Trapped Electron Mode Research Articles

Gyrokinetic simulations of electrostatic microturbulence in ADITYA-U tokamak

Global gyrokinetic simulations of the electrostatic microturbulence driven by the pressure gradients of thermal ions and electrons are carried out for the ADITYA-U tokamak geometry using its experimental plasma profiles and with collisional effects. The dominant instability is trapped electron mode (TEM) based on the linear eigenmode structure and its propagation in the electron diamagnetic direction. Collisional effects suppress turbulence and transport to a certain extent. Zonal flow is not playing a critical role in the TEM saturation, which is dominated by the inverse cascade. The frequency spectrum of the electrostatic fluctuations is in broad agreement with the experimentally recorded spectrum in the ADITYA-U, with a bandwidth ranging from to 50 kHz.

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.

Stabilization of trapped electron mode through effective diffusion in electron temperature gradient turbulence

Multi-scale gyrokinetic theory and simulations of a toroidal magnetized plasma have revealed the existence of cross-scale interactions of the trapped electron mode (TEM) and the electron temperature gradient (ETG) turbulence. Reduction of the TEM instability growth rate in the ETG turbulence is clearly identified, and is well represented in the form of effective diffusion. A theoretical model based on the stochastic forcing by the ETG turbulence well describes the turbulent diffusion coefficient observed in multi-scale turbulence simulations.

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, $\delta <0$ is found to lead to a reduction of fluxes when $s>1$ but not anymore when shear is reduced. In certain parameter regimes, this effect can be inverted, up to obtaining higher fluxes when $\delta <0$ with respect to its $\delta >0$ counterpart.

Global gyrokinetic simulation of edge coherent mode in EAST

Linear and nonlinear simulations are carried out for the edge coherent mode (ECM) using the global gyrokinetic code GEM based on the EAST experimental parameters. The linear simulation results show that ECM is an electrostatic mode with dominant toroidal mode number n = 18 and frequency about 48 kHz, and propagates along the direction of electron diamagnetic drift, which are consistent with the experimental results. In addition, the density and electron temperature gradients destabilize the mode, while the collision stabilizes the mode. The nonlinear simulation results show that the saturated particle and heat fluxes induced by ECM are mainly due to the perturbed electrostatic ExB drift, and the fluxes of electrons and ions are almost equal. The ECM drives significant outward particle and heat fluxes, thus greatly promoting the maintenance of the long pulse H-mode. The Fourier decomposition of fluxes and potentials demonstrate that the intermediate-n modes of n = 14, 18 grow fastest in the linear phase, while in the nonlinear saturation phase, the low-n modes such as n = 4, 6 dominate and the fluxes are mainly contributed by the mode of n = 10. It is found that zonal flow is not the dominant saturation mechanism of the turbulence. The inverse spectral cascade of turbulence is inevitably observed in the nonlinear saturation process, indicating that it is a more universal turbulence saturation mechanism. It is also found that radial electric field can greatly reduce the turbulence intensity and transport level. From the analyses of frequency and transport channels, it can be concluded that ECM appears to be the collisionless trapped electron mode.

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.

Features of transport induced by ion-driven trapped-electron modes in tokamak plasmas

As an obstacle in high-performance discharge in future fusion devices, disruptions may do great damages to the reactors through causing strong electromagnetic forces, heat loads and so on. The drift waves in tokamak are illustrated to play essential roles in the confinement performance as well. Depending on the plasma parameters and mode perpendicular wavelength, the mode phase velocity is either in the direction of electron diamagnetic velocity (namely, typical trapped electron mode) or in the direction of ion diamagnetic velocity (namely, the ubiquitous mode). Among them, the ubiquitous mode is directly investigated using gyro-fluid simulation associating with gyro-fluid equations for drift waves in tokamak plasmas. The ubiquitous mode is charactered by the short wavelength and propagates in ion diamagnetic direction. It is suggested that the density gradient is essential for the occurrence of the ubiquitous mode. However, the ubiquitous mode is also influenced by the temperature gradients and other plasma parameters including the magnetic shear and the fraction of trapped electrons. Furthermore, the ubiquitous mode may play essential roles in the turbulent transport. Meanwhile, the relevant parameters are scanned using a great number of electrostatic gyro-fluid simulations. The stability map is taken into consideration with the micro-instabilities contributing to the turbulent transport. The stability valley of the growth rates occurs with the assumption of the normalized temperature gradient equaling to the normalized density gradient.

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.

Existence of finite and anisotropic heavy ion parallel compressibility pinch in the gyrokinetic turbulence

Turbulence-driven heavy ion transport in hot magnetized plasma is investigated by means of the gyrokinetic theory and simulations. A finite heavy ion parallel compressibility pinch (${\mathrm{\ensuremath{\Gamma}}}_{s,\ensuremath{\parallel}}$) is found in the gyrokinetic framework, in contrast to the conventional understanding that ${\mathrm{\ensuremath{\Gamma}}}_{s,\ensuremath{\parallel}}$ is negligible. A perturbation theory clarifies the turbulence frequency dependence of ${\mathrm{\ensuremath{\Gamma}}}_{s,\ensuremath{\parallel}}$, resolving the discrepancy with experimental observations. It is also predicted by a nonlocal approach of the parallel advection term that ${\mathrm{\ensuremath{\Gamma}}}_{s,\ensuremath{\parallel}}$ is strongly anisotropic on a magnetic surface. The parameter dependence shows that decreasing the heavy ion mass ${m}_{s}$ strongly enhances ${\mathrm{\ensuremath{\Gamma}}}_{s,\ensuremath{\parallel}}$ through kinetic effects, leading to a deviation from the $1/{m}_{s}$ scaling. Moreover, the pinch direction can be reversed in nonlinear trapped electron mode turbulence through the inverse cascade.

Quasi-coherent mode in core plasma of SUNIST spherical tokamak

A quasi-coherent (QC) mode was observed in the core region of low-density ohmic plasmas in Sino-UNIted Spherical Tokamak. In experiments on the QC mode, two sets of moveable Langmuir probes (LPs) were used to measure the local parameters including floating potential, electron temperature, electron density, and so on, as well as their profiles. To monitor the magnetohydrodynamic activities, a Mirnov probe was used to measure the poloidal magnetic fluctuation. The QC mode can be seen in the spectra of floating potential, but there is no similar peak in the spectra of magnetic fluctuation. Thus, the QC mode is probably electrostatic. By analyzing the electrostatic potential fluctuations from the LPs, the features of the QC mode including frequency, wavenumber, propagation direction, and dependence on collisionality are identified, which are consistent with the characteristics of dissipative trapped electron mode.

Progress on physics understanding of improved confinement with fishbone instability at low q 95 < 3.5 operation regime in EAST

Improved confinement at the low q 95 < 3.5 operation regime with fishbone instability compared to sawtooth oscillation has been observed and investigated on the EAST under the dominant electron heating condition with a tungsten divertor. The formation of an internal transport barrier in the ion thermal channel strongly correlates to the excitation of the fishbone, accompanied by reduced particle outward transport in the core region identified by a central peaked density profile. Current density distribution is found to change from a monotonic shape with q 0 < 1 during sawtooth oscillation to a central flat structure, magnetic shear s ∼ 0 at ρ < 0.4, with the fishbone instability at where the higher off-axis bootstrap current fraction might play a critical role. Linear gyrokinetic simulation by NLT code was carried out to investigate the turbulent transport characteristics, which is qualitatively in good agreement with experimental measurements from CO2 laser collective scattering diagnostics. The electron-scale trapped electron mode that dominates the turbulent transport during sawtooth is found to be stabilized with the fishbone at identical heating power and plasma configurations.

Feasibility study of a high spatial and time resolution beam emission spectroscopy diagnostic for localized density fluctuation measurements in Lithium Tokamak eXperiment-β (LTX-β).

Trapped electron mode (TEM) is the main source of turbulence predicted for the unique operation regime of a flat temperature profile under low-recycling conditions in the LTX-β tokamak, while ion temperature gradient driven turbulence may also occur with gas fueling from the edge. To investigate mainly TEM scale density fluctuations, a high spatial and time resolution 2D beam emission spectroscopy (BES) diagnostic is being developed. Apart from spatially localized density turbulence measurement, BES can provide turbulence flow and flow shear dynamics. This BES system will be realized using an avalanche photodiode-based camera and narrow band interference filter. The system can acquire data at 2MHz. Simulations with the Simulation of Spectra (SOS) code indicate that a high signal to noise ratio can be achieved with the proposed system. This will enable sampling the density fluctuations at this high time resolution. The design considerations and system optimization using the SOS code are presented.

Global gyrokinetic study of shaping effects on electromagnetic modes at NSTX aspect ratio with ad hoc parallel magnetic perturbation effects

Plasma shaping may have a stronger effect on global turbulence in tight-aspect-ratio tokamaks than in conventional-aspect-ratio tokamaks due to the higher toroidicity and more acute poloidal asymmetry in the magnetic field. In addition, previous local gyrokinetic studies have shown that it is necessary to include parallel magnetic field perturbations in order to accurately compute growth rates of electromagnetic modes in tight-aspect-ratio tokamaks. In this work, the effects of elongation and triangularity on global, ion-scale, linear electromagnetic modes are studied at National Spherical Torus Experiment (NSTX) aspect ratio and high plasma β using the global gyrokinetic particle-in-cell code XGC. The effects of compressional magnetic perturbations are approximated via a well-known modification to the particle drifts that was developed for flux-tube simulations [Joiner et al., Phys. Plasmas 17, 072104 (2010)], without proof of its validity in a global simulation, with the gyrokinetic codes GENE and GEM being used for local verification and global cross-verification. Magnetic equilibria are re-constructed for each distinct plasma profile that is used. Coulomb collision effects are not considered. Within the limitations imposed by the present study, it is found that linear growth rates of electromagnetic modes (collisionless microtearing modes and kinetic ballooning modes) are significantly reduced in a high-elongation and high-triangularity NSTX-like geometry compared to a circular NSTX-like geometry. For example, growth rates of kinetic ballooning modes at high-β are reduced to the level of that of collisionless trapped electron modes.

Impact of impurities on drift wave instabilities in reversed-field pinch plasmas.

The drift wave in the presence of impurity ions was investigated numerically in reversed-field pinch plasmas, using the gyrokinetic integral eigenmode equation. By comparing the results of regular and hollow plasma density profiles, it was found that the ion temperature gradient mode for the hollow density profile case is much harder to excite. For the impurity effects, when the impurity density gradient is opposite to the electrons, namely when L_{ez} (L_{ez}=L_{ne}/L_{nz} with 1/L_{n} being the density gradient scale length, and the subscript "e" and "z" indicates electrons and impurity ions, respectively) is negative, the impurities can enhance the instability. On the contrary, when L_{ez} is positive, the instability is stabilized. Regarding the trapped electron mode (TEM), the growth rate for plasmas with a hollow density profile remains smaller than that of the standard density gradient. There exists a threshold in L_{ez}. When L_{ez} is less than this value, the impurities destabilize the TEMs, while when L_{ez} is greater than this value, the impurities stabilize the TEMs. In addition, the influence of the collisionality on the TEMs was also studied.

Effects of alpha particles on the transport of helium ash driven by collisionless trapped electron mode turbulence

The effects of alpha (α) particles on the transport of helium ash driven by collisionless trapped electron mode (CTEM) turbulence are analytically studied using quasi-linear theory in tokamak deuterium (D) and tritium (T) plasmas. Under the parameters used in this work, the transport of helium ash is mainly determined by the diffusion due to very weak convection. It is found that the ratio between helium ash diffusivity and effective electron thermal conductivity (D He/χ eff) driven by CTEM turbulence, which is a proper normalized parameter for quantifying the efficiency of helium ash removal, is smaller than unity. This indicates the less efficient removal of helium ash through CTEM turbulence as compared with ion temperature gradient (ITG) turbulence in [Angioni et al 2009 Nucl. Fusion 49 055013]. However, the efficiency of helium ash removal is increased 55% by the presence of 3% α particles with their density gradient being equivalent to that of electrons, and this enhancement can be further strengthened by steeper profile of α particles. This is mainly because the enhancement of helium ash diffusivity by α particles is stronger than that of the effective electron thermal conductivity. Moreover, the higher fraction of T ions, higher temperature ratio between electrons and thermal ions as well as flatter electron density profile, the stronger enhancement of D He/χ eff, and α particles further strengthen the favorable effects of these parameters on the removal of helium ash.

Global gyrokinetic simulations of electrostatic microturbulent transport using kinetic electrons in LHD stellarator

Global gyrokinetic simulations of ion temperature gradient (ITG) and trapped electron mode (TEM) in the LHD stellarator are carried out using the gyrokinetic toroidal code (GTC) with kinetic electrons. ITG simulations show that kinetic electron effects increase the growth rate by more than 50% and more than double the turbulent transport levels compared with simulations using adiabatic electrons. Zonal flow dominates the saturation mechanism in the ITG turbulence. Nonlinear simulations of the TEM turbulence show that the main saturation mechanism is not the zonal flow but the inverse cascade of high to low toroidal harmonics. Further nonlinear simulations with various pressure profiles indicate that the ITG turbulence is more effective in driving heat conductivity whereas the TEM turbulence is more effective for particle diffusivity.

Global gyro-kinetic study of magnetic shaping effects on linear trapped electron mode instability in normal/reversed magnetic shear plasmas

A linear δf version of the gyro-kinetic Vlasov code GKNET (Gyro-Kinetic Numerical Experiment of Tokamak) is extended to the global cylindrical coordinates (R, φ, Z) and includes the kinetic electron response, to study the shaping effect on linear drift-wave instabilities in Tokamak plasmas. Cross-verifications are performed between three GKNET versions that use different electron models, i.e. the adiabatic electron model, hybrid electron model (only trapped electrons are calculated kinetically) and full-kinetic electron model (all electrons are calculated kinetically). A destabilizing effect of non-adiabatic passing electrons is observed in the full-kinetic case for the ion temperature gradient (ITG) mode in the short wavelength region and the trapped electron mode (TEM). The ion-to-electron mass ratio and the electron–electron collisionality have weak impacts on the destabilization of ITG/TEM. Utilizing magnetohydrodynamic equilibria designed with normal and reversed magnetic shear (NS and RS), the characteristics of linear TEMs and the corresponding impact of plasma shaping are studied based on the GKNET code with full-kinetic electrons. Due to the change in temperature/density gradient and magnetic shear either measured locally in the low field side (LFS) or averaged over the flux surface, plasma shaping shows different impacts on linear TEMs in NS and RS configurations. For the elongation κ, the increase in κ always stabilizes linear TEMs due to the reduction in the effective profile gradient over the flux surface. For the triangularity δ, in the NS case, the change in δ shows weak dependence on TEM linear growth rates due to the balance between variations of profile gradients and magnetic shear in the LFS. In the RS case, local magnetic shear in the peak gradient region is nearly zero. Thus, the variation in local profile gradient plays a dominant role on the linear growth in a plasma shaping scan. Consequently, the negative triangularity (δ < 0) has a destabilizing effect on the linear TEMs in the RS configuration mainly due to the upshift in local profile gradient in the LFS.

Extraction of quasi-coherent modes based on reflectometry data

The identification of turbulence sources would drive to a deeper understanding of confinement dynamics in tokamak plasmas. Turbulence results from a mixture of instabilities corresponding to sources at different timescales and spatial scales. Using poloidal correlation reflectometry and multi-pin Langmuir probe, it was shown in the T-10 and the Tokamak Experiment for Technology Oriented Research (TEXTOR) tokamaks that the reflectometry frequency spectrum is the superposition of several components: broadband component, quasi-coherent (QC) modes and low-frequency components. The relevance of QC modes is associated with their link with the trapped electron mode instability. This link was exhibited in the transition from the linear ohmic confinement (LOC) to the saturated ohmic confinement (SOC) regime. A method is presented in this paper to extract the QC mode component from the reflectometry data, enabling its separation from the broadband component and the study of its time evolution. It is a first step toward the discrimination of turbulence sources. The central idea explores a way to combine the approach of signal processing and machine learning. The continuous wavelet transform on the basis of complex Morlet wavelet has proved to be efficient in providing a decomposition of a signal at different scales over time for fluctuation tackling; clustering techniques, such as the mini-batch K-means, are able to tackle clusters at different scales. The method was applied to Tore Supra and TEXTOR reflectometry data. In Tore Supra, the amplitude of the extracted QC mode component decreases during the LOC–SOC transition. In TEXTOR, the amplitude of the coherent spectra of the extracted QC mode component is similar to the experimental coherent spectra obtained through correlation reflectometry. The developed method permits the extraction of components, preserving their physical and statistical properties.