Tearing Mode Stability Research Articles

Effect of runaway electrons on tearing mode stability: with or without favorable curvature stabilization

An MHD-RE hybrid model is developed and implemented into the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681), where the runaway electrons (REs) are treated as a fluid species. The model is utilized to study the tearing mode (TM) stability in a tokamak plasma, with the numerical results compared to that of the analytic theory. The RE effect on the n = 1 TM is systematically investigated in the absence or presence of the favorable average curvature stabilization (the GGJ-effect). Without the GGJ-effect, for a force-free toroidal plasma equilibrium, REs are found to destabilize the TM and induce a finite real frequency to the mode (in a plasma with vanishing equilibrium flow). The RE contribution is found to significantly enhance the toroidal mode coupling. In the presence of the GGJ-effect, for a plasma with finite equilibrium pressure, the MARS-F hybrid model finds that REs destroy the symmetry in the TM spectrum and introduce extra branch of the TM solution due to the eigenvalue bifurcation. This happens because REs lead to coupling to a stable fluid TM mode and destabilize this mode. Despite complicated mode spectrum introduced by REs, we find that the latter play an overall destabilizing role for the TM also in the presence of the GGJ-effect. The MARS-F computed eigenvalues are well fitted with the analytic dispersion relation derived by Liu et al (2020 Phys. Plasmas 27 092507) for the force-free equilibrium. Less satisfactory is the fitting result with a TM dispersion relation that includes both the GGJ-effect and the RE contribution, suggesting further improvement of the proposed dispersion relation.

Tearing mode stabilization by electron cyclotron resonant heating in EAST tokamak experiments

Tearing mode stabilization by electron cyclotron waves (ECWs) has been carried out in Experimental advanced superconductiong tokamak (EAST) experiments. The effects of the amount of ECW power and the radial wave deposition location on stabilizing the m/n = 2/1 magnetic island are investigated, where m/n is the poloidal/toroidal mode number. The local heating is found to dominate the mode stabilization in these experiments. The stabilization is more effective when the wave is deposited closer to the radial island location, as expected. With increasing ECW power, however, the tearing modes are not stabilized completely, and the island width saturates at a finite width. Moreover, the island rotation frequency is found to decrease when the ECW deposition is close to the island such that the island width is reduced significantly. Using externally applied, rotating resonant magnetic perturbations to generate slowly rotating magnetic islands, the locked island stabilization by ECW has also been studied, and the island width reduction and nonuniform island rotation are observed when the island’s center passes through the ECW deposition region.

On the merit of hot ion mode for tearing mode stabilization

The stabilization of tearing modes with rf driven current benefits from the cooperative feedback loop between rf power deposition and electron temperature within the island. This effect, termed rf current condensation, can greatly enhance and localize current driven within magnetic islands. It has previously been shown that the condensation effect opens the possibility of passive stabilization with broad rf profiles, as would be typical of LHCD for steady state operation. Here we show that this self-healing effect can be dramatically amplified by operation in a hot ion mode, due to the additional electron heat source provided by the hotter ions.

Nonlinear feedback algorithm for tearing-mode magnetic control in tokamak

Results of calculations and analysis of the tearing-mode evolution under the effect of resonant magnetic perturbation produced by a nonlinear feedback system in rotating tokamak plasma are presented. The TEAR-code used for calculations is based on the visco-resistive magnetohydrodynamic approximation that gives coupled diffusion-type equations for the magnetic flux perturbation and for the plasma rotation velocities in toroidal and poloidal directions. The code is supplemented by a computational unit simulating the nonlinear algorithm of the feedback system. The feedback gain and phase shift are automatically regulated in real time. The gain depends on the tearing-mode amplitude. At high feedback input signals, the gain does not exceed some finite value to reduce technical requirements for the feedback actuator and to mitigate the phase instability. In the process of the tearing-mode suppression, the gain gradually increases to provide the mode control under reduction of feedback input signal and rise of the intrinsic tearing-mode stability index. Besides that, the real-time control of the feedback phase shift is provided to additionally mitigate the phase instability. According to simulation, the used nonlinear characteristics of the feedback algorithm improve the efficiency of the tearing-mode suppression.

Two-fluid model of rf current condensation in magnetic islands

The stabilization of tearing modes with rf waves is subject to a nonlinear effect, termed rf current condensation, that has the potential to greatly enhance and localize current driven within magnetic islands. Here we extend previous investigations of this effect with a two fluid model that captures the balance of diffusive and thermal equilibration processes within the island. We show that the effective power and resulting strength of the condensation effect can be greatly enhanced by avoiding collisional heat loss to the ions. The relative impact of collisions on the overall power balance within the island depends on the ratio of the characteristic diffusion timescale and the electron–ion equilibration time, rather than the latter alone. Although relative heat loss to ions increases with island size, the heating efficiency does as well. In particular, we show that the latter safely dominates for large deposition profiles, as is typically the case for lower hybrid current drive. This supports the possibility of passive stabilization of neoclassical tearing modes without the precise aiming of the rf waves required for electron cyclotron current drive stabilization.

Neoclassical tearing mode stabilization by electron cyclotron current drive for HL-2M tokamak* *Project supported by the National Key Research and Development Program of China (Grant Nos. 2018YFE0303102, 2018YFE0301100, and 2017YFE0301702), the National Natural Science Foundation of China (Grant Nos. 11905109 and 11947238), U.S. DOE SciDAC ISEP, users with Excellence Program (on EAST tokamak) of Hefei Science Center CAS under (Grant

Investigation of neoclassical tearing mode and its suppression by electron cyclotron current drive (ECCD) has been carried out in HL-2M tokamak. The current driving capability of the electron cyclotron wave is evaluated. It is found that the deposition location can be effectively controlled by changing the poloidal angle. The validation of electron cyclotron wave heating and current driving has been demonstrated for the upper launcher port. We show that 3.0 MW and 2.5 MW modulated ECCD can completely stabilize (2,1) and (3,2) NTMs, respectively. The non-modulated ECCD, radial misalignment as well as current profile broadening have deleterious effect on the NTM stabilization. The time required for suppression of (3,2) mode is shorter than that required for the suppression of (2,1) mode. Moreover, the time needed for complete stabilization at different initial island width has been quantitatively presented and analyzed.

Modelling effects of edge density fluctuations on electron-cyclotron current drive used for neoclassical tearing mode stabilization

In this work we study the undesired effects of electron density fluctuations (in the form of blob structures which may exist in the edge region of tokamak plasmas) to the electron-cyclotron wave propagation and current drive in connection to the efficiency of neoclassical tearing mode stabilization. Our model involves the evaluation of the driven current in the presence of density perturbations, by using a combination of a wave solver based on the transfer matrix and electromagnetic homogenization methods for the propagation part prior to and inside the region of these structures (where standard asymptotic propagation methods may not be valid due to the short-wavelength limit breakdown), with a ray tracing code including island geometry effects and current drive computation for the propagation past the perturbed region. The computed driven current is input into the modified Rutherford equation in order to estimate the consequences of the wave deformation (driven by the density fluctuations) to the mode stabilization.

Generation of localized lower-hybrid current drive by temperature perturbations

Despite high demonstrated efficiency, lower-hybrid current drive (LHCD) has not been considered localized enough for neoclassical tearing mode (NTM) stabilization in tokamaks. This assessment must be reconsidered in view of the radiofrequency current condensation effect. We show that an island with a central hot spot induces significant localization of LHCD. Furthermore, in steady state tokamaks where a significant amount of current is provided by LHCD, passive stabilization of NTMs may occur automatically, particularly as islands become large, without requiring precise aiming of the wave power.

Direct prediction of nonlinear tearing mode saturation using a variational principle

It is shown that the variational principle of multi-region relaxed magnetohydrodynamics (MRxMHD) can be used to predict the stability and nonlinear saturation of tearing modes in strong guide field configurations without resolving the dynamics and without explicit dependence on the plasma resistivity. While the magnetic helicity is not a good invariant for tearing modes, we show that the saturated tearing mode can be obtained as an MRxMHD state of a priori unknown helicity by appropriately constraining the current profile. The predicted saturated island width in a tearing-unstable force-free slab equilibrium is shown to reproduce the theoretical scaling at small values of Δ′ and the scaling obtained from resistive magnetohydrodynamics simulations at large Δ′.

Pulsed RF schemes for tearing mode stabilization

The RF stabilization of tearing modes with current condensation has the potential to increase stabilization efficiency and loosen power localization requirements. Such benefits stem from the cooperative feedback between the RF deposition and the resulting island temperature perturbation governed by diffusion. A self-consistent treatment of the damping of an rf ray as it traverses the island shows that low damping scenarios can require unfavorably high powers to overcome initial power leakage and effectively capitalize on the nonlinear effect. In this work, it is demonstrated that for such regimes, modulated stabilization schemes can achieve significant improvements in heating and current drive contributions to stabilization for the same average power as a continuous wave scheme. The impact of modulation frequency and duty cycle on the performance is explored, the results of which suggest modulation strategies in which the pulsing periods are kept on the order of a diffusive time.

GTC simulation of linear stability of tearing mode and a model magnetic island stabilization by ECCD in toroidal plasma

Stabilization of a model magnetic island in tokamaks by localized electron cyclotron current drive (ECCD) has been studied using a fluid-kinetic hybrid model coupled with ray tracing and Fokker−Planck equations. Even though a gyrokinetic toroidal code at present is not able to simulate the long-time evolution of tearing modes, which starts from small perturbation and evolves to the Rutherford regime, we can still calculate a model magnetic island and its stabilization by ECCD. Gyrokinetic simulations find that the model magnetic island can be fully stabilized by the ECCD with the 1 MW 68 GHz X2-mode in HL-2A-like equilibrium, while the model magnetic island in the DIII-D tokamak is only partially stabilized with the same ECCD power. A helicoidal current drive is more efficient than a continuous ECCD to stabilize the model magnetic island. Simulation results further indicate that, without external current drive, thermal ion kinetic effects could also reduce the magnetic island width and the linear growth rate of tearing modes.

Non-linear simulations of neoclassical tearing mode control by externally driven RF current and heating, with application to ITER

Neoclassical tearing modes (NTM) must be controlled or suppressed to prevent a degradation of the energy confinement in tokamak plasmas. This can be done applying RF-current via electron cyclotron current drive and -heating at the rational surface where the instability appears. Both the current and heating generated by the RF waves are known to provide a stabilizing effect on the magnetic island. In the present work, we address the issue of neoclassical tearing mode stabilization by heating and current drive in an ITER-like configuration, using a stiff transport model. From a revised generalized Rutherford equation, we revisit the criterion on the RF current and power required to stabilize an NTM, showing that the level of plasma background heating (residual heat sources) in ITER significantly lowers the benefit of the RF heating contribution. Nonlinear magnetohydrodynamic simulations with the XTOR code, where a stiff transport model as well as RF-power and -current drive are implemented, are performed to compute the NTM stabilization efficiency. The stabilization efficiency due to the RF current contribution is found to be less than theoretically predicted in the case of continuous application, but consistent with theory in the modulated control scheme, suggesting an enhanced destabilization at the X-point. The role of RF heating for continuous application is found to be moderate for the range of power envisaged in ITER, essentially because of the detrimental effect of residual heat sources. This numerical work confirms the capability of the ITER RF system to control the NTM.

Influence of deeply trapped energetic ions on tearing modes

The effects of deeply trapped energetic ions (DTEIs) on the stability of tearing modes through stability criterion Δ′ are studied. In contrast to the stabilizing adiabatic effect of background plasma pressure, the adiabatic contribution of the DTEI destabilizes due to the direct coupling between the bad curvature and asymmetrical pressure of energetic ions. When the orbit width is much larger than the island width, the nonadiabatic effect of the DTEI stabilizes, which counteracts the major destabilizing adiabatic contribution. DTEIs are shown to have a net destabilizing effect on the tearing mode. The main physics of destabilization of Δ′ comes from the modification of the Mercier index.

Multi-scale interactions between turbulence and magnetic islands and parity mixture—a review

This paper presents a review of multi-scale interactions between small-scale turbulence and large scale magnetic islands. In finite beta plasmas, zonal flows are relatively weak, and thus another electromagnetic coherent structure formation such as magnetic islands becomes important for regulating turbulence. In multi-scale interactions, large-scale modes dominate turbulent fluctuations even when the growth rate of the large-scale mode is much smaller than small-scale modes. On the other hand, small-scale modes influence large-scale modes when the large-scale modes are stable/marginally stable. Thus, the multi-scale interactions are categorized according to the stability of tearing mode (TM), which drives large-scale magnetic islands. When the TM is unstable, wide magnetic islands are produced, and as a result of the multi-scale interactions, the turbulent transport is significantly enhanced inside the separatrix of the island, because large-scale stable modes are excited by mutual interactions between turbulence and the island. On the other hand, a steep temperature gradient is formed around the separatrix of the island, which is consistent with zonal flow shear appearing at the separatrix. When the TM is stable/marginally stable, turbulence drives and sustains magnetic islands of width equal to multiples of the Larmor radius. This excitation of islands by turbulence can be related to the seed island formation of neo-classical TMs. The parity of fluctuations plays crucial role in the multi-scale nonlinear interactions, because pure twisting parity mode does not satisfy the nonlinear fluid/gyrokinetic equations. Magnetic islands belongs to the tearing parity mode and drift-wave instabilities normally belong to the twisting parity mode, and each parity is conserved in the linear growth of the instability. However, when the amplitude of the twisting parity mode becomes finite, the nonlinear energy transfer takes place from the twisting parity to tearing parity modes. Through this nonlinear parity mixture, the magnetic islands are produced by the turbulence. The influence of anomalous current drive and polarization current on the multi-scale interactions is discussed as well.

Hazard function exploration of tokamak tearing mode stability boundaries

The technical feasibility of hazard function learning and exploration on multi-scenario tokamak plasma time-series datasets is demonstrated. In particular, the onset intensity (events per time) of born-rotating tearing mode instabilities in DIII-D tokamak plasmas is modeled as a function (the hazard) of gross plasma equilibrium covariates. It is shown that the hazard function is calibrated in a precise probabilistic sense. Partial dependence visualizations of this function suggest that the approach can be developed into powerful tokamak database query software geared towards physics discovery.

Induction and stabilization of neoclassical tearing modes on HL-2A tokamak

The induction and stabilization characteristics of neoclassical tearing modes (NTMs) on Hl-2A tokamak are presented. NTMs are induced by sawtooth oscillations of the m/n = 1/1 mode via toroidal coupling and by gas puffing fuelling in the experiments of HL-2A tokamak. The evolutions of NTMs are modeled with a two dimensional non-linear cylindrical tearing mode code and compared with the experimental observations. The stabilization of NTMs with electron cyclotron current drive (ECCD) is numerically studied. It is found that a driven current as low as 0.015 of total plasma current can stabilize or even fully suppress NTMs. On the other hand, a small radial misalignment decreases the stabilizing effect considerably. In addition, a phase misalignment blocks the NTM stabilization and results in island width saturation at a moderate value. The effects of island rotation frequency on NTM stabilization are explored. Furthermore, it is found that the stabilizing effect can be improved efficiently by applying ECCD when the island width is less than a threshold value.

Stabilization of tearing modes by modulated electron cyclotron current drive

The influence of modulated-ECCD on m/n=2/1 resistive tearing mode is investigated by a three-dimensional toroidal and non-reduced MHD code CLT. It is found that, after applying a modulated-ECCD, tearing mode instabilities are suppressed and magnetic islands are gradually reduced to a low level, then the width of the magnetic islands exhibit periodic oscillation with the time scale of ECCD modulation frequency. The minimum width of magnetic islands decreases with the decrease of ECCD modulation frequency and increases with the increase of the buildup time of the driven current.

Millimeter-wave beam scattering by edge-plasma density fluctuations in TCV

In magnetically confined fusion devices, the use of millimeter waves (mmw) at the electron cyclotron (EC) frequencies ranges from plasma diagnostics to plasma heating, current drive and core confinement preservation. For large tokamaks such as ITER, numerical simulations and analytical estimates suggest that plasma edge turbulence could significantly broaden the EC-beam, possibly preventing tearing modes stabilization at the designed power levels. We report measurements of mmw-beam scattering by plasma turbulence in the TCV tokamak. A mmw-Gaussian beam is injected from the top of the device and the transmitted power is measured at the bottom. We show that the measured plasma density fluctuations in the upper part of the scrape-off layer (SOL) are the cause of fluctuations of the transmitted mmw-power. A full-wave model based on COMSOL multiphysics is presented and compared against the wave-kinetic-equation solver WKBeam in a TCV case. Using the SOL turbulence simulations from the GBS code, comparison between the scattering effect on the mmw-beam with both the full-wave simulations and the experiments are ongoing. We also present experimental observations of rapid changes in the transmitted power caused by ELMs in ELMy H-mode plasma.

Tearing modes stabilized by sawtooth activity

Control of the tearing mode by sawtooth activity has been achieved in the Joint European Torus tokamak experiments. It has been shown that the tearing mode can be stabilized by short-period sawtooth oscillation. Based on the experimental results, a model for the tearing mode stabilized by sawtooth activity has been proposed, which mainly focuses on the periodic variation of the current during sawtooth activity. Both the current oscillation and the induced electric field which is due to the rapid variation of the current play important roles in the tearing mode stabilization.

Interchange destabilization of collisionless tearing modes by temperature gradient

Using a fluid theory, the stability of collisionless tearing modes in plasmas is analyzed in the presence of an inhomogeneous magnetic field, electron temperature and density gradients. It is shown that small scale modes, characterized by a negative stability parameter (Δ′<0), can be driven unstable due to a combination of the magnetic field and electron temperature gradients. The destabilization mechanism is identified as of the interchange type similar to that for toroidal electron temperature gradient modes.