Spectrum of the Velocity Distribution Function in the Slab Ion Temperature Gradient Driven Turbulence

A spectral analysis of the velocity distribution function in the slab ion temperature gradient (ITG) driven turbulence is done by using high-resolution Eulerian kinetic simulation results. It is clarified how the entropy variable associated with the fine-scale structure of the distribution function is produced by the turbulent heat transport in the presence of the temperature gradient, transferred from macro to microscales in the velocity space through phase- mixing processes, and dissipated by collisions. An interesting analogy between the entropy spectrum in the ITG turbulence and the spectrum of a passive scalar quantity in a turbulent fluid is pointed out. The entropy spectral function is analytically derived and confirmed by the simulation result. It is shown that the entropy spectrum obeys a power law in the range that is free from instability sources and collisional dissipation

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

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

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

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

Polarization and magnetization in collisional and turbulent transport processes

Expressions of polarization and magnetization in magnetically confined plasmas are derived, which include full expansions in the gyroradius to treat effects of both equilibrium and microscopic electromagnetic turbulence. Using the obtained expressions, densities and flows of particles are related to those of gyrocenters. To the first order in the normalized gyroradius expansion, the mean part of the particle flow is given by the sum of the gyrocenter flow and the magnetization flow, which corresponds to the so-called magnetization law in drift kinetics, while the turbulent part contains the polarization flow as well. Collisions make an additional contribution to the second-order particle flow. The mean particle flux across the magnetic surface is of the second-order, and it contains classical, neoclassical, and turbulent transport processes. The Lagrangian variational principle is used to derive the gyrokinetic Poisson and Ampère equations, which properly include mean and turbulent parts so as to be useful for full-f global electromagnetic gyrokinetic simulations. It is found that the second-order Lagrangian term given by the inner product of the turbulent vector potential and the drift velocity consisting of the curvature drift and the ∇B drift should be retained in order for the derived Ampère equation to correctly include the diamagnetic current, which is necessary especially for the full-f high-beta plasma simulations. The turbulent parts of these gyrokinetic Poisson and Ampère equations are confirmed to agree with the results derived from the WKB representation in earlier works

Reduced models of turbulent transport in helical plasmas including effects of zonal flows and trapped electrons

Using transport models, the impacts of trapped electrons on zonal flows and turbulence in helical field configurations are studied. The effect of the trapped electrons on the characteristic quantities of the linear response for zonal flows is investigated for two different field configurations in the Large Helical Device. The turbulent potential fluctuation, zonal flow potential fluctuation and ion energy transport are quickly predicted by the reduced models for which the linear and nonlinear simulation results are used to determine dimensionless parameters related to turbulent saturation levels and typical zonal flow wavenumbers. The effects of zonal flows on the turbulent transport for the case of the kinetic electron response are much smaller than or comparable to those in an adiabatic electron condition for the two different field configurations. It is clarified that the effect of zonal flows on the turbulent transport due to the trapped electrons changes, depending on the field configurations