A possible hybrid dissipative trapped electron ion temperature gradient mode

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.

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.

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.

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 linear stability of dissipative drift electrostatic modes in tokamak plasmas is studied numerically with an extended version of the gyrokinetic code Kinezero [C. Bourdelle et al., Nucl. Fusion 42, 892 (2002)] including a modified Krook collision operator to account for collisional effects on the trapped electron response. This new version of Kinezero has been successfully tested and benchmarked against the results of a more sophisticated and complete gyrokinetic solver, GS2 [M. Romanelli, C. Bourdelle, and W. Dorland, Phys. Plasmas 11, 3845 (2004)]. The critical density and temperature gradients for ion gradient driven modes (ITG) and trapped electron modes (TEM) have been computed for different values of collisionality. The threshold for TEM disappears as the collisionality increases. A detailed study of the dependence of the growth rate of the dissipative TEM on collisionality and density gradient is presented in the paper. The range of parameters where the dissipative trapped electron modes are destabilized by increasing collisionality corresponds to very steep density gradients that can hardly be achieved in today's large tokamaks.

Ion temperature profiles of neutral beam heated plasmas in JT‐60 have been simulated by using models of ion thermal diffusivity, χi, based on ion temperature gradient mode (ηi mode) turbulence and drift wave turbulence (trapped electron mode and circulating electron mode). Three different χi models proposed by Dominguez and Waltz, Lee and Diamond, and Romanelli are adopted and the predicted Ti profiles are compared with those measured by CXRS (charge exchange recombination spectroscopy). All three χi models can fit the Ti profile over wide range of plasma parameters of JT‐60 L‐mode plasmas except for 1 MA limiter cases. However, in the high ion temperature (high Ti) plasmas, the predicted Ti profiles are much broader than that of experiment.

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.

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.

The unified fluid/kinetic equations developed in Part I [Phys. Fluids B 4, ▪▪▪ (1992)] of this work are used to study plasma-drift-type microinstabilities. A generalized perturbed Ohm’s law is derived (for a sheared slab magnetic field model) that is uniformly valid for arbitrary collisionality ω/ν and adiabaticity ω/k∥vt. Applications to electron drift waves, ion temperature gradient modes (ηi modes) and electron electromagnetic modes (microtearing modes) are addressed. It is shown that the unified equations exhibit their simple and uniformed features in the plasma microinstability analysis. The well-known results of these instability branches in both fluid and adiabatic limits are easily recovered using the new fluid/kinetic equations. Generalization of the two-field Hasegawa–Wakatani turbulent equations [Phys. Rev. Lett. 50, 682 (1983)] to include electron temperature fluctuations and linear Landau damping effects is also discussed. Finally, a new method is presented to facilitate the study of magnetic trapped particle modes using the present kinetic closure procedure. It is found that by including the trapped particle effects in the closure relations, the usual separation of the fluid equations into trapped and untrapped components becomes unnecessary.

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.

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.

The energy confinement properties of different regimes of JET plasmas are investigated. The results of local transport analysis in both L- and H-mode regimes are discussed and the properties of H-mode plasmas produced by neutral beam injection and/or ion cyclotron resonance heating are compared. Two aspects of transport analysis are addressed. Firstly, the relative importance of the electron and ion heat conductivities and a comparison with the effective particle diffusivity since this determines the nature of the turbulence responsible for the degradation in confinement. The second issue is whether theoretical models adequately describe the radial dependence of the measured heat flux. Several theoretical models are considered: the ion temperature gradient driven turbulence model, the Rebut-Lallia critical temperature gradient model, the dissipative and collisionless trapped electron drift wave mode, the Carreras-Diamond resistive ballooning model and the neoclassical pressure gradient driven turbulence model.

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.

The stability properties of the toroidal ion temperature gradient (ITG) mode change dramatically for plasmas with flat density profiles, as found in H-mode plasmas. Even though ηi ≫ 1, the relevant stability parameter is is the ion temperature gradient scale length and R is the major radius). It is proposed that a significant element in the improved confinement observed in the L- to H-mode transient is the diminution of ITG mode turbulence, mediated by broader H-mode ion temperature profiles. Confinement results of L- and H-mode simulations of DIII-D, based on a simplified energy transport equation, are presented to support this hypothesis.