We present experimental observations suggesting that the non-diffusive avalanche-like events are a prevalent and universal process of the electron turbulent heat transport in tokamak core plasmas. They are observed in the low confinement mode and the weak internal transport barrier tokamak plasmas in the absence of magnetohydrodynamic instabilities. In addition, the electron temperature profile corrugation, which indicates the existence of the E × B shear flow layers, is clearly demonstrated as well as their dynamical interaction with the avalanche-like events. The measured width of the profile corrugation is around 45ρ i , which implies the mesoscale nature of the structure. a)

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Nonlinear bounce-averaged kinetic theory [B. H. Fong and T. S. Hahm, Phys. Plasmas 6, 188 (1999)] is used for magnetically trapped electron dynamics for the purpose of achieving efficient gyrokinetic simulations of Trapped Electron Mode (TEM) and Ion Temperature Gradient mode with trapped electrons (ITG-TEM) in shaped tokamak plasmas. The bounce-averaged kinetic equations are explicitly extended to shaped plasma equilibria from the previous ones for concentric circular plasmas, and implemented to a global nonlinear gyrokinetic code, Gyro-Kinetic Plasma Simulation Program (gKPSP) [J. M. Kwon et al., Nucl. Fusion 52, 013004 (2012)]. Verification of gKPSP with the bounce-averaged kinetic trapped electrons in shaped plasmas is successfully carried out for linear properties of the ITG-TEM mode and Rosenbluth-Hinton residual zonal flow [M. N. Rosenbluth and F. L. Hinton, Phys. Rev. Lett. 80, 724 (1998)]. Physics responsible for stabilizing effects of elongation on both ITG mode and TEM is identified using global gKPSP simulations. These can be understood in terms of magnetic flux expansion, leading to the effective temperature gradient R/LT(1−E′) [P. Angelino et al., Phys. Rev. Lett. 102, 195002 (2009)] and poloidal wave length contraction at low field side, resulting in the effective poloidal wave number kθρi/κ.

The linear physics of lower hybrid waves (LHWs) and their nonlinear interaction with particles through Landau damping are studied with the gyrokinetic electron and fully kinetic ion (GeFi) particle simulation model in the electrostatic limit. Unlike most other wave modes, the LHWs can resonantly interact with both electrons and ions, with the former being highly magnetized and latter nearly unmagnetized around the lower hybrid frequency. Direct interactions of LHWs with electrons and/or ions are investigated for cases with various k∥/k,Ti/Te, and wave amplitudes. In the linear electron Landau damping (ELD), the dispersion relation and the linear damping rate obtained from our simulation agree well with the analytical linear theory. As the wave amplitude increases, the nonlinear Landau effects are present, and a transition from strong decay at smaller amplitudes to weak decay at larger amplitudes is observed. In the nonlinear stage, the LHWs in the long time evolution finally exhibit a steady Bernstein-Greene-Kruskal mode, in which the wave amplitude is saturated above the noise level. While the resonant electrons are trapped in the wave field in the nonlinear ELD, the resonant ions are untrapped in the LHW time scales. The ion Landau damping is thus predominantly in a linear fashion, leading to a wave saturation level significantly lower than that in the ELD. On the long time scales, however, the ions are still weakly trapped. The results show a coupling between the LHW frequency and the ion cyclotron frequency during the long-time LHW evolution.

The first principle nonlinear gyrokinetic numerical simulation successfully reproduces the experimental observations of non-diffusive large scale avalanching events in a KSTAR MHD-quiescent L-mode plasma. Power law scaling of electron temperature fluctuation δT e and Hurst exponent factor H from simulation and experiment are in good agreement. In addition, the simulation verifies that the global pattern of mean zonal flow is corrugated with staircase-like structure and responsible for the creased profile of δT e, which is also observed in the experiment. We report on a novel finding that the zonal flow staircase constrains the radial extent of electron heat avalanches through shearing the electron temperature gradient fluctuation, while previous studies were mostly on ion heat transport.