Sawtooth-like oscillations and steady states caused by the m/n=2/1 double tearing mode

The sawtooth-like oscillations resulting from the m/n=2/1 double tearing mode (DTM) are numerically investigated through the three-dimensional, toroidal, nonlinear resistive-MHD code (CLT). We find that the nonlinear evolution of the m/n=2/1 DTM can lead to sawtooth-like oscillations, which are similar to those driven by the kink mode. The perpendicular thermal conductivity and the external heating rate can significantly alter the behaviors of the DTM driven sawtooth-like oscillations. With a high perpendicular thermal conductivity, the system quickly evolves into a steady state with m/n=2/1 magnetic islands and helical flow. However, with a low perpendicular thermal conductivity, the system tends to exhibit sawtooth-like oscillations. With a sufficiently high or low heating rate, the system exhibits sawtooth-like oscillations, while with an intermediate heating rate, the system quickly evolves into a steady state. At the steady state, there exist the non-axisymmetric magnetic field and strong radial flow, and both are with helicity of m/n=2/1. Like the steady state with m/n=1/1 radial flow, which is beneficial for preventing the Helium ash accumulation in the core, the steady state with m/n=2/1 radial flow might also be a good candidate for the advanced steady-state operations in future fusion reactors. We also find that the behaviors of the sawtooth-like oscillations are almost independent of Tokamak geometry, which implies that the steady state with saturated m/n=2/1 islands might exist in different Tokamaks.

Prevention of ECCD triggering explosive bursts in reversed magnetic shear tokamak plasmas for disruption avoidance

The explosive burst excited by neoclassical tearing mode (NTM) is one of the possible candidates of disruptive terminations in reversed magnetic shear (RMS) tokamak plasmas. For the purpose of disruption avoidance, numerical investigations have been implemented on the prevention of explosive burst triggered by the ill-advised application of electron cyclotron current drive (ECCD) in RMS configuration. Under the situation of controlling NTMs by ECCD in RMS tokamak plasmas, a threshold in EC driven current has been found. Below the threshold, not only are the NTM islands not effectively suppressed, but also a deleterious explosive burst could be triggered, which might contribute to the major disruption of tokamak plasmas. In order to prevent this ECCD triggering explosive burst, three control strategies have been attempted in this work and two of them have been recognized to be effective. One is to apply differential poloidal plasma rotation in the proximity of outer rational surface during the ECCD control process; The other is to apply two ECCDs to control NTM islands on both rational surfaces at the same time. In the former strategy, the threshold is diminished due to the modification of classical TM index. In the latter strategy, the prevention is accomplished as a consequence of the reduction of the coupling strength between the two rational surfaces via the stabilization of inner islands. Moreover, the physical mechanism behind the excitation of the explosive burst and the control processes by different control strategies have all been discussed in detail.

Effect of poloidal equilibrium flow and pressure gradient on the m/n = 2/1 tearing mode

The effect of equilibrium poloidal flow and pressure gradient on the m/n = 2/1 (m is the poloidal mode number and n is the toroidal mode number) tearing mode instability for tokamak plasmas is investigated. Based on the condition of ≠0 ( is plasma pressure), the radial part of motion equation is derived and approximately solved for large poloidal mode numbers (m). By solving partial differential equation (Whittaker equation) containing second order singularity, the tearing mode stability index Δ′ is obtained. It is shown that, the effect of equilibrium poloidal flow and pressure gradient has the adverse effect on the tearing mode instability when the pressure gradient is nonzero. The poloidal equilibrium flow with pressure perturbation partially reduces the stability of the classical tearing mode. But the larger pressure gradient in a certain poloidal flow velocity range can abate the adverse influence of equilibrium poloidal flow and pressure gradient. The numerical results do also indicate that the derivative of pressure gradient has a significant influence on the determination of instability region of the poloidal flow with pressure perturbation.

Transport and losses of fusion-born alpha particles in the presence of tearing modes using the new Toroidal Accelerated P Article Simulator (TAPAS)

The transport and losses of fusion-born alpha particles is studied in the presence of a single-helicity tearing mode, characterized by (m=2,n=1). The analysis is performed by means of the recently developed Toroidal Accelerated PArticle Simulator (TAPAS). Although such modes have been usually believed to result only in a local flattening of the radial profiles, it is shown that the density profile can exhibit a global modification leading to significant losses of alpha particles. This is due to the fact that, although the magnetic field does not exhibit any chaotic behaviour, the trajectories of alpha particles do, as revealed by their Poincaré maps. Such result is in qualitative agreement with past observations and simulations of energetic particles generated by neutral beam injection in TFTR, DIII-D and AUG tokamaks. In-depth analysis is carried out to characterize the impact of the tearing mode on the transport and losses of fusion-born alpha-particles with a realistic density profile. The impact of the amplitude is evidenced. Moreover, the effect of the island rotation frequency is assessed based on a detailed analysis of the linear resonances in phase-space, in agreement with the simulation results. Finally, the probability density function of the exit time has been computed and the transport of alpha particles has been found to be anomalous.

Integrated control of individual plasma scalars with simultaneous Neoclassical Tearing-Mode suppression

Simulations using the Control-Oriented Transport SIMulator (COTSIM) and DIII-D experiments have been carried out to demonstrate the performance of a novel integrated-control architecture for simultaneous regulation of individual-scalar magnitudes. The individual scalars considered in this work include kinetic variables, such as the thermal stored-energy or volume-average toroidal rotation, and magnetic variables such as the safety factor profile at different spatial locations. Separate control algorithms have been designed independently for each of these individual variables that use robust, nonlinear control techniques. In addition, the individual-scalar controllers have been integrated with Neoclassical Tearing-Mode (NTM) suppression algorithms, supervisory and exception handling algorithms, and an actuator manager, both within COTSIM and in the Plasma Control System (PCS) of the DIII-D tokamak. The resulting architecture has a high level of integration and some of the functionalities that will be required to fulfill the advanced-control requirements anticipated for ITER. Initial simulations using COTSIM suggest that the plasma performance and its Magneto-HydroDynamic (MHD) stability may be improved under integrated feedback control. These simulation results also show good qualitative agreement with DIII-D experimental results in the steady-state high-$q_{min}$ scenario, which is one of the candidates for steady-state operation in ITER. By means of individual-scalar feedback-control techniques in conjunction with NTM-suppression techniques, the confinement deterioration caused by NTMs in these scenarios may be significantly ameliorated.

Zonal flow generation and toroidal Alfvén eigenmode excitation due to tearing mode induced energetic particle redistribution

Generation of the n = 0 zonal flow and excitation of the n = 1 toroidal Alfvén eigenmode (TAE) due to the redistribution of energetic particles (EPs) by the m/n = 2/1 tearing mode (TM) are systematically studied with the hybrid drift-kinetic magnetohydrodynamic (MHD) simulations (m and n represent the poloidal and toroidal mode number, respectively). In the presence of the m/n = 2/1 TM, the amplitude of the n = 1 TAE shows a slower decay after its first saturation due to the wave-particle nonlinearity and the nonlinear generation of the n = 0 & higher-n (n ≥ 2) sidebands. Meanwhile, a strong n = 0 zonal flow component is nonlinearly generated when both TAE and TM grow to large amplitudes. The redistribution of EPs by the m/n = 2/1 magnetic island results in a continuous drive on the background plasma, and finally produces the zonal flow through the MHD nonlinearity. In addition, the large m/n = 2/1 magnetic island is found to be responsible for the formation of the strong spatial gradient of the EP distribution through the resonance between EPs and TM, which can lead to burst of unstable TAE and destabilization of originally stable TAE.

MHD simulations of cold bubble formation from 2/1 tearing mode during massive gas injection in a tokamak

Massive gas injection (MGI) experiments have been carried out in many tokamaks to study disruption dynamics and mitigation schemes. Two events often observed in those experiments are the excitation of the m = 2, n = 1 magnetohydrodynamic (MHD) mode, and the formation of cold bubble structure in the temperature distribution before the thermal quench (TQ). Here m is the poloidal mode number, n the toroidal mode number. The physics mechanisms underlying those phenomena, however, have not been entirely clear. In this work, our recent NIMROD simulations of the MGI process in a tokamak have reproduced the main features of both events, which has allowed us to examine and establish the causal relation between them. In these simulations, the 3/1 and 2/1 islands are found to form successively after the arrival of impurity ion cold front at the corresponding q = 3 and q = 2 rational surfaces. At the interface between impurity and plasma, a local thin current sheet forms due to an enhanced local pressure gradient and moves inward following the gas cold front, this may contribute to the formation of a dominant 2/1 mode. Following the growth of the 2/1 tearing mode, the impurity penetration into the core region inside the q = 2 surface gives rise to the formation of the cold bubble temperature structure and initiates the final TQ. A subdominant 1/1 mode developed earlier near the q = 1 surface alone does not cause such a cold bubble formation, however, the exact manner of the preceding impurity penetration depends on the nature of the 1/1 mode: kink-tearing or quasi-interchange.

Probing Current Sheet Instabilities from Flare Ribbon Dynamics

The presence of current sheet instabilities, such as the tearing mode instability, are needed to account for the observed rate of energy release in solar flares. Insights into these current sheet dynamics can be revealed by the behavior of flare ribbon substructure, as magnetic reconnection accelerates particles down newly reconnected field lines into the chromosphere to mark the flare footpoints. Behavior in the ribbons can therefore be used to probe processes occurring in the current sheet. In this study, we use high-cadence (1.7 s) IRIS Slit Jaw Imager observations to probe for the growth and evolution of key spatial scales along the flare ribbons—resulting from dynamics across the current sheet of a small solar flare on 2016 December 6. Combining analyses of spatial scale growth with Si iv nonthermal velocities, we piece together a timeline of flare onset for this confined event, and provide evidence of the tearing mode instability triggering a cascade and inverse cascade toward a power spectrum consistent with plasma turbulence.