG, including impurity modes) turbulence driven transport in the presence of tungsten impurity ions in tokamak plasma is studied by employing the gyrokinetic theory. The effect of heavy (tungsten) impurity ions on ITG and impurity mode is revealed to modify significantly the isotope mass dependence and effective charge effect. As the charge number of impurity ions (Z) or impurity charge concentration (fz) changes, the theoretical scaling law of ITG turbulence transport varies substantially in a relatively large range. The maximum growth rate of ITG mode scales as Mi-0.48 -0.12, whilst that of impurity mode scales as Mi-0.46 -0.3. Here, Mi is the mass number of primary ion in the plasma. In both cases the fitting index with Mi deviates further away from -0.5 when impurity charge concentration fz increases. The isotope mass dependence of ITG turbulence gradually weakens when the effective charge number Zeff increases. The isotope mass dependence of impurity mode turbulence also weakens with Zeff increasing for the same impurity ion charge number (Z). In contrast, the isotope mass dependence gradually strengthens with effective charge number Zeff increasing for the same impurity charge concentration (fz). On average, the maximum growth rates of impurity mode scale roughly as max~Mi-0.35Zeff1.5 and max~Mi-0.4Zeff1, respectively, for Zeff 3 and Zeff 3. The reason for the deviation of isotope scaling law from the normal case is investigated deliberately, and it is demonstrated that the isotope scaling index deviates from -0.5 more or less due to the fact that the impurity species, charge number and impurity concentrations vary in a certain range. These results demonstrate that it is impossible to deduce a unique isotope scaling law due to the variety of micro-instabilities and various plasma parameter regimes in tokamak plasma, which is consistent with the experimental observations. These results may contribute to the transport study involving heavy (tungsten) impurity ions in ITER discharge scenario investigation.

The effect of electron cyclotron heating on density fluctuations at ion and electron scales in ITER baseline scenario discharges on the DIII-D tokamak

Experiments simulating the ITER baseline scenario on the DIII-D tokamak show that torque-free pure electron heating, when coupled to plasmas subject to a net co-current beam torque, affects density fluctuations at electron scales on a sub-confinement time scale, whereas fluctuations at ion scales change only after profiles have evolved to a new stationary state. Modifications to the density fluctuations measured by the phase contrast imaging diagnostic (PCI) are assessed by analyzing the time evolution following the switch-off of electron cyclotron heating (ECH), thus going from mixed beam/ECH to pure neutral beam heating at fixed . Within 20 ms after turning off ECH, the intensity of fluctuations is observed to increase at frequencies higher than 200 kHz; in contrast, fluctuations at lower frequency are seen to decrease in intensity on a longer time scale, after other equilibrium quantities have evolved. Non-linear gyro-kinetic modeling at ion and electron scales scales suggest that, while the low frequency response of the diagnostic is consistent with the dominant ITG modes being weakened by the slow-time increase in flow shear, the high frequency response is due to prompt changes to the electron temperature profile that enhance electron modes and generate a larger heat flux and an inward particle pinch. These results suggest that electron heated regimes in ITER will feature multi-scale fluctuations that might affect fusion performance via modifications to profiles.

Modification of argon impurity transport by electron cyclotron heating in KSTAR H-mode plasmas

Experiments with a small amount of Ar gas injection as a trace impurity were conducted in the Korea Superconducting Tokamak Advanced Research (KSTAR) H-mode plasma ( = 2.8 T, = 0.6 MA, and = 4.0 MW). 170 GHz electron cyclotron resonance heating (ECH) at 600 and 800 kW was focused along the mid-plane with a fixed major radial position of = 1.66 m. The emissivity of the Ar16+ (3.949 ) and Ar15+ (353.860 ) spectral lines were measured by x-ray imaging crystal spectroscopy (XICS) and a vacuum UV (VUV) spectrometer, respectively. ECH reduces the peak Ar15+ emission and increases the Ar16+ emission, an effect largest with 800 kW. The ADAS-SANCO impurity transport code was used to evaluate the Ar transport coefficients. It was found that the inward convective velocity found in the plasma core without ECH was decreased with ECH, while diffusion remained approximately constant resulting in a less-peaked Ar density profile. Theoretical results from the NEO code suggest that neoclassical transport is not responsible for the change in transport, while the microstability analysis using GKW predicts a dominant ITG mode during both ECH and non-ECH plasmas.