Overall entropy balances and radial dynamics for thermodynamic entropy and conventional fluctuation entropy are investigated by means of newly derived coupled equations and the full-f gyrokinetic simulations for toroidal flux-driven ion-temperature-gradient turbulence. When the equations are integrated over the radial direction, in the quasi-steady state, fluctuation entropy production due to collisional dissipation in velocity space and thermodynamic entropy reduction due to energy input/output in real space are found to be balanced through the generation of a heat flux and associated phase mixing. The cross-correlation analysis indicates that collisional dissipation occurs after the formation of fine-scale structures by phase mixing, while there exists an in-phase relationship between thermodynamic entropy production due to profile relaxation and heat flux. However, when the radial dynamics are retained in the equations, this relationship is found to be violated in regions exhibiting heat avalanches. This is because the thermodynamic entropy is dominated by advection, leading to a time lag between heat flux and temperature variation.
Full-f gyrokinetic simulations of ion temperature gradient (ITG) turbulence in the presence of a magnetic island are performed. A newly developed method for evaluating the flux-surface average is implemented to treat adiabatic electrons inside the magnetic island precisely. A neoclassical simulation below the threshold for linear ITG instability shows that the density profile does not relax at the O-point, although the ion temperature profile is flattened there. This results from the force balance in the direction of the magnetic field between the pressure gradient related to ion parallel motion and the mean radial electric field. A flux-driven ITG turbulence simulation shows a quasi-periodic transport reduction due to interaction between the background temperature profile and the vortex mode, which is a nonlinearly generated mesoscale structure with the same mode numbers as the magnetic island. These results indicate that not only the parallel streaming but also the equilibrium electric field and turbulence contribute significantly to profile formation around a magnetic island.
In this study, global gyrokinetic simulations of the toroidal impurity mode (tIM) turbulence are performed. A linear analysis shows that the tIM is an instability that occurs in the bad curvature region when the density gradients of bulk ions and impurities are in opposite directions. The tIM can be unstable even when the temperature profiles are flat. In the presence of temperature gradients, the tIM and toroidal ion temperature gradient (tITG) mode could coexist. For the small temperature gradient, the tIM is found to be dominant. The tIM turbulence drives the large inward impurity and outward ion particle transports. Furthermore, the inward ion heat flux driven by the tIM turbulence causes the ion temperature profile to be more peaked than the initial one. For the large temperature gradient, while such inward ion heat flux does not occur because of the dominant tITG mode, the large inward impurity and outward ion particle fluxes are still observed due to the subdominant tIM. These results indicate that the tIM plays an important role in turbulent heat and particle transport when impurities are injected.
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