Ion Temperature Gradient Research Articles

Gyrokinetic simulations of core turbulence and thermal transport in the high-β P discharge on EAST

The properties of core turbulence and thermal transport are investigated for EAST high-β P (β P ∼ 3.1) plasmas with dominant electron heating (T e/T i > 1) via gyrokinetic simulation with the NLT code. Linear simulations identify that the electrostatic -driven trapped electron mode (-TEM) dominates in the core region (ρ< 0.7) and the ion temperature gradient (ITG) mode dominates in the out region (ρ⩾ 0.7), consistent with the linear threshold analysis of micro-instabilities. Sensitivity analysis shows that the normalized electron density gradient (R/L ne) and ITG (R/L Ti) are two effective parameters to stabilize TEM instability. Nonlinear simulations are also carried out and compared with the experimental results, which show that the electron thermal internal transport barrier (ITB) in EAST high-β P plasma is determined by the TEM-induced turbulence. A higher zonal flow shearing rate is observed in the ITB region (0.2 < ρ < 0.34), which can regulate energy transport induced by TEM turbulence and facilitate the formation of e-ITB. A plausible positive feedback mechanism to mitigate turbulence transport and improve energy confinement via enhanced ion heating is proposed for future experiments.

Global gyrofluid simulations of turbulence in tokamak plasmas

We develop a tokamak plasma turbulence simulation code based on a fluid model using the BOUT++ framework. The model corresponds to a global extension of the local gyrofluid model (Beer and Hammett, 1996 [11]), where external sources and neoclassical equilibrium flows are included but some higher-order kinetic effect terms are ignored for the global nonlinear simulation. Hyper-viscous damping terms are introduced to compensate for the stabilizing effect of the missing kinetic terms. With an appropriate hyper-viscosity, we obtain reasonable linear and nonlinear results on ion temperature gradient modes compared to global gyrokinetic simulations. We perform global flux-driven simulations with self-consistently evolving profiles with external heat sources/sinks. A spectral analysis of heat flux in flux-driven turbulence exhibits a broad 1/f (f is the frequency) spectrum observed in gyrokinetic simulations, indicating the prevalence of self-organized criticality-like heat avalanches. We also investigate the effect of an externally imposed vorticity source on turbulence suppression and transport barrier formation. It is shown that internal transport barrier can form even for a monotonic safety factor profile when a sufficiently strong vorticity source is applied.

The internal transport barrier formation on EAST tokamak during the fishbone instability

The internal transport barrier (ITB) which is related to the fishbone instability has been observed on the Experimental Advanced Superconducting Tokamak (EAST) in ELMy H-mode discharges. An interpretation of the formation of the ITB on EAST tokamak is provided, based on both analytical and numerical calculations. The fishbone instability induces the redistribution of fast ions and leads to the accumulation of fast ions in a local region where the ITB is going to appear. Correspondingly, the gradients of fast ions are enhanced, where the ion temperature gradient (ITG) mode exists. Fast ions can interact with the ITG mode through the dilution, Shafranov shift and wave-particle resonance mechanisms. It is found that the ITG mode is stabilized by fast ions and the stabilizing effects are determined mainly by the density, temperature and their gradients of fast ions. The enhanced density and temperature gradients of fast ions lead to a stronger stabilizing effect on ITG mode. Compared with the stabilizing effect before the appearance of fishbone instability, the stabilization on ITG mode is enhanced after the fishbone instability, which is beneficial to the formation of the ITB.

Transition from ITG to MTM linear instabilities near pedestals of high density plasmas

Investigation of linear gyrokinetic ion-scale modes ( k θ ρ s = 0.3) finds that a transition from ion temperature gradient to microtearing mode (MTM) dominance occurs as the density is increased near the pedestal region of a parameterized DIII-D sized tokamak. H-modes profile densities, temperatures, and equilibria are parameterized utilizing the OMFIT PRO_create module. With these profiles, linear gyrokinetic ion-scale instabilities are predicted with CGYRO. This transition (nMTM) has a weak dependence on radial location in the region near the top of the pedestal ( ρ = 0.7 − 0.9), which allows simulating single radii to examine the approximate scaling of nMTM with global parameters. The critical nMTM is found to scale with plasma current. Additionally, increasing the minor radius by decreasing the aspect ratio and increasing the major radius are found to reduce nMTM. However, any relationship between nMTM and density limit physics remains unclear as nMTM increases relative to the Greenwald density with larger minor radius and with larger magnetic field, suggesting that the transport due to MTM may be less important for a reactor. Additionally, nMTM is sensitive to the pedestal temperature, the local electron and ion gradients, the ratio of ion to electron temperature T i / T e, and the current profile. MTMs are predicted to be the dominant instability in the core at similar Greenwald fractions for DIII-D, NSTX, and NSTX-U H-mode experiments, supporting the results of the parameterized study. Additionally, MTMs continue to be the dominant linear instability in a DIII-D L-mode after an H–L transition as the plasma approaches a density limit disruption despite the large change in plasma profiles.

Electrostatic turbulence in EAST plasmas with internal transport barrier

Based on first-principles nonlinear gyrokinetic simulations, the electrostatic turbulence properties in the internal transport barrier (ITB) region of an Experimental Advanced Superconducting Tokamak discharge (#93890) are investigated. Specifically, ITBs with steep density and temperature gradients are located in the weakly negative magnetic shear region at the plasma center. In the linear stage, the growth rate and frequency of the ion temperature gradient (ITG) mode increase significantly due to resonant excitation by trapped electrons. That is, the resonance between trapped electrons and the ITG becomes strong due to the precession drift reversal of trapped electrons by the negative magnetic shear and Shafranov shift. Meanwhile, the trapped electron mode is stable in the ITB region due to only a very small fraction of electrons precessing in the direction of the electron diamagnetic drift. Nonlinear simulations show that, after considering the non-adiabatic effect of trapped electrons, the heat conductivity of ions and the turbulence intensity increase by at least a factor of 7 compared with the results only considering the adiabatic effect of electrons. The zonal charge density of trapped electrons can partially cancel that of ions, which weakens the intensity of the zonal flow, and consequently reduces the zonal flow regulation and enhances the turbulent transport.

Study of correlations between LOC/SOC transition, intrinsic toroidal rotation reversal and TEM/ITG bifurcation with different working gases in TCV

The effects of different working gases on the transition from linear ohmic confinement (LOC) regime to saturated ohmic confinement (SOC) regime and its relation to the intrinsic toroidal rotation reversal phenomenon were explored in the TCV tokamak. The energy confinement saturation was studied across D, H and He density ramps, and a range of ECRH injection power and through variations of ohmic plasma current. The occurrence of rotation reversal, concomitantly with the LOC–SOC transition, was observed only for certain cases, making us formally exclude a causal relation between the two phenomena. A strong correlation between the evolution of toroidal rotation profiles and electron density gradients was, however, observed, in agreement with previous works (Lebschy et al 2017 Nucl. Fusion 58 026013; Hornsby et al 2018 Nucl. Fusion 58 056008). Linear gyrokinetic simulations were performed to probe the turbulent regime of these discharges, showing a dominance of trapped electron mode (TEM) during the LOC phase and a mixture of TEM and ion temperature gradient (ITG) following the transition to SOC regime in D. Such a TEM/ITG bifurcation was less pronounced in H and He. MHD activity was monitored throughout the discharges and possible correlations between sawteeth instability activity, energy confinement time saturation and rotation reversal are highlighted.

A simplified model to estimate nonlinear turbulent transport by linear dynamics in plasma turbulence

A simplified model to estimate nonlinear turbulent transport only by linear calculations is proposed, where the turbulent heat diffusivity in tokamak ion temperature gradient(ITG) driven turbulence is reproduced for a wide parameter range including near- and far-marginal ITG stability. The optimal nonlinear functional relation(NFR) between the turbulent diffusivity, the turbulence intensity mathcal{T}, and the zonal-flow intensity mathcal{Z} is determined by means of mathematical optimization methods. Then, an extended modeling for mathcal{T} and mathcal{Z} to incorporate the turbulence suppression effects and the temperature gradient dependence is carried out. The simplified transport model is expressed as a modified nonlinear function composed of the linear growth rate and the linear zonal-flow decay time. Good accuracy and wide applicability of the model are demonstrated, where the regression error of sigma _{textrm{model}} = 0.157 indicates improvement by a factor of about 1/4 in comparison to that in the previous works.

Global linear stability analysis of kinetic trapped ion mode (TIM) in tokamak plasma using the spectral method

Trapped ion modes (TIMs) belong to the family of ion temperature gradient (ITG) modes, which are one of the important ingredients in heat turbulent transport at the ion scale in tokamak plasmas. A global linear analysis of a reduced gyro-bounce kinetic model for trapped particle modes is performed, and a spectral method is proposed to solve the dispersion relation. Importantly, the radial profile of the particle drift velocity is taken into account in the linear analysis by considering the magnetic flux ψ dependency of the equilibrium Hamiltonian in both the quasi-neutrality equation and equilibrium gyro-bounce averaged distribution function . Using this spectral method, linear growth rates of TIM instability in the presence of different temperature profiles and precession frequencies of trapped ions, with an approximated constant Hamiltonian and the exact ψ dependent equilibrium Hamiltonian, are investigated. The growth rate depends on the logarithmic gradient of temperature κ T , density κ n and equilibrium Hamiltonian . With the exact ψ dependent Hamiltonian, the growth rates and potential profiles are modified significantly, compared to the cases with an approximated constant Hamiltonian. All the results from the global linear analysis agree with a semi-Lagrangian based linear Vlasov solver with good accuracy. This spectral method is very fast and requires much less computation resources compared to a linear version of the Vlasov-solver based on a semi-Lagrangian scheme.

Edge turbulence transport during ELM suppression with n = 4 resonant magnetic perturbation on EAST

The edge turbulence characteristics and the induced radial transport have been investigated in edge localized mode (ELM) suppression by using the 4 resonant magnetic perturbation coils on EAST, with 3.6 and the electron collisionality 0.5. During ELM suppression, the edge turbulence is enhanced dramatically, as measured by the reciprocating probe and the poloidal correlation reflectometry. In the near SOL, the low frequency turbulence (<30 kHz) has a large fluctuation level and propagates along the ion diamagnetic drift direction with a speed of 0.35 km s−1 in the plasma frame; an electromagnetic mode around 120 kHz with a small (∼0.15 cm−1) appears when the ELM is suppressed; weak broadband turbulence between 40–120 kHz propagates in the electron diamagnetic drift direction with a velocity of 3.4 km s−1 in the plasma frame. During the ELM suppression, the radial turbulent particle flux, calculated in both the time and frequency domains, is much higher (can be up to five times) than that in the inter-ELM phase. Furthermore, the low frequency turbulence (<30 kHz) dominates the cross-field particle transport. The 120 kHz electromagnetic mode also contributes to outward particle flux, which is relatively small. A set of CGYRO simulations are performed to illustrate the nature of the 120 kHz electromagnetic mode and the low frequency turbulence, suggesting that the former is the micro-tearing mode and the latter is the ion temperature gradient mode. The bispectral analysis suggests a strong three-wave coupling between the low frequency and high frequency turbulence (>250 kHz), which could be beneficial to form the observed turbulent transport. The estimated upstream cross-field particle flux is consistent with the total particle flux deposited on divertor targets, demonstrating that the enhanced radial turbulent particle transport is an important mechanism for particle exhaust in ELM suppression.

Peaking and hollowness of low-Z impurity profiles: an interplay between ITG and TEM induced turbulent transport

The transport of low-Z impurities in fusion plasmas is dominated, in many regimes of interest, by ion temperature gradient (ITG) and trapped electron mode (TEM) turbulence. We use a statistical test-particle approach to analyze the effects of these drift instabilities on the transport coefficients. It is found that the convection of motion by the polarization drift drives an outward radial pinch via ITG and an inward pinch via TEM turbulence. Opposite radial pinches are driven by turbulent motion along magnetic field-lines. The interplay between these effects can explain the co-existence of peaked and hollow impurity density profiles observed in tokamak plasmas. The theoretical framework is validated through comparison with experimental data on the transport of Boron impurities.

Simulation on the transition of electrostatic instabilities in EAST steady-state scenario

The parameter dependence of transition between electrostatic instabilities is studied using gyrokinetic simulation based on a real discharge of steady-state scenario in the Experimental Advanced Superconducting Tokamak. The scan of radial locations shows that trapped electron mode (TEM) dominates around the core while the ion temperature gradient mode (ITG) simultaneously dominates outside. The maximum growth rate of TEM appears around ρ = 0.24, where the maximum electron temperature gradient R/L Te locates, ρ is the normalized poloidal flux. Effects of the parameters on the transition between TEM and ITG instability are studied at ρ = 0.24. It is found that TEM dominates in the scanning with individually changing R/L Te from 2.50 to 25.02 or the density gradient R/L n from 1.38 to 13.76. Meanwhile, the electron-ion temperature ratio T e/T i is found to destabilize TEM, the effect of T e is more sensitive than that of T i. The dominant instability diagrams in the (R/L Te, R/L Ti) plane at different T e/T i and R/L n are numerically obtained, which clearly show the parameter range of the dominant TEM or dominant ITG instability region. It is found that the dominant TEM region becomes narrower in the plane by decreasing R/L n when T e/T i > 0.5.

Interplay between magnetic shear and triangularity in ion temperature gradient and trapped electron mode dominated plasmas

Local gyrokinetic simulations, performed with the GENE code, are used to investigate the interaction between (negative) triangularity $\delta$ and magnetic shear $s$ , in both ion temperature gradient and trapped electron mode dominated plasmas. Magnetic shear turns out to influence in a non-trivial way the effect of negative triangularity. Also, $\delta &lt;0$ is found to lead to a reduction of fluxes when $s&gt;1$ but not anymore when shear is reduced. In certain parameter regimes, this effect can be inverted, up to obtaining higher fluxes when $\delta &lt;0$ with respect to its $\delta &gt;0$ counterpart.

Characteristics of constrained turbulent transport in flux-driven toroidal plasmas.

We study the dynamics of turbulence transport subject to a constraint on the profile formation and relaxation, dominated by the ion temperature gradient modes, within the framework of adiabatic electron response using a flux-driven global gyro-kinetic toroidal code, GKNET. We observe exponentially constrained profiles, with two different scale lengths, that are spatially constant in each region in higher input power regimes. The profiles are smoothly connected in the knee region located at [Formula: see text] of the minor radius, outside which the gradient is steepened and shows a weak confinement improvement. Based on the probability density function analysis of heat flux eddies, the power law demonstrates a dependence on the eddy size S, as [Formula: see text], which distinguishes events into diffusive and non-diffusive parts including the validation of quasi-linear hypotheses. Radially localized avalanches and global bursts, which exhibit different spatial scales, play central roles in giving rise to constrained profiles on an equal footing. It is also found that the [Formula: see text] shear layers are initiated by the global bursts, which evolve downward on a slow time scale across the knee region and play a role in adjusting the profile by increasing the gradient. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Plasma elongation effect on the parity change in global electromagnetic ion temperature gradient modes and intrinsic rotation generation

A study is made of the effect of plasma elongation (κ) on parity of a global electromagnetic (EM) ion temperature gradient mode and intrinsic rotation generation. An odd parity component of the mode is generated by global EM effects and increases with β (=plasma thermal energy/magnetic energy), enhancing the symmetry breaking and subsequent Reynolds stress [Kaang et al., Phys. Plasmas 25, 012505 (2018)]. The plasma elongation is shown to diminish the parity change via the reduction in the effective ion temperature gradient by a factor α=1−E′, where E=r(κ−1)/(κ+1). A quasi-linear analysis indicates that plasma elongation can weaken the generation of intrinsic torque induced by the global EM effect as a result of the decline of the parity change.

Effect of radial electric field on ion-temperature gradient driven mode stability

To understand the effect of given radial electric field on ion-temperature gradient driven mode (ITG) stability in tokamak plasmas, we derive the eigenmode equation for ITG including the poloidal rotation and density modulation associated with radial electric field by using nonlinear gyrokinetic theory. The equation is solved for the eigenfrequency, growth rate and parallel mode structure of ITG both in short- and long-wavelength limit with energetic-particle-induced geodesic acoustic mode (EGAM) as a specific form. The eigenmode equation is not only solved analytically, but also solved numerically to validate the analytic solutions. It is found that, the radial electric field induced poloidal rotation can significantly stabilize ITG, while the density perturbation of the radial electric field may slightly distort the ITG parallel mode structure, but has little effect on ITG stability. The result is consistent with the common picture of turbulence suppression by poloidal shear flow. The general model is also applicable to the investigation of the indirect interaction of ITG and energetic particle driven Alfvén instabilities via zonal structures generation, by introducing poloidal rotation and density modulation associated with zonal structures spontaneously excited by Alfvén instabilities. The indirect channel is supplement to the direct interaction of microturbulences and energetic particle driven Alfvén instabilities.

ITB formation in gyrokinetic flux-driven ITG/TEM turbulence

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

Transition of turbulence regime during neutral beam injection on EAST

In recent experiments on EAST with neutral beam injection (NBI) and radio frequency (RF) waves (lower hybrid wave (LHW) and electron cyclotron waves) heating, it was observed that an increase in the line-averaged electron density and a decrease in the plasma internal inductance occurred in the duration of NBI. To explain the experimental observation, the simulations are conducted by using the equilibrium code EFIT and the transport codes ONETWO and TGYRO. It is shown that L-H transition is triggered right after neutral beam is injected, leading to the formation of density pedestal, the plasma density gradient in the outer region (0.4 < ρ < 0.75) is thus changed, which leads to an increase in η i (, where and ), where ρ is the normalized square root of the toroidal magnetic flux. A transition from a trapped electron modes (TEM) to an ion temperature gradient (ITG) modes dominant turbulence regime then happens due to the increase of η i in the region (0.4 < ρ < 0.75), which results in an inward particle pinch. As a result of the rise of plasma density, the parallel refractive index and ray trajectories of the LHW are affected and more power is deposited outside ρ > 0.6, which drives more off-axis current and therefore the internal inductance is reduced.

Spectral transition of multiscale turbulence in the tokamak pedestal

The transition in the turbulence spectrum from ion-scale dominated regimes to multiscale transport regimes that couple ion and electron scales is studied with gyrokinetic simulations of turbulent transport. The simulations are based on DIII-D high-confinement mode (H-mode) plasma parameters in the tokamak pedestal. The transition is initiated by varying the ion temperature gradient. To our knowledge, no full multiscale simulations of pedestal-like transport have been done previously. The experimental parameters lie in a bifurcation region between the two regimes. At long wavelengths, a complex, ion-direction hybrid mode is the dominant linearly unstable drift wave, while an electron temperature gradient-driven mode is unstable at short wavelengths. In the transition from the multiscale branch to the ion-scale branch, the magnitude of the ion-scale poloidal wavenumber spectrum of the nonlinear turbulent energy flux increases and the magnitude of the high-wavenumber spectrum decreases. The decrease in the electron-scale transport is due to nonlinear mixing with ion-scale fluctuations and the ion-scale-driven zonal flows. A shift in the total energy associated with the fluctuating electrostatic potential intensity from dominantly drift kinetic energy in the multiscale regime to dominantly potential intensity in the ion-scale regime is well-correlated with the trend in the total energy flux.

Peripheral temperature gradient screening of high-Z impurities in optimised ‘hybrid’ scenario H-mode plasmas in JET-ILW

Screening of high-Z (W) impurities from the confined plasma by the temperature gradient at the plasma periphery of fusion-grade H-mode plasmas has been demonstrated in the JET-ILW (ITER-like wall) tokamak. Through careful optimisation of the hybrid-scenario, deuterium plasmas with sufficient heating power ( 32 MW), high enough ion temperature gradients at the H-mode pedestal top can be achieved for the collisional, neo-classical convection of the W impurities to be directed outwards, expelling them from the confined plasma. Measurements of the W impurity fluxes between and during edge-localised modes (ELMs) based on fast bolometry measurements show that in such plasmas there is a net efflux (loss) between ELMs but that ELMs often allow some W back into the confined plasma. Provided steady, high-power heating is maintained, this mechanism allows such plasmas to sustain high performance, with an average D–D neutron rate of s−1 over a period of ∼3 s, after an initial overshoot (equivalent to a D–T fusion power of ∼9.4 MW), without an uncontrolled rise in W impurity radiation, giving added confidence that impurity screening by the pedestal may also occur in ITER, as has previously been predicted (Dux et al 2017 Nucl. Mater. Energy 12 28–35).

Vlasov equation, waves and dispersion relations in fractal dimensions: Landau damping and the toroidal ion temperature gradient instability problem

In this study, we have used the concept of ‘product-like fractal measure’ introduced by Li and Ostoja-Starzewski in their formulation of anisotropic and elastic media to introduce Vlasov equation in fractal dimension. We have been motivated by this new concept since it is safely applied to several systems with length scales bounded by lower and upper cutoffs via the dimensional regularization technique. We have considered through this study collisionless plasma in fractal dimension and we have analyzed the impacts of the Vlasov equation in some points in plasma physics starting from the Hamiltonian dynamics. Several results have been obtained and discussed accordingly. The main outcomes of the present study concern first the facts that waves in cold plasma are associated with low fractal dimensions and hence by low complexity and that the effective damping is affected by the sign of the fractal dimension and differs from the conventional Landau damping in magnitude and in sign for negative dimension. Besides, for a very low fractal dimension, the Landau damping is negligible or removed. This result was observed in kinetic turbulent plasmas and may solve the paradox problem emerging in the application of critical balance to a kinetic turbulence cascade.