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The effectiveness of multiple electron cyclotron resonance (ECR) harmonics has been thoroughly investigated in context of high current drive efficiency, generally observed in fully non-inductive operation of the low aspect ratio EXL-50 spherical tokamak (ST) powered by electron cyclotron (EC) waves. The Fokker-Plank equation is numerically solved to obtain electron distribution function, under steady state of the relativistic nonlinear Coulomb collision and quasi-linear diffusion operators, for calculating plasma current driven by the injected EC wave. For the extra-ordinary EC wave, simulation results unfold a mechanism by which electrons moving around the cold second harmonic ECR layer strongly resonate with higher harmonics via the relativistic Doppler shifted resonance condition. This feature is in fact evident above a certain value of input EC wave power in simulation, indicating it to be a non-linear phenomenon. Similar to the experimental observation, high efficiency in current drive (over 1 A/W) has indeed been found in simulation for a typical low density ($\sim 1\times10^{18}~m^{-3}$), low temperature ($\lesssim 100$ eV) plasma of EXL-50 by taking into account multi-pass absorptions in our simulation model. However, such characteristic is not found in the ordinary EC-wave study for both single-pass and multi-pass simulations, suggesting it as inefficient in driving current on our ST device., Comment: 22 pages, 15 figures. Submitted to the Nuclear Fusion journal

To help reveal the complete picture of linear kinetic drift modes, four independent numerical approaches, based on integral equation, Euler initial value simulation, Euler matrix eigenvalue solution and Lagrangian particle simulation, respectively, are used to solve the linear gyrokinetic electrostatic drift modes equation in Z-pinch with slab simplification and in tokamak with ballooning space coordinate. We identify that these approaches can yield the same solution with the difference smaller than 1\%, and the discrepancies mainly come from the numerical convergence, which is the first detailed benchmark of four independent numerical approaches for gyrokinetic linear drift modes. Using these approaches, we find that the entropy mode and interchange mode are on the same branch in Z-pinch, and the entropy mode can have both electron and ion branches. And, at strong gradient, more than one eigenstate of the ion temperature gradient mode (ITG) can be unstable and the most unstable one can be on non-ground eigenstates. The propagation of ITGs from ion to electron diamagnetic direction at strong gradient is also observed, which implies that the propagation direction is not a decisive criterion for the experimental diagnosis of turbulent mode at the edge plasmas., Comment: 12 pages, 10 figures, accept by Physics of Plasmas

First principle gyrokinetic simulation of the edge turbulent transport in toroidal plasmas finds a reverse trend in the turbulent transport coefficients under strong gradients. It is found that there exist both linear and nonlinear critical gradients for the nonmonotonicity of transport characteristics. The discontinuity of transport flux slope around the turning gradient shows features of second order phase transition. Under strong gradient the most unstable modes are in non-ground eigenstates with unconventional mode structures, which significantly reduces the effective correlation length and thus reverse the transport trend. Our results suggest a completely new mechanism for the low to high confinement mode transition without invoking shear flow or zonal flow., Comment: 5 pages, 7 figures, accepted by Phys. Rev. Lett

With strong gradients in the pedestal of high confinement mode (H-mode) fusion plasmas, gyrokinetic simulations are carried out for the trapped electron and ion temperature gradient modes. A broad class of unconventional mode structures is found to localize at arbitrary poloidal positions or with multiple peaks. It is found that these unconventional ballooning structures are associated with different eigen states for the most unstable mode. At weak gradient (low confinement mode or L-mode), the most unstable mode is usually in the ground eigen state, which corresponds to a conventional ballooning mode structure peaking in the outboard mid-plane of tokamaks. However, at strong gradient (H-mode), the most unstable mode is usually not the ground eigen state and the ballooning mode structure becomes unconventional. This result implies that the pedestal of H-mode could have better confinement than L-mode., Comment: 5 pages, 6 figures