Multiscale gyrokinetic turbulence simulations with the real ion-to-electron mass ratio and β value are realized for the first time, where the β value is given by the ratio of plasma pressure to magnetic pressure and characterizes electromagnetic effects on microinstabilities. Numerical analysis at both the electron scale and the ion scale is used to reveal the mechanism of their cross-scale interactions. Even with the real-mass scale separation, ion-scale turbulence eliminates electron-scale streamers and dominates heat transport, not only of ions but also of electrons. Suppression of electron-scale turbulence by ion-scale eddies, rather than by long-wavelength zonal flows, is also demonstrated by means of direct measurement of nonlinear mode-to-mode coupling. When the ion-scale modes are stabilized by finite-β effects, the contribution of the electron-scale dynamics to the turbulent transport becomes non-negligible and turns out to enhance ion-scale turbulent transport. Damping of the ion-scale zonal flows by electron-scale turbulence is responsible for the enhancement of ion-scale transport.

Gyrokinetic simulations of electromagnetic turbulence in magnetically confined torus plasmas including tokamak and heliotron/stellarator are reviewed. Numerical simulation of turbulence in finite beta plasmas is an important task for predicting the performance of fusion reactors and a great challenge in computational science due to multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The simulation becomes further challenging in non-axisymmetric plasmas. In finite beta plasmas, magnetic perturbation appears and influences some key mechanisms of turbulent transport, which include linear instability and zonal flow production. Linear analysis shows that the ion-temperature gradient (ITG) instability, which is essentially an electrostatic instability, is unstable at low beta and its growth rate is reduced by magnetic field line bending at finite beta. On the other hand, the kinetic ballooning mode (KBM), which is an electromagnetic instability, is destabilized at high beta. In addition, trapped electron modes (TEMs), electron temperature gradient (ETG) modes, and micro-tearing modes (MTMs) can be destabilized. These instabilities are classified into two categories: ballooning parity and tearing parity modes. These parities are mixed by nonlinear interactions, so that, for instance, the ITG mode excites tearing parity modes. In the nonlinear evolution, the zonal flow shear acts to regulate the ITG driven turbulence at low beta. On the other hand, at finite beta, interplay between the turbulence and zonal flows becomes complicated because the production of zonal flow is influenced by the finite beta effects. When the zonal flows are too weak, turbulence continues to grow beyond a physically relevant level of saturation in finite-beta tokamaks. Nonlinear mode coupling to stable modes can play a role in the saturation of finite beta ITG mode and KBM. Since there is a quadratic conserved quantity, evaluating nonlinear transfer of the conserved quantity from unstable modes to stable modes is useful for understanding the saturation mechanism of turbulence.

Gyrokinetic turbulence simulations are applied for the first time to the cross-scale interactions of microtearing modes (MTMs) and electron-temperature-gradient (ETG) modes. The investigation of the fluctuation response in a multiscale simulation including both types of instabilities indicates that MTMs are suppressed by ETG turbulence. A detailed analysis of nonlinear mode coupling reveals that radially localized current-sheet structures of MTMs are strongly distorted by fine-scale E×B flows of ETG turbulence. Consequently, electron heat transport caused by the magnetic flutter of MTMs is significantly reduced and ETG turbulence dominates electron heat transport.

Turbulent transport in a high ion temperature discharge of the Large Helical Device (LHD) is investigated by means of electromagnetic gyrokinetic simulations, which include kinetic electrons, magnetic perturbations, and full geometrical effects. Including kinetic electrons enables us to firstly evaluate the particle and the electron heat fluxes caused by turbulence in LHD plasmas. It is found that the electron energy transport reproduces the experimental result, and that the particle flux is negative. The contribution of magnetic perturbation to the transport is small because of very low beta. The turbulence is driven by the ion temperature gradient (ITG) instability, and the effect of kinetic electrons enhances the growth rate larger than that from the adiabatic electron calculation. The ion energy flux is larger than that observed in the experiment, while the flux is close to the experimental observation when the temperature gradient is reduced 20% in the simulation. This significant sensitivity of the energy flux implies that the profile in the experiment is close to the critical temperature gradient. The critical gradient for turbulent energy flux is similar to that for the linear instability, i.e., the Dimits shift is small. This is because the zonal flow in the LHD is weaker than that in tokamaks.

confined plasmas, such as GKV+/EM solving the gyrokinetic equations for ions and electrons and GKV+/EMH solving the hybrid model of gyrokinetic ion and fluid electron equations, are newly developed. These codes are applied to the linear and nonlinear analyses of micro-instabilities of finite beta plasmas in the Cyclone base case tokamak and in a model configuration of standard LHD 1) . Accuracy of the hybrid model is confirmed through comparison with linear and nonlinear simulation results for the tokamak and the LHD plasmas obtained by the full gyrokinetic code. The comparison in the linear analysis confirms good agreement in the growth rates and real frequencies of KBMs in high-beta regime. In nonlinear simulations the hybrid code can run with about four times faster speed than that of the full gyrokinetic code. The hybrid code is especially useful for nonlinear analysis of LHD for which full gyrokinetic simulation is difficult because of large computational cost.The nonlinear simulation of KBM turbulence in the CBC with β = 2% and η e = 0 shows that the ion heat (particle) transport coefficient given by electrostatic perturbations is about 0.6 (0.5) v T i ρ 2 i /L n . The magnetic perturbation of KBM turbulence has small pinch effects on the ion heat and particle transport, which is in contrast with Rechester-Rosenbluth model. The electron heat flux is about 0.4. The analysis of beta scaling of these fluxes and a comparison between the kinetic simulation results and our previous fluid simulation results will be made in our future work. Turbulent fluctuation of KBM satisfies the entropy balance equation, and the entropy (or free energy) is transferred from ions to electrons.Although it has been shown that the zonal flow produced by KBM is weak compared to ITG with the adiabatic electron, it is valuable to study the production of zonal structure in KBM turbulence. By using the entropy balance relation it is shown that the entropy transfer to the zonal component from magnetic (electrostatic) nonlinearity is positive (negative). It is noticed that the magnetic (electrostatic) nonlinearity corresponds to the Maxwell (Reynolds) stress in the fluid limit. This zonal structure production is in contrast with the production (reduction) of zonal flow by the Reynolds (Maxwell) stress in two-fluid simulations 2) . Linear analysis of KBM in the model configuration of standard LHD plasmas by means of the full kinetic code shows that the ITG mode is stabilized around β = 0.8% and the critical value of KBM onset is about β = 1.5% for η i = 3, η e = 0 andŝ = −0.85. When η e = 3, the growth rate of ITG is suppressed with beta but it is not stabilized completely and KBM appears in β > 1%. One of the significant feature of KBM in the standard LHD is that the most unstable mode has a finite radial wavenumber. This is in contrast to ITG in the LHD and micro-instabilities in tokamaks, where the most unstable mode has vanishing radial wavenumber, which is then set by the magnetic shear length scale.The first nonlinear simulation of t...