Magnetic Island Width Research Articles

The Coupling Structure Features Between (2,1) NTM and (1,1) Internal Mode in EAST Tokamak**supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2014GB103000, 2011GB101000 and 2013GB102000) and sponsored in part by National Natural Science Foundation of China (Nos. 10725523, 10990212 and 11205199)

In the discharge of EAST tokamak, it is observed that (2,1) neoclassical tearing mode (NTM) is triggered by mode coupling with a (1,1) internal mode. Using singular value decomposition (SVD) method for soft X-ray emission and for electron cyclotron emission (ECE), the coupling spatial structures and coupling process between these two modes are analyzed in detail. The results of SVD for ECE reveal that the phase difference between these two modes equals to zero. This is consistent with the perfect coupling condition. Finally, performing statistical analysis of r1/1, ξ1/1 and w2/1, we find that r1/1 more accurately represents the coupling strength than ξ1/1, and r1/1 is also strongly related to the (2,1) NTM triggering, where r1/1 is the width of (1,1) internal mode, ξ1/1 is the perturbed amplitude of (1,1) internal mode, and w2/1 denot es the magnetic island width of (2,1) NTM.

Theoretical and Numerical Study of Electron Transport Through Magnetic Island

We investigate electron heat diffusion across a low mode magnetic island numerically in cylindrical geometry and compare with the theory in tokomak plasma physics. In order to keep the simulation results reliable, a modified simulation code, TM8P, was used in our simulation work. The correlation of the effective radial heat conductivity, χr, and several high ratio of parallel magnetic field heat diffusion coefficient to the perpendicular coefficient, \( {{\chi_{\parallel } } \mathord{\left/ {\vphantom {{\chi_{\parallel } } {\chi_{ \bot } }}} \right. \kern-0pt} {\chi_{ \bot } }} \), is studied in this article. It’s found that the theoretical prediction by Yu conform with the numerical results of TM8P when \( {{\chi_{\parallel } } \mathord{\left/ {\vphantom {{\chi_{\parallel } } {\chi_{ \bot } }}} \right. \kern-0pt} {\chi_{ \bot } }} \) is not bigger than 1012, i.e. the value of width of magnetic island to the width of diffusive layer, w/wc, is a small number.

Response of microscale turbulence and transport to the evolution of resistive magnetohydrodynamic magnetic island

Nonlinear evolution of microscale turbulence interacting with a naturally growing MHD magnetic island is simulated based on a Landau-fluid model. Here, we report on a new short wavelength magnetic-island-induced ion temperature gradient (ITG) instability triggered by a critical threshold of magnetic island width in multiscale turbulence, which is referred to as sw-MITG mode. The sw-MITG mode is characterized by a substantially low stability threshold and a global structure propagating along the ion diamagnetic drift direction. Its generation results from the response of microscale fluctuations to turbulent cross-field heat transport associated with increasing boundary layer width about the island separatrix. An intermittency of heat transport is caused by the sw-MITG mode interacting with dynamical magnetic island and microturbulence.

The effect of biased limiter on the magnetic island width in tokamak plasma

AbstractIn this work the effects of Cold Biased Limiter (CBL) and Emissive Biased Limiter (EBL) have been individually investigated, in both positive and negative polarities, on the width and frequency of magnetic islands. The effects were examined using singular value decomposition and wavelet techniques on mirnov coil signals. The results show that the application of EBL with both positive and negative polarities has been more effective on plasma stability compared with CBL. Comparing different polarities of CBL and EBL revealed that the positive polarity was more effective on the width of magnetic islands than negative polarity. The greatest impact occurs during EBL with positive polarity, in which reduction is observed in both width of magnetic islands and emission of Hα radiation. Besides, intensity and frequency of magnetic islands are reduced from 50 to 25 kHz in around 1 ms after bias application. Meanwhile, the minimal effect on width and frequency of magnetic field occurs in CBL with negative polarity.

Excitation of (2,1) neoclassical tearing modes by mode coupling with (1,1) internal mode in EAST

Neoclassical tearing modes (NTM) are observed in discharges with auxiliary heating LH+ICRF and LH only during H-mode in EAST. The m/n = 2/1 NTM is triggered by strongly coupling with an m/n = 1/1 internal mode. Here, LH and ICRF are the abbreviations of lower hybrid resonance heating and ion cyclotron resonance frequency heating, respectively. The mode number of the NTM is m/n = 2/1, where m is the poloidal mode number and n is the toroidal mode number. Just before the triggering of NTMs, an m/n = 1/1 internal mode appears in the soft x-ray emission at plasma centre when the intensity of hard x-ray (IHX) reaches a critical value. The mode, characterized by frequency chirping in the spectrum, may be related to suprathermal electrons produced by LH. The saturated magnetic island width wsat of the NTM is strongly correlated with poloidal βp. Normalized βN,onset and the magnetic island critical width wcrit increase with electron temperature Te.

Measurement of Magnetic Island Width by Multi-Channel ECE Radiometer on HT-7 Tokamak

A 16-channel electron cyclotron emission (ECE) radiometer has been employed to observe the (m, n) = (2, 1) magnetic island structure on HT-7 tokamak, where m and n represent the poloidal and toroidal mode number respectively. The results indicate that the island width is about 7 cm when the magnetic island is saturated during the m/n = 2/1 mode. The location of resonance surface can be determined by plotting the contour of ECE relative fluctuation. This method could be applied to the HT-7 and EAST campaigns in the future for the research of neoclassical tearing modes (NTMs).

Evidence of Neoclassical Toroidal Viscosity on the Neoclassical Tearing Modes in TCV tokamak

The interplay between the plasma toroidal rotation and the onset of magnetohydrodynamics instabilities, such as the Neoclassical Tearing Modes (NTMs), is an important issue for tokamak performance. An interesting mechanism characterizing this interaction is the breaking of axisymmetry due to the NTM helical structure, which is the source of a magnetic viscous drag parallel to the toroidal field. This effect, known as Neoclassical Toroidal Viscosity (NTV) depends on magnetic island width, and is responsible of the nearly global slowing down of the toroidal velocity across the profile. In the TCV tokamak the spontaneous plasma toroidal rotation profile, observed even in absence of other external momentum sources [1], can be modified by nearly central electron cyclotron heating (ECH) with a slight poloidal asymmetry and current drive (ECCD) [1,2,3]. The evidence of NTV effect on the plasma toroidal velocity profile of TCV is apparent as a pronounced flattening at the onset of m/n=3/2 and 2/1 tearing instabilities in the neoclassical regime in TCV discharges (Ip~150 kA, ne_av~2 1019 m−3 Te~3 keV) with 1.5 MW EC ramp up/down phases. Comparison of the measured and calculated toroidal plasma velocity is performed using the NTV formulation [4,5] applicable in the collisionless regimes. The different aspects of the NTM onset associated both with the ECH-coECCD effect on the current profile and with NTV observed in several TCV discharges are discussed, in the frame of classical and neoclassical tearing modes theory applied to 3/2 and 2/1 modes.

Hybrid-like 2/1 flux-pumping and magnetic island evolution due to edge localized mode-neoclassical tearing mode coupling in DIII-D

Direct analysis of internal magnetic field pitch angles measured using the motional Stark effect diagnostic shows m/n=2/1 neoclassical tearing modes exhibit stronger poloidal magnetic flux-pumping than typical hybrids containing m/n=3/2 modes. This flux-pumping causes the avoidance of sawteeth, and is present during partial electron cyclotron current drive suppression of the tearing mode. This finding could lead to hybrid discharges with higher normalized fusion performance at lower q95. The degree of edge localized mode-neoclassical tearing mode (ELM-NTM) coupling and the strength of flux-pumping increase with beta and the proximity of the modes to the ELMing pedestal. Flux-pumping appears independent of magnetic island width. Individual ELM-NTM coupling events show a rapid timescale drop in the island width followed by a resistive recovery that is successfully modeled using the modified Rutherford equation. The fast transient drop in island width increases with ELM size.

Compressibility effects on double tearing mode interlocking in differentially rotating plasmas

Effects of compressibility on the double tearing modes (DTMs) in rotating plasmas are numerically investigated by using a compressible magnetohydrodynamics (MHD) model. It is found that due to the compressibility effects, the threshold of the interlocking magnetic island width in the slow and intermediate rotation regimes is larger than the counterpart in the incompressible plasmas. In the fast rotation regime, the compressible effect makes the DTM islands interlock more easily and faster. Moreover, in the very fast rotation regime, the plasma rotation can more effectively suppress the DTM islands. The scalings of the interlocking threshold in the different rotation regimes are obtained. Effects of plasma viscosity and beta on the DTM interlocking in the compressible plasmas are also discussed.

Analytical solutions for Tokamak equilibria with reversed toroidal current

In tokamaks, an advanced plasma confinement regime has been investigated with a central hollow electric current with negative density which gives rise to non-nested magnetic surfaces. We present analytical solutions for the magnetohydrodynamic equilibria of this regime in terms of non-orthogonal toroidal polar coordinates. These solutions are obtained for large aspect ratio tokamaks and they are valid for any kind of reversed hollow current density profiles. The zero order solution of the poloidal magnetic flux function describes nested toroidal magnetic surfaces with a magnetic axis displaced due to the toroidal geometry. The first order correction introduces a poloidal field asymmetry and, consequently, magnetic islands arise around the zero order surface with null poloidal magnetic flux gradient. An analytic expression for the magnetic island width is deduced in terms of the equilibrium parameters. We give examples of the equilibrium plasma profiles and islands obtained for a class of current density profile.

Numerical simulation on edge localized mode control capability of resonant magnetic perturbation in the KSTAR tokamak

Numerical simulations are carried out to investigate the applicability of resonant magnetic perturbation (RMP) to KSTAR plasmas for a possible control of edge localized mode (ELM) to suppress or mitigate its damages to divertor materials. For the verification of the feasibility of RMP application, magnetic island configurations, resonant normal fields, magnetic island widths and Chirikov parameters are calculated for two types of KSTAR operation scenarios: steady state and hybrid. Field error correction (FEC) coils in KSTAR are considered to produce externally perturbed magnetic fields for RMP, and the directions of coil currents determine the toroidal mode n and the parity (even or odd). The RMP configurations are described by vacuum superposition of the equilibrium magnetic fields and the perturbed ones induced by FEC coils. The numerical simulations for n = 2 toroidal mode in both operation scenarios show that when the pitches of the equilibrium and perturbed magnetic fields are well aligned, magnetic islands are formed for a series of m poloidal modes and the adjacent islands are overlapped to generate a stochastic layer in the edge region. Even parity turns out to be more effective in making the magnetic islands overlapped to become stochastic field lines in the steady-state operation, while odd parity in the hybrid operation. The formation of the stochastic layer is verified by the calculated Chirikov parameters, which also give basic information on the current requirement of FEC coils. Additionally, lobe structures of stochastic field lines are found in the edge region extended to the divertor plate in the hybrid scenario. Based on the standard vacuum criteria for RMP, the simulation results indicate that the FEC coils will be feasible for control of ELMs and mitigation of divertor heat load by RMP in both steady-state and hybrid operation scenarios.

Local measurements of tearing mode flows and the magnetohydrodynamic dynamo in the Madison Symmetric Torus reversed-field pinch

The first localized measurements of tearing mode flows in the core of a hot plasma are presented using nonperturbing measurements of the impurity ion flow. Emission from charge exchange recombination is collected by a novel high optical throughput duo spectrometer providing localized (±1 cm) measurements of C+6 impurity ion velocities resolved to <500 m/s with high bandwidth (100 kHz). Poloidal tearing mode flows in the Madison Symmetric Torus reversed-field pinch are observed to be localized to the mode resonant surface with a radial extent much broader than predicted by linear magnetohydrodynamic (MHD) theory but comparable to the magnetic island width. The relative poloidal flow amplitudes among the dominant core modes do not reflect the proportions of the magnetic amplitudes. The largest correlated flows are associated with modes having smaller magnetic amplitudes resonant near the midradius. The MHD dynamo due to these flows on the magnetic axis is measured to be adequate to balance the mean Ohm’s law during reduced tearing activity and is significant but does not exclude other dynamo mechanisms from contributing during a surge in reconnection activity.

Effect of Magnetic Island Associated with Neoclassical Tearing Modes on Plasma Rotation in JT-60U

This paper describes the dependence of the rotation frequency of an m/n = 2/1 neoclassical tearing mode (NTM) on its magnetic island width in JT-60U (m and n are the poloidal and toroidal mode numbers, respectively). Throughout the experiments, the island width is actively controlled by changing the location of the electron cyclotron current drive (ECCD), based on the fact that aligned ECCD and misaligned ECCD make the NTM islands shrink and grow, respectively. The NTM frequency was found to gradually decrease with the increasing island width. While the frequency is 5.5 kHz for zero island width, it is 3 kHz for the full island width of about 15% of the plasma minor radius. Also, the mode frequency suddenly decreases (typically by 80%) shortly after the misaligned ECCD, during which the increment in the island width is only less than 10%. A sudden increase in the mode frequency is observed shortly after the ECCD turnoff, which is nearly the reverse process of the sudden decrease, but with a hysteresis in the island width at which downward and upward frequency changes occur. The downward frequency change occurs when the frequency decreases to about half of that without the NTM.

Magnetic Island Formation by External Cyclic Perturbation in Rotating and Non-rotating Plasmas

Effects of a non-monotonically evolving external perturbation on a plasma, that is stable against tearing modes, are numerically investigated. It is found that for a magnetic island driven by an external single-cycle magnetic perturbation, the time constants during the phases of growth and decay are different. This difference in time constants causes a finite magnetic island to form even after the external perturbation is removed. Therefore, the saturation width of a magnetic island driven by a successive applications of an external single-cycle perturbation becomes larger than the maximum magnetic island width driven by a single application of that. For a rotating plasma, the background rotation is damped as the magnetic island grows due to an external perturbation [R. Fitzpatrick, Phys. Plasmas 5, 3325(1998)]. Therefore, for a rotating plasma, the driven magnetic island can enter an explosive growth stage due to successive applications of a single-cycle perturbation even with amplitude smaller than the critical value for the onset of the rapid growth in the case of a monotonically increasing or step-function type external perturbation. These features are important in explaining the explosive growth of magnetic islands and the onset of neoclassical tearing mode due to non-monotonically growing MHD phenomena such as sawtooth, fishbones and ELM.

On the merits of heating and current drive for tearing mode stabilization

Neoclassical tearing modes (NTMs) are magnetohydrodynamic modes that can limit the performance of high β discharges in a tokamak, leading eventually to a plasma disruption. A NTM is sustained by the perturbation of the ‘bootstrap’ current, which is a consequence of the pressure flattening across a magnetic island. Control and suppression of this mode can be achieved by means of electron cyclotron waves (ECWs) which allow the deposition of highly localized power at the island location. The ECW power replenishes the missing bootstrap current by generating a current perturbation either inductively, through a temperature perturbation (electron cyclotron resonance heating), or non-inductively by direct current drive (electron cyclotron current drive). Although both methods have been applied successfully to experiments showing a predominance of ECRH for medium-sized limiter tokamaks (TEXTOR, T-10) and of ECCD for mid-to-large-sized divertor tokamaks (AUG, DIII-D, JT-60), conditions determining their relative importance are still unclear. We address this problem with a numerical study focused on the contributions of heating and current drive to the temporal evolution of NTMs as described by the modified Rutherford equation. For the effects of both heating as well as current drive, simple analytical expressions have been found in terms of an efficiency fore-factor times a ‘geometrical’ term depending on the power deposition width wdep, location and modulation. When the magnetic island width w equals the width of the deposition profile, w ≈ wdep, both geometric terms are practically identical. Whereas for current drive the geometric term approaches a constant for small island widths and is inversely proportional to (w/wdep)2 for large island widths, the heating term approaches a constant for large island widths and is proportional to (w/wdep) for small island widths. For medium-sized tokamaks (TEXTOR, AUG) the heating and current drive efficiencies are of the same order of magnitude, whereas in a future, large reactor like ITER the current drive efficiency is expected to be significantly larger.

The stabilizing effect of flow shear on m/n=3/2 magnetic island width in DIII-D

It is found that flow shear has a stabilizing effect on m/n=3/2 neoclassical tearing mode islands through a more negative classical tearing stability index Δ′ in the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] tokamak. The heating neutral beams are mixed between co- and counter-directions to vary the torque on the plasma and thus the plasma flow (rotation) and flow shear. This is done “shot to shot” in the presence of a saturated m/n=3/2 neoclassical tearing mode (NTM) while slowly raising the plasma beta up to the limit of the onset of an m/n=2/1 mode. A heuristic model for the stabilizing effect of flow shear on Δ′ is shown to explain how flow shear acts to reduce NTM island size and obviate the effect of higher beta and concomitant destabilizing helically perturbed bootstrap current.

Model for current drive stabilization of neoclassical tearing modes

A model derivation is presented for the effect of current drive on the saturated width of magnetic islands driven by the neoclassical tearing mode instability in axisymmetric plasmas. The derivation is carried out for continuous current drive as well as for modulated current that is driven at the same angle as the island O-point. The results of the derivation are implemented in a revision of the ISLAND module to compute saturated magnetic island widths. It is found that the greatest stabilizing effect of both modulated and continuous current drive on the island width is achieved when current is driven at the island center. In addition, narrow current drive is more effective at stabilizing the magnetic islands than wide current drive, for which more current falls outside the island. When modulated and continuous current drives are compared for equal total driven current, the modulated current is shown to be more effective, particularly as the offset from the island center increases.

H-mode plasma transport simulation in ITER with effect of neoclassical tearing mode

For the prediction of the ITER plasmas, the effect of the neoclassical tearing mode (NTM) on the plasma confinement has been calculated using the 1.5-dimensional equilibrium and transport simulation code TOTAL. The time evolution of the NTM magnetic island has been analyzed using the modified Rutherford equation for ITER normal shear plasmas. The anomalous transport model used here is GLF23. The saturated magnetic island widths are w/a ∼ 0.048 at 3/2 mode and w/a∼0.21 at 2/1 mode, and the reduction in fusion power output by NTM is 27% at the 3/2 mode, and 82% at the 2/1 mode. The stabilization effect of the electron cyclotron current drive (ECCD) with EC is also clarified. The threshold of ECCD power for the full stabilization at high beta NTM island formation is ∼10 MW against the 3/2 mode, and ∼23 MW against the 2/1 mode.

Locking of neoclassical tearing modes by error fields and its stabilization by RF current

The locking of neoclassical tearing modes (NTMs) by error fields is studied numerically. In the regime with low mode frequency and large plasma viscosity, the required field amplitude for mode locking is found to be proportional to the plasma viscosity and the mode frequency but inversely proportional to the square of the magnetic island width and the Alfven velocity, being similar to that of the classical tearing mode. This indicates that NTMs will be locked to low amplitude error fields in a fusion reactor. The stabilization of NTMs by RF current in the presence of a static helical field is therefore further investigated. The applied helical field allows one to control the location of the island's o-point to be in the RF wave deposition region, to enable the NTM stabilization by RF current after mode locking. When the island is large enough to be locked by a small amplitude helical field in the desired phase, the island is reduced to a smaller width by RF current compared with the case without the helical field. This suggests a possible way to enhance the stabilization of NTMs by RF current.

Neoclassical tearing mode saturation in periodic current sheets

The saturation of Neoclassical Tearing Mode islands in a periodic slab configuration is investigated. Several theoretical models, all based on a generalization of Rutherford’s procedure, that aim at reducing the complete system to a single equation of the magnetic island width, are compared against numerical simulations. When the effects of the bootstrap current and of the second derivative of the equilibrium current profile are included, the numerical saturation levels are well matched with the predictions of this equation in a wide region of the stability diagram. However, the numerical results diverge from the standard theory when evaluating the threshold for nonlinear destabilization, since the theoretical value appears to be strongly conservative. In other words, the standard generalization of Rutherford’s equation is not able to capture the minimum value of the linear stability parameter and of the island width such that below them the Neoclassical Tearing Mode is always suppressed. To correct this discrepancy, a new theoretical model in which the transverse propagation of the island affects the bootstrap current term is proposed.