Ion Temperature Gradient Research Articles

The role of ion-scale micro-turbulence in pedestal width of the DIII-D wide-pedestal QH mode

Abstract The low-edge rotation, intrinsically ELM-free, and improved confinement wide-pedestal quiescent H-mode (QH-mode), discovered in DIII-D tokamak, has pedestal widths exceeding the EPED-KBM model scaling typically by at least 25%. Ion-scale (k_y ρ_s<1) microturbulence and its role in setting the pedestal structure is investigated using the radially local δf gyrokinetic code CGYRO. The electromagnetic trapped electron mode (TEM) is unstable at the pedestal top, while plasma beta (β_e) is ~60% below the kinetic-ballooning mode (KBM) onset threshold and the electron temperature gradient (ETG) mode is found to be unstable in the peak gradient region. Nonlinear simulation reveals that the ion-scale turbulence could produce electron energy flux consistent with the flux inferred from power balance at the pedestal top, with a reasonable variation of the local E×B shearing rate; and the local neoclassical transport from NEO is dominant over the simulated turbulent transport in the ion energy flux channel. The simulated ion-scale turbulence produces much lower electron energy flux than inferred from experiment in the pedestal peak gradient region. A correction to the EPED-KBM pedestal width scaling is obtained based on the two-dimensional scan of pedestal top plasma beta (β_e) and normalized electron density and temperature scale lengths, a⁄L_(n_e ) , a⁄L_(T_e ) using CGYRO linear simulations. Mode transitions among TEM, micro-tearing mode (MTM), ion-temperature gradient (ITG) mode and KBM, are observed in the 2D scan at the pedestal top. A fixed normalized growth rate for these drift-type modes is taken to determine the pedestal width scaling, which shows good consistency with the QH experimental database on pedestal heights and widths. The onset of KBM instabilities and the local ExB shear suppression criterion set the lower and upper limit for the pedestal width of standard QH-mode, wide-pedestal QH-mode and type-I ELMy H mode. A potentially higher and wider pedestal is expected from the new scaling of pedestal width. This work presents an improved understanding of the ion-scale micro-turbulence of wide-pedestal QH-mode and sheds light on a promising scenario for future reactors, including ITER and beyond.

Effect of ion temperature anisotropy on ITG mode in reversed field pinch plasmas

Abstract The Ion Temperature Gradient (ITG) mode instability in the Reversed-Field-Pinch (RFP) plasmas with anisotropies in ion temperature and its gradient, is studied for the first time using the gyrokinetic integral eigen-mode equation. Detailed numerical results indicate that ITG instability is reduced by ion temperature anisotropy, specifically when the temperature is higher in the direction perpendicular to the magnetic field or sufficiently high in the direction parallel to the magnetic field, with Landau damping playing a significant role. Moreover, the driving force of the ion temperature gradient in the parallel direction for the ITG mode is stronger than that in the perpendicular direction, particularly when the parallel ion temperature is higher. In addition, the study provides detailed insights into the synergistic effects of ion temperature anisotropy with magnetic shear, poloidal wave number, safety factor, and density gradient on ITG mode. It also elucidates the threshold of the ion temperature gradient necessary for mode excitation.

Ion temperature gradient mode mitigation by energetic particles, mediated by forced-driven zonal flows

Ion temperature gradient mode mitigation by energetic particles, mediated by forced-driven zonal flows

Linear and nonlinear dynamics of self-consistent collisionless tearing modes in toroidal gyrokinetic simulations

We investigate tearing modes (TM) driven by current density gradient in collisionless tokamak plasmas by using the electromagnetic gyrokinetic simulation code ORB5. We elucidate the TM width by simulations for flat profiles, as the absence of background diamagnetic flows implies a small rotation speed, while finite gradients are included to investigate the TM rotation. For flat profiles, the initial saturation width of nonlinearly driven magnetic islands is related to the TM linear growth rate; however, large islands in the initial saturation phase are prone to current density redistribution that reduces the island width in the following evolution. Island-induced E×B and diamagnetic sheared flows develop at the separatrix, able to destabilize the Kelvin–Helmholtz instability (KHI). The KHI turbulence enhances a strong quadrupole vortex flow that reinforces the island decay, resulting in a strong reduction of the island width in an eventual steady state. This process is enhanced by trapped electrons. For finite gradients profile, the TM usually rotates in the electron diamagnetic direction but can change direction when the ion temperature gradient dominates the other gradients. The reduced growth of the TM by diamagnetic effects results in a moderate island size, which remains almost unchanged after the initial saturation. At steady state, strong zonal flows are nonlinearly excited and dominate the island rotation, as expected from previous theoretical and numerical studies. When β is increased, the TM mode is suppressed and a mode with the same helicity but with twisting parity, coupled with the neighboring poloidal harmonics, is destabilized, similar to the kinetic ballooning mode.

Drift waves and ion temperature gradient instabilities in the large linear device SPEKTRE

Drift waves and ion temperature gradient instabilities in the large linear device SPEKTRE

On how finite β and three-dimensional magnetic perturbations affect the instability of toroidal ion temperature gradient mode

Abstract The effects of finite β (the ratio of plasma kinetic pressure to magnetic pressure) and three-dimensional (3D) magnetic perturbations (MPs) on the instability of toroidal ion temperature gradient (ITG) mode are studied in this work. The expression of ion magnetic drift frequency ω_di modified by the effects from both finite β and 3D MPs is firstly derived based on the local 3D equilibrium model. Then, under the assumptions of adiabatic electrons and localized mode structure around the outboard mid-plane (ϑ_p=0), the dispersion equation of the long wavelength toroidal ITG mode with considering the parallel ion dynamics is derived and solved. The results show that the distribution of ω_di around the outboard mid-plane, including both ω_(di,0)=├ ω_di ┤|_(ϑ_p=0) and ω_(di,0)^''≡├ (d^2 ω_di \/dϑ_p^2 )┤|_(ϑ_p=0) (twist parameter quantifying the degree of concave or convex of ω_di), is the key for affecting the toroidal ITG mode instability. The diamagnetic effects from finite β and the effects from 3D MPs can suppress the instability by reducing |ω_(di,0) |. Via reducing |ω_(di,0)^'' | under the prerequisite of unchanged sign of ω_(di,0)^'', there also exist stabilization effects on the instability from 3D MPs and the modification of local magnetic shear by finite β effects. In addition, the stabilization effects induced by reducing |ω_(di,0)^'' | are closely associated with the global magnetic shear. The mechanisms for the effects of finite β and 3D MPs on the instability of toroidal ITG mode revealed in this work are helpful to the comprehensive understanding of the relationship between internal kink mode induced non-axisymmetric flux surface distortion and internal transport barrier physics in tokamak plasmas.

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.

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.

Influence of temperature gradients on helium diffusion and clustering in tungsten: A molecular dynamics study

Tungsten and its alloys, used as plasma-facing materials in fusion reactors, endure high-flux, low-energy helium ion irradiation and temperature gradients induced by thermal load and shocks. This study utilizes molecular dynamics (MD) simulations to explore the diffusion and clustering behavior of helium (He) in tungsten (W) under temperature gradients. The migration behavior of isolated helium atoms, small helium clusters, and helium self-interstitial atom (He-SIA) clusters within tungsten is analyzed. It is revealed that both helium and He-SIA clusters tend to migrate towards higher temperature regions, exhibiting negative thermophoresis. The nucleation of helium clusters, the formation of Frenkel pairs, and the interactions between self-interstitial clusters and helium clusters are also investigated. The results indicate that helium concentration significantly impacts He nucleation behavior. Directional diffusion may lead to areas of high concentration over time, potentially promoting the formation of He clusters and bubbles. These insights enhance the understanding of tungsten's performance and durability as a plasma-facing component in fusion reactors.

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.

Full-f gyrokinetic simulations of hydrogen isotope mixing in tokamak plasmas

Hydrogen isotope mixing phenomena in tokamak plasmas are analyzed using global full-f gyrokinetic simulations. Model plasma parameters are chosen based on hydrogen isotope pellet experiments on JET, in which fast hydrogen isotope mixing in the timescale of the energy confinement time τE occurred after injecting deuterium (D) pellets into hydrogen (H) plasmas. Two numerical experiments are conducted using plasma profiles before and after the pellet injection. In both cases, turbulent fluctuations in the plasma core are characterized by ion temperature gradient driven turbulence. In the former case, the density profile of bulk H ions is kept in a quasi-steady state, and the particle confinement time of bulk H ions τH is an order of magnitude longer than τE. In the latter case, the density profiles of bulk H ions and pellet D ions show transient relaxation in the timescale of τE, and both τH and the timescale of particle pinch τD become comparable to τE, indicating the fast hydrogen isotope mixing. In the toroidal angular momentum balance, it is found that the enhanced ion particle transport leading to the fast hydrogen isotope mixing is driven by the toroidal field stress.

Non-linear MHD modelling of transients in tokamaks: a review of recent advances with the JOREK code

Abstract Transient MHD events like edge localized modes (ELMs) or disruptions are a concern for magnetic confinement fusion power plants. Research with the MHD code JOREK towards understanding control of such instabilities is reviewed here. Experimental validation for unmitigated vertical displacement events (VDEs) progressed. The mechanism of vertical force mitigation by impurity injection was identified. Two-way eddy current coupling to CARIDDI was completed. Shattered pellet injection (SPI) was simulated in JET, KSTAR and ASDEX Upgrade (AUG) and ITER. Benign runaway electron (RE) beam termination in JET and ITER was studied. Coupling of kinetic REs to the MHD is ongoing and a virtual RE synchrotron radiation diagnostic was developed. Regarding pedestal physics, regimes devoid of large ELMs in AUG were simulated and predictive JT60-SA simulations are ongoing. For ELM suppression by resonant magnetic perturbations (RMPs), AUG, ITER and EAST simulations were performed. A free boundary RMP model was validated against experiments. Evidence for penetrated magnetic islands at the pedestal top based on AUG experiments and simulations was found. Simulations of the naturally ELM-free quiescent H-mode (QH) in AUG and HL-3 show external kink mode formation prevents pedestal build-up towards an ELM within windows of the edge safety factor. With kinetic neutral particles, high field side high density (HFSHD) formation in ITER was simulated and with kinetic impurities, tungsten transport in AUG RMP plasmas was studied. To capture turbulent transport, electro-static full-f PiC models for ion temperature gradient (ITG) and trapped electron modes (TEM) were established and benchmarked. Application to RMP plasmas shows enhanced turbulence in comparison to unperturbed states. Energetic particle (EP) interactions with MHD were studied. Flux-pumping that prevents the safety factor on axis from dropping below unity was simulated. First non-linear stellarator applications include current relaxation in l=2 stellarators, while verification for advanced stellarators progresses.

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.

Drift instabilities driven by slab ion temperature gradient in suprathermal plasmas

Abstract The drift instabilities driven by the slab ion temperature gradient (ITG) in Kappa-distributed plasmas are investigated by the kinetic method. The linear dispersion relation is given in an integral representation involving only the standard plasma dispersion function. The wave frequency and growth rate are derived without the density inhomogeneity. Numerical solutions of the dispersion equation are conducted to show the different effects of the suprathermal ions and electrons. We find that the suprathermal ions can enhance the instability in large wavenumbers but suppress it in small wavenumbers. Thus, the suprathermalization of ions could be one of the factors leading to a lower limit of wavenumbers for the ITG instabilities. Besides, the numerical calculations also imply that the thermal speed ratio affects the intensities of the suprathermal effects. Finally, in the presence of density inhomogeneity, the ITG instability boundary is numerically analyzed.

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.

Effect of adiabatic trapping of electrons on the nonlinear evolution of ion temperature gradient driven drift mode in a dispersive plasma

We have theoretically investigated the effect of adiabatic trapping of electrons on ion temperature gradient (ITG) driven nonlinear drift mode in a warm and dispersive electron-ion plasma. For this purpose, we have incorporated the gradients in the background plasma density, ion temperature and ambient magnetic field and derived two different nonlinear partial differential equations (NLPDEs). One of them contains only fractional nonlinearity while the other one incorporates the effect of both quadratic and fractional nonlinearities. We have obtained the exact solutions of these NLPDEs by using the functional variable method. We have used the graphical analysis to carry out the parametric study of the obtained solutions for the Tokamak plasma parameters. We have shown that the amplitude and the width of these nonlinear structures depend on the plasma parameters like T e , T i and η i . This work may be helpful to understand the effect of electron trapping on the low frequency drift type modes in laboratory and space plasmas.

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.

Interpretive modeling of tungsten divertor leakage during experiments with neon gas seeding

Many existing and future tokamaks with tungsten divertors operate, or will operate, with low-Z impurity seeding, but the direct effect of these seeded impurities on tungsten Scrape-off-Layer (SOL) transport has not been explored in detail. This paper reports on a DIII-D experiment designed to test how tungsten divertor leakage from the Small-Angle Slot V-Shaped, tungsten-coated divertor is impacted by neon seeding at a variety of injection rates and poloidal injection locations. Measurements from the experiment show an inverse relationship between the neon injection rate and the tungsten core penetration factor. Interpretive modeling is performed with a combination of the SOLPS-ITER and DIVIMP codes to assess the underlying tungsten behavior. The modeling results show that the reduction in tungsten divertor leakage is driven by both an increase in the divertor collisionality as well as a reduction in the ion temperature gradient near the divertor target. Collisions between low-Z impurities and tungsten impurities are found to have a significant impact on the tungsten SOL transport, such that ignoring the low-Z impurity collisional effects on the tungsten transport can result in an overestimate of the divertor leakage by an order-of-magnitude. Given the importance of these localized interactions, neon seeding from the closed, slot-like divertor has a clear advantage in being able to reduce tungsten divertor leakage without the high levels of neon core contamination that occur when seeding from other poloidal locations.

Ion-temperature- and density-gradient-driven instabilities and turbulence in Wendelstein 7-X close to the stability threshold

Electrostatic gyrokinetic instabilities and turbulence in the Wendelstein 7-X stellarator are studied. Particular attention is paid to the ion-temperature-gradient (ITG) instability and its character close to marginal stability [Floquet-type turbulence (Zocco et al., Phys. Rev. E, vol. 106, 2022, p. L013202) with no electron temperature gradient]. The flux tube version of the $\delta f$ code stella (Barnes et al., J. Comput. Phys., vol. 391, 2019, pp. 365–380) is used to run linear and nonlinear gyrokinetic simulations with kinetic electrons. The nature of the dominant instability depends on the wavelength perpendicular to the magnetic field, and the results are conveniently displayed in stability diagrams that take this dependence into account. This approach highlights the presence of universal instabilities, which are less unstable but have longer wavelengths than other modes. A quasi-linear estimate of the heat flux suggests they are relevant for transport. Close to the stability threshold, the linear eigenmodes and turbulence form highly extended structures along the computational domain if the magnetic shear is small. Numerical experiments and diagnostics are undertaken to assess the resulting radial localisation of the turbulence, which affects the interaction of the latter with zonal flows. Increasing the amplitude of the magnetic shear (e.g.through current drive) has a stabilising effect on the turbulence and, thus, reduces the nonlinear energy transport.

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.