Ion temperature gradient mode and H-mode confinement

It is shown that the toroidal ion temperature gradient (ITG) mode has an upper ηi (higher ηi) stability regime for experimentally relevant parameter values in addition to the lower regime with the stability threshold at ηi around one ( where Ln and LT1 are the characteristic lengths for the density and ion temperature gradients). The ITG mode is studied with a focus on the upper ηi stability regime and the β dependence (β = plasma pressure/magnetic pressure). The results of a gyrokinetic and a two-fluid model as well as a semilocal approximation are compared. It is shown that the upper stability threshold is very sensitive to and considerably reduced by finite-β effects. It is also sensitive to finite Larmor radius (FLR) effects and to (LB is the characteristic length for the toroidal magnetic field gradient). Predictions and comparisons are made with data from a joint European torus (JET) optimized shear discharge and a JET hot ion H-mode (high-performance mode) discharge.

(Received 7 December 2012 /Accepted 10 May 2013)To study the nonlinear saturation mechanism in turbulent plasmas, we plan to obseve ion temperature gra-dient (ITG) modes in the Plasma Assembly for Nonlinear Turbulence Analysis (PANTA). Linear growth ratesof ITG modes in the linear device are analyzed to determine their excitation conditions using a three-field fluidmodel to describe the ion motion. Parameter scans of the linear growth rate show the threshold for ITG modeexcitation, and the typical plasma parameters of the PANTA are found in the unstable domain.

Linear gyrokinetic simulations have been performed using the GTC code to investigate the effects of fast ions on dominant instability changes from TEM to ITG in the EAST. The effects of fractions (5%, 7.5%, and 10%) and temperatures (10 keV, 20 keV, and 30 keV) of fast ions are investigated. The dominant mode transitions from trapped electron mode (TEM) to ion temperature gradient (ITG) mode under different plasma parameters. A transition of the dominant instability is observed at 0.7 ≤ kθρs ≤ 0.8 and shifts to kθρs ≈ 0.7 when fast ions are considered. In addition, fast ions stabilize ITG modes, and the effect becomes more significant as the fraction of fast ions increases, reducing the growth rate by approximately 10% when the fraction of fast ions is 10%. The stabilizing effect increases with increasing temperature of fast ions, but varies little for Tf > 20 keV. Fast ions reduce the ion temperature gradient R/LTi threshold of the dominant instability changes from TEM to ITG. The threshold decreases with decreasing temperature of fast ions, with a reduction of about 10%-20% when the fraction reaches 10% in hydrogen plasmas, and about 3%-12% when deuterium is the main ion. Furthermore, the normalized electron temperature gradient R/LTe for the dominant instability changes from ITG to TEM is lower in hydrogen plasmas, decreasing from 5.4 to 4.1 as Tf increases from 10 keV to 30 keV, while in deuterium plasmas it decreases from 10.5 to 9.5. Moreover, electron–electron collisions lead to the dominant instability changes from TEM to ITG at 0.4 ≤ kθρs ≤ 0.8 and strongly stabilize the ITG mode, reducing its growth rate about 50%, while ion–ion collisions have little influence on TEM and ITG.

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.

The gyrokinetic equations predict that various drift type waves or modes can be unstable in a tokamak. For some of these modes, such as the ion temperature gradient mode and the electron temperature gradient mode, there exists a critical gradient, above which the mode is unstable. There are also drift type modes, such as the trapped electron mode, which do not have a critical ion temperature gradient, but have a threshold which depends upon a variety of parameters. Since the existence of unstable modes can cause increased transport, plasmas which are centrally heated tend to increase in temperature gradient until the modes become unstable. Here the measured ion temperature gradients are compared to the “critical” gradients as calculated by a gyrokinetic linear stability (GKS) code [M. Kotschenreuther et al., Phys. Plasmas 2, 2381 (1995)]. Also, the maximum linear growth rate as calculated by this code is compared to experimentally derived transport coefficients. The results show that for low confinement mode (L-mode) discharges, the measured ion temperature gradient is significantly greater than the GKS calculated critical gradient over a large region of the plasma. This is the same region of the plasma where the ion thermal diffusivity is large. For high confinement mode (H-mode) discharges the ion temperature gradient is closer to the critical gradient, but often still greater than the critical gradient over some region. For the best H-mode discharges, the ion temperature is less than or equal to the critical gradient over the whole plasma. In general, the position in the plasma where the ion thermal diffusivity starts to increase rapidly is where the maximum linear growth rate is greater than the E×B shearing rate.

The effects of dissipative trapped electrons on ion temperature gradient-driven instability (ηi mode) in tokamak plasmas are considered. A sheared slab geometry is adopted and a linearized fluid model of ion temperature gradient (ITG) mode including dissipative trapped electrons, which are described by means of the well-known formula of the nonadiabatic electron response [P. L. Similon and P. H. Diamond, Phys. Fluids 27, 916 (1984)], is presented. Results show that in tokamak plasmas not only is there a modification of the dissipative trapped electrons on the ηi mode, but also there may exist an intrinsic oscillation mode, namely, a hybrid dissipative trapped electron ion temperature gradient mode. The higher the dissipative trapped electron fraction, the more it drives the ηi mode, that is, when the trapped electron fraction is sufficient high and the trapped electrons are dissipated strongly, the mode is dominated by the trapped electron dynamics and propagates in the electron diamagnetic direction. These analytical results can be reduced to the usual predictions of the ion temperature gradient-driven instability in the absence of the dissipative trapped electron. Numerical results further show that (a) there may be a hybrid dissipative trapped electron ITG mode and the dissipative trapped electron effect is a destabilizing effect on this mode; and (b) when the trapped electron fraction is sufficiently high and the trapped electrons are dissipated strongly, the mode is determined by the trapped electron dynamics. These conclusions are in agreement with the experimental observations in the latest simulated tokamak experiment on the Columbia Linear Machine [J. Chen and A. K. Sen, Phys. Rev. Lett. 72, 3997 (1994)].

Hot ion mode has been achieved on HL-2A tokamak with a low electron density and a moderate neutral beam injection power. It is characterized by a high ratio of ion temperature (T_i) and electron temperature (T_e). The T_i/T_e is higher than 3 and ion temperature reaches to 3.5keV in the experiments with heating power no more than 1.3MW. Strong internal transport barrier (ITB), fishbone modes, kinetic ballooning modes (KBM) and ion temperature gradient (ITG) modes are also observed in the hot ion plasma. Power balance analysis given by TRANSP code suggests that electron heating is dominant but thermal ion heat diffusivity is lower than the neoclassical diffusivity in ITB region. Further analysis based on GENE code shows the ITG modes induced heat transport is dominant in experiment, but KBM induced transport will play a more critical role when the electron beta reaches to 0.48\%. More interesting, the heat flux shows a great drop when the fast ions are taken into account. Those results may indicate that the fast ions have a stabilization effect on plasma turbulence, then reduce the thermal ion transport and finally contribute to achievement of high ion temperature and formation of hot ion mode.

Effects of low central fuelling on density and ion temperature profiles have been investigated using negative ion based neutral beam injection and electron cyclotron heating (ECH) in reversed shear plasmas on JT-60U. Strong internal transport barrier (ITB) was maintained in density and ion temperature profiles, when central fuelling was decreased by switching positive ion based neutral beam injection to ECH after the strong ITB formation. Similar density and ion temperature ITBs were formed for the low and high central fuelling cases during the plasma current ramp-up phase. Strong correlation between the density gradient and the ion temperature gradient was observed, indicating that particle transport and ion thermal transport are strongly coupled or the density gradient assists the ion temperature ITB formation through suppression of drift wave instabilities such as ion temperature gradient mode. These results support that the density and ion temperature ITBs can be formed under reactor relevant conditions.

With the term microinstabilities, we indicate a class of plasma drift waves such as the ion temperature gradient (ITG) mode, the trapped electron mode (TEM), and the electromagnetic Alfvénic ion temperature gradient (AITG) mode. They are usually driven by spatial gradients in the plasma and they are held responsible for anomalous transport and enhanced heat flux in tokamaks. Their understanding is therefore crucial for the development of magnetically confined plasma fusion devices. Our approach is based on the gyrokinetic model (Hahm 1988) for particle dynamics. The gyrokinetic nonlinear Vlasov equation, in the presence of an electromagnetic perturbation (Brizard 1989, 1995), is derived using Lie perturbation theory (Cary and Littlejohn 1983) to average out the fast particle motion around the gyrocenter. We have linearized the gyrokinetic Vlasov equation and added the quasi‐neutrality equation and Ampère's law, providing closure to the system. A temporal spectral formulation is used, ensuring the absence of numerical instabilities due to high frequency modes. The equations are simplified with a large aspect ratio approximation for an axisymmetric toroidal configuration. The fields are expanded in a Fourier series in the three spatial directions (radial, poloidal, and toroidal) reducing the problem in a matrix form. The code EM‐GLOGYSTO (Brunner et al. 1998; Falchetto et al. 2003; Joint Varenna‐Lausanne International Workshop 2002) has been developed to look at its solutions. Recently, we have included in the model an electrostatic equilibrium potential in order to provide E×B sheared flow. The code has been optimized for running in a parallel environment using MPI routines, and it allows us to study frequencies, growth rates, and mode structures of electromagnetic microinstabilities. Results on an AITG mode are shown to illustrate these features.

In this study, global nonlinear electromagnetic gyrokinetic simulations are conducted to investigate turbulence 
in the internal transport barrier (ITB) region of the EAST discharge with weakly reversed magnetic shear. 
Linear simulations reveal two dominant ion temperature gradient (ITG) modes: 
a higher frequency mode at the $q=1$ surface, which dominates in the electrostatic limit, 
and a lower frequency mode near the $q_{\min}$ surface, which prevails under the experimental $\beta$ 
(the ratio of plasma pressure to magnetic pressure).
Therefore, electromagnetic effects play a important role in stabilizing ITG modes, 
and in causing the transition between the most unstable mode at different radial positions.
The linear growth rate of the unstable mode in the electrostatic limit is approximately 1.25 times higher than that of the dominant mode in the electromagnetic case.
However, in the electromagnetic nonlinear regime,
the thermal ion heat conductivity is reduced by at least a factor of 4.
This reduction primarily results from nonlinear electromagnetic effects enhancing the shearing effect of zonal flows, 
thereby further suppressing microturbulence.
It is emphasized that the electromagnetic effect on ITG with weak magnetic shear 
should be included to accurately calculate the turbulent transport.

Using the averaged magnetic drift model and a first-order finite Larmor radius expansion, the eigenvalue equation for the ion temperature gradient (ITG) mode in tokamak plasmas is reduced to a Schrödinger-type differential equation. By invoking generalized translational invariance, the model is extended to reversed magnetic shear (RMS) configurations and benchmarked against global gyrokinetic simulations from GTC, showing good quantitative agreement. The analysis reveals a characteristic double-well potential unique to RMS profiles, which gives rise to the degeneracy between the lowest-order even and first-order odd eigenmodes when the two potential wells are sufficiently separated radially. The ITG instability is also found to resonate with the magnetic drift frequency, and its maximum growth occurs when the two rational surfaces are slightly separated. These results provide new physical insight into ITG mode behavior under RMS and offer a compact, accurate theoretical framework that bridges simplified analytic models and global simulations.

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.

The effect of poloidal shear flow on the global structure and stability of toroidal ion temperature gradient mode is studied theoretically and also numerically using a toroidal particle simulation code. Reasonable agreements are found between the theoretical and simulation results; both indicating that with increasing shear flow the toroidal ion temperature gradient mode is stabilized in the increase of poloidal asymmetry and in the reduction of radial mode width.

The linearized gyrokinetic equation governing electrostatic microinstabilities in the presence of sheared equilibrium flow in both the {cflx z} and {cflx y} directions has been systematically derived for a sheared slab geometry, where in the large aspect ratio limit {cflx z} and {cflx y} directions correspond to the toroidal and poloidal directions respectively. In the familiar long perpendicular wavelength regime ({kappa}{perpendicular}{rho}i > 1), the analysis leads to a comprehensive kinetic differential eigenmode equation which is solved numerically. The numerical results have been successfully cross-checked against analytic estimates in the fluid limit. For typical conditions, the Ion Temperature Gradient ({eta}i) modes are found to be stabilized for {cflx y}-direction flows with a velocity shear scale comparable to that of the ion temperature gradient and velocities of a few percent of the sound speed. Sheared flows in the {cflx z}-direction taken along are usually destabilizing, with the effect being independent of the sign of the flow. However, when both types are simultaneously considered, it is found that in the presence of shared {cflx z}-direction flow, sheared {cflx y}-direction flow can be either stabilizing or destabilizing depending on the relative sign of these flows. However, for sufficiently large values of {upsilon}{prime}{sub y} the mode is completely stabilized regardless of the sign of {upsilon}{prime}{sub z} {upsilon}{prime}{sub y}. The importance of a proper kinetic treatment of this problem is supported by comparisons with fluid estimates. In particular, when such effects are favorable, significantly smaller values of sheared {cflx y}-direction flow are required for stability than fluid estimates would indicate.

Quasi-coherent (QC) modes, known as a type of the trapped electron mode (TEM) turbulence, have been measured in the outboard core region of low-density electron cyclotron resonant heating (ECH) injected and ohmically heated L-mode plasmas on the Korea Superconducting Tokamak Advanced Research (KSTAR) device. It appears that QC modes of 20–60 kHz occur or strengthen with an increase of the electron temperature to ion temperature ratio, but weaken or are fully suppressed by increased density/collisionality. Toroidal rotation shear, which is strongly related to the density/collisionality, also seems to stabilize the QC modes. Linear gyrokinetic simulations indicate that TEM is the most unstable mode at low densities where the QC modes are observed for both the ECH and ohmic plasmas. At high densities where the QC modes are suppressed, the most unstable mode is the ion temperature gradient (ITG) mode for the ECH plasmas but still TEM for the ohmic plasmas. In the ECH plasmas, it is found that the direction of the core toroidal intrinsic rotation is gradually reversed from the co-current to counter-current direction and the QC mode is suppressed as the line-averaged density increases, which can be explained by the transition of dominant micro-turbulence (TEM to ITG). However, in the ohmically heated plasmas, the acceleration of the core toroidal rotation is not fully explained by the TEM-ITG transition since the direction of the core toroidal rotation is counter-current direction when the QC mode is observed. Furthermore, the core toroidal rotation is accelerated to the counter-current direction even the line-averaged density decreases.