Trapped Electron Mode Research Articles

Impurity pinch generated by trapped particle driven turbulence

Impurity turbulent transport in tokamak plasmas is investigated in the case of trapped ion mode (TIM) and trapped electron mode (TEM) using a non-linear bounce-averaged gyrokinetic model. In particular, we focus on the thermo-diffusive pinch and the curvature-driven pinch observed in non-linear simulations. Thermodiffusion is analyzed independently of curvature pinch by disabling the latter artificially. A parameter scan shows that the direction of thermodiffusion depends mainly on two factors. First, it depends on the sign of the turbulence phase velocity, and the resulting transport is inward in the case of TEM whereas it is outward in the case of TIM. Second, it depends on the sign of the impurity temperature gradient. Moreover, the magnitude of the thermodiffusion tends to decrease with respect to the impurity charge Z, while it is proportional to the intensity of background turbulence. Lastly, the direction of the curvature pinch is investigated as a function of the magnetic shear. The results of non-linear simulations are compared with quasi-linear theory. The Kubo number is calculated for our non-linear simulations to justify this comparison. Quasi-linear theory is found to be in qualitative agreement with our gyrokinetic numerical observations.

Multi-scale multi-mode nonlinear interaction in tokamak plasma turbulence with moderate small-scale shear flow

Effects of moderate small-scale shear flow, e.g., which may be created by the trapped electron mode, on electromagnetic (EM) ion-scale turbulence in tokamak plasmas are numerically investigated via a self-consistent Landau-fluid model. A modeling analysis is carried out in slab geometry to reveal the underlying mechanism of the multi-scale multi-mode nonlinear interaction. Results show that while a Kelvin–Helmholtz (KH) instability with long wavelengths may be excited by the shear flows to dominate the multi-scale EM fluctuation, shorter wavelength ion temperature gradient (ITG) modes experience multiple quasi-steady (QS) stages with enhanced fluctuation level through different driving and saturation mechanisms. One mechanism is the secondary ITG instability due to the decrease in flow stabilization modified by the zonal flow. Meanwhile, the other one is the modulational interaction between the EM ITG and KH modes through the nonlinear mode coupling. Moreover, the synergism of these two mechanisms may sustain the final QS state near the marginal KH instability threshold. Complex linear and nonlinear interactions among multiple modes and external flow, as well as self-generated zonal flow, result in a weak dependence of the final saturation level of the dominant EM ITG mode on the small-scale flow amplitude. The turbulent heat transport is visibly suppressed by weaker shear flow, but is almost not affected by stronger shear flows. The underlying mechanism is elaborated.

Dependence of the impurity transport on the dominant turbulent regime in ELM-y H-mode discharges on the DIII-D tokamak

Laser blow-off injections of aluminum and tungsten have been performed on the DIII-D tokamak to investigate the variation of impurity transport in a set of dedicated ion and electron heating scans with a fixed value of the external torque. The particle transport is quantified via the Bayesian inference method, which, constrained by a combination of a charge exchange recombination spectroscopy, soft x-ray measurements, and vacuum ultraviolet spectroscopy provides a detailed uncertainty quantification of transport coefficients. Contrasting discharge phases with a dominant electron and ion heating reveal a threefold drop in the impurity confinement time and order of magnitude increase in midradius impurity diffusion, when additional electron heating is applied. Furthermore, the calculated stationary aluminum density profiles reverse from peaked in electron heated to hollow in the ion heated case, following a similar trend to electron and carbon density. Comparable values of a core diffusion have been observed for W and Al ions, while differences in the propagation dynamics of these impurities are attributed to pedestal and edge transport. Modeling of the core transport with non-linear gyrokinetics code CGYRO [J. Candy and E. Belly, J. Comput. Phys. 324, 73 (2016)], significantly underpredicts the magnitude of the variation in Al transport. Diffusion increases three-times steeper with additional electron heat flux, and 10-times lower diffusion is observed in ion heated case than predicted by the modeling. The CGYRO model quantitatively matches the increase in the Al diffusion when approaching the linear threshold for the transition from the ion temperature gradient to trapped electron mode.

Comparison of edge turbulence characteristics between DIII-D and C-Mod simulations with XGC1

The physical processes taking place at the separatrix and scrape-off layer regions are crucial for the operation of tokamaks as they govern the interaction of hot plasma with the vessel walls. Numerical modeling of the edge with state-of-the-art codes attempts to elucidate the complex interactions between neoclassical drifts, turbulence, poloidal, and parallel flows that control the physical set-up of the SOL region. Here, we present the post-processing analysis of simulation results from the gyrokinetic code XGC1, comparing and contrasting edge turbulence characteristics from a simulation of the DIII-D tokamak against a simulation of the Alcator C-Mod tokamak. We find that the equilibrium E × B flux across the separatrix has a similar poloidal pattern in both discharges, which can be explained by ∇B-drifts and trapped ion excursions. However, collisionality is noted to play a major role in the way that it prevents local charge accumulations from having more global effects in the C-Mod case. In both cases, turbulent electron heat flux is observed to be higher than the ion one and is possibly related to the need of electrons to maintain quasineutrality through the only channel available to them for exiting the confinement. By Fourier analysis, we identify turbulent frequencies and growth rates of the dominant mode in both simulations. In the case of C-Mod, these numbers point to the presence of a drift wave. In the DIII-D case, further linear simulations with the Gene code reveal a trapped electron mode. Furthermore, using a blob detection and tracking tool, we present the amplitude and size distributions of the blobs from both simulations. The amplitude distributions are in qualitative agreement with experimental observations, while the size distributions are consistent with the fact that most of the blobs are not connecting to the divertor plates and suggest that they are generated by the shearing of the turbulent modes.

Influence of toroidal rotation from electron cyclotron resonance heating in KSTAR

Toroidal rotation behaviors from electron cyclotron resonance heating (ECH) injected Ohmic and high confinement mode (H-mode) plasmas are investigated in KSTAR. The on-axis ECH injection induces core toroidal rotation reversal by neoclassical toroidal viscosity (NTV) damping torque coincided with trapped electron mode (TEM)-driven co-current rotation torque in the countercurrent rotating Ohmic plasmas. In the ECH triggered H-mode plasmas with enhanced heating power, the toroidal rotation in the central region turns to the countercurrent direction and co-current direction in the outer region of the plasma.

Effects of temperature gradient driven turbulence and core MHD instability on particle transport in HL-2A L-mode plasmas

Experiments in L-mode plasmas in the HL-2A tokamak show that the electron and trace Al impurity transport is related to the normalized electron temperature gradient with opposite trends. Increasing in the confinement zone (0.25 ⩽ ρ⩽ 0.5, ρ is the normalized minor radius) tends to pump out electrons but accumulate impurity, leading to slightly hollow electron density profiles meanwhile with an overall stronger inward convection of injected impurity. Moreover, after the injection of Al impurity by laser blow-off (LBO), the impurity density profiles remain deeply hollow due to the combined effect of the impurity expulsion by core magneto-hydrodynamic (MHD) activity in the plasma centre and the inward impurity convection driven by turbulence in the outer confinement region. Gyrokinetic simulation results reveal that the local change of affects the relative strength of the trapped electron mode (TEM) and the ion temperature gradient (ITG) mode, eventually determining the electron particle transport in a way consistent with the experimental observations. Comparison of simulations with and without collisionallity shows that the plasma collisionality can significantly reduce the growth rate of the TEM and the associated outward particle flux.

Evidence and modeling of turbulence bifurcation in L-mode confinement transitions on Alcator C-Mod

Analysis and modeling of rotation reversal hysteresis experiments show that a single turbulent bifurcation is responsible for the Linear to Saturated Ohmic Confinement (LOC/SOC) transition and concomitant intrinsic rotation reversal on Alcator C-Mod. Plasmas on either side of the reversal exhibit different toroidal rotation profiles and therefore different turbulence characteristics despite the profiles of density and temperature, which are indistinguishable within measurement uncertainty. Elements of this bifurcation are also shown to persist for auxiliary heated L-modes. The deactivation of subdominant (in the linear growth rate and contribution to heat transport) ion temperature gradient and trapped electron mode instabilities is identified as the only possible change in turbulence within a reduced quasilinear transport model across the reversal, which is consistent with the measured profiles and inferred heat and particle fluxes. Experimental constraints on a possible change from strong to weak turbulence, outside the description of the quasilinear model, are also discussed. These results indicate an explanation for the LOC/SOC transition that provides a mechanism for the hysteresis through the dynamics of subdominant modes and changes in their relative populations and does not involve a change in the most linearly unstable ion-scale drift-wave instability.

Modulation of the trapped electron driven turbulence by m/n = 2/1 tearing mode in the core of HL-2A plasmas

Turbulent fluctuations within a quasi-coherent frequency range (peak frequency of ∼130 kHz, Δf ≈ tens of kHz) are modulated by the rotation of low frequency tearing modes in the core of HL-2A ohmic plasmas. The quasi-coherent modes (QCMs) emerge outside the island boundary as the island O-point passes by in the large island cases (W > 4.5 cm), where the local electron temperature profile is steepened. Statistical analysis shows that for the QCM excitation, a threshold value of temperature gradient is identified and the QCM is solely observed in low density discharges, consistent with the linear ohmic confinement regime. These experimental evidence suggests that the observed QCMs are driven by the trapped electron mode, in agreement with linear stability calculations. Cross-correlation analysis reveals that the QCMs have long-range poloidal correlations and radially propagate outwards. Besides, the bispectral analysis indicates: (i) there exists non-linear coupling between the tearing mode and micro-turbulence, most significantly in the QCM frequency range; (ii) the QCMs nonlinearly couple by themselves to excite the second harmonic, whereas no non-linear interaction is observed between the QCMs and ambient turbulence.

First implementation of gyrokinetic exact linearized Landau collision operator and comparison with models

Gyrokinetic simulations are fundamental to understanding and predicting turbulent transport in magnetically confined fusion plasmas. Previous simulations have used model collision operators with approximate field-particle terms of unknown accuracy and/or have neglected collisional finite Larmor radius (FLR) effects. We have implemented the linearized Fokker–Planck collision operator with exact field-particle terms and full FLR effects in a gyrokinetic code (GENE). The new operator, referred to as “exact” in this paper, allows the accuracy of model collision operators to be assessed. The conservative Landau form is implemented because its symmetry underlies the conservation laws and the H-theorem, and enables numerical methods to preserve this conservation, independent of resolution. The implementation utilizes the finite-volume method recently employed to discretize the Sugama collision model in GENE, allowing direct comparison between the two operators. Results show that the Sugama model appears accurate for the growth rates of trapped electron modes (TEMs) driven only by density gradients, but appreciably underestimates the growth rates as the collisionality and electron temperature gradient increase. The TEM turbulent fluxes near the nonlinear threshold using the exact operator are similar to the Sugama model for the ηe=d ln Te/d ln ne=0 case, but substantially larger than the Sugama model for the ηe=1 case. The FLR effects reduce the growth rates increasingly with wavenumber, deepening a “valley” at the intermediate binormal wavenumber as the unstable mode extends from the TEM regime to the electron temperature gradient instability regime. Application to the Hinton–Rosenbluth problem shows that zonal flows decay faster as the radial wavenumber increases and the exact operator yields weaker decay rates.

Impact of fast ions on a trapped-electron-mode dominated plasma in a JT-60U hybrid scenario

The impact of fast ions on a trapped electron mode (TEM) is extensively analysed by linear and nonlinear gyrokinetic simulations for a JT-60U plasma at high and low magnetic shear using the Gene code in local approximation. For the first time, it is shown that TEM-induced turbulent transport may remain unaffected by the steep fast ion pressure profile generated by the neutral beam injection. Unlike recent observations of ion temperature gradient (ITG)-induced turbulent transport reductions due to fast ions, TEM-dominated systems could act differently in the presence of a significant fast ion population. The possible role of zonal flows as a saturation mechanism is analyzed, showing that their weak impact in the reported JT-60U scenario might lead to different behaviour of fast ions with respect to the ITG-dominated discharges. It is also shown that Alfvénic shear modes are destabilized at low wave numbers (). They are identified as drift Alfvén waves destabilized by ITG, which is a form of Alfvénic ITG instabilities. Deep numerical analysis provides the physical parameter range in which ITG-driven BAEs are stabilized. These results open the way to new possibilities of tailoring future experimental scenarios in order to benefit from transport reduction by fast ions.

Modeling of the transition mechanism from electrostatic drift-type modes to electromagnetic kinetic ballooning mode-dominant regime in high poloidal-beta discharges

Recent analyses (for example, see the paper by Staebler et al (2018 Phys. Plasmas 056113)) indicate that in DIII-D high poloidal-beta discharges turbulent transport, particularly for ions, is governed by the electromagnetic kinetic ballooning mode (KBM) in most radial regions, including the outer core between the internal and external transport barriers (ITBs and ETBs). Considering that in the usual L- or H-mode plasmas turbulent transport is widely believed to be dominated by the electrostatic drift-type modes, such as the ion temperature gradient (ITG) or trapped electron mode (TEM), a modeling study is presented to show how this transition of dominant modes can occur. In the ITB region, where there already exist several theoretical models, the focus is put on clarifying the relative role between the Shafranov shift and linear electromagnetic effects. While these two can play an important role in the transition or ITB formation by stabilizing the electrostatic drift-type modes, a significant difference is found in that the former mainly works on the TEM, while the latter works on the ITG. In contrast to the ITB region, in the outer core between the ITB and ETB the transition appears to be more relevant to the destabilization of the KBM itself, rather than the stabilization of electrostatic modes. A jump of edge plasma beta through the pedestal formation is shown to play the critical role in this destabilization by making the KBM threshold temperature gradient smaller than that of the ITG/TEM, thus allowing an earlier excitation of KBM when background temperature gradients increase by external heating.

Nonlinear gyrokinetic analysis of linear ohmic confinement to saturated ohmic confinement transition

This work presents a nonlinear gyrokinetic analysis, which addresses one of the perennial conundrums in ohmically heated fusion plasmas. The widely observed linear ohmic confinement (LOC) to saturated ohmic confinement (SOC) transition of the energy confinement time with increasing density is successfully reproduced from nonlinear gyrokinetic simulations for the first time. Suppression of trapped electron turbulence by collisional detrapping due to increasing density is found to be responsible for the transition. The microturbulence transition from trapped electron modes to ion temperature gradient modes is found to coincide, but is not a necessary condition for the LOC–SOC transition. Damping of nonlinearly generated zonal flow by increasing collisionality with density can be responsible for the energy confinement degradation in the SOC regime.

Numerical study of ubiquitous modes in tokamak plasmas in the presence of impurities

As an important branch of trapped electron modes (TEMs), the ubiquitous mode (UM) is a favored subject for the investigation of anomalous energy losses in magnetic fusion plasmas. In this paper, the numerical study of UMs was carried out in tokamak plasmas in the presence of impurities. The physical model and the gyrokinetic equations for TEM (and UM) instability is introduced, including the impurity effect. The numerical results show that impurity species impose significant impacts on the UM instability in many ways, one of which is that impurity effect on UMs is generally stabilizing, and on the whole the stabilizing effect is most pronounced for the case of −0.8 ≲ Lez < 0 ( with ). As the impurity charge concentration increases, or for the heavier or lower-ionized impurity ions, the UM instability is weaker. Compared to the ion and electron temperature gradient effects, impurity temperature gradient (expressed by ) has only a minor effect, while the ratio of electron to impurity temperature has a relatively larger effect on UMs, embodied in the mode linear growth rates and instability windows. The investigation of wavenumber threshold for UM showed that the mode was a fluid-like instability when and the presence of impurity resulted in the modification of the UM instability window. By surveying the parametric dependences of UMs in the presence of impurities, it is revealed that comparatively, the stabilizing effects of impurity is more pronounced in the regime of larger wavenumber, while the weakening effects of (i) decreasing the fraction of trapped electrons, (ii) increasing the magnetic shear, or (iii) decreasing the electron density gradient on UM instability are relatively more pronounced in the regime of smaller wavenumber. It also indicates that the stabilizing effect of impurity on UMs is owing to the non-resonant mechanism of the UM.

Comparison of edge turbulence characteristics between DIII-D and C-Mod simulations with XGC1

The physical processes taking place at the separatrix and scrape-off layer regions are crucial for the operation of tokamaks as they govern the interaction of hot plasma with the vessel walls. Numerical modeling of the edge with state-of-the-art codes attempts to elucidate the complex interactions between neoclassical drifts, turbulence, poloidal, and parallel flows that control the physical set-up of the SOL region. Here, we present the post-processing analysis of simulation results from the gyrokinetic code XGC1, comparing and contrasting edge turbulence characteristics from a simulation of the DIII-D tokamak against a simulation of the Alcator C-Mod tokamak. We find that the equilibrium E × B flux across the separatrix has a similar poloidal pattern in both discharges, which can be explained by ∇ B-drifts and trapped ion excursions. However, collisionality is noted to play a major role in the way that it prevents local charge accumulations from having more global effects in the C-Mod case. In both cases, turbulent electron heat flux is observed to be higher than the ion one and is possibly related to the need of electrons to maintain quasineutrality through the only channel available to them for exiting the confinement. By Fourier analysis, we identify turbulent frequencies and growth rates of the dominant mode in both simulations. In the case of C-Mod, these numbers point to the presence of a drift wave. In the DIII-D case, further linear simulations with the Gene code reveal a trapped electron mode. Furthermore, using a blob detection and tracking tool, we present the amplitude and size distributions of the blobs from both simulations. The amplitude distributions are in qualitative agreement with experimental observations, while the size distributions are consistent with the fact that most of the blobs are not connecting to the divertor plates and suggest that they are generated by the shearing of the turbulent modes.

The dominant micro-turbulence instabilities in the lower q95 high βp plasmas on DIII-D and predict-first extrapolation

Large-radius internal transport barriers (ITB) are the signature of high scenarios on DIII-D. Previous studies show that a large Shafranov shift, rather the shear, suppresses the turbulence and helps in the formation of the large-radius ITB. New gyrokinetic simulations suggest that the remaining micro-instabilities in lower q95 (<7.0), high ITB plasmas are drift wave instabilities, including the collisionless trapped electron mode in the core and ITB peak gradient region, the electron temperature gradient mode in the ITB peak gradient region and at the ITB foot and the ion temperature gradient mode at the ITB foot. Gyrokinetic simulation results qualitatively agree with the density fluctuation analysis from beam emission spectroscopy, which suggests the existence of a low-k ion mode at the ITB foot. The gyrokinetic simulations also predict that a larger Shafranov shift can overwhelm the driving sources for turbulence from the profile gradients at higher , leading to stronger turbulence suppression and stronger ITBs in lower q95, high plasmas.

Scaling study for positive magnetic shear ELMy H-mode plasmas in JT-60U

Scaling of the density peaking for positive magnetic shear ELMy H-mode plasmas in JT-60U has been developed. Although the density peaking generally depends on collisionality, a variation of the density peaking factor for the same collisionality exists, and the variation is different between plasmas with co-directed and ctr-directed toroidal rotation(co-VT plasmas and ctr-VT plasmas). The variation of the co-VT plasmas can be explained by particle source profile. As a result of scaling, the peaking factor of the co-VT plasmas depends on the particle source rate profile from neutral beams (NBs) as much as collisionality. The dataset of the ctr-VT plasmas has a larger variation of the peaking factor compared to that of the co-VT plasmas. The larger variation stems from that the peaking factor of the ctr-VT plasmas also depends on the normalized ion temperature gradient at the edge region. As a result of scaling, the normalized ion temperature gradient influences the peaking factor as much as or a little larger than collisionality. The parameter regime of the ctr-VT plasmas ranges from the trapped electron mode (TEM) to the ion temperature gradient mode (ITG mode). The plasmas with the positive correlation between the normalized density gradient and the normalized ion temperature gradient are dominated by the TEM. On the other hand, the plasmas with the negative correlation are dominated by the ITG mode.

Effects of collisionality and Te/Ti on fluctuations in positive and negative δ tokamak plasmas

The effects of negative triangularity () on confinement and fluctuations in plasmas covering a large range of parameters were investigated on the tokamak à configuration variable (TCV). The conditions explored in this paper include discharges where neutral beam (NB) heating was employed to obtain an electron-ion temperature ratio across a large fraction of the plasma profile. This significantly extended the range of negative plasmas studied on TCV towards conditions more relevant to future reactor-like tokamaks. Negative triangularity was found to improve confinement over the full range of collisionality studied () and (). The amplitude of radiative temperature fluctuations, measured using a correlation electron cyclotron emission diagnostic over the range , was found to be reduced, in negative with respect to positive plasmas, for all combinations of parameters explored. This was, in particular, verified for a pair of positive and negative plasmas with comparable density and under different conditions of NB heating. Linear gyrokinetic simulations found the dominant turbulence regime, in the strongly NB heated discharges, to be a mixture of trapped electron modes (TEMs) and ion temperature gradient driven modes. This is in contrast to ohmic or electron cyclotron heated discharges, for which the dominant turbulence regime was found to be pure TEM. Negative triangularity was found to lead to partial stabilization of the most unstable modes for low wavenumbers in both turbulence regimes. These findings demonstrate that negative triangularity could provide significant confinement improvement over a large range of parameters, that include conditions closer to future reactor-like machines (, low collisionality).

Turbulent transport in TCV plasmas with positive and negative triangularity

Local gyrokinetic simulations with the GENE code are used to investigate the turbulent transport for different levels of neutral beam injection heating power in the Tokamak à Configuration Variable (TCV) for plasmas with both positive and negative edge triangularity. The sensitivity of the heat fluxes with respect to the main plasma parameters, including background gradients, impurity content, and electron temperature, is systematically studied. The experimentally measured transport levels are recovered with variations of profiles compatible with experimental error bars. When considering experimental conditions, trapped electron modes are the dominant instabilities for all heating powers and both types of shapes, whereas ion temperature gradients (ITGs) are not found. A numerical experiment, considering plasma profiles that strongly destabilize ITG modes, is thus performed. Negative triangularity is found to reduce the transport level also in this regime.

Formation of a High Pressure Staircase Pedestal with Suppressed Edge Localized Modes in the DIII-D Tokamak.

We observe the formation of a high-pressure staircase pedestal (≈16-20 kPa) in the DIII-D tokamak when large amplitude edge localized modes are suppressed using resonant magnetic perturbations. The staircase pedestal is characterized by a flattening of the density and temperature profiles in midpedestal creating a two-step staircase pedestal structure correlated with the appearance of midpedestal broadband fluctuations. The pedestal oscillates between the staircase and single-step structure every 40-60ms, correlated with oscillations in the heat and particle flux to the divertor.Gyrokinetic analysis using the cgyro code shows that when the heat and particle flux to the divertor decreases, the pedestal broadens and the E×B shear at the midpedestal decreases, triggering a transport bifurcation from the kinetic ballooning mode (KBM) to trapped electron mode (TEM) limited transport that flattens the density and temperature profiles at midpedestal and results in the formation of the staircase pedestal. As the heat flux to the divertor increases, the pedestal narrows and the E×B shear at the midpedestal increases, triggering a back transition from TEM to KBM limited transport. The pedestal pressure increases during the staircase phase, indicating that enhanced midpedestal turbulence can be beneficial for confinement.

Gyrokinetic GENE simulations of DIII-D near-edge L-mode plasmas

We present gyrokinetic simulations with the GENE code addressing the near-edge region of an L-mode plasma in the DIII-D tokamak. At radial position ρ = 0.80, simulations with the ion temperature gradient (ITG) increased by 40% above the nominal value give electron and ion heat fluxes that are in simultaneous agreement with the experiment. This gradient increase is consistent with the combined statistical and systematic uncertainty σ of the charge exchange recombination spectroscopy measurements at the 1.6σ level. Multiscale simulations are carried out with a realistic mass ratio and geometry for the first time in the near-edge. These multiscale simulations suggest that the highly unstable ion temperature gradient (ITG) modes of the flux-matched ion-scale simulations suppress electron-scale transport, such that ion-scale simulations are sufficient at this location. At radial position ρ = 0.90, nonlinear simulations show a hybrid state of ITG and trapped electron modes, which was not expected from linear simulations. The nonlinear simulations reproduce the total experimental heat flux with the inclusion of E × B shear effects and an increase in the electron temperature gradient by ∼23%. This gradient increase is compatible with the combined statistical and systematic uncertainty of the Thomson scattering data at the 1.3σ level. These results are consistent with previous findings that gyrokinetic simulations are able to reproduce the experimental heat fluxes by varying input parameters close to their experimental uncertainties, pushing the validation frontier closer to the edge region.