The effects of magnetic island on toroidal ion temperature gradient mode instability

In this work, we have investigated the influences of magnetic island (MI) on electrostatic toroidal ion temperature gradient (ITG) mode, where the ions are described by gyro-kinetic equations including MI, and adiabatic approximation is used for electrons. The eigen-equation for short-wavelength toroidal ITG mode in Fourier-ballooning representation is derived, and the corresponding eigen-value as well as mode structure are solved. Both the flattening effects of MI on plasma pressure and MI-scale shear flow are considered. It is found that when only considering the flattening effects of MI, ITG mode can be stabilized as compared to the case without MI. While, the effective drive of toroidal ITG mode could be enhanced by including MI-scale flow, which indicates the dominant destabilizing by MI-scale flow over the stabilizing by flattening profile and results in higher growth rate than the case without MI. It is also found that the total flow shearing may prevent the ITG turbulence spreading from X-point of MI but not strong enough to prevent spreading from the seperatrix across O-point of larger MI via comparison between the flow shearing rate and the linear growth rate. Furthermore, the corresponding width of lowest-order mode structure in ballooning angle is slightly widened (narrowed) for the case without (with) MI-scale flow, as compared to the case without MI. Besides, the shifted even symmetry in ballooning angle is not qualitatively influenced by the presence of MI. The mode structure is radially asymmetric, but is symmetric with respect to the phase of MI at the O-point.

Spurious free thickness shear bulk acoustic resonators on lithium niobate using standard and broadband piston mode designs

This paper describes design and fabrication of sprious-free thickness shear bulk acoustic resonators (TSBARs) using the lithium niobate (LN) plate. Previously, the authors conjected from the experiment on the TSBAR that cutoff edges with crystal LN X-plane serve as ideal reflectors for the piston mode operation, and complete suppression is possible by adding the standard piston mode design to the other edges normal to the X-axis. Following to this conjecture, the traditional piston mode structure is designed by the traditional two-dimensional finite element method, and the TSBAR is fabricated following to the design. The experiment showed complete suppression of the transverse mode resonances, and the conjecture was verified.

Mode structure symmetry breaking of reversed shear Alfvén eigenmodes and its impact on the generation of parallel velocity asymmetries in energetic particle distribution

In this work, the gyrokinetic eigenvalue code LIGKA, the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of Reversed Shear Alfv\'en Eigenmodes (RSAEs). Using the parameters from an ASDEX-Upgrade plasma, a benchmark with the three different physical models for RSAE without and with Energetic Particles (EPs) is carried out. Reasonable agreement has been found for the mode frequency and the growth rate. Mode structure symmetry breaking (MSSB) is observed when EPs are included, due to the EPs' non-perturbative effects. It is found that the MSSB properties are featured by a finite radial wave phase velocity, and the linear mode structure can be well described by an analytical complex Gaussian expression $\Phi(s)=e^{- \sigma (s-s_0)^2}$ with complex parameters $\sigma$ and $s_0$, where $s$ is the normalized radial coordinate. The mode structure is distorted in opposite {manners} when the EP drive shifted from one side of $q_{min}$ to the other side, and specifically, a non-zero average radial wave number $\langle k_s\rangle$ with opposite signs is generated. The initial EP density profiles and the corresponding mode structures have been used as the input of HAGIS code to study the EP transport. The parallel velocity of EPs is generated in opposite directions, due to different values of the average radial wave number $\langle k_s\rangle$, corresponding to different initial EP density profiles with EP drive shifted away from the $q_{min}$.

Experimental evidence of nonlinear avalanche dynamics of energetic particle modes

Recent observations in HL-2A tokamak give new experimental evidences of energetic particle mode (EPM) avalanche. In a strong EPM burst, the mode structure propagates radially outward within two hundred Alfvén time, while the frequency of the dominant mode changes self-consistently to maximize wave-particle power exchange and mode growth. This suggests that significant energetic particle transport occurs in this avalanche phase, in agreement with theoretical framework of EPM convective amplification. A simplified relay runner model yields satisfactory interpretations of the measurements. The results can help understanding the nonlinear dynamics of energetic particle driven modes in future burning plasmas, such as ITER.

Nonlinear MHD simulation of core plasma collapse events in Wendelstein 7-X

Three-dimensional nonlinear MHD simulations study the core collapse events observed in a stellarator experiment, Wendelstein 7-X. In the low magnetic shear configuration like the Wendelstein 7-X, the rotational transform profile is very sensitive to the toroidal current density. The 3D equilibrium with localized toroidal current density is studied. If the toroidal current density follows locally in the middle of the minor radius, the rotational transform is also changed locally. Sometimes, the magnetic topology changes due to appearing the magnetic island. A full three-dimensional nonlinear MHD code studies the nonlinear behaviors of the MHD instability. It was found that the following sequence. At first, the high-n ballooning-type mode structure appears in the plasma core, and then the mode linearly grows. The high-n ballooning modes nonlinearly couple and saturate. The mode structure changes to the low-n mode. The magnetic field structure becomes strongly stochastic into the plasma core due to the nonlinear coupling in that phase. Finally, the plasma pressure diffuses along the stochastic field lines, and then the core plasma pressure drops. This is a crucial result to interpret the core collapse event by strong nonlinear coupling.