Modes In Tokamaks Research Articles

Dual effects of impurity seeding on pedestal turbulence and ELMs in the HL-2A tokamak

The control of the edge localized mode (ELM) in tokamaks has been intensively investigated with different techniques. Recently, ELM control with impurity seeding has also raised to be a hot topic. This paper reports the effect of the laser blow-off impurity seeding on the pedestal turbulence and ELMs. It has been found that the seeded impurity could have dual impacts on pedestal instabilities, depending on the quantity of the injected impurity. The impurity enhances the pedestal turbulence and further mitigates the ELMs when its quantity exceeds a lower threshold. Instead, the impurities suppress the pedestal turbulence and suppress ELMs when the quantity of the injected particles reaches a second higher threshold. It has also been observed that the ion toroidal velocity increases due to the impurity seeding while the collision rate is increasing. In addition, the impurities reduce the velocity shear rate by changing the toroidal velocity term rather than by changing the pressure gradient term as observed in ELM mitigation with LHCD. The reduction of the E × B velocity shear rate enhances the pedestal turbulence possibly through the turbulence spectral shift process during ELM mitigation.

Experimental signatures of electron cyclotron wave energy condensation in magnetic islands

Bifurcation of the electron temperature perturbation (ΔT e) in magnetic islands due to electron cyclotron current drive (ECCD) is reported for the first time in toroidal plasmas. In this DIII-D experiment ΔT e spontaneously increases by 50% in a growing 2, 1 island which in turn rapidly shrinks, consistent with improved stabilization by the ECCD due to the temperature bifurcation. This non-linearity of ΔT e maps out a hysteresis in the island evolution cycle, in qualitative agreement with the theoretically predicted radio frequency current condensation effect Reiman and Fisch 2018 (Phys. Rev. Lett. 121 225001). Therefore, this observed bifurcation can be critical for the avoidance of disruptions caused by tearing modes in tokamaks.

Transition of a network of nonlinear interactions into a regime of strong nonlinear fluctuations: A paradigm for the edge localized mode onset

We study how a network of nonlinear oscillators transits into a regime of strong nonlinear fluctuations when perturbed by a triad. In this regime, most of the potential energy contained in the waves is made available to the system through strong nonlinear fluctuations. This analysis is motivated by recent experimental observations [Dominski and Diallo, Plasma Phys. Control. Fusion 62, 095011 (2020)] where it was found that magnetic fluctuations trigger the onset of edge localized modes by suddenly exciting a network of nonlinear interactions. In our study, we consider the simplest system of many harmonic oscillators that are organized in a network of nonlinear triads. We model and simulate the sudden transition of this network of triads into a regime of strong nonlinear fluctuations—reminiscent of the onset of edge localized modes in tokamaks. This transition is triggered by the activation of a nonlinear perturbation. An abrupt rise of the system's disorder (an entropy-like quantity) is measured during the transition. This transition from weak to strong nonlinear fluctuations is even more abrupt when these fluctuations are chaotic, i.e., when the timescale of the nonlinear interaction is comparable to the timescale of the wave oscillations.

Effect of the toroidal flow and flow shear on the m/n 2/1 tearing mode in J-TEXT tokamak

The effect of the toroidal flow and flow shear on the m/n 2/1 tearing mode (TM) has been investigated in J-TEXT tokamak, where m and n are the poloidal and toroidal mode numbers. It is found that the toroidal flow increment is linearly modulated by the bias current/return current. The frequency of the 2/1 TM is also found to be proportional to the toroidal flow during the bias phase, which is consistent with the theoretical expectation. The electron diamagnetic drift frequency is almost constant before and during the bias phase. Moreover, the statistical analysis shows that the saturated island width of the TM is more correlated to the toroidal flow amplitude than the flow shear, which reveals that the effect of the TM depends on the magnitude of the toroidal flow rather than the flow shear. This result may illustrate the process of the 2/1 TM controlled by the electrode biasing, and suggests that changing the magnitude of toroidal flow is a possible method for stabilizing the TM.

Disruption mitigation using ion cyclotron wave in ADITYA tokamak

Controlling and mitigating plasma disruptions are a matter of serious concern for tokamak operation since they can cause serious damage to the machine. Dedicated experiments on disruption mitigation have been carried out in ADITYA (R = 75 cm, a = 25 cm), an Ohmically heated circular limiter tokamak. A rapid growth of magneto hydrodynamic (MHD) modes is found to be the major cause of disruptions in ADITYA tokamak. Stimulated disruptions induced by hydrogen gas puffing are successfully mitigated through stabilization of these MHD modes by applying a biased-electrode placed inside the last-closed flux surface prior to the gas injection. However, as biased electrodes cannot be placed inside the plasma in bigger tokamaks, the application of ion-cyclotron waves (ICWs) prior to disruption has been successfully attempted to mitigate disruptions through stabilization of MHD modes in ADITYA tokamak. The amplitude of MHD modes (m/n = 3/1, 2/1) is significantly reduced upon the application of ICW prior to disruption, and the stimulated disruptions are successfully mitigated by preventing the growth and overlapping of these MHD modes. These experimental results demonstrate that MHD driven disruptions may be mitigated due to stabilization of m = 2 modes by ponderomotive force of the IC waves.

Gyrokinetic simulation of low-frequency Alfvénic modes in DIII-D tokamak

Global gyrokinetic simulations find that a beta-induced Alfvén eigenmode (BAE) and a low-frequency mode (LFM) co-exist in the DIII-D tokamak experiments. The simulated LFM mode structure and many of its parametric dependencies are consistent with experimental observations. The LFM can be excited without fast ions and has a frequency inside the gap of the beta-induced Alfvén-acoustic eigenmode (BAAE). However, an antenna scan shows that it is NOT the conventional BAAE. Instead, the LFM is an interchange-like electromagnetic mode excited by non-resonant drive of pressure gradients. Furthermore, the simulated BAE mode structure is consistent with the experiment but the frequency is lower than the experiment. The compressible magnetic perturbations significantly increase the growth rates of the BAE and LFM. On the other hand, trapped electrons and equilibrium current have modest effects on the BAE and LFM.

Excitation of fishbone-like mode in tokamaks due to bounce resonances of trapped thermal ions

When the drift kinetic effect of thermal ions is taken into account, a high-frequency fishbone-like mode (FLM) is found to be driven unstable by trapped thermal ions (TTIs) in tokamak plasmas, according to self-consistent magneto-hydrodynamic (MHD)-kinetic hybrid modeling utilizing the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] as well as an analytic theory. It is found that, similar to energetic particles, TTIs can also stabilize the internal kink mode, whereas the FLM is excited when the effective beta of TTIs exceeds a threshold value. The real frequency of the FLM is comparable to the bounce frequency of TTIs. The mode structure of the FLM can be significantly different from the conventional step-like function for the associated plasma radial displacement. This drift kinetic induced modification of the mode structure near the q = 1 surface is captured by non-perturbative MHD-kinetic hybrid computations with MARS-K. Furthermore, the FLM can only be triggered by TTIs at sufficiently high thermal temperatures. Both the FLM and the internal kink can be stabilized by sufficiently fast plasma toroidal rotation and parallel sound wave damping. These two conditions of high thermal temperature and (fast) flow stabilization, though making it challenging to observe the TTI-driven FLM in present day experiments, are favorable for the mode excitation in future reactor scale devices.

Sideways force due to coupled rotating kink modes in tokamaks

The possibility of generation of the rotating sideways force on the wall by the kink modes is analytically investigated. The approach is basically the same as that developed earlier in (Mironov and Pustovitov 2017 Phys. Plasmas 24 092508) for the locked modes, but now their rotation is allowed. Its main elements are ∂b/∂t ≠ 0 (described by the growth rate γ and angular rotation frequency ω of the magnetic perturbation b), resistive dissipation in the wall, and the requirement of zero sideways force on the plasma. These make the approach greatly different from those resulting in the so-called Noll’s formula. The result is also different; it predicts a force an order of magnitude smaller. Nevertheless, such a force can be dangerous at the resonance frequency of the vacuum vessel. The derived relations show that the rotating force must be maximal at ωτ w = O(1), where τ w is the resistive wall time. For the faster modes it decreases roughly as ∼1/ω.

Group velocity in spatiotemporal representation of collisionless trapped electron mode in tokamak

The multiple scale derivative expansion method is used to manipulate the electron drift kinetic equation, following the theoretical framework of drift wave–zonal flow system developed by Zhang et al. [Zhang Y Z, Liu Z Y, Mahajan S M, Xie T, Liu J <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.1063/1.4995302"> 2017 <i>Phys. Plasmas</i> <b>24</b> 122304 </ext-link>]. At the zeroth order it is the linear eigenmode equation describing the trapped electron mode on a mirco-scale. At the first order it is the envelop equation for trapped electron mode modulated by the zonal flow on a meso-scale. The eigenmode equation has been solved by Xie et al. [Xie T, Zhang Y Z, Mahajan S M, Wu F, He Hongda, Liu Z Y <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1063/1.5048538"> 2019 <i>Phys. Plasmas</i> <b>26</b> 022503 </ext-link>] to obtain the eigenvalue and two-dimensional mode structure of trapped electron mode. These are essential components in calculating group velocities contained in the envelop equation. The radial group velocity arises from the geodesic curvature of magnetic field in tokamak. The poloidal group velocity stems from the normal curvature and diamagnetic drift velocity, which yields the mapping between the poloidal angle and time. Since the radial group velocity is also a function of poloidal angle, it is mapped to a periodic function of time with a period of milliseconds. The numerical results indicate the rapid zero-crossing, which is significant in the drift wave – zonal flow system and provides a sound foundation for studying zonal flow driven by trapped electron mode.

Locking effects of error fields on a tearing mode in tokamak

Locking effects of error fields on a tearing mode in Tokamak are studied numerically using the three-dimensional toroidal code based on a full set of magnetohydrodynamic equations. It is found that a threshold of the error field for mode locking exists and depends on the plasma rotation and the ramp-up time of the error field. The mode locking threshold increases with increasing the rotation frequency and the ramp-up time of the error field. Moreover, the results from the multiple helical error field suggest that the m/n = 3/1 and 4/2 error field along with the m/n = 2/1 error field can increase both the m/n = 2/1 perturbation and its higher-harmonics through the mode coupling due to both the toroidal and nonlinear effects, but it becomes more effective if the 4/2 error field is imposed directly. The 3/1 error field in-phase (anti-phase) with the 2/1 error field leads to a positive (negative) contribution to intensification of the 2/1 tearing mode and mode locking.

Structure and overstability of resistive modes with runaway electrons

We investigate the effects of runaway electron current on the dispersion relation of resistive magnetohydrodynamic modes in tokamaks. We present a new theoretical model to derive the dispersion relation, which is based on the asymptotic analysis of the resistive layer structure of the modes. It is found that in addition to the conventional resistive layer, a new runaway current layer can emerge whose properties depend on the ratio of the Alfvén velocity to the runaway electron convection speed. Due to the contribution from this layer, both the tearing mode and kink mode will have a real frequency in addition to a growth rate. The derived dispersion relation has been compared with numerical results using both a simplified eigenvalue calculation and a M3D-C1 linear simulation, and good agreement is found in both cases.

Simulation studies of the radiation-driven tearing mode in tokamaks

The influence of bremsstrahlung and cyclotron radiation on the evolution and saturation of the resistive tearing mode is investigated by using a three-dimensional toroidal magnetohydrodynamic code. It is found that accumulation of impurities (such as tungsten) in magnetic islands has a destabilizing effect on the tearing mode due to an imbalance of local radiative cooling and Ohmic heating inside the island. The asymmetry current effect and the nonlinear mode coupling play an important role on evolution of the radiation-driven tearing mode instability. As a result, the magnetic island width could increase over 20% of the minor radius (disruption scale). Along with higher mode burst, multi-mode interaction makes magnetic field lines become stochastic. Moreover, the core pressure is reduced due to the radiation cooling inside the magnetic island. Consequently, the whole discharge area is shifted towards the high-field side, which leads to a strong intensification of the mode.

The effects of toroidal equilibrium flow on the stabilization of ballooning modes in tokamaks

Effects of toroidal flows on ballooning mode instabilities have been studied extensively in recent years. In the published works, toroidal flow effects are taken into account only in the perturbation equation while the tokamak equilibrium is assumed to be unchanged. In this work, the influence of a toroidal flow on ballooning mode instabilities is numerically investigated by using the BOUT++ code while the modification of the tokamak equilibrium due to the flow has been taken into account in fixing the profiles of the quasi-toroidal magnetic field, quasi-density, and quasi-pressure and only changing the toroidal Mach number. A toroidal flow can significantly modify the safety factor q profile and the pressure gradient ∇P, which then affects the ballooning instability. The simulation results show that in the presence of shear flows, the growth rate of the ballooning mode will be affected if the modified equilibrium is considered. For a shear flow, the growth rates of high-n modes are significantly reduced.

Role of Hall effect on the resistive kink mode in tokamaks

The influence of the Hall effect on the nonlinear evolution of the m/n = 1/1 resistive-kink mode is numerically investigated by the three-dimensional toroidal Hall-MHD code CLT. It is found that the Hall effect can lead to the explosive growth of the resistive-kink mode at the nonlinear stage. The explosive nonlinear growth of the resistive-kink mode mainly results from the structural transition of the current sheet in the Hall-MHD simulations. At the nonlinear stage, the geometry of the current sheet turns into X-type from Y-type, resulting in the significant acceleration of the reconnection process. The fast reconnection induced by the Hall effect may explain the fast crash observed in large tokamaks. We also found that there exists a critical value of the ion inertial length that is resulted from the acceleration of magnetic reconnection due to the decoupling motions of ions and electrons and the suppression effect by the electron diamagnetic rotation in the Hall MHD. The critical value of decreases with increasing thermal conductivity When exceeds a critical value, the peak growth rate decreases with increasing

Role of thermal conduction on resistive tearing mode in Tokamaks

We investigate the role of thermal conductivity on the evolution and saturation of the m/n = 2/1 resistive tearing mode (m and n are, respectively, the poloidal and toroidal Fourier mode numbers), by using a 3D toroidal MHD code (CLT). It is found that thermal conductivity has great influence on pressure and current profiles, and further affects the dynamic evolution of the tearing mode. Our simulation results indicate that the linear growth rate of the tearing mode increases, but the saturation level of magnetic islands decreases with increase of thermal conductivity. With a small thermal conductivity, a flattened distribution of the thermal pressure inside magnetic islands leads to a large pressure gradient at the edge that drives a ballooning mode to be unstable. We further found that the radial electric field at the magnetic island boundary and the vortex-like flow inside the magnetic island lead to a poloidally asymmetric transport barrier and reduce the thermal conductivity at the magnetic island boundary, which contributes to formation of an internal transport barrier.

Singular global components and frequency shift of the geodesic acoustic continuum modes in shaped tokamaks

Within the ideal magnetohydrodynamic (MHD) model, the geodesic acoustic modes (GAMs) in tokamaks derived by Winsor et al (1968 Phys. Fluids 11 2448) belong to the continuous spectrum, characterised by unbounded non-square integrable eigenfunctions (delta functions) at the singular surfaces (Goedbloed 1975 Phys. Fluids 18 1258). The eigenfunctions of the MHD continua in cylindrical as well as toroidal plasmas include, in addition, components that exist outside the singular surfaces and have singularities of type or where is a flux function that labels the magnetic surfaces, and defines the singular surface (Pao 1975 Nucl. Fusion 15 631). Using a large aspect ratio approximation of tokamak plasmas it is shown in this paper that the GAMs indeed include such singular components. Hence, in addition to the non-square integrable and components of the plasma flow and of the density and pressure perturbations at the GAM surface, the GAM continua also include accompanying and singular components varying as This gives the and components of each GAM in the continuum radially extended profiles and a global character also within ideal theory. To the same order in the expansion, effects of a finite aspect ratio and a non-circular plasma cross section on the GAM frequency are also calculated, and we recover the dependence on inverse aspect ratio and Shafranov shift of the real GAM frequency previously calculated within gyrokinetic theory by Gao (2010 Phys. Plasmas 17 092503). Furthermore, while the dominating shaping effect on the GAM frequency comes from plasma elongation, as shown previously, it is shown in this paper that there is a higher-order triangularity effect that can also be significant. The calculated triangularity effect predicts a nearly linearly increasing GAM frequency with increasing triangularity, a phenomenon observed also in the TCV tokamak.

Core-crash sawtooth associated with m/n = 2/1 double tearing mode in Tokamak

The core-crash sawtooth caused by m/n = 2/1 double tearing mode (DTM) in Tokamak is investigated using a three-dimensional toroidal MHD code (CLT). It is found that mode–mode coupling effect plays a crucial role during the core-crash sawtooth. The n = 0 component and n > 1 components generated by mode–mode coupling of the n = 1 modes take up more than 40% of the total kinetic energy and become unneglectable during the core-crash sawtooth. The n = 0 component is crucial for the saturation of DTM. Without the n = 0 component, the DTM will not saturate. The high n components are responsible for the explosive growth of the DTM that finally results in the fast crash of the core plasma temperature.

The two-dimensional kinetic ballooning theory for trapped electron mode in tokamak

The two-dimensional (2D) kinetic theory for a collisionless trapped electron mode is developed based on the Fourier-ballooning transform in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The system consists of two equations: the ballooning (integral) equation with a parameterized Floquet phase and a second order differential equation for the distribution of the Floquet phase. The coupled equations are, then, numerically solved as an eigenvalue problem yielding the 2D mode structure (in real space) as well as the global (phase-independent) eigenvalue for an L-mode parameter set. The 2D mode structure exhibits apparent radial-poloidal asymmetry; due to the poloidal coupling, the radial correlation length is found to be, at least, twice as large as the poloidal one. The global (phase-independent) eigenvalue of the mode differs considerably from the conventional local (phase-dependent) estimate. This paper shares many technical aspects with a published paper that works out the 2D kinetic theory for the ion temperature gradient mode [Xie et al., Phys. Plasmas 24, 102506 (2017)].

Mode rotation control in a tokamak with a feedback-driven biased electrode.

Rotation of the plasma and MHD modes in tokamaks has been shown to stabilize resistive wall and tearing modes as well as improve confinement through suppression of edge turbulence. In this work, we control mode rotation with a biased electrode inserted into the plasma of the High Beta Tokamak-Extended Pulse's facility in conjunction with its active GPU (Graphical Processing Unit) feedback system. We first characterize a negative linear relationship between the electrode voltage and mode rotation. Using this relationship, we design, simulate, and implement a proof-of-concept, GPU-based active-control system, which shows consistent success in controlling mode rotation in both feedforward and feedback operation. Controllability is limited by operating conditions, the electrode's voltage range, and by the electrode's proximity to the vessel's walls. The final control system has a 15 μs cycle time, but the addition of various signal filters results in a full cycle latency of 200 μs.

Nonlinear saturation of kinetic ballooning modes by zonal fields in toroidal plasmas

Kinetic ballooning modes (KBMs) are widely believed to play a critical role in disruptive dynamics as well as turbulent transport in magnetic fusion and space plasmas. While the nonlinear evolution of the ballooning modes has been proposed as a mechanism for “detonation” in various scenarios such as the edge localized modes in tokamaks, the role of the kinetic effects in such nonlinear dynamics remains largely unexplored. In this work, global gyrokinetic simulation results of KBM nonlinear behavior are presented. Instead of the finite-time singularity predicted by ideal magnetohydrodynamic theory, the kinetic instability is shown to develop into an intermediate nonlinear regime of exponential growth, followed by a nonlinear saturation regulated by spontaneously generated zonal fields. In the intermediate nonlinear regime, rapid growth of localized current sheets, which can induce magnetic reconnection, is observed.