Shinya Maeyama

Gyrokinetic turbulence simulations of high-beta tokamak and helical plasmas with full-kinetic and hybrid models

Turbulent transport in high-beta toroidal plasmas is investigated by means of an electromagnetic gyrokinetic model and a newly developed electromagnetic hybrid model consisting of the gyrokinetic equation for ions and drift-Landau-fluid equations for electrons. Full gyrokinetic simulation results for Cyclone base case tokamak and for Large Helical Device (LHD) plasmas are quickly and accurately reproduced by the hybrid simulation. In the kinetic ballooning mode (KBM)-driven turbulence the ion heat and particle fluxes are mainly caused by electrostatic perturbation, and the contribution of magnetic perturbation is small and negative. The electron heat flux is caused by both electrostatic and magnetic perturbations. The numerical solutions satisfy the entropy balance equation, and the entropy is transferred from ions to electrons through electrostatic and magnetic perturbations. An analysis based on the entropy balance equation shows that the zonal structure is produced by magnetic nonlinearity corresponding to the Maxwell stress in the fluid limit but is weakened by the electrostatic one related to the Reynolds stress. A linear analysis on the standard configuration of LHD plasmas shows the suppression of the ion temperature gradient mode by finite-beta effects and the destabilization of KBM at high beta.

Numerical techniques for parallel dynamics in electromagnetic gyrokinetic Vlasov simulations

Abstract Numerical techniques for parallel dynamics in electromagnetic gyrokinetic simulations are introduced to regulate unphysical grid-size oscillations in the field-aligned coordinate. It is found that a fixed boundary condition and the nonlinear mode coupling in the field-aligned coordinate, as well as numerical errors of non-dissipative finite difference methods, produce fluctuations with high parallel wave numbers. The theoretical and numerical analyses demonstrate that an outflow boundary condition and a low-pass filter efficiently remove the numerical oscillations, providing small but acceptable errors of the entropy variables. The new method is advantageous for quantitative evaluation of the entropy balance that is required for obtaining a steady state in gyrokinetic turbulence.

Electromagnetic gyrokinetic turbulence in finite-beta helical plasmasa)

A saturation mechanism for microturbulence in a regime of weak zonal flow generation is investigated by means of electromagnetic gyrokinetic simulations. The study identifies a new saturation process of the kinetic ballooning mode (KBM) turbulence originating from the spatial structure of the KBM instabilities in a finite-beta Large Helical Device (LHD) plasma. Specifically, the most unstable KBM in LHD has an inclined mode structure with respect to the mid-plane of a torus, i.e., it has a finite radial wave-number in flux tube coordinates, in contrast to KBMs in tokamaks as well as ion-temperature gradient modes in tokamaks and helical systems. The simulations reveal that the growth of KBMs in LHD is saturated by nonlinear interactions of oppositely inclined convection cells through mutual shearing as well as by the zonal flow. The saturation mechanism is quantitatively investigated by analysis of the nonlinear entropy transfer that shows not only the mutual shearing but also a self-interaction with an e...

Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

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.

Turbulent transport of heat and particles in a high ion temperature discharge of the Large Helical Device

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 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.

A hybrid method of semi-Lagrangian and additive semi-implicit Runge–Kutta schemes for gyrokinetic Vlasov simulations

Abstract A hybrid method of semi-Lagrangian and additive semi-implicit Runge–Kutta schemes is developed for gyrokinetic Vlasov simulations in a flux tube geometry. The time-integration scheme is free from the Courant–Friedrichs–Lewy condition for the linear advection terms in the gyrokinetic equation. The new method is applied to simulations of the ion-temperature-gradient instability in fusion plasmas confined by helical magnetic fields, where the parallel advection term severely restricts the time step size for explicit Eulerian schemes. Linear and nonlinear results show good agreements with those obtained by using the explicit Runge–Kutta–Gill scheme, while the new method substantially reduces the computational cost.

Comparison between kinetic-ballooning-mode-driven turbulence and ion-temperature-gradient-driven turbulence

Electromagnetic turbulence driven by kinetic ballooning modes (KBMs) in high-β plasma is investigated based on the local gyrokinetic model. Analysis of turbulent fluxes, norms, and phases of fluctuations shows that KBM turbulence gives narrower spectra and smaller phase factors than those in ion-temperature-gradient (ITG)-driven turbulence. This leads to the smaller transport fluxes in KBM turbulence than those in ITG turbulence even when they have similar linear growth rates. From the analysis of the entropy balance relation, it is found that the entropy transfer from ions to electrons through the field-particle interactions mainly drives electron perturbations, which creates radial twisted modes by rapid parallel motions of electrons in a sheared magnetic geometry. The nonlinear coupling between the dominant unstable mode and its twisted modes is important for the saturation of KBM turbulence, in contrast to the importance of zonal flow shearing in ITG turbulence. The coupling depends on the flux-tube domain with the one-poloidal-turn parallel length and on the torus periodicity constraint.

Effects of time-varying E × B flow on slab ion-temperature-gradient turbulence

Effects of time-varying sheared E×B flow on turbulence driven by slab ion temperature gradient instabilities are investigated by means of Landau fluid simulation. Here, the E×B flow, which consists of stationary and time-periodic oscillatory parts, is externally imposed to the turbulence. The dependence on the amplitude and frequency of E×B flow is examined in the case that the amplitude of oscillatory part is the same or less than that of stationary part. The ion heat transport caused by turbulence oscillates with the same period as the E×B flow and the time-averaged transport coefficient is larger than the coefficient which is evaluated without the oscillatory part. The time-averaged coefficient is maximized when the amplitude of oscillatory part is equal to that of stationary part. As the frequency of E×B flow increases, the time-averaged coefficient decreases and is close to the coefficient which is evaluated without the oscillatory part. This mechanism is explained by introducing a kind of the logist...

Impact of plasma parameter on self-organization of electron temperature gradient driven turbulence

Self-organization in the slab electron temperature gradient driven (ETG) turbulence is investigated based on gyrokinetic simulations and the Hasegawa-Mima (HM) equation. The scale and the anisotropy of self-organized turbulent structures vary depending on the Rhines scale and the characteristic scale given by the adiabatic response term in the HM equation. The former is determined by competition between the linear wave dispersion and the nonlinear turbulent cascade, while the latter is given as the scale, at which the turbulent cascade is impeded. These scales are controlled by plasma parameters such as the density and temperature gradient, and the temperature ratio of ion to electron. It is found that depending on the plasma parameters, the ETG turbulence shows either isotropic turbulence or zonal flows, which give significantly different transport levels. Although the modulational instability excites zonal modes regardless of the plasma parameters, the final turbulent structure is determined by the self...

Suppression of Ion-Scale Microtearing Modes by Electron-Scale Turbulence via Cross-Scale Nonlinear Interactions in Tokamak Plasmas

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.