Ion Temperature Gradient Mode Research Articles

Performance prediction applying different reduced turbulence models to the SMART tokamak

Abstract The SMall Aspect Ratio Tokamak (SMART) is currently being
commissioned at the University of Seville and will be able to compare the
performance of positive and negative triangularity plasmas at low aspect ratio.
Predictive simulations have been performed for different machine scenarios and
heating schemes using the TRANSP code. The objectives of these simulations
are to predict the parameters expected in positive triangularity plasmas, to
guide diagnostic development, and to validate transport models. Several reduced
turbulence models have been used to predict electron and ion temperatures for the
operational phase 2. All models provide similar results from approximately midradius
to the separatrix but important discrepancies are found in the core region.
These positive triangularity results are compared with experiments from a similar
size machine like GLOBUS-M2. The multi-mode model (MMM) shows the best
agreement. Simulations with different boundary conditions have been performed
and no strong differences have been observed between them. The impact of neutral
beam injection (NBI) on the predicted profiles has also been addressed. Rotation
reduces turbulence levels so higher temperatures are achieved when included in
the simulations. Studying the different contributions to the thermal diffusivities,
it is observed that electron temperature gradient (ETG) turbulence dominates
at the plasma core while mictro-tearing modes (MTM) dominate at the edge
in the electron channel. In the ion channel, the neoclassical contribution is
dominant at the core and at the very edge while the Weiland component, which
includes ion temperature gradient mode (ITG), trapped electron mode (TEM),
kinetic ballooning mode (KBM), peeling mode (PM) and collisionless and collision
dominated magnetohydrodynamic (MHD) modes governs the mid-radius region.
For phase 3, two plasmas with different electron densities have been studied. The
case with lower density matches well a specific discharge of GLOBUS-M2. The
higher density plasma shows high performance with βN ≈ 3.8.

Ion temperature gradient modes modulational stability with kappa-distribution

We investigated the modulational stability and instability of the ion temperature gradient (ITG) mode in electron-ion plasma. Ions are dynamic species, whereas electrons follow a Kappa distribution. We used the reduction perturbation approach to determine the linear dispersion relation for the fluid under consideration. The nonlinear Schrodinger equation describes nonlinear features such as nonlinear modulational stability or instability in the ITG mode. The product of dissipation and nonlinear coefficients, known as LM, contains both modulational stability and instability in the ion temperature gradient mode. Theoretical results are expanded numerically, showing the influence of various plasma parameters on modulational stability and instability, particularly the superthermality coefficient κ e . The current observations may be extended to space and laboratory plasma for modification.

First results of turbulence investigation on Globus-M2 using radial correlation Doppler reflectometry

The first results of investigation of the turbulence structure using Doppler backscattering (DBS) on the Globus-M2 tokamak are presented. A one-channel DBS system with a variable probing frequency within the 18–26 GHz range was installed to investigate the edge plasma at normalized minor radii 0.9–1.1. Radial correlation Doppler reflectometry was used to study the changes in turbulence eddies after the LH transition. Correlation analysis was applied to the phase derivative of complex in-phase and quadrature (IQ) signals of the DBS diagnostic as it contains information about the poloidal plasma rotation velocity. In L-mode, the radial correlation length L r is estimated to be 3 cm and after transition to H-mode reduces to approximately 2 cm. Gyrokinetic modelling in a linear local approximation using code GENE indicates that the instability with positive growth rate at the normalized minor radius 0.75 in L-mode and H-mode on Globus-M2 was the ion temperature gradient (ITG) mode.

Magnetic shaping effects on turbulence in ADITYA-U tokamak

The work reported in this paper addresses two aspects. In the first part, numerical simulations are conducted to examine the impact of magnetic equilibrium shaping (elongation and triangularity), on both conventional Ion Temperature Gradient (ITG) modes and Short Wavelength ITG modes. This analysis is performed considering the experimental profiles and parameters of the ADITYA-U tokamak, employing the nonlinear global gyrokinetic Particle-in-Cell code ORB5. The linear and nonlinear collisionless electrostatic simulation of these modes are carried out with kinetic ions and adiabatic electrons. From the linear results, it has been observed that the magnetic equilibrium shaping slighty reduced the growth rates and widened the spectrum, and the maxima of growth rate curve is shifted to higher toroidal wave number. We find that the heat flux is reduced by a significant ≃35% for the true circular magnetohydrodynamic magnetic equilibrium as compared to ad hoc concentric circular equilibrium reported in Singh et al (2023 Nucl. Fusion 63 086029). A further ≃10% reduction in the heat flux is seen with magnetic equilibrium shaping. In the second part, linear collisionless electrostatic simulation studies of ITG coupled with fully kinetic electrons (both trapped and passing electrons are treated kinetically) using a drift-kinetic ordering is performed. It can be seen from the linear results that, in presence of kinetic electrons, the growth rate and real frequency of the ITG mode are increased significantly for ADITYA-U parameters and a mode propagating in the electron diamagnetic direction is identified at high toroidal wavenumbers.

Verification and validation of electrostatic turbulence simulation for numerical Lie transform code

Abstract This paper reports the verification and validation of a new gyrokinetic (GK) code, numerical Lie transform (NLT), for electrostatic turbulence simulation in tokamak plasmas. Based on the standard cyclone base case (CBC), NLT has been verified against two typical GK codes, GK toroidal code (GTC) and GK numerical experiment of tokamak, by simulating the ion temperature gradient mode and trapped electron mode. The linear dispersion relation and mode structure agree well among all these codes. In nonlinear simulation, the time evolution of ion heat diffusivity obtained from NLT is consistent with the GTC results. Furthermore, utilizing experimental equilibria with obvious turbulence features from HL-2A shot #22388, the validation of NLT for real tokamak simulation has been carried out. The profiles of ion turbulent thermal diffusivity calculated by NLT match well with experimental results.

Ti/Te effects on transport in EAST low q95 plasmas

Enhanced confinement is observed in EAST low q95 ( q95<3.5 ) plasmas with the temperature ratio ( Ti/Te ) increasing. A statistically significant positive correlation between H98y2 and Ti/Te has been established. Increased Ti triggerd by Neutral Beam Injection in experiments maintaining constant Te leads initially to an improved Ti/Te ratio, which subsequently mitigates heat transport in the ion channel. The Trapped Gyro–Landau Fluid transport model was applied to analyse the dependence of the turbulent transport on Ti/Te . Simulation results demonstrate that the Ion Temperature Gradient mode is stabilized in high Ti/Te plasma, with ion flux results from predictive modelling further validating this effect. These findings corroborate the Weiland model and complement one another. This study contributes to a deeper understanding of how the dimensionless parameter Ti/Te influences plasma transport, and helps demonstrate the feasibility of operations under the low q95 condition required for the ITER-inductive scenario in the new Ti/Te regime.

Effects of hydrogen isotope species on ITG microturbulence in LHD

The linear and nonlinear effects of hydrogen isotope species on ion temperature gradient (ITG) instability in the Large Helical Device (LHD) stellarator are studied using radially global gyrokinetic simulation. We found that the coupling range of linear toroidal harmonics depends on the ion mass of the hydrogen isotope. The growth rates of ITG mode are almost the same for H, D, and T plasmas, indicating a gyro-Bohm scaling of ion-mass dependence. The nonlinear electrostatic simulations show that the zonal flow breaks the radially elongated eigenmode structures and reduces the size of the turbulence eddies, which suppresses the turbulence and the ion heat transport in the LHD. The turbulence amplitude without the zonal flow is almost the same for H, D, and T plasmas, while it decreases with increasing ion mass of the hydrogen isotope when the zonal flow is present. The reduction of the turbulent transport with larger ion mass is mostly due to the enhancement of zonal flows by larger ion mass. The ion heat conductivity deviates from the gyro-Bohm scaling for both cases with and without the zonal flow.

Assessing core ion thermal confinement in critical-gradient-optimized stellarators

We investigate the core confinement properties of two recently devised quasi-helically symmetric stellarator configurations, HSK and QSTK. Both have been optimized for large critical gradients of the ion temperature gradient mode, which is an important driver of turbulent transport in magnetic confinement fusion devices. To predict the resulting core plasma profiles, assuming a fixed edge temperature, we utilize an advanced theoretical framework based on the gyrokinetic codes GENE and GENE-3D, coupled to the transport code TANGO. Compared to the HSX stellarator, both HSK and QSTK achieve significantly higher core-to-edge temperature ratios, partly thanks to their smaller aspect ratios, with the other part due to more detailed shaping of the magnetic geometry achieved during optimization. The computed core confinement time, however, is less sensitive to core temperature than the fixed edge temperature, simply due to the disproportionate influence, the edge has on stored plasma energy. We, therefore, emphasize the possible benefits of further optimizing turbulence in the outer core region, and the need to include accurate modeling of confinement in the edge region in order to assess overall plasma performance of turbulence optimized stellarators.

Gyro-kinetic simulations of trapped electron collision effects on low-frequency drift-wave instabilities in tokamak plasmas

Low-frequency drift-wave instabilities play a crucial role in the radial transport of present-day tokamaks, and trapped electron collisions can significantly influence these instabilities. In this paper, the effects of trapped electron collisions on these instabilities are investigated based on linear gyro-kinetic simulations. The basic numerical techniques including dispersion relation integral method and orthogonal basis function expansion are presented in detail with necessary benchmark work. The results demonstrate that in medium gradients, the increase of trapped electron proportions promotes the growth rate and radial heat transport largely for quasi-linear trapped electron modes (TEMs) and ion temperature gradient (ITG) modes. Moreover, trapped electron collisions have strong stabilizing effects, especially for TEMs driven by electron temperature gradients. Two distinctive branches, namely Mode #1 and #2, are investigated in steep gradients. Both behave in a varied instability nature during different ranges of the normalized wave vector k^θ . Mode #1 mainly induces radial heat transport during k^θ<0.5 and is significantly suppressed by the collisions. Mode #2 mainly induces radial heat transport during 0.4<k^θ<0.8 , and is largely enhanced by the collisions. When the collisionality is large enough, Mode #2 has stronger transport capacity than the other. Mode #2 at the medium wave vector, known as dissipative TEM, may provide the mechanism of the edge coherent mode observed in EAST H-mode plasmas, wherein collisionality plays an important role in the mode excitation.

Ion temperature gradient mode modulational stability analysis with cairn’s distribution

In this manuscript, we have studied electron-ion plasma with inhomogeneity in equilibrium number density and temperature. Ions are the dynamic species, and lighter particles in plasma obey the cairn’s distribution. We introduce Brajinskii’s equation for dynamic species and get the linear dispersion relation and the nonlinear Schrodinger equation by the reduction perturbation method. From the linear dispersion relation, we found the mode frequency and phase velocity, while from the nonlinear Schrodinger equation, we obtained the stability and instability of the ion temperature gradient mode modulation. Findings show that phase velocity is dependent on the superthermality coefficient and other plasma parameters like ion temperature, ion density, and mode parameter η i . Further, the modulational stability and instability of the mode vary with the superthermality coefficient and other plasma parameters, especially the η i . We can apply these observations equally to the laboratory as well as to the space plasma.

Reduction of electrostatic turbulence in a quasi-helically symmetric stellarator via critical gradient optimization

We present a stellarator configuration optimized for a large threshold (‘critical gradient’) for the onset of the ion temperature gradient (ITG) driven mode, which achieves the largest critical gradient we have seen in any stellarator. Above this threshold, gyrokinetic simulations show that the configuration has low turbulence levels over an experimentally relevant range of the drive strength. The applied optimization seeks to maximize the drift curvature, leading to enhanced local-shear stabilization of toroidal ITG modes, and the associated turbulence. These benefits are combined with excellent quasi-symmetry, yielding low neoclassical transport and vanishingly small alpha particle losses. Analysis of the resulting configuration suggests a trade-off between magnetohydrodynamic (MHD) and ITG stability, as the new configuration possesses a vacuum magnetic hill.

Finite pedestal width formation from early L-H transition stage with a strong edge safety-factor dependence through the resistive ballooning mode

An approximate modeling of the low- to high-confinement (L-H) transition dynamics is given using the method, similar to that by Hinton et al. [Phys. Fluid B 5, 1281 (1993)], but considering more explicitly the L-mode edge turbulence which is here assumed to be dominated by the resistive ballooning mode (RBM) near the separatrix, while the ion temperature gradient (ITG) mode in the inner edge–core region. It is shown that the L-H transition can then be initiated from an inner edge near the ITG-RBM transition point with a finite width. Especially, this width is found to have a strong edge safety-factor or poloidal field dependence, similar to that shown by the EPED1 model. Meanwhile, unlike the pedestal width, the H-mode threshold power appears to be much less sensitive to the edge safety-factor, in qualitative agreement with the observed weak dependence of the threshold power on plasma current (IP). From an additional brief check, these dependences on IP are also found to be quite different from the behavior of other parameters (ion mass, toroidal field, plasma density, and effective Z-number) where the threshold power depends relatively strongly while the initial width depends somewhat weakly on most of them, except the effective Z-number.

Experimental Investigations of Quasi-Coherent Micro-Instabilities in J-TEXT Ohmic Plasmas

Quasi-coherent micro-instabilities is one of the key topics of magnetic confinement fusion. This work focuses on the quasi-coherent spectra of ion temperature gradient (ITG) and trapped-electron-mode instabilities using newly developed far-forward collective scattering measurements within ohmic plasmas in the J-TEXT tokamak. The ITG mode is characterized by frequencies ranging from 30 to 100 kHz and wavenumbers (kθρ s) less than 0.3. Beyond a critical plasma density threshold, the ITG mode undergoes a bifurcation, which is marked by a reduction in frequency and an enhancement in amplitude. Concurrently, enhancements in ion energy loss and degradation in confinement are observed. This ground-breaking discovery represents the first instance of direct experimental evidence that establishes a clear link between ITG instability and ion thermal transport.

Simulation of ion temperature gradient driven modes with 6D kinetic Vlasov code

With the increase in computational capabilities over the last few years, it becomes possible to simulate more and more complex and accurate physical models. Gyrokinetic theory has been introduced in the 1960s and 1970s in the need of describing a plasma with more accurate models than fluid equations but eliminating the complexity of the fast gyration about the magnetic field lines. Although results from current gyrokinetic computer simulations are in fair agreement with experimental results in core physics, crucial assumptions made in the derivation make it unreliable in regimes of higher fluctuations and stronger gradient, such as the tokamak edge. With our novel optimized and scalable semi-Lagrangian solver, we are able to simulate ion temperature gradient modes with the 6D kinetic model including the turbulent saturation. After thoroughly testing our simulation code against analytical computations and gyrokinetic simulations (with the gyrokinetic code GYRO), it has been possible to show first plasma properties that go beyond standard gyrokinetic simulations. This includes the explicit description of the complete perpendicular energy fluxes and the excitation of high-frequency waves (around the Larmor frequency) in the nonlinear saturation phase.

Research of turbulent transport due to dissipative trapped electron mode in tokamak plasmas

The purpose of this article is to study turbulent transport for laboratory plasmas in toroidal devices by gyrokinetic analyses. Linear analysis is performed to clarify the dominant mode for tokamak plasmas. The dissipative trapped electron mode (d-TEM) and the ion temperature gradient (ITG) mode are predicted using the Sugama collision model operator [Sugama et al., Phys. Plasmas 16, 112503 (2009)]. Nonlinear gyrokinetic analysis is used to quantify turbulent transport. The nonlinear simulation results show the levels of particle and energy transport, where the d-TEM and ITG mode are unstable. The effect of zonal flows is studied by the linear and nonlinear simulation results. The results of the analysis are compared when two types of model collision operator, which are the Sugama and Lenard–Bernstein [Phys. Rev. 112, 1456 (1958)] collision model operators, are used. In this study, the simulation results using the Sugama collision operator show a stronger effect of the zonal flows on the turbulent transport than those using the Lenard–Bernstein collision operator, as predicted by the linear simulation result such as the zonal flow decay time.

Isotope effects on transport characteristics of edge and core plasmas heated by neutral beam injection (NBI) in an inward shifted configuration at the Large Helical Device

Isotope effects have been investigated in Neutral Beam Injection (NBI) heated plasmas on the Large Helical Device with similar operational parameters between Hydrogen (H) and Deuterium (D) plasmas. Experimental results show that the global energy confinement has no significant dependence on the isotope mass under similar discharge conditions with nearly the same heating power, line-averaged density ( nˉe ) and magnetic field. For both electron and ion energy transport, the transport coefficients, which are obtained based on local power balance analysis, have analogous profiles between H and D dominant plasmas. For neoclassical χe and χi values, they are almost equal between H and D dominant plasmas in low nˉe discharges, whereas in high nˉe cases they are lower in H plasmas than those in D ones. At low nˉe , the electron and ion thermal transport in both H and D plasmas are dominated by neoclassical transport at a certain zone ( ρ≈0.6−0.85 ), while the anomalous transport process has primary effects in the remaining area, and the density fluctuations exhibit ion temperature gradient mode nature. With increase of nˉe , the anomalous transport becomes prevailing and the density fluctuations propagate along electron diamagnetic drift direction. Bispectral analysis reveals that the H plasma has stronger nonlinear coupling in edge density fluctuations in both low and high density discharges, which is probably due to that the D plasma has stronger damping rate for the nonlinear interaction of turbulence. For a comparative study, the present results have been compared with those observed in the ECRH discharges (Tanaka et al 2019 Nucl. Fusion 59 126040). The reasons for the similarities and dissimilarities between these two different heating manners are not clear yet. To unravel the underlying physics, essential inputs from theories and simulations are required.

Simulation Prediction of Heat Transport with Machine Learning in Tokamak Plasmas

Machine learning opens up new possibilities for research of plasma confinement. Specifically, models constructed using machine learning algorithms may effectively simplify the simulation process. Previous first-principles simulations could provide physics-based transport information, but not fast enough for real-time applications or plasma control. To address this issue, this study proposes SExFC, a surrogate model of the Gyro-Landau Extended Fluid Code (ExFC). As an extended version of our previous model ExFC-NN, SExFC can capture more features of transport driven by the ion temperature gradient mode and trapped electron mode, using an extended database initially generated with ExFC simulations. In addition to predicting the dominant instability, radially averaged fluxes and radial profiles of fluxes, the well-trained SExFC may also be suitable for physics-based rapid predictions that can be considered in real-time plasma control systems in the future.

Effect of coherent edge-localized mode on transition to high-performance hybrid scenarios in KSTAR

This paper deals with one of the origins and trigger mechanisms responsible for the observed performance enhancements in the hybrid scenario experiments conducted in Korea Superconducting Tokamak Advanced Research (KSTAR). The major contribution to the performance improvement comes from a broader and higher pedestal formation. The increase of fast ion pressure due to a plasma density decrease also contributes substantially to the global beta. Although the reduced core plasma volume resulting from the pedestal expansion has a negative effect on the core thermal energy, a considerable confinement improvement observed in the inner core region limits the degradation. The one significant characteristic of high-performance discharges is the presence of Coherent Edge-localized Mode (CEM) activity. CEM is triggered during the pedestal recovery phase between typical ELM crashes and has been found to be related to the increase of particle and heat transport. It appears to underlie two commonly observed phenomena in high-performance hybrid scenario discharges in KSTAR; pedestal broadening and continuous density decrease. Despite the associated transport increase, CEM activities can induce performance enhancement. With the pedestal broadening, ELM crashes become delayed and weakened, which, in turn, allows for a higher pedestal. Moreover, the density decrease directly increases fast ion pressure by extending the beam-slowing-down time. The linear gyrokinetic analysis reveals that the increase of fast ions could initiate positive feedback loops, leading to the stabilization of Ion Temperature Gradient mode in the inner core region.

Gyrokinetic analysis of turbulent transport by electromagnetic turbulence in finite β plasmas with weak magnetic shear on HL-2A

Turbulent transport and zonal flow (ZF) dynamics in the mixed kinetic ballooning mode (KBM) and ion temperature gradient (ITG) mode dominated turbulence states are analyzed by gyrokinetic simulations based on the experimental observations of KBMs in the HL-2A Internal Transport Barrier (ITB) plasmas with weak magnetic shear configuration. Results have shown that KBMs and ITGs are the main candidates for turbulent transport and the inclusion of fast ions (FIs) can destabilize both instabilities, which is resulted by the decrease of ballooning parameter αMHD hence reduced Shafranov shift stabilization due to the negative FI density gradient, making them more unstable according to the ŝ-αMHD diagram. In addition, the ITGs are suppressed by both dilution and finite-β stabilization effects caused by FIs. Nonlinear simulations excluding the effects of FIs indicate that the transport is minimum at βe=βeexp as the turbulence predominated by ITGs is strongly suppressed by the nonlinear electromagnetic (EM) stabilization and enhancement of ZFs. However, the transport is further increased with β e although the ZFs become stronger due to the transition from ITG to KBM dominated turbulence state. The presence of FIs can modify the relation between ZF shearing rate and β e. The transport level is insensitive to β e when βe⩽βeexp but increases significantly because of the KBM destabilization. Meanwhile, the ZF amplitude reaches maximum at βe=βeexp whereas it suffers an erosion at higher values, implying that the plasma might be a self-organized critical state owning to the interactions among ZFs, KBMs and FI effects hence setting the plasma β around β exp. The results have also provided a possible explanation that the destabilization of EM turbulence is responsible for the ion heat transport stiffness under weak magnetic shear configurations in the off-axis neutral beam injection heated ITB plasmas on HL-2A.

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.