Magnetic Island Width Research Articles

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.

Structure bifurcation induced by wide magnetic islands

Magnetic islands resulting from magnetic reconnection play significantly important roles in critical issues of magnetic fusion plasmas, because they essentially change magnetic topology and significantly degrade plasma confinement. In this paper, we report that the wide islands can lead to a structure bifurcation of flow parity inside islands, then induce a state with a large vortex flow. The mechanism is identified as an instability in the configuration with magnetic islands, in which the eigenmode parity is contrary to the conventional tearing mode and the radial profile of zonal flow also changes. The critical values of the width of magnetic island for the bifurcation are obtained and discussed. The dependence of bifurcation on various physical parameters is studied in detail. It is found that tearing instability parameter and diamagnetic drift flow have significant impacts on the bifurcation. Moreover, the characteristics of the bifurcation show the qualitative agreement with the experimental observation on the Large Helical Device.

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.

Theory of edge localized mode suppression by static resonant magnetic perturbations in the DIII-D tokamak

According to a recent paper [Hu et al., Phys. Plasmas 26, 120702 (2019)], mode penetration at the top of the pedestal is a necessary and sufficient condition for the suppression of edge localized modes (ELMs) by a resonant magnetic perturbation (RMPs) in an H-mode tokamak discharge. This paper employs asymptotic matching theory to model a particular DIII-D discharge in which ELMs were suppressed by an externally generated, static, n = 2, RMP whose amplitude was modulated at a frequency of 1 Hz. It is demonstrated that the response of the plasma to the applied RMP, in the immediate vicinities of the rational (i.e., resonant) surfaces, is governed by nonlinear, rather than by linear, physics. This is the case because the magnetic island widths associated with driven reconnection exceed the linear layer widths, even in cases where driven reconnection is strongly suppressed by plasma rotation. The natural frequency at a given rational surface (i.e., the helical frequency at which the locally resonant component of the RMP would need to propagate in order to maximize driven reconnection) is found to be offset from the local E×B frame in the ion diamagnetic direction. The size of the offset is mostly determined by neoclassical poloidal rotation. Finally, the predictions of a fully nonlinear plasma response model are found to be broadly consistent with the DIII-D experimental data.

Beta-induced Alfvén eigenmodes destabilized by resonant magnetic perturbations in the J-TEXT tokamak

Investigations of beta-induced Alfvén eigenmodes (BAEs) destabilized by resonant magnetic perturbations (RMPs) have been conducted on the J-TEXT tokamak. In the Ohmic discharges, with RMPs having finite perturbed amplitudes, two different types of Alfvén eigenmodes have been observed and identified. One is considered as m-BAE, due to the strong correlation with magnetic island in some noticeable aspects, for example, frequency characteristic, mode number and driving mechanism. Specifically, the standing wave nodes of m-BAE are located at the O point and X point of the magnetic island. Another one is discerned as the magnetic island-induced AE (labeled as the MIAE-like mode in this work), which is consistent with the prediction of theory (Biancalani et al 2010 Phys. Rev. Lett. 105 095002). The frequency of MIAE-like mode is found to be approximately proportional to the square of magnetic island width.

Transition from ion-coupled to electron-only reconnection: Basic physics and implications for plasma turbulence

Using 2.5 dimensional kinetic particle-in-cell simulations, we simulate reconnection conditions appropriate for the magnetosheath and solar wind, i.e., plasma beta (ratio of gas pressure to magnetic pressure) greater than 1 and low magnetic shear (strong guide field). Changing the simulation domain size, we find that the ion response varies greatly. For reconnecting regions with scales comparable to the ion inertial length, the ions do not respond to the reconnection dynamics leading to “electron-only” reconnection with very large quasisteady reconnection rates. Note that in these simulations, the ion Larmor radius is comparable to the ion inertial length. The transition to a more traditional “ion-coupled” reconnection is gradual as the reconnection domain size increases, with the ions becoming frozen-in in the exhaust when the magnetic island width in the normal direction reaches many ion inertial lengths. During this transition, the quasisteady reconnection rate decreases until the ions are fully coupled, ultimately reaching an asymptotic value. The scaling of the ion outflow velocity with the exhaust width during this electron-only to ion-coupled transition is found to be consistent with a theoretical model of a newly reconnected field line. In order to have a fully frozen-in ion exhaust with ion flows comparable to the reconnection Alfvén speed, an exhaust width of at least several ion inertial lengths is needed. In turbulent systems with reconnection occurring between magnetic bubbles associated with fluctuations, using geometric arguments, we estimate that fully ion-coupled reconnection requires magnetic bubble length scales of at least several tens of ion inertial lengths.

On the effect of electron cyclotron waves on the evolution of neoclassical tearing modes in tokamak plasmas

In this paper we study the generation of current in a tokamak plasma in the presence of a magnetic island, using electron cyclotron (EC) waves in a process known as electron cyclotron current drive. We study some features related to the efficiency of the method, adopting a simplified model for a tokamak which incorporates the existence of a magnetic island associated with the occurrence of a neoclassical tearing mode instability. The study utilizes a self-consistent treatment of the interaction of EC waves with the plasma in the tokamak and the consequent current generation, taking into account the existence of the tokamak loop voltage and the occurrence of radial transport of particles, and also the existence of induced effects. The formalism also includes an approximate self-consistent description of the evolution of the width of the magnetic islands, which depends on the plasma current through the so-called modified Rutherford equation. The evolution of the islands depends on classical effects, which are driven mainly by the equilibrium current gradient, on neoclassical effects related to the perturbed bootstrap current and on the current generated by the radio waves. The results obtained in our numerical analyses confirm that the width of the islands can be substantially reduced by the use of EC waves, and lead to an estimate of the minimum amount of EC power required to be effective in reducing the width of magnetic islands. The results also show that, although the density of current generated by EC waves in the island region decreases along late time evolution, the total amount of plasma current is increased compared with the case in which the width of the island is assumed to remain constant.

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.

Tearing Mode Behavior in the Globus-M Spherical Tokamak Plasma

The 2/1 tearing mode instability during the plateau phase of the plasma current time evolution has been observed since the start of the Globus-M spherical tokamak operation. Because of a small amount of shots in a database, the poloidal beta dependence of the instability growth rate had been investigated with an insufficient accuracy. In this work, a more detailed analysis has been produced that proves the fact that the observed modes can be treated as neoclassical. The saturated island width as a function of poloidal beta has been obtained; a time evolution of the magnetic island has been calculated from the Mirnov magnetic coil signals and compared to the modified Rutherford theory, and the critical magnetic island width has been found for the neoclassical tearing mode (NTM) of the Globus-M tokamak.

Estimation of magnetic island width by the fluctuations of electron cyclotron emission radiometer on J-TEXT

The width of a magnetic island is an important parameter for the quantitative analysis of magnetohydrodynamic-related physics. An electron cyclotron emission radiometer (ECE) is a powerful tool that can be used to obtain this width, which can usually be determined from the flat temperature distribution at the O-point phase or the maxima temperature perturbation. An improved method to estimate the width of a magnetic island is proposed in this paper, and it is independent of calibration. With this method and the existing 24-channel ECE system, the width of a rotation magnetic island can be estimated. Additionally, by filtering the fluctuation ECE signal, the evolution of the magnetic island can be obtained. The results of this method are consistent with those of the integrated magnetic probe signals, which represent the relative change of the magnetic island.

Estimation of orbit island width from static magnetic island width, using safety factor and orbit pitch

In order to account for the effect of field perturbations on the transport of fast ions in integrated codes used for the simulation of operational scenarios, it is crucial to develop computationally efficient reduced transport models. Such modeling efforts may greatly benefit from a simple method that determines the width of the island-like structures, which are produced by resonant perturbations in the phase space of the fast ion guiding centers and are known to play a key role for fast ion transport enhancement. In this paper, we present a method for estimating the widths of such ‘orbit islands’ for passing particles in the presence of static magnetic perturbations. The method consists of mapping the boundaries of magnetic islands from magnetic flux space () into the canonical angular momentum space () of the fast ions. As a working example, we consider co-passing neutral beam (NB) ions subject to a resonant magnetic perturbation (RMP) in a KSTAR tokamak plasma. The estimated orbit island width deviates by less than 25% from the value obtained from Poincaré plots of the actual guiding center trajectories, even when the magnetic drifts are large (here, up to 50% of the minor radius). Our analysis also shows that most of the fast ion transport can be attributed to the effect of isolated islands, which means that stochastization of particle trajectories due to resonance overlaps does not play a major role in the case studied here. The island mapping method proposed here eliminates the need to compute and analyze Poincaré maps of particle trajectories, so that computation times can be reduced tremendously by several orders of magnitude. A further speed-up may be achieved by the development of a method for estimating the width of magnetic islands under realistic conditions.

Influence of magnetic flutter on tearing growth in linear and nonlinear theory

Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.

Effect of electron cyclotron beam width to neoclassical tearing mode stabilization by minimum seeking control in ITER

We report the effect of the electron cyclotron (EC) beam width on the full suppression time of neoclassical tearing mode (NTM) using the finite difference method (FDM) based minimum seeking controller in ITER. An integrated numerical system is setup for time-dependent simulations of the NTM evolution in ITER by solving the modified Rutherford equation together with the plasma equilibrium, transport, and EC heating and current drive. The calculated magnetic island width and growth rate is converted to the Mirnov diagnostic signal as an input to the controller to mimic the real experiment. In addition, 10% of the noise is enforced to this diagnostic signal to evaluate the robustness of the controller. To test the dependency of the NTM stabilization time on the EC beam width, the EC beam width scan is performed for a perfectly aligned case first, then for cases with the feedback control using the minimum seeking controller. When the EC beam is perfectly aligned, the narrower the EC beam width, the smaller the NTM stabilization time is observed. As the beam width increases, the required EC power increases exponentially. On the other hand, when the minimum seeking controller is applied, NTM stabilization sometimes fails as the EC beam width decreases. This is consistently observed in the simulation with various representations of the noise as well as without the noise in the Mirnov signal. The higher relative misalignment, misalignment divided by the beam width, is found to be the reason for the failure with the narrower beam widths. The EC stabilization effect can be lower for the narrower beam widths than the broader ones even at the same misalignment due to the smaller ECCD at the island O-point. On the other hand, if the EC beam is too wide, the NTM stabilization time takes too long. Accordingly, the optimal EC beam width range is revealed to exist in the feedback stabilization of NTM.

EC power management in ITER for NTM control: the path from the commissioning phase to demonstration discharges

Time dependent simulations that evolve consistently the magnetic equilibrium and plasma pressure profiles and the width and frequency rotation of magnetic islands under the effect of the Electron Cyclotron feedback system are used to assess whether the control of NTMs on ITER is compatible with other simulataneous functionalities of the EC system, like core heating and current profile tailoring, or sawtooth control. Results indicate that the power needs for control can be reduced if the EC power is reserved and if pre-emptive control is used as opposed to an active search for an already developed island.

On the threshold of magnetic island width in nonlinear mutual destabilization of tearing mode and ion temperature gradient mode

Nonlinear multi-scale interactions between the tearing mode and the ion temperature gradient (ITG) mode are investigated by means of numerical simulations in a self-consistent 5-field Landau-fluid model. It is observed that there exists a threshold of magnetic island width in the nonlinear evolution of interaction, above which the ITG turbulence can enhance the island growth significantly. Dependence of the threshold on basic plasma parameters is deeply analyzed. It is found that the higher ion viscosity may raise the threshold through its effect on the E×B drift and the diamagnetic drift of electron density gradient in different ways, both of which play a synergetic role in determining the threshold. Moreover, the effects of plasma resistivity, gradient length of equilibrium current sheet as well as magnetic shear of field line on the threshold are discussed based on the analyses of the initial growth rate of islands.

Reduction of neoclassical polarization current contribution to NTM evolution

The neoclassical polarization current, which can be generated by a time-dependent electric field resulting from magnetic island rotation, is believed to play an important role in the initial stage of the neoclassical tearing mode (NTM) evolution in tokamak plasmas. In the previous analytical description of the neoclassical polarization current contribution to the evolution of NTMs in the limit of low collision frequency (νii≪εω, νii is ion collision frequency, ε is the inverse aspect ratio, and ω is the island propagation frequency in the plasma rest frame), the width of magnetic islands has been assumed to be much larger than the finite-banana-width (FBW) of the trapped ions in order to solve the drift-kinetic equation of ions by using the perturbation method. In this paper, we introduce a new analytical approach to investigate the neoclassical polarization current contribution to the NTM evolution without the assumption of the large island width by solving the drift-kinetic equation in a so-called ion-banana-center coordinate system. The results show that, when the island width is comparable to the FBW of the thermal ion, the neoclassical polarization current term in the equation of the NTM evolution is much smaller than the previous analytical expression but matches well with the empirical anticipation commonly adopted in experiments.

Nonlinear tearing modes stabilization by oscillating the resonant surface

The stabilization of the nonlinear tearing mode by rapidly oscillating the resonant surface has been investigated numerically in a large aspect ratio tokamak with a circular cross-section. By means of the radio frequency current drive, the plasma current can be modulated to make the resonant surface (rs) oscillate in time near its mean position. Previous results show that the linear tearing mode can be suppressed by oscillating the resonant surface with a suitable frequency and amplitude. At the nonlinear stage, the tearing mode stabilization shows different properties. The suppression effects not only depend on the modulation frequency and the oscillation width of the resonant surface but also depend on the relative size of χ0 to δ (here, χ0 is the oscillation width of the resonant surface and δ is the width of tearing layer) and the relative width of χ0 to the magnetic island width W.

Nonlinear evolution of multi-helicity neo-classical tearing modes in rotating tokamak plasmas

Plasma perturbations from the core and/or boundary regions of tokamaks can provide seed islands for the excitation of neo-classical tearing modes (NTMs) with negative , where is the linear instability parameter of the classical tearing mode. In this work, by means of reduced magnetohydrodynamic simulations, we numerically investigate the nonlinear evolution of multi-helicity NTMs in rotating tokamak plasmas with these two types of plasma perturbations with different boundary conditions. In the first case of initial plasma perturbations from the core region with a zero boundary condition, the meta-stable property of seed-island triggered NTM with negative is verified in the single helicity simulation. Nevertheless in the multiple helicity simulation, this seed-island triggered NTM with negative can be suppressed by a spontaneous NTM with positive through the competitive interaction between NTMs with different helicities. If a fixed poloidal rotation is taken into account in the first case, two different helicity NTMs could coexist in the saturation stage, which is different qualitatively from the process without plasma rotation. In the second case of initial plasma perturbations from the boundary region with a nonzero boundary condition, as the amplitude of plasma perturbations on the boundary increases, the mode with negative gradually changes from the driven-reconnection state to the NTM state, accompanied by an enhancement of magnetic island width in the single helicity simulation. Nevertheless in the multi-helicity simulation, the spontaneous NTM with positive can make the driven-reconnection triggered NTM with negative transfer from the NTM state back to the driven-reconnection state again. The underlying mechanism behind these transitions is analyzed step by step. Effects of fixed and unfixed poloidal rotations on the nonlinear interaction processes are also investigated in detail. In addition, the appearance and disappearance of the magnetic stochasticity resulting from the nonlinear coupling among the multi-helicity NTMs are discussed in the second case.

Numerical Modeling on Heat Transport Across Stochastic Magnetic Field

AbstractThe heat diffusion across the stochastic magnetic field is studied numerically. The stochastic field is generated by the overlap of two magnetic islands. The parameter w/wc, is found tobe an important parameter in charactering the transport, where w is the magnetic island width, and wc is the critical island width for flattening the electron temperature across an island. For w/wc < 1, the enhanced radial heat diffusivity χr is proportional to the parallel heat diffusivity χ∥, and the heat transport is dominated by the additive effect of individual islands. For w/wc > 3, χr is also proportional to χ∥ and the additional degradation of the energy confinement due to stochastic magnetic field becomes apparent. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The effect of sheared toroidal rotation on pressure driven magnetic islands in toroidal plasmas

The impact of sheared toroidal rotation on the evolution of pressure driven magnetic islands in tokamak plasmas is investigated using a resistive magnetohydrodynamics model augmented by a neoclassical Ohm's law. Particular attention is paid to the asymptotic matching data as the Mercier indices are altered in the presence of sheared flow. Analysis of the nonlinear island Grad-Shafranov equation shows that sheared flows tend to amplify the stabilizing pressure/curvature contribution to pressure driven islands in toroidal tokamaks relative to the island bootstrap current contribution. As such, sheared toroidal rotation tends to reduce saturated magnetic island widths.