Tearing Mode Research Articles

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.

Investigation of fracture behaviour of asymmetric spur gear

As a high power transmission capacity and long durability constitute an essential requirement for mechanical machinery, the mechanical transmission gears need to be modified to improve the performance. The increasing drive side pressure angle is one of the methods for enhancing load-carrying capacity of the spur gear. The fracture characteristics of asymmetric gears need to be investigated to estimate the fatigue life. The location and magnitude of stress intensity factors mainly depend on gear tooth geometry, gear parameters, crack tip location, and applied force. Most of the literature study of fracture analysis carried out for the symmetric gears and the majority of them are two-dimensional analysis. In this study, a parametric analysis carried out for asymmetric spur gears to examine the fracture behaviour under mixed-mode fracture condition and explore the significance of each gear parameters. The maximum bending stress location for each gear pair is determined and the crack is introduced at that region. The stress intensity factor (SIF) for each mode is estimated and the effective stress intensity factor at each node along the face width is determined. In addition, the effect of opening mode, sliding mode and tearing mode on effective stress intensity factor for fillet crack is examined. This analysis inferred that the effect of opening mode fracture is predominant in the effective stress intensity factor irrespective of gear parameters.

Coriolis Force Effect on Suppression of Neo-Classical Tearing Mode Triggered Explosive Burst in Reversed Magnetic Shear Tokamak PlasmasSupported by the National Natural Science Foundation of China (Grant Nos. 11925501, 11875099, and 11575158), the Liaoning Revitalization Talents Program (Grant No. XLYC1802009), and the China Scholarship Council (Grant No. 201806060036).

We numerically investigate the Coriolis force effect on the suppression of an explosive burst, triggered by the neo-classical tearing mode, in reversed magnetic shear configuration tokamak plasmas, using a reduced magnetohydrodynamic model, including bootstrap current. Previous works have shown that applying differential poloidal rotation, with rotation shear located near the outer rational surface, is an effective way to suppress an explosive burst. In comparison with cases where there is no Coriolis force, the amplitude of differential poloidal rotation required to effectively suppress the explosive burst is clearly reduced once the effect of Coriolis force is taken into consideration. Moreover, the effective radial region of the rotation shear location is broadened in cases where the Coriolis force effect is present. Applying rotation with shear located between the radial positions of q min and the outer rational surface always serves to effectively suppress explosive bursts, which we anticipate will reduce operational difficulties in controlling explosive bursts, and will consequently prevent plasma disruption in tokamak experiments.

New methodology for measuring electron density perturbations caused by plasma coherent modes using profile reflectometry: Magnitudes and radial profiles in DIII-D.

New capabilities of fast-sweep frequency-modulated profile reflectometry are explored to measure electron density ne perturbation magnitudes and radial profiles due to plasma coherent modes in DIII-D. The first approach is based on the frequency analysis of phase perturbations associated with high frequency (∼MHz) Alfvén eigenmodes (AEs). The measurement of ∼5.5MHz fast-ion-driven global Alfvén eigenmodes (GAEs) is demonstrated in a neutral beam-heated DIII-D plasma. The GAE induced a broad radial distribution of phase perturbations in the profile reflectometer data. Analysis of these data determined the effective cutoff location displacement and the estimated ne fluctuation profile. In the second approach, high resolution ne profiles are used directly to determine the radial structure of ne perturbations due to a neo-classical tearing mode. These new measurements broaden the application of profile reflectometry and advance the development of AE spectroscopy as a tool for non-invasive diagnosis of fast-ion-driven modes in DIII-D and burning plasmas such as ITER.

Electromagnetic torque measurements in DIII-D using internal/external magnetic field decomposition

Given spatially resolved measurements of normal and tangential components of the magnetic field just outside the surface of a magnetically confined plasma, the field at the measurement location can be uniquely decomposed into contributions from the plasma and from external sources. This principle allows direct measurement of the electromagnetic torque on the plasma without knowledge of the distribution of the internal and external currents, similar to the more well-known formalism using the Maxwell stress tensor. The internal/external field decomposition also enables a mixed approach that incorporates any explicitly known current distributions (e.g., from non-axisymmetric coils). We discuss the requirements and limitations of such an approach to torque measurements. Experimental measurements of the torque evolution as a rotating tearing mode locks to the wall in the DIII-D tokamak are consistent with a simple model.

Disruption avoidance via radio frequency current condensation in magnetic islands produced by off-normal events

This paper discusses the use of radio frequency (RF) current drive to stabilize large islands, focusing on nonlinear effects that appear when relatively high powers are used to stabilize large islands. We are interested in developing a capability to stabilize large islands via RF driven currents to avoid the need for mitigation to the extent possible. As tokamaks are designed and built with increasing levels of stored energy in the plasma, disruptions become increasingly dangerous. It has been reported that 95% of the disruptions in the Joint European Torus tokamak with the ITER-like wall are preceded by the growth of large locked islands. These large islands are mostly produced by off-normal events other than neoclassical tearing modes. This paper presents theory and modeling for a nonlinear “RF current condensation” effect that can concentrate the RF driven current near the center of a large island, thereby increasing the efficiency of the stabilization. A nonlinear shadowing effect can hinder the stabilization of islands if the aiming of the ray trajectories does not properly consider the nonlinear effects.

Drift kinetic theory of neoclassical tearing modes in a low collisionality tokamak plasma: magnetic island threshold physics

A new drift kinetic theory for the plasma response to the neoclassical tearing mode (NTM) magnetic perturbation is presented. Small magnetic islands of width, (a is the tokamak minor radius) are assumed, retaining the limit w ∼ ρ bi (ρ bi is the ion banana orbit width) to include finite orbit width effects. When collisions are small, the ions/electrons follow streamlines in phase space; for passing particles, these lie in surfaces that reproduce the magnetic island structure but have a radial shift by an amount, proportional to , where is the ion/electron poloidal Larmor radius. This shift is associated with the curvature and ∇B drifts and is found to be in opposite directions for , where is the component of velocity parallel to the magnetic field. The particle distribution function is then found to be flattened across these shifted or drift islands rather than the magnetic island. This results in the pressure gradient being sustained across the magnetic island for and hence reduces the neoclassical drive for NTMs when w is small. This provides a physics basis for the NTM threshold, which is quantified. In Imada et al (2019 Nucl. Fusion 59 046016, and references therein), a 4D drift kinetic non-linear code has been applied to describe these modes. In the present paper, the drift island formalism is employed. Valid at low collisionality, it allows a dimensionality reduction to a 3D problem, simplifying the numerical task and efficiently resolving the collisional boundary layer across the trapped-passing boundary. An improved model is adopted for the magnetic drift frequency. This decreases the NTM threshold, compared to the results shown in Imada et al (2019 Nucl. Fusion 59 046016, and references therein), making it in quantitative agreement with experimental observations, with , where w c is the threshold magnetic island half-width, or 2.85ρ bi for the full threshold island width, predicted for our equilibrium.

Numerical investigation of alpha particle confinement under the perturbation of neoclassical tearing modes and toroidal field ripple in CFETR

The confinement of alpha particles in burning plasma is a key issue in fusion reactor design, including particle interaction with instabilities. This paper includes two topics: the effect of neoclassical tearing modes (NTMs) and toroidal field ripple on alpha particle loss, and the assessment of particle redistribution under an NTM with a reduced model. We consider Chinese fusion engineering test reactor parameters, the alpha particle distribution given by TRANSP/NUBEAM and the NTM perturbation function given by the initial value code TM1. We show that the synergistic effect of the NTM and ripple is negligible; the particle loss fraction does not change with increasing NTM amplitude. Only passing particles are affected by the mode particle resonance, producing profile flattening but no increased loss because only trapped particles are influenced by ripple. To study alpha particle profile flattening, the work adopts an innovative method of phase vector rotation to determine regions of good and broken Kolmogorov–Arnold–Moser surfaces and equilibrates the particle density according to local stochasticity.

Transition from no-ELM response to pellet ELM triggering during pedestal build-up—insights from extended MHD simulations

Pellet edge localized mode (ELM) triggering is a well-established scheme for decreasing the time between two successive ELM crashes below its natural value. Reliable ELM pacing has been demonstrated experimentally in several devices, increasing the ELM frequency considerably. However, it was also shown that the frequency cannot be increased arbitrarily due to a so-called lag-time. During this time, after a preceding natural or triggered ELM crash, neither a natural ELM crash occurs nor is it possible to trigger an ELM crash by pellet injection. For this article, pellet ELM triggering simulations are advanced beyond previous studies in two ways. Firstly, realistic E × B and diamagnetic background flows are included. And secondly, the pellet is injected at different stages of the pedestal build-up. This allows us to recover the lag time for the first time in simulations and investigate it in detail. A series of nonlinear extended MHD simulations is performed to investigate the plasma dynamics resulting from an injection at different time points during the pedestal build-up. The experimentally observed lag-time is qualitatively reproduced. In particular, a sharp transition is observed between the regime where no ELMs can be triggered and the regime where pellet injection causes an ELM crash. Via variations of pellet parameters and injection time, the two regimes are studied and compared in detail, revealing pronounced differences in the nonlinear dynamics. The toroidal mode spectrum is significantly broader when an ELM crash is triggered, enhancing the stochasticity and therefore also the losses of thermal energy along magnetic field lines. In the heat fluxes to the divertor targets, pronounced toroidal asymmetries are observed. In the case of high injection velocities leading to deep penetration, the excitation of core modes like the 2/1 neoclassical tearing mode is also observed.

Noise suppression for MHD characterization with electron cyclotron emission imaging 1D technique

Significant noise suppression for magnetohydrodynamics (MHD) mode characterization in the spatial and spectral domain is achieved by processing two-dimensional (2D) electron cyclotron emission imaging (ECEI) data with a one-dimensional (1D) ECEI technique using a short time window (). The technique is applied to detect toroidal Alfven eigenmodes (TAEs) in the temporal spectrum and fit their radial envelope using the data from the DIII-D tokamak W-band 2D ECEI system. Using the data length (time window) of only 1 , the 1D ECEI can clearly detect the TAEs (∼100 ) on the spectrum, while similar spectrum quality requires ∼10 data length with the cross power spectrum between two midplane ECEI channels. The 1D ECEI technique also effectively avoids biased fitting when resolving the fine structure of the TAE’s radial envelope. The radially spatial resolution of 1D ECEI is constrained by the finite ECE radiation volume of the ECEI receiver. With forward radiation modeling, we find the DIII-D ECEI system can sensitively measure the even parity MHD activities, for which the mode width is >15 mm, and tearing modes (odd parity MHD activities), for which the island full width is >30 mm.

Non-Resonant n = 1 Helical Core Induced by m/n = 2/1 Neoclassical Tearing Mode in JT-60U

In JT-60U, simultaneous excitation of n = 1 helical cores (HCs) and m/n = 2/1 Tearing Modes (TMs) was observed [T. Bando et al., Plasma Phys. Control. Fusion 61 115014 (2019)]. In this paper, we have investigated the excitation mechanism of n = 1 HCs with m/n = 2/1 TMs based on the experimental observations and a simple quasi-linear MHD model. In the previous study, it was reported that a "coupling" on the phase of the MHD mode is observed between n = 1 HCs and m/n = 2/1 TMs. In this study, it is found that the coupling is observed with the mode frequency from several Hz to 6 kHz. This indicates that the resistive wall and the plasma control system do not induce the coupling because the both time scales are different from the mode frequency. In addition, n = 1 HCs appear to be the non-resonant mode from the two observations: n = 1 HCs do not rotate with the plasma around the q = 1 surface in the core and the coupling is also observed even when qmin > 1. It is also observed that the electron fluctuation due to an n = 1 HC in the core region disappears with the stabilization of an m/n = 2/1 neoclassical tearing mode by electron cyclotron current drive, implying that n = 1 HCs are driven by m/n = 2/1 TMs. This perspective, n = 1 HCs are driven by m/n = 2/1 TMs, is supported by the observation that the saturated amplitude of the m/n = 1/1 component of the radial displacement in the core is smaller than that of the m/n = 2/1 component. Finally, we revisit a quasi-linear MHD model where the m/n = 1/1 HC is induced directly by the sideband of the current for the m/n = 2/1 TM, which allows to excite the non-resonant m/n = 1/1 mode. The model also describes the characteristic of the coupling, fm/n=1/1(HC) = 2fm/n=2/1(TM).

Onset of tearing modes in plasma termination on JET: the role of temperature hollowing and edge cooling

In this work the onset of tearing modes in the termination phase of plasma pulses on JET is investigated. It is shown that the broadening or the shrinking of the current density profile, as a consequence of a core hollowing or an edge cooling of the electron temperature profile, strongly increases the probability of destabilizing a 2/1 tearing mode also in absence of an external trigger (e.g. a sawtooth crash). Two parameters are defined to highlight changes in the shape of the temperature profile that can lead to MHD instabilities and an empirical stability diagram is introduced into the space of the two new parameters. A large data-set of pulses carried out in the high-current scenario at JET with ITER-like wall is analyzed and criteria for the development of disruption alerts based on the two risk indicators for MHD instabilities are discussed, taking into account the different dynamics of the observed phenomena leading to the onset of 2/1 tearing modes.

Assessment of measurement performance for a low field side IDTT plasma position reflectometry system

The Italian Divertor Test Tokamak (IDTT) facility will study advanced exhaust solutions applicable to DEMO. This new machine also opens the possibility to test and validate relevant non-magnetic control diagnostics in support of a DEMO design implementation. Reflectometry, compatible with a full grade reactor implementation, has been proposed as a source of real-time (RT) plasma position and shape measurements for control purposes, in replacement or complement of standard magnetic measurements, to ensure reliability and safety on the machine. Additionally, such a system can be useful to obtain the characteristics of edge turbulence, useful for Neoclassical Tearing Mode (NTM) control or to improve the efficiency of other diagnostics as Collective Thomson Scattering (CTS). This new control technique based on multiple, poloidally distributed, non-magnetic measurements, must be tested, in all of its aspects, before it can be fully implemented in future fusion reactors. IDTT will be one of the best candidates to implement and build a knowledge database of nonstandard reflectometry (away from the equatorial plane) that will be needed on DEMO and is currently unavailable. The performance of three Ordinary mode (O-mode) Plasma Position Reflectometers (PPR) at the Lower Field Side (LFS) on IDTT is assessed using the two-dimensional (2D) full-wave Finite-Difference Time-Domain (FDTD) code, REFMULF, in two of the foreseen IDTT plasma scenarios: 5MA Single Null (SN) and Double Null (DN) configurations.

Phase relation between rotating phase locked (2, 1) and (3, 1) tearing modes in ASDEX Upgrade

Tearing modes are a major concern for large tokamak devices. Therefore their detection and characterization is of importance for timely countermeasures to avoid significant impact on the discharge or at least prevent possible machine damage. In case of phase-locked tearing modes, the poloidal variation of induced magnetic field fluctuation depends on the amplitudes of and the phase difference between the individual modes. This affects mode detection and identification when not considered appropriately. The phase between phase-locked (2, 1) and (3, 1) tearing modes in ASDEX Upgrade has been determined from local electron temperature and magnetic measurements independently. It is shown that the modes can be in phase at any poloidal position starting from the low field side plasma midplane over the plasma top to the high field side midplane. This observation invalidates the widespread assumption that phase-locked tearing modes are in phase near the low field side midplane. Dependence of the in-phase position on both, the plasma pressure and the plasma rotation velocity, is observed.

Suppression of neoclassical tearing mode instability at the initial stage by electron cyclotron current drive

The suppression of the neoclassical tearing mode (NTM) by the electron cyclotron wave current drive (ECCD) is studied numerically based on the reduced MHD equations. The required current drive for the NTM stabilization is shown to be significantly reduced if ECCD is applied at the initial stage when the magnetic island is not too large. The modulated ECCD is more effective than a continued one to suppress the NTM, as expected. The value of the duty circle of modulated ECCD is also found to affect the result.

Effect of resistive wall on thermal quench in JET disruptions

Experimental data, simulations, and theory are presented for a JET tokamak thermal quench. The emphasis is on the timescale of the bulk plasma thermal energy loss. The simulations suggest that the thermal energy loss is caused by a resistive wall tearing mode, and experimental data are consistent with this conclusion. The timescale of the thermal quench is the inverse of the mode growth rate.

Computational general relativistic force-free electrodynamics

Scientific codes are an indispensable link between theory and experiment; in (astro-)plasma physics, such numerical tools are one window into the universe’s most extreme flows of energy. The discretization of Maxwell’s equations – needed to make highly magnetized (astro)physical plasma amenable to its numerical modeling – introduces numerical diffusion. It acts as a source of dissipation independent of the system’s physical constituents. Understanding the numerical diffusion of scientific codes is the key to classifying their reliability. It gives specific limits in which the results of numerical experiments are physical. We aim at quantifying and characterizing the numerical diffusion properties of our recently developed numerical tool for the simulation of general relativistic force-free electrodynamics by calibrating and comparing it with other strategies found in the literature. Our code correctly models smooth waves of highly magnetized plasma. We evaluate the limits of general relativistic force-free electrodynamics in the context of current sheets and tearing mode instabilities. We identify that the current parallel to the magnetic field (j∥), in combination with the breakdown of general relativistic force-free electrodynamics across current sheets, impairs the physical modeling of resistive instabilities. We find that at least eight numerical cells per characteristic size of interest (e.g., the wavelength in plasma waves or the transverse width of a current sheet) are needed to find consistency between resistivity of numerical and of physical origins. High-order discretization of the force-free current allows us to provide almost ideal orders of convergence for (smooth) plasma wave dynamics. The physical modeling of resistive layers requires suitable current prescriptions or a sub-grid modeling for the evolution of j∥.

Experimental Observation of Magnetic Island Heteroclinic Bifurcation in Tokamaks.

We report empirical observations of magnetic island heteroclinic bifurcation for the first time. This behavior is observed in interacting coupled 2/1 tearing modes in the core of a DIII-D tokamak plasma. Poincaré maps constrained by measured magnetic amplitudes and phasing show bifurcation from heteroclinic to homoclinic topology in the 2/1 island as the 4/2 relative amplitude (R_{4/2}) decreases. Initially, the local electron temperature peak in the 2/1 island splits, consistent with two O points. As R_{4/2} decreases a single peak forms, consistent with one O point. These call for developing tearing stability theory and control solutions for heteroclinic islands in tokamaks.

Nonlinear evolution and secondary island formation of the double tearing mode in a hybrid simulation

Double tearing modes (DTMs), induced by double current sheet configurations or two neighboring rational surfaces with the same safety factor in tokamaks, are widely observed in solar, space, and fusion plasmas. In this paper, the evolution of DTMs without a guide field is investigated numerically using a hybrid model (electron fluid + ion PIC). The overall evolution processes of DTMs are qualitatively consistent with previous works using other models. The particle dynamics during the evolution of DTMs is analyzed in detail. Behaviors of ions and electrons present different characteristics around the reconnection region which gives rise to Hall effects producing the out-of-plane quadrupole magnetic field. In the explosive reconnection process with interactions between two DTMs islands, the asymmetric drive and the thin current layer feature lead to the emergence of secondary magnetic islands which develop with the late evolution of the DTMs.

Experimental observation of the localized coupling between geodesic acoustic mode and magnetic islands in tokamak plasmas

The localized coupling among geodesic acoustic mode (GAM), tearing modes (TMs) and twin counter-propagating beta-induced Alfvén eigenmodes (BAEs) waves has been investigated in the experimental advanced superconducting tokamak. Before the appearance of TMs, typical continuous GAM is observed through the multi-channel Doppler backscattering (DBS) diagnostic. The twin BAEs can be excited after the burst of magnetic islands, which are localized to the q = 4 rational surface that is confirmed by the measurement of DBS array, where the GAM and twin BAEs are observed synchronically at R ≈ 2.23 m (normalized radius ρ ≈ 0.8). One reasonable excitation mechanism is proposed that the twin BAEs can be excited by the nonlinear interaction between GAM and magnetic islands. As the width of magnetic islands increases, the electromagnetic twin BAEs increase synchronically with the decreasing of electrostatic GAM, strongly suggesting that the electromagnetic components are pumped from three-wave interaction between electrostatic GAM and magnetic islands.