Tearing Modes In Tokamak Plasmas Research Articles

Enhancement of ECCD by the current condensation effect for stabilizing large magnetic islands caused by neoclassical tearing modes in tokamak plasmas

The radio frequency current condensation effect reported in Reiman and Fisch (2018 Phys. Rev. Lett. 121 225001) is modeled in the nonlinear resistive magnetohydrodynamic code. A series of numerical investigations have been performed to investigate the enhancement of electron cyclotron current drive (ECCD) by the current condensation effect during the control of neoclassical tearing mode (NTM) in tokamak plasmas. In the numerical model, both the parallel transport and the perpendicular transport of electron temperature are considered. The EC driven current and driven perturbed electron temperature can nonlinearly evolve within the given magnetic configuration and eventually reach saturation states. The input power threshold of ECCD and the fold bifurcation phenomenon are numerically verified via nonlinear simulations. The numerical results show good agreements with the analytical results. Moreover, spatial distributions of EC current for the two solutions at different condensed level are displayed. The control effectiveness of ECCD for large NTM islands has been evaluated while considering the current condensation effect. While taking into account current condensation effect, for a sufficiently large input power, a larger island can be more effectively stabilized than a smaller one, which suggests a reassessment of the previous idea that the ECCD should always be turned on as early as possible. The potential physics mechanism behind the ECCD control have all been discussed in detail. Furthermore, the condensation effect is found to have favorable effects on the radial misalignment of ECCD. In the consideration of the situation for extremely localized control needs, a highly peaked heating profile is adopted to verify that the fold bifurcation phenomenon still exists and the current condensation effect can still take effect in this extreme condition.

Drift kinetic theory of neoclassical tearing modes in tokamak plasmas: polarisation current and its effect on magnetic island threshold physics

A nonlinear 4-dimensional drift island theory derived in (Imada et al 2019 Nucl. Fusion 59 046016 and references therein) provides qualitative predictions of the plasma response to a stationary neoclassical tearing mode (NTM) magnetic island in a low beta, large aspect ratio tokamak plasma. (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) refines a model for the magnetic drift frequency and exploits the limit of rare collisions, reducing this theory to 3-dimensional and thus providing a more accurate treatment of the trapped-passing boundary layer. The drift island theory is further improved in (Dudkovskaia et al 2023 Nucl. Fusion 63 016020) by introducing plasma shaping and finite beta effects. In the present paper, an improved model is adopted to resolve the drift island separatrix boundary layer, allowing one to investigate the polarisation current contribution that exists around the magnetic island separatrix, including in the presence of the background electric field. In particular, different magnetic topologies from both sides of the separatrix generate a radial discontinuity in the distribution function gradient there, when collisions are neglected. Allowing for collisional dissipation in the leading order distribution function around the separatrix resolves this discontinuity, smoothing the density distribution. The overall effect of the polarisation current on the NTM threshold is then combined from the outer contributions that exist outside the layer, as well as the separatrix layer piece, and self-consistently accounts for the electrostatic potential reconstructed from plasma quasi-neutrality. The corresponding NTM threshold is quantified and compared with previous predictions of (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001, Dudkovskaia et al 2023 Nucl. Fusion 63 016020).

Effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes in tokamak plasmas with reversed magnetic shear

Effects of plasma radiation on the nonlinear evolution of neo-classical double tearing modes (NDTMs) in tokamak plasmas with reversed magnetic shear are numerically investigated based on a set of reduced magnetohydrodynamics (MHD) equations. Cases with different separations Δ rs = |r s2–r s1| between the two same rational surfaces are considered. In the small Δ rs cases, the plasma radiation destabilizes the NDTMs and makes the kinetic energy still grow gradually in the late nonlinear phase. Moreover, the NDTM harmonics with high mode numbers reach a high level in the presence of plasma radiation, forming a broad spectrum of MHD perturbations that induces a radially broadened region of MHD turbulence. As a result, the profiles of safety factors also enter a nonlinear oscillation phase. In the intermediate Δ rs case, the plasma radiation can advance the explosive burst of kinetic energy that results from the fast driven reconnection between the two rational surfaces, because it can further promote the destabilizing effects of bootstrap current perturbation on the magnetic island near the outer rational surfaces. In the large Δ rs case, through destabilizing the outer islands significantly, the plasma radiation can even induce the explosive burst in the reversed magnetic shear configuration where the burst cannot be induced in the absence of plasma radiation.

Influence of two simultaneous driven currents on multiple tearing modes in tokamak plasmas

The influence of two driven currents simultaneously and respectively imposed on the m/n = 2/1 and 3/2 resistive tearing modes in tokamak plasmas is researched by using a three-dimensional toroidal magnetohydrodynamic code CLT. The simulation results show that using two suitable driven currents can better suppress multiple tearing modes than using only one of the two driven currents. When the two suitable driven currents are simultaneously imposed on both the m/n = 2/1 and 3/2 modes, respectively, the two modes may be well suppressed. If only one of the driven currents is imposed on the m/n = 2/1 mode, then the m/n = 2/1 mode may be well suppressed but the m/n = 3/2 mode may be not. Conversely, if only the other of the two driven currents is imposed on the m/n = 3/2 mode, both the two modes may be not suppressed. Moreover, it should be noted that the parameters of using two driven currents to suppress multiple tearing modes must be appropriate; otherwise, some new modes (such as m/n = 5/3 mode) may be excited and grown due to the interaction among the driven currents and multiple modes.

Multi-harmonic Rutherford island theory

Rutherford island theory, which governs the nonlinear evolution of tearing modes in tokamak plasmas, is generalized to take into account situations in which the conventional one-harmonic approximation is not valid. The analysis incorporates non-inductive currents driven by radio frequency (RF) electromagnetic waves injected into the plasma. A multi-harmonic tearing mode dispersion relation is derived that takes the form of a nonlinear inhomogeneous matrix eigenvalue problem. The dispersion relation is solved in the so-called two-harmonic approximation, in which only the principal Fourier harmonic of the perturbed magnetic flux and its first overtone are included in the calculation. In the absence of RF current drive, the nonlinear behavior of a tearing mode predicted in the two-harmonic approximation does not differ substantially from that predicted in the one-harmonic approximation. On the other hand, RF current drive that is sufficiently localized in the vicinity of the O-points of the mode's magnetic island chain is capable of triggering bifurcations of the O-points (which is impossible in the one-harmonic approximation). However, the current drive is incapable of triggering bifurcations of the island X-points. This finding is significant because Bardóczi and Evans [Phys. Rev. Lett. 126, 085003 (2021)] recently observed bifurcations of magnetic island chain O-points in the presence of RF current drive in the DIII-D tokamak but did not observe bifurcations of the X-points. Finally, the changes in the topology of the magnetic island flux-surfaces induced by RF current drive are found to facilitate the stabilization of the tearing mode.

Effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes in tokamak plasmas

The effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes are investigated based on a set of reduced magnetohydrodynamic equations. It is found that the radiation can reduce the pressure near the rational surface. During the nonlinear evolution, the magnitude of perturbed bootstrap current is drastically enhanced in the presence of the radiation. Besides, the radiation can increase the growth rate of the magnetic islands by diminishing the pressure, such that the magnetic islands do not saturate compared with that without radiation. On the other hand, with the increase of the ratio of parallel to perpendicular transport coefficient the reduction of pressure can further increase the growth rate of magnetic islands in the presence of plasma radiation. Finally, the mechanisms of the destabilizing effects driven by the radiation are discussed in detail as well.

Destabilization and nonlinear interaction of tearing modes in tokamak plasmas with locally reversed shear

Linear destabilization and nonlinear dynamics of m/n = 2 tearing modes in tokamak plasmas with locally reversed shear have been investigated in a reduced magnetohydrodynamic model. It is found that a transformation from the single tearing mode structure to the global double tearing mode structure takes place depending on the local shear parameter. The resistivity scaling law of the mode growth rate also changes from ∼SHp−3/5 to ∼ SHp−1/3 with qmin decreasing, where SHp is the magnetic Reynolds number, and qmin is the local minimum q value at position outsider q = 2 surfaces. Nonlinear simulation shows that once qmin < 2, the fast growing islands on the outer rational surfaces interact each other and trigger a plasmoid instability, which can couple with the inner tearing mode and generate a turbulent structure finally. This might provide an implication for understanding of relative nonlinear physics in ITER or astrophysical plasmas.

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.

Influence of the poloidal equilibrium flow and flow shear on the tearing mode instabilities in tokamak plasmas

The effect of the poloidal equilibrium flow and flow shear on the tearing mode instabilities for tokamak plasmas is investigated. The vorticity equation is derived and approximately solved for large poloidal mode numbers (m). Asymptotic matching of the inner solution to the outer solution can approximately give the classical tearing mode stability index Δ′. For typical plasma parameters with positive flow shear, we notice that the poloidal mean flows have a beneficial effect on the classical tearing mode and vice versa. To study the modes with arbitrary poloidal mode numbers, we numerically solve the vorticity equation for delta prime (Δ′) for typical plasma parameters with positive flow shear at the rational surface and the resulting Δ′ with large m also decreases with increasing poloidal flow velocity, consistent with the approximate analytical large m results. Our numerical calculations indicate that the poloidal mean flow with positive flow shear has beneficial influence on the stabilization of classical tearing modes in tokamak plasmas.

Fast island phase identification for tearing mode feedback control on J-TEXT tokamak.

A new method to control the tearing mode (TM) in tokamaks has been proposed [Q. Hu and Q. Yu, Nucl. Fusion 56, 034001 (5pp.) (2016)], according to which, the external resonant magnetic perturbation needs to be applied in certain magnetic island phase regions. Therefore, it is very important to identify the helical phase of magnetic islands in real time. The TM in tokamak plasmas is normally rotating and carries magnetic oscillations, which are known as Mirnov oscillations and can be detected by Mirnov probes. When the O-point or X-point of the magnetic island passes through the probe, the signal will experience a zero-crossing. A poloidal Mirnov probe array and a corresponding island phase identification method are presented. A field-programmable gate array is used to provide the magnetic island helical phase in real time by using multichannel zero crossing detection. This system has been developed on the J-TEXT tokamak and works well. This paper introduces the establishment of the fast magnetic island phase identifying system.

A resistive magnetodynamics analysis of sawtooth driven tearing modes in tokamak plasmas

In this paper, a resistive magnetohydrodynamics model is applied to study the effect of sawtooth driven on classical/neoclassical tearing modes in tokamak plasmas. In a model of forced reconnection, the sawtooth is considered as a boundary disturbance for m>1 modes and causes the islands growth of m/n = 2/1 and 3/2 modes through toroidal coupling. Theoretical and numerical analyses show that the linear growth of the modes is driven by precursors of the sawtooth through the linear mode coupling, while differential rotation has great effect on both the linear and the nonlinear development of the modes. It is believed that the tearing mode can be suppressed by control of the sawtooth by radio frequency heating or current drive.

An improved neoclassical drift-magnetohydrodynamical fluid model of helical magnetic island equilibria in tokamak plasmas

The effect of the perturbed ion polarization current on the stability of neoclassical tearing modes in tokamak plasmas is calculated using an improved, neoclassical, four-field, drift-magnetohydrodynamical model. The calculation involves the self-consistent determination of the pressure and scalar electric potential profiles in the vicinity of the associated magnetic island chain, which allows the chain's propagation velocity to be fixed. Two regimes are considered. First, a regime in which neoclassical ion poloidal flow damping is not strong enough to enhance the magnitude of the polarization current (relative to that found in slab geometry). Second, a regime in which neoclassical ion poloidal flow damping is strong enough to significantly enhance the magnitude of the polarization current. In both regimes, two types of solution are considered. First, a freely rotating solution (i.e., an island chain that is not interacting with a static, resonant, magnetic perturbation). Second, a locked solution (i.e., an island chain that has been brought to rest in the laboratory frame via interaction with a static, resonant, magnetic perturbation). In all cases, the polarization current is found to be either always stabilizing or stabilizing provided that ηi≡dlnTi/dlnne does not exceed some threshold value. In certain ranges of ηi, the polarization current is found to have a stabilizing effect on a freely rotating island, but a destabilizing effect on a corresponding locked island.

Phase locking of multi-helicity neoclassical tearing modes in tokamak plasmas

The attractive “hybrid” tokamak scenario combines comparatively high q95 operation with improved confinement compared with the conventional H98,y2 scaling law. Somewhat unusually, hybrid discharges often exhibit multiple neoclassical tearing modes (NTMs) possessing different mode numbers. The various NTMs are eventually observed to phase lock to one another, giving rise to a significant flattening, or even an inversion, of the core toroidal plasma rotation profile. This behavior is highly undesirable because the loss of core plasma rotation is known to have a deleterious effect on plasma stability. This paper presents a simple, single-fluid, cylindrical model of the phase locking of two NTMs with different poloidal and toroidal mode numbers in a tokamak plasma. Such locking takes place via a combination of nonlinear three-wave coupling and conventional toroidal coupling. In accordance with experimental observations, the model predicts that there is a bifurcation to a phase-locked state when the frequency mismatch between the modes is reduced to one half of its original value. In further accordance, the phase-locked state is characterized by the permanent alignment of one of the X-points of NTM island chains on the outboard mid-plane of the plasma, and a modified toroidal angular velocity profile, interior to the outermost coupled rational surface, which is such that the core rotation is flattened, or even inverted.

Development of a high power diplexer with short-slotted metal half mirrors for electron cyclotron current drive

A new type wideband diplexer as a fast switching device of high power millimeter wave has been developed for an electron cyclotron current driving system. A main purpose of fast switching is a stabilization of neoclassical tearing mode in tokamak plasmas. The short-slotted metal half mirror, which is one of the key components of a wideband diplexer is proposed. Two types of short-slotted metal half mirrors were designed and tested. One is periodic slot, and the other is non-periodic slot in a longitudinal direction. The switching operation of a mock-up diplexer with short-slotted metal half mirrors was verified at the frequency band from 169.5GHz to 170.5GHz at low power.

Hybrid simulation of energetic particle effects on tearing modes in tokamak plasmas

The effects of energetic ions on stability of tearing mode are investigated by global kinetic/MHD hybrid simulations in a low beta tokamak plasma. The kinetic effects of counter circulating energetic ions from the non-adiabatic response are found to be strongly destabilizing while the effects from the adiabatic response are stabilizing. The net effect with both adiabatic and non-adiabatic contributions is destabilizing. On the other hand, the kinetic effects of co-circulating energetic ions from the non-adiabatic response are calculated to be weakly stabilizing while the corresponding adiabatic contribution is destabilizing for small energetic ion beta. The net effect is weakly stabilizing. The dependence of kinetic effects on energetic ion beta, gyroradius, and speed is studied systematically and the results agree in large part with the previous analytic results for the kinetic effects of circulating particles. For trapped energetic ions, their effects on tearing mode stability are dominated by the adiabatic response due to large banana orbit width and strong poloidal variation of particle pressure. The net effect of trapped energetic particles on tearing modes is much more destabilizing as compared to that of counter circulating particles at the same beta value.

The influence of the ion polarization current on magnetic island stability in a tokamak plasma

The influence of the ion polarization current on the stability of a constant-ψ magnetic island in a tokamak plasma is investigated numerically using a reduced two-fluid model in two-dimensional slab geometry. The polarization current is found to be negligibly small when the island is either too narrow or too wide. However, under certain circumstances, there exists an intermediate regime in which the polarization current is appreciable, and has a stabilizing influence on the island. This effect may account for the metastable nature of neoclassical tearing modes in tokamak plasmas.

Nonlinear three-dimensional MHD simulations of tearing modes in tokamak plasmas

The comprehension of the dynamics of classical and neoclassical tearing modes is a key issue in high-performance tokamak plasmas. Avoiding these instabilities requires a good knowledge of all the physical mechanisms involved in their linear and/or nonlinear onset. Our tridimensional time evolution code XTOR, which solves the full magnetohydrodynamic (MHD) equations including thermal transport, is used to tackle this difficult problem. In this paper, to show the state of art in full-scale nonlinear MHD simulations of tokamak plasmas, we investigate the effect of plasma curvature on the tearing mode dynamics. For a realistic picture of this dynamics, heat diffusion is required in the linear regimes as well, as in the nonlinear regimes. We present a new dispersion relation including perpendicular and parallel transport, and show that it matches the linear and nonlinear regimes. This leads to a new tearing mode island evolution equation including curvature effects, valid for every island size in tokamak plasmas. This equation predicts a nonlinearly unstable regime for tearing instabilities, i.e. a regime which is linearly stable, but where the tearing mode can be destabilized nonlinearly by a finite-size seed island. These theoretical predictions are in good agreement with XTOR simulations. In particular, the nonlinear instability due to curvature effects is reproduced. Our results have an important impact on the onset mechanism of neoclassical tearing modes. They indeed predict that curvature effects lead to a resistive MHD threshold.

Modelling of macroscopic magnetic islands in tokamaks

The article presents experimental and theoretical investigations on thedynamics of sawteeth and neoclassical tearing modes in tokamakplasmas. The main findings of these investigations are: (1) Theexperimental validation, on the basis of FTU and TCV data, of a model for the prediction of the sawtooth period and amplitude; (2) the importance of diamagnetic effects in determining the threshold for sawtoothcrashes and the rotation of non-linear tearing modes; (3) a clarification of collisionless reconnection processes, in particular the role of phase mixing in association with magnetic island growth and saturation in dissipationless regimes. The interplay between ECRH and macroscopic island dynamics is alsodiscussed.

Helical temperature perturbations associated with tearing modes in tokamak plasmas

An investigation is made into the electron temperature perturbations associated with tearing modes in tokamak plasmas. It is found that there is a critical magnetic island width below which the conventional picture where the temperature is flattened inside the separatrix is invalid. This effect comes about because of the stagnation of magnetic field lines in the vicinity of the rational surface and the finite parallel thermal conductivity of the plasma. Islands whose widths lie below the critical value are not destabilized by the perturbed bootstrap current, unlike conventional magnetic islands. This effect may provide an explanation for some puzzling experimental results regarding error field-induced magnetic reconnection. The critical island width is found to be fairly substantial in conventional tokamak plasmas, provided that the long mean-free path nature of parallel heat transport and the anomalous nature of perpendicular heat transport are taken into account in the calculation.

Stability of tearing modes in tokamak plasmas

The stability properties of m≥2 tearing instabilities in tokamak plasmas are analyzed. A boundary layer theory is used to find asymptotic solutions to the ideal external kink equation, which are used to obtain a simple analytic expression for the tearing instability parameter Δ′. This calculation generalizes previous work on this topic by considering more general toroidal equilibria (however, toroidal coupling effects are ignored.) Constructions of Δ′ are obtained for plasmas with finite beta and for islands that have nonzero width. A simple heuristic estimate is given for the value of the saturated island width when the instability criterion is violated. A connection is made between the calculation of the asymptotic matching parameter in the finite beta and island width case to the nonlinear analog of the Glasser effect [Phys. Fluids 18, 875 (1975)].