Plasma Turbulent Transport and Fine-Scale Structures of Phase Space Distribution Function

Recent results from kinetic simulations of steady and quasisteady states of the ion temperature gradient (ITG) driven turbulence are reviewed in focus on the fine-scale structures of the phase space distribution function associated with the anomalous transport. Importance of proper treatment for the fine structures in numerical simulations of the collisionless ITG turbulence is emphasized by a parameter survey for the velocity space resolution. Preliminary results of the flux tube simulation of the toroidal ITG mode are also given for the linear benchmark test and the collisionless damping in a tokamak configuration

Kinetic simulation of a quasisteady state in collisionless ion temperature gradient driven turbulence

Existence of a quasisteady state with a mean transport flux in the collisionless ion temperature gradient driven turbulence has been confirmed by means of a direct numerical simulation of a basic kinetic equation for the perturbed ion velocity distribution function deltaf. The phase mixing generates fine-scale fluctuations of deltaf and leads to continuous growth of high-order moments which balances the transport flux. The phase relation between the temperature and the parallel heat flux is also examined and compared with a fluid closure model

Collisionless damping of zonal flows in helical systems

Collisionless time evolution of zonal flows in helical systems is investigated. An analytical expression describing the collisionless response of the zonal-flow potential to the initial potential and a given turbulence source is derived from the gyrokinetic equations combined with the quasineutrality condition. The dispersion relation for the geodesic acoustic mode (GAM) in helical systems is derived from the short-time response kernel for the zonal-flow potential. It is found that helical ripples in the magnetic-field strength as well as finite orbit widths of passing ions enhance the GAM damping. The radial drift motions of particles trapped in helical ripples cause the residual zonal-flow level in the collisionless long-time limit to be lower for longer radial wavelengths and deeper helical ripples. On the other hand, a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport. The validity of our analytical results is verified by gyrokinetic Vlasov simulation

Linear Gyrokinetic Analyses of ITG Modes and Zonal Flows in LHD with High Ion Temperature

Ion temperature (Ti) gradient modes (ITG modes) and zonal flows for high Ti discharges in the Large Helical Device (LHD) are investigated by linear gyrokinetic Vlasov simulation. In recent LHD experiments, high Ti plasmas are generated by neutral beam injection, and spatial profiles of density fluctuations are measured by phase contrast imaging (PCI) [K. Tanaka et al., Plasma Fusion Res. 5, S2053 (2010)]. The observed fluctuations most likely propagate in the direction of the ion diamagnetic rotation in the plasma frame, and their amplitudes increase with the growth of the temperature gradient. The results show the characteristics of ITG turbulence. To investigate the ITG modes and zonal flows in the experiment, linear gyrokinetic simulations were performed in the corresponding equilibria with different Ti profiles by using the GKV-X code [M. Nunami et al., Plasma Fusion Res. 5, 016 (2010)]. The simulation results predict unstable regions for the ITG modes in radial, wavenumber, and phase velocity spaces, in agreement with the PCI measurements. Thus, the fluctuations observed in the experiment are attributed to ITG instability. The responses of the zonal flows show clear contrasts in different field spectra that depend on the Ti profile and the radial position. In addition to the dependence on the field spectra, the zonal flow residual levels are enhanced by increasing the radial wavenumber as theoretically predicted

Impact of hydrogen isotope species on microinstabilities in helical plasmas

The impact of isotope ion mass on ion-scale and electron-scale microinstabilities such as ion temperature gradient (ITG) mode, trapped electron mode (TEM), and electron temperature gradient (ETG) mode in helical plasmas are investigated by using gyrokinetic Vlasov simulations with a hydrogen isotope and real-mass kinetic electrons. Comprehensive scans for the equilibrium parameters and magnetic configurations clarify the transition from ITG mode to TEM instability, where a significant TEM enhancement is revealed in the case of inward-shifted plasma compared to that in the standard configuration. It is elucidated that the ion-mass dependence on the ratio of the electron–ion collision frequency to the ion transit one, i.e. ${{\nu}_{\text{ei}}}/{{\omega}_{\text{ti}}}\propto {{\left({{m}_{\text{i}}}/{{m}_{\text{e}}}\right)}^{1/2}}$ , leads to a stabilization of the TEM for heavier isotope ions. The ITG growth rate indicates a gyro-Bohm-like ion-mass dependence, where the mixing-length estimate of diffusivity yields $\gamma /k_{\bot}^{2}\propto m_{\text{i}}^{1/2}$ . On the other hand, a weak isotope dependence of the ETG growth rate is identified. A collisionality scan also reveals that the TEM stabilization by the isotope ions becomes more significant for relatively higher collisionality in a banana regime

Isotope Effects on Trapped-Electron-Mode Driven Turbulence and Zonal Flows in Helical and Tokamak Plasmas

Impacts of isotope ion mass on trapped-electron-mode (TEM)-driven turbulence and zonal flows in magnetically confined fusion plasmas are investigated. Gyrokinetic simulations of TEM-driven turbulence in three-dimensional magnetic configuration of helical plasmas with hydrogen isotope ions and real-mass kinetic electrons are realized for the first time, and the linear and the nonlinear nature of the isotope and collisional effects on the turbulent transport and zonal-flow generation are clarified. It is newly found that combined effects of the collisional TEM stabilization by the isotope ions and the associated increase in the impacts of the steady zonal flows at the near-marginal linear stability lead to the significant transport reduction with the opposite ion mass dependence in comparison to the conventional gyro-Bohm scaling. The universal nature of the isotope effects on the TEM-driven turbulence and zonal flows is verified for a wide variety of toroidal plasmas, e.g., axisymmetric tokamak and non-axisymmetric helical or stellarator systems

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

Modeling of turbulent particle and heat transport in helical plasmas based on gyrokinetic analysis

The particle and heat transport driven by the ion temperature gradient instability in helical plasmas is investigated by the gyrokinetic analysis taking into account the kinetic electron response. High and low ion temperature plasma cases for the discharge in the Large Helical Device (LHD) are studied. Two types of transport models with a lower computational cost to reproduce the nonlinear gyrokinetic simulation results within allowable errors are presented for application in quick transport analyses. The turbulent electron and ion heat diffusivity models are given in terms of the linear growth rate and the characteristic quantity for the linear response of zonal flows, while the model of the effective particle diffusivity is not obtained for the flattened density profile observed in the LHD. The quasilinear flux model is also shown for the heat transport. The quasilinear flux models for the energy fluxes are found to reproduce the nonlinear simulation results at the accuracy similar to that of the heat diffusivity models. In addition, the quasilinear particle flux model, which is applicable to the transport analysis for LHD plasmas, is constructed. These turbulent reduced models enable coupling to the other simulation in the integrated codes for the LHD