Ion Temperature Gradient Research Articles

Gyrokinetic simulations of the kinetic electron effects on the electrostatic instabilities on the ITER baseline scenario

The linear and nonlinear simulations are carried out using the gyrokinetic code NLT for the electrostatic instabilities in the core region of a deuterium plasma based on the International Thermonuclear Experimental Reactor (ITER) baseline scenario. The kinetic electron effects on the linear frequency and nonlinear transport are studied by adopting the adiabatic electron model and the fully drift-kinetic electron model in the NLT code, respectively. The linear simulations focus on the dependence of linear frequency on the plasma parameters, such as the ion and electron temperature gradients , the density gradient and the ion–electron temperature ratio . Here, is the major radius, and and denote the electron and ion temperatures, respectively. is the gradient scale length, with denoting the density, the ion and electron temperatures, respectively. In the kinetic electron model, the ion temperature gradient (ITG) instability and the trapped electron mode (TEM) dominate in the small and large region, respectively, where is the poloidal wavenumber. The TEM-dominant region becomes wider by increasing (decreasing) ( ) or by decreasing . For the nominal parameters of the ITER baseline scenario, the maximum growth rate of dominant ITG instability in the kinetic electron model is about three times larger than that in the adiabatic electron model. The normalized linear frequency depends on the value of , rather than the value of or , in both the adiabatic and kinetic electron models. The nonlinear simulation results show that the ion heat diffusivity in the kinetic electron model is quite a lot larger than that in the adiabatic electron model, the radial structure is finer and the time oscillation is more rapid. In addition, the magnitude of the fluctuated potential at the saturated stage peaks in the ITG-dominated region, and contributions from the TEM (dominating in the higher region) to the nonlinear transport can be neglected. In the adiabatic electron model, the zonal radial electric field is found to be mainly driven by the turbulent energy flux, and the contribution of turbulent poloidal Reynolds stress is quite small due to the toroidal shielding effect. However, in the kinetic electron model, the turbulent energy flux is not strong enough to drive the zonal radial electric field in the nonlinear saturated stage. The kinetic electron effects on the mechanism of the turbulence-driven zonal radial electric field should be further investigated.

Facilitated core-edge integration through divertor nitrogen seeding in the HL-2A tokamak

A divertor detachment with sustainable high-performance plasmas has been achieved through divertor nitrogen seeding in the HL-2A tokamak. The closed divertor structure facilitates achieving high divertor neutral pressure due to its efficient particle containment effect as demonstrated by both experimental and SOLPS simulation results, which aids in achieving the divertor detachment. The radiative divertor is conducive to high-frequency small edge localized modes (ELMs) operation, characterized by a reduced pedestal ion temperature gradient ∇Ti and the enhanced electron density gradient ∇ne . The presence of minority nitrogen at the edge plasma, which results from the divertor nitrogen seeding, contributes to the increase of ion temperature Ti in the confinement region by suppressing the turbulence through the impurity dilution effect and E×B shear. The increased ion temperature Ti and electron density ne compensate the energy loss resulting from the increased edge radiation during detachment, which contributes to the confinement sustainment combined with reduced pedestal energy loss caused by small ELMs. This work advances our understanding of the fundamental physics governing closed divertor detachment with sustainable high-performance plasmas through divertor nitrogen seeding.

Turbulent particle pinch in gyrokinetic flux-driven ITG/TEM turbulence

Aiming at a fuel supply through particle pinch effects, turbulent particle transport is studied by gyrokinetic flux-driven Ion-Temperature-Gradient/Trapped-Electron-Mode (ITG/TEM) simulations. It is found that ITG/TEM turbulence can drive ion particle pinch by E × B drift (n ≠ 0) when the ion temperature gradient is steep enough. Electron particle pinch is also driven by E × B drift (n ≠ 0) in the case with the steep electron temperature gradient. Such an electron particle pinch can trigger an ambipolar electric field, leading to additional ion particle pinch by not only magnetic drift but also E × B drift (n = 0). These results suggest that a density peaking of bulk ions due to turbulent fluctuations can be achieved by sufficiently strong both ion and electron heating.

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.

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.

Predictive modeling of NSTX discharges with the updated multi-mode anomalous transport module

The objective of this study is twofold: firstly, to demonstrate the consistency between the anomalous transport results produced by updated Multi-Mode Model (MMM) version 9.0.4 and those obtained through gyrokinetic simulations; and secondly, to showcase MMM’s ability to predict electron and ion temperature profiles in low aspect ratio, high beta NSTX discharges. MMM encompasses a range of transport mechanisms driven by electron and ion temperature gradients, trapped electrons, kinetic ballooning, peeling, microtearing, and drift resistive inertial ballooning modes. These modes within MMM are being verified through corresponding gyrokinetic results. The modes that potentially contribute to ion thermal transport are stable in MMM, aligning with both experimental data and findings from linear CGYRO simulations. The isotope effects on these modes are also studied and higher mass is found to be stabilizing, consistent with the experimental trend. The electron thermal power across the flux surface is computed within MMM and compared to experimental measurements and nonlinear CGYRO simulation results. Specifically, the electron temperature gradient modes (ETGM) within MMM account for 2.0 MW of thermal power, consistent with experimental findings. It is noteworthy that the ETGM model requires approximately 5.0 ms of computation time on a standard desktop, while nonlinear CGYRO simulations necessitate 8.0 h on 8 K cores. MMM proves to be highly computationally efficient, a crucial attribute for various applications, including real-time control, tokamak scenario optimization, and uncertainty quantification of experimental data.

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.

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.

Cross-scale interaction between microturbulence and meso-scale reversed shear Alfvén eigenmodes in DIII-D plasmas

This paper reports global nonlinear gyrokinetic simulations that couple meso-scale reversed shear Alfvén eigenmodes (RSAEs) driven by energetic particles (EPs) and ion temperature gradient (ITG) microturbulence driven by thermal plasma, using equilibrium and profiles from DIII-D discharge #159243. In simulations focusing only on the ITG, electrostatic ITG drives a huge thermal ion heat transport, which is reduced by a factor of 10 to a level close to the experimental value in electromagnetic simulation due to finite β effect. In the simulations coupling the RSAE and ITG, ITG can scatter the resonant EP nonlinearly trapped by the RSAE and damp the zonal flows generated by the RSAE. The regulation of the RSAE by the ITG greatly reduces the initial saturation amplitude of the RSAE but increases the RSAE amplitude and associated EP transport to experimental levels in the quasi-steady state. The RSAE effects on the ITG, specifically the stronger zonal flows generated by the RSAE and the RSAE frequency modulation of the ITG-induced thermal ion heat transport, in turn, leads to a reduction of the thermal ion heat transport by more than a factor of 2 . For a stronger background ITG, the regulation of the RSAE by the ITG is stronger, while the RSAE effects on the ITG are weaker. This work highlights the importance of cross-scale coupling in the dynamics of the AE turbulence and EP transport.

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.

Flow-shear destabilization of multiscale electron turbulence

The impact of sheared E×B flow on multiscale turbulence is studied with nonlinear gyrokinetic simulations. Simulations are based on DIII-D-like, high-confinement mode (H-mode) pedestal parameters in the regime of low ion temperature gradient drive, where there is a broad spectrum of electron temperature gradient (ETG)-driven turbulence. It is found that E×B shear can have a significant effect on ETG-driven electron transport, with an unexpected transition from a turbulence stabilization regime at moderate to large shearing rates γ E to a novel turbulence destabilization regime at low levels of γ E . In the turbulence stabilization regime, the electron energy flux decreases monotonically with γ E , even when γ E is small compared to electron mode growth rates. The stabilizing effect comes dominantly from the electron, not ion, gyrokinetic equation. In the novel destabilization regime, reduction of zonal energy results from the interaction of γ E -modulated nonlinear drive in the zonal ion gyrokinetic equation, increasing the electron transport over a broad range of shearing rates. Neither of these effects have been observed in previous electron-scale simulations.

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.

Linear gyrokinetic theory of two-dimensional ion-temperature-gradient mode in tokamaks

The investigation of the two-dimensional (2D) linear ion-temperature-gradient (ITG) mode in toroidal plasma is carried out in ballooning mode representation. A novel approach to solve the radial envelope structure is proposed by constructing radial differential eigenequation. The important lemma (∂ω/∂θk)|θk=0=0 is proved and employed to construct a numerically solvable eigenequation. We have developed a numerical solver which gives the 2D solution consistent with the results obtained by the gyrokinetic global simulation code. Our newly proposed method presents an alternative solution to the 2D ITG eigenvalue problem.

Simultaneous reproduction of experimental profiles, fluxes, transport coefficients, and turbulence characteristics via nonlinear gyrokinetic profile predictions in a DIII-D ITER similar shape plasma

Experimental conditions obtained on the DIII-D tokamak in the ITER Similar Shape (ISS) have been compared extensively with nonlinear gyrokinetic simulation using the CGYRO code [Candy et al., J. Comput. Phys. 324, 73–93 (2016)] with comparisons spanning ion and electron heat fluxes, electron and impurity particle transport, and turbulent fluctuation levels and characteristics. Bayesian optimization techniques [Rodriguez-Fernandez et al., Nucl. Fusion 62(7), 076036 (2022)], combined with nonlinear gyrokinetics, have been used to obtain simultaneously Qi, Qe, and Γe flux-matched profiles that are found to be in good agreement with experimental profile measurements. Synthetic diagnostics were used to compare measured beam emission spectroscopy and correlation electron cyclotron emission turbulent fluctuations with nonlinear simulation. Although some disagreements exist, nonlinear simulations are found to be in generally good agreement with measured fluctuation levels, spectral shapes, and measured radial trends in low-k δne/ne and δTe/Te. Low (Li and C) and mid-Z (Ca) impurity transport was also compared with these flux-matched simulations. Fully stripped, low-Z impurities are well reproduced by the gyrokinetic modeling while clear disagreement exists in comparisons with mid-Z impurities. Nonlinear gyrokinetic investigation into the Z dependence of impurity transport in the ISS conditions is also performed, demonstrating clear trends of impurity diffusion with impurity Z (both D∝Z and D∝1/Z) that vary with the radial location studied. These trends are shown to result from the local dominance of ion temperature gradient or ∇n driven trapped electron mode turbulence and may contribute to the disagreement between simulation and experiment in mid-Z impurity transport. The results of this work represent one of the most complete validation studies of the gyrokinetic model performed to date and provide an example of new capabilities for predicting performance in future fusion devices.