Nonlinear Interaction of Edge-Localized Modes and Turbulent Eddies in Toroidal Plasma undern=1Magnetic Perturbation

Abstract

The effect of static n ¼ 1 resonant magnetic perturbation (RMP) on the spatial structure and temporal dynamics of edge-localized modes (ELMs) and edge turbulence in tokamak plasma has been investigated. Two-dimensional images measured by a millimeter-wave camera on the KSTAR tokamak revealed that the coherent filamentary modes (i.e., ELMs) are still present in the edge region when the usual large scale collapse of the edge confinement, i.e., the ELM crash, is completely suppressed by n ¼ 1 RMP. Cross-correlation analyses on the 2D images show that (1) the RMP enhances turbulent fluctuations in the edge toward the ELM-crash-suppression phase, (2) the induced turbulence has a clear dispersion relation for wide ranges of wave number and frequency, and (3) the turbulence involves a net radially outward energy transport. Nonlinear interactions of the turbulent eddies with the coexisting ELMs are clearly observed by bispectral analysis, which implies that the exchange of energy between them may be the key to the prevention of large scale crashes.

Non-linear modeling of the threshold between ELM mitigation and ELM suppression by resonant magnetic perturbations in ASDEX upgrade

“…This rotation braking likely induces the braking of the modes: edge modes are forced to be in phase with the penetrated mode induced by RMPs and thus to become static. The mode penetration inducing the sudden braking of the electron perpendicular velocity was observed in ELM suppression regimes in the experiments of DIII-D [29,30] and KSTAR [31,32]. The reduction below 1km/s of the velocity of saturated edge modes observed in non-bursting ELM suppression regimes of KSTAR [31,32], as well as the phase-locking of edge peeling-kink modes with static RMPs in grassy-ELM suppression regimes of DIII-D [33] is consistent with the edge mode locking found in this modeling.…”

Nonlinear wave interactions generate high-harmonic cyclotron emission from fusion-born protons during a KSTAR ELM crash

“…For general information see [34][35][36][37] and for plasma-specific applications see, for example, [37,[42][43][44][45]. An early account of the application of higher order spectral techniques to plasma physics is given in [38].…”

“…The bicoherence defined by equation (B.2) measures the strength of nonlinear wave coupling only, whereas equation (B.1) measures the strength of nonlinear energy flow. Bispectral analysis has been successfully applied to the MCI [23] and experimental plasma measurements [42][43][44], including those in the KSTAR tokamak [45].…”

Effect of time-varying flow-shear on the nonlinear stability of the boundary of magnetized toroidal plasmas

“…11 To study the dynamics of coupled modes P 1 and P 2 , we derived equations (12)-(13). We confirmed that the linear growth terms are crucial to determine the long-time behavior of P 1 and P 2 (Figs.5-6).…”

“…Magnetic perturbations have been used successfully to mitigate or suppress the crash [9][10][11] but the underlying mechanisms of mitigation and suppression are still unclear. Accordingly, it is crucial to understand the dynamics of ELM for more reliable and robust methods to avoid the crash.…”