Double Tearing Modes Research Articles

Control of neo-classical double tearing modes by differential poloidal rotation in reversed magnetic shear tokamak plasmas

The control of neo-classical tearing modes (NTMs) by the differential rotation in the reversed magnetic shear (RMS) configuration with different separations between two rational surfaces is numerically studied by means of reduced magnetohydrodynamic (MHD) simulations. It is found that the differential rotation with a strong shear at the outer resonant surface can effectively suppress the explosive burst of double tearing modes (DTMs)/NTMs. Critical values of the strength of rotation to suppress the burst are also presented for different bootstrap current fractions . Furthermore, a couple of measurable parameters , corresponding respectively to the triangularity and elongation of the magnetic islands at the outer resonant surface, are introduced to characterize the deformation of islands in the nonlinear phase. It is found that the triangularity is more likely to precisely predict the onset of burst than the island width and elongation . For a given , the critical value of triangularity is obtained by scanning different plasma parameters. Establishing such a database of is helpful to effectively control the development of NTMs in the RMS experimental discharges.

Effects of energetic ions on double tearing modes in reversed shear plasmas

The modified dispersion relation of qs = m/n double tearing modes (DTMs) with trapped energetic ions is derived by the matching procedure of mode structures in the ideal region and resistive layer. It is found that a mode transition between the DTM and the fishbone-like mode can be triggered, depending on fast ion driving, which provides a possible explanation for the observation of experiments (Günter et al 1999 Nucl. Fusion 39 1793; Maget et al 2006 Nucl. Fusion 46 797). The resistivity scaling of DTMs is changed significantly by on/off-axis heating beams. The effects of beam energy, electron inertia, magnetic shear and plasma resistivity on the stability of the mode and mode transition are discussed in detail.

Effect of toroidal plasma rotation on double tearing modes in cylindrical geometry

The effect of toroidal plasma rotation on q = 3 double tearing modes (DTMs) was studied numerically in cylindrical geometry using the method of reduced magnetohydrodynamic simulation. The results indicate that toroidal plasma rotation can reduce the growth rate of DTMs, but the magnitude of toroidal velocity has weak effect, especially without shear. When the shear of toroidal velocity exists, the suppression effect becomes better. Whether the velocity flow has shear or not, the growth rate of DTMs decreases as the magnitude of toroidal velocity increases. With the increase of velocity shear, the DTMs grow slowly. And the suppression effect of toroidal plasma rotation in early growth and transition stage is better, which means that the toroidal plasma rotation can suppress the linear growth of islands. Furthermore, the toroidal plasma rotation can suppress the evolution of poloidal stream. And the toroidal velocity shear on the q = 3 rational surface is more dominant than the magnitude of toroidal velocity in determining the DTM characteristics.

Influence of driven current on resistive tearing mode in Tokamaks

The influence of driven current on the m/n=2/1 resistive tearing mode is studied systematically using a three-dimensional toroidal magnetohydrodynamic code. A uniform driven current with Gaussian distribution in the radial direction is imposed around the unperturbed rational surface. It is found that the driven current can locally modify the profiles of the current and safety factor, such that the tearing mode becomes linearly stable. The stabilizing effect increases with the increase of the driven current Icd or the decrease of its width δcd, unless an excessively large driven current reverses the magnetic shear near the rational surface and drives other instabilities such as double or triple tearing modes. The stabilizing effect can be negligible or becomes reversed if the maximum driven current density is not at the unperturbed rational surface.

The effect of radial pressure force on rotating double tearing mode in compressible plasmas

The role of radial pressure force in the interlocking dynamics of double tearing modes (DTMs) is investigated by force balance analysis based on the compressible magnetohydrodynamics (MHD) model. It is found that the stability of symmetric DTMs is dominated by the radial pressure force rather than the field line bending force. Owing to the compressibility of rotating plasmas, unbalanced radial forces can just result in the rotating islands drift toward each other in the radial direction but do not trigger the explosive growth of the mode in the interlocking process, which is different from that of antisymmetric DTM without flow.

Nonlinear evolution of the Kelvin-Helmholtz instability in the double current sheet configuration

The nonlinear evolution of the Kelvin-Helmholtz (KH) instability driven by a radially antisymmetric shear flow in the double current sheet configuration is numerically investigated based on a reduced magnetohydrodynamic model. Simulations reveal different nonlinear fate of the KH instability depending on the amplitude of the shear flow, which restricts the strength of the KH instability. For strong shear flows far above the KH instability threshold, the linear electrostatic-type KH instability saturates and achieves a vortex flow dominated quasi-steady state of the electromagnetic (EM) KH turbulence with large-amplitude zonal flows as well as zonal fields. The magnetic surfaces are twisted significantly due to strong vortices but without the formation of magnetic islands. However, for the shear flow just over the KH instability threshold, a weak EM-type KH instability is saturated and remarkably damped by zonal flows through modifying the equilibrium shear flow. Interestingly, a secondary double tearing mode (DTM) is excited subsequently in highly damped KH turbulence, behaving as a pure DTM in a flowing plasma as described in Mao et al. [Phys. Plasmas 21, 052304 (2014)]. However, the explosive growth phenomenon is replaced by a gradually growing oscillation due to the extremely twisted islands. As a result, the release of the magnetic energy becomes slow and the global magnetic reconnection tends to be gentle. A complex nonlinear interaction between the EM KH turbulence and the DTMs occurs for the medium shear flows above the KH instability threshold, turbulent EM fluctuations experience oscillatory nonlinear growth of the DTMs, finally achieves a quasi-steady state with the interplay of the fluctuations between the DTMs and the EM KH instability.

Verification of gyrokinetic particle simulation of current-driven instability in fusion plasmas. III. Collisionless tearing mode

A finite-mass electron fluid model for low frequency electromagnetic fluctuations, particularly the collisionless tearing mode, has been implemented in the gyrokinetic toroidal code. Using this fluid model, linear properties of the collisionless tearing mode have been verified. Simulations verify that the linear growth rate of the single collisionless tearing mode is proportional to De2, where De is the electron skin depth. On the other hand, the growth rate of a double tearing mode is proportional to De in the parameter regime of fusion plasmas.

Study of nonlinear evolution of tearing modes induced by anomalous electron viscosity

The nonlinear development of double tearing modes (DTMs) induced by anomalous electron viscosity, which may be present in magnetically confined plasmas due to electromagnetic turbulence and structures such as braiding of magnetic field lines, in a periodic cylinder is simulated. Comparing the evolution of the helical magnetic flux contours, the nonlinear development of magnetic reconnection of the DTMs is studied for different distances between the two resonant rational flux surfaces. There are three clear phases in the nonlinear evolution of DTMs when the distance between the two resonant flux surfaces is large: linear growing, nonlinearly driven growing, and saturation. There are four phases when the distance is medium: linear growing, nonlinearly driven growing, fast growing, and decaying. Finally, there are three phases of evolution when the distance is quite small, which are different from the phases when the distance is large: linear growing, nonlinearly driven growing, and decaying,. The coupling between the fastest-growing modes at the two resonant surfaces drives the nonlinear evolution of the system.

Thermal synchrotron radiation from RRMHD simulations of the double tearing mode reconnection – application to the Crab flares

We study the magneto-hydrodynamic tearing instability occurring in a double current sheet configuration when a guide field is present. This is investigated by means of resistive relativistic magneto-hydrodynamic (RRMHD) simulations. Following the dynamics of the double tearing mode (DTM), we are able to compute synthetic synchrotron spectra in the explosive reconnection phase. The pulsar striped wind model represents a site where such current sheets are formed, including a guide field. The variability of the Crab nebula/pulsar system, seen as flares, can be therefore naturally explained by the DTM explosive phase in the striped wind. Our results indicate that the Crab GeV flare can be explained by the double tearing mode in the striped wind region if the magnetization parameter $\sigma$ is around $10^5$.

Effects of electron cyclotron current drive on the evolution of double tearing mode

The effects of electron cyclotron current drive (ECCD) on the double tearing mode (DTM) in slab geometry are investigated by using two-dimensional compressible magnetohydrodynamics equations. It is found that, mainly, the double tearing mode is suppressed by the emergence of the secondary island, due to the deposition of driven current on the X-point of magnetic island at one rational surface, which forms a new non-complete symmetric magnetic topology structure (defined as a non-complete symmetric structure, NSS). The effects of driven current with different parameters (magnitude, initial time of deposition, duration time, and location of deposition) on the evolution of DTM are analyzed elaborately. The optimal magnitude or optimal deposition duration of driven current is the one which makes the duration of NSS the longest, which depends on the mutual effect between ECCD and the background plasma. Moreover, driven current introduced at the early Sweet-Parker phase has the best suppression effect; and the optimal moment also exists, depending on the duration of the NSS. Finally, the effects varied by the driven current disposition location are studied. It is verified that the favorable location of driven current is the X-point which is completely different from the result of single tearing mode.

On the behavior of plasma with a negative current in the L-2M stellarator

The behavior of plasma with a negative current in the range of 5 kA ≤ |J| ≤ 16 kA in the L-2M stellarator is studied. Plasma is created and heated by means of electron cyclotron resonance heating (ECRH). Here, the definition “negative” stands for a toroidal current directed in such a way that it reduces the initial rotational transform µ in absolute value. It is shown that, only at relatively small values of the negative current (|J| ~ 6 kA), the increase in the shear leads to a reduction in electromagnetic turbulence. As |J| rises, the average level of magnetic fluctuations in the stationary phase of the discharge gradually increases. After ECRH is switched off (i.e., when plasma cools down), there is a time interval in which the amplitude of magnetic field fluctuations increases. No coherent three-dimensional modes (e.g., double tearing modes) that could accompany the penetration of the current into the plasma were observed. As for axisymmetric perturbations with m ≠ 0, analysis of the experimental data shows that they are absent at |J| ≤ 8 kA, appear in some discharges at |J| = 9 kA, and are observed in each discharge at |J| ≥ 10 kA. The frequency of these oscillations is on the order of 10 kHz, the poloidal mode number is m = 2, and the duration is 4–6 ms. The absence of oscillations with m = 1 and the small value of the external magnetic field for the m = 2 perturbation indicate that the radial size of the magnetic island is less than 1 cm. This, in turn, suggests that the radial profile of the plasma current changes with increasing |J|.

Nonlinear evolution of neo-classical tearing modes in reversed magnetic shear tokamak plasmas

Linear and nonlinear neo-classical double tearing modes (NDTMs) in the reversed magnetic shear configuration with different separations Δrs between two same rational surfaces are numerically studied by means of reduced magnetohydrodynamic simulations, taking into account different bootstrap current fractions fb. It is found that in the case of large Δrs, an explosive burst of fast reconnection, which was previously observed only in the intermediate Δrs case with fb = 0 (Ishii Y. et al 2002 Phys. Rev. Lett. 89 205002), can also be induced if the fraction of bootstrap current fb is sufficiently high. In the case of intermediate Δrs, such explosive bursts can effectively be brought forward, since the bootstrap current significantly destabilizes the tearing mode on the outer rational surface. In the case of small Δrs, higher order harmonics of the NDTMs become dominantly unstable in the linear phase, if fb continues increasing. In its nonlinear phase, the local modification of bootstrap current near the magnetic islands makes the islands move inwards, while the recovery of the Ohm current tends to make them move outwards. The different dynamics of complicated motions of magnetic islands (or rational surfaces) determined by these two effects are analysed in detail in the cases of different fb values.

Explosive reconnection of the double tearing mode in relativistic plasmas with application to the Crab nebula

The Crab pulsar and its surrounding nebula is a well-known relic of a massive star that exploded in 1054 AD. The Crab nebula was generally believed to be a good standard candle in gamma rays. Recently, this view has been challenged by sudden increases in the gamma-ray flux in a narrow spectral band within a few hundred MeV. These flares are short but powerful; their duration is between a few hours and up to several days with a rising/falling time of a few hours/days. To date it is neither clear what mechanism powers these flares nor where exactly in the nebula they should be located. However, recent models seem to favor emission sites inside the nebula. In the present work, we study the magneto-hydrodynamic tearing instability occurring in a double current sheet configuration with application to the Crab flares. This is investigated by means of resistive relativistic magneto-hydrodynamic simulations. These put some constraints on the maximum Lorentz factor of the striped wind, Γ≲150 and on the localization of the emission region, r ≈ 50 rL where rL = c/Ω is the light-cylinder radius, c is the speed of light and Ω is the rotation speed of the pulsar. Sites close to but outside the light-cylinder are favored in our model.

Intermittent bursts induced by double tearing mode reconnection

Reversed magnetic shear (RMS) configuration is assumed to be the steady-state operation scenario for the future advanced tokamaks like International Thermonuclear Experimental Reactor. In this work, we numerically discover a phenomenon of violent intermittent bursts induced by self-organized double tearing mode (DTM) reconnection in the RMS configuration during the very long evolution, which may continuously lead to annular sawtooth crashes and thus badly impact the desired steady-state operation of the future advanced RMS tokamaks. The key process of the intermittent bursts in the off-axis region is similar to that of the typical sawtooth relaxation oscillation in the positive magnetic shear configuration. It is interestingly found that in the decay phase of the DTM reconnection, the zonal field significantly counteracts equilibrium field to make the magnetic shear between the two rational surfaces so weak that the residual self-generated vortices of the previous DTM burst are able to trigger a reverse DTM reconnection by curling the field lines.

Bi-fluid and neoclassical effect on a Double-Tearing mode in Tore Supra

Tearing modes associated to hollow current profiles are prone to grow in moderate performance plasmas and often constrain the realization of non-inductive discharges in the Tore Supra tokamak, where long pulse duration is performed using Lower Hybrid waves for providing most of the plasma current. The prediction of MHD boundaries in such scenarios is complicated by the importance of diamagnetic effects, combined with curvature stabilization, which determine the stability of these modes. We show that diamagnetic effects, as well as neoclassical forces, are playing a key role in the linear and nonlinear regimes of Double-Tearing Modes on q = 5/3 and q = 2 in these experimental conditions. Detailed comparison with experimental measurements, combined with a scaling in plasma resistivity, give constraints about the experimental equilibrium. Resistive-Interchange Modes destabilized by diamagnetic rotation could also play a role in degrading the energy confinement in the negative magnetic shear region.

Zonal flow dynamics in the double tearing mode with antisymmetric shear flows

The generation dynamics and the structural characteristics of zonal flows are investigated in the double tearing mode (DTM) with antisymmetric shear flows. Two kinds of zonal flow oscillations are revealed based on reduced resistive magnetohydrodynamics simulations, which depend on the shear flow amplitudes corresponding to different DTM eigen mode states, elaborated by Mao et al. [Phys. Plasmas 20, 022114 (2013)]. For the weak shear flows below an amplitude threshold, vc, at which two DTM eigen states with antisymmetric or symmetric magnetic island structure are degenerated, the zonal flows grow oscillatorily in the Rutherford regime during the nonlinear evolution of the DTMs. It is identified that the oscillation mechanism results from the nonlinear interaction between the distorted islands and the zonal flows through the modification of shear flows. However, for the medium shear flows above vc but below the critical threshold of the Kelvin-Helmholtz instability, an oscillatory growing zonal flow occurs in the linear phase of the DTM evolution. It is demonstrated that the zonal flow oscillation originates from the three-wave mode coupling or a modulation instability pumped by two DTM eigen modes with the same frequency but opposite propagating direction. With the shear flows increasing, the amplitude of zonal flow oscillation increases first and then decreases, whilst the oscillation frequency as twice of the Doppler frequency shift increases. Furthermore, impacts of the oscillatory zonal flows on the nonlinear evolution of DTM islands and the global reconnection are also discussed briefly.

Nonlinear evolution of double tearing modes in tokamak plasmas via multiple helicity simulation

Nonlinear evolution of multiple double tearing modes (multi-DTMs) with different helicities (DHs) in several reversed magnetic shear configurations is investigated by employing a reduced magnetohydrodynamic model in cylindrical geometry. It is found that the basic characterizations of the nonlinear evolution process of the system depend on the linear unstable spectrum of multi-DTMs with DHs. In the case that the linear growth rates of multi-DTMs with DHs are comparable to each other, continuous bursts occur one after another due to a sequence of magnetic energy release induced by multi-DTMs reconnections on different pairs of resonant surfaces with DHs. Moreover, the overlapping of the magnetic island chains of multi-DTMs during the continuous bursts process results in the strong magnetic stochasticity in the off-axis region. Such unique nonlinear evolution of multi-DTMs with DHs cannot be reproduced by the single helicity simulation. However, in the case that the linear growth rates of DTMs with the dominant helicity are much larger than the counterparts of DTMs with the other helicities, the main nonlinear physical process obtained by the multiple helicity simulation can be reproduced by the single helicity simulation.

Explosive reconnection of double tearing modes in relativistic plasmas: application to the Crab flares

Abstract Magnetic reconnection associated to the double tearing mode is investigated by means of resistive relativistic magnetohydrodynamic simulations. A linearly unstable double current sheet system in two-dimensional Cartesian geometry is considered. For initial perturbations of large enough longitudinal wavelengths, a fast reconnection event is triggered by a secondary instability that is structurally driven by the non-linear evolution of the magnetic islands. The latter reconnection phase and time-scale appear to weakly depend on the plasma resistivity and magnetization parameter. We discuss the possible role of such explosive reconnection dynamics to explain the MeV flares observed in the Crab Pulsar nebula. Indeed, the time-scale and the critical minimum wavelength give constraints on the Lorentz factor of the striped wind and on the location of the emission region, respectively.

The effects of a shear flow on nonlinear evolutions of double tearing mode in Hall magnetohydrodynamics

Abstract The effects of a shear flow on nonlinear evolution of double tearing mode in Hall magnetohydrodynamics are investigated. The parallel shear flow displays a suppressing effect on the double tearing mode. Due to the effect of the shear flow, the relative displacements between the magnetic islands are changed, and therefore their mutual interactions become weak. Furthermore, the nonlinear impulsive growth phase of the double tearing mode is delayed with increasing the shear flow velocity. When the magnetic islands are pushing against each other, the width of current sheets decreases drastically, and therefore the Hall effects are dominant and the magnetic reconnection enhances greatly.

Error-field penetration in reversed magnetic shear configurations

Error-field penetration in reversed magnetic shear (RMS) configurations is numerically investigated by using a two-dimensional resistive magnetohydrodynamic model in slab geometry. To explore different dynamic processes in locked modes, three equilibrium states are adopted. Stable, marginal, and unstable current profiles for double tearing modes are designed by varying the current intensity between two resonant surfaces separated by a certain distance. Further, the dynamic characteristics of locked modes in the three RMS states are identified, and the relevant physics mechanisms are elucidated. The scaling behavior of critical perturbation value with initial plasma velocity is numerically obtained, which obeys previously established relevant analytical theory in the viscoresistive regime.