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The problem of dispersion of geodesic acoustic modes is revisited with two different methods for the solution of the kinetic equation. The dispersive corrections to the mode frequency are calculated by including the m = 2 poloidal harmonics. Our obtained results agree with some earlier results but differ in various ways with other previous works. Limitations and advantages of different approaches are discussed.

The simulation study of nonlocal transport from edge to core in tokamak plasmas is performed using the 4-field reduced MHD model. A toroidally-elongated cylindrical particle source is applied in the plasma edge, after saturation of the resistive ballooning turbulence is attained. After a short time, the source is switched off and plasma response is investigated in detail. The nonlocal transport appears at the location far from the edge source. It is found that the particle source induces (0,0) and (±1, 0) modes of density fluctuations, where (m, n) indicates the set of poloidal mode number m and the toroidal mode number n. These modes interact with each other by the nonlinear and/or toroidal couplings. The symmetry of (±1, 0) modes breaks after switching-off the source and the formation of the spiral structure with poloidal rotation is observed, which yields a connection between core and edge regions. In this simulation, the convective cell mode such as (1,0) mode contributes the nonlocal transport. The simulation result indicates that two dimensional transport plays an essential role to produce the nonlocal transport. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Spatio-temporal measurements of the impurity ion temperature, density, and rotation profiles around the plasma edge region have been made in the JT-60U tokamak, allowing the determination of radial electric field, Er, with the key dimensionless parameter (poloidal Mach number, Upm) at the L-H transition in a number of operational regimes. We found that there is variation in the L-H transition in terms of its time-scale; not only “hard” type transition with a faster time-scale than that seen in the plasma transport (as represented by an energy confinement time, τE) as seen in the many conventional tokamaks, but also “soft” one with a slow time-scale (≈τE) is possible solution, including a complex multi-stage Er transition in the later H-phase. The most important point is that the critical condition for the L-H transition predicted by ion-orbit loss model could be applicable only for “hard” transition (occurred at Upm ≥ 1), and not necessary for “slow” one (occurred even at Upm < 1). Characteristics of the turbulent density fluctuation with the frequency range of 100 kHz at the plasma edge region, in addition to a uniform toroidal MHD oscillation (i.e., n = 0), during ELM-free H-phase are also reported. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

It is found that new channels of energy exchange between macro- and microscopic dynamics exist in plasmas. They are induced by macroscopic plasma flow. This finding is based on the kinetic-magnetohydrodynamic (MHD) theory, which analyses interaction between macroscopic (MHD-scale) motion and microscopic (particle-scale) dynamics. The kinetic-MHD theory is extended to include effects of macroscopic plasma flow self-consistently. The extension is realised by generalising an energy exchange term due to wave-particle resonance, denoted by δ WK. The first extension is generalisation of the particle’s Lagrangian, and the second one stems from modification to the particle distribution function due to flow. These extensions lead to a generalised expression of δ WK, which affects the MHD stability of plasmas.

Zonal flow behaviour and its effect on turbulent transport in tokamak plasmas with reversed magnetic shear are investigated by global fluid simulations of electrostatic ion temperature gradient driven turbulence. It is found that for high q (safety factor) turbulent transport is high even at a minimum-q region because oscillatory zonal flows called geodesic acoustic modes (GAMs) are dominant. The turbulent transport is reduced in the neighbourhood of a minimum-q surface when q is low enough to damp the GAMs. The difference in zonal flow behaviour causes a difference in turbulent transport and may trigger the formation of ion internal transport barriers in reversed shear tokamaks.

Using a global Landau-fluid code in toroidal geometry, an electromagnetic ion temperature gradient (ITG) driven turbulence–zonal mode system is investigated. Two different types of zonal flows, i.e. stationary zonal flows in a low q (safety factor) region and oscillatory ones in a high q region, which are called geodesic acoustic modes, are found to be simultaneously excited in a torus. The stationary flows efficiently suppress turbulent transport, while the oscillatory ones weakly affect the turbulence due to their time varying nature. Therefore, in the low q region where the zonal flows are almost stationary, they are dominant over the turbulence. On the other hand, the turbulence is still active in the high q region where the zonal flows are oscillatory.

Nonlinear behaviour of resistive drift-Alfven mode is described by a three-field model composed of vorticity equation, Ohm's law and continuity equation. Resistive drift-Alfven instabilities occur in the cylindrical plasma where both resistivity and plasma β value are finite. The resistive drift-Alfven instabilities assuming single helicity generate poloidal sheared flow via the Reynolds stress by nonlinear mode couplings. The poloidal sheared flow stabilizes several unstable modes including the most unstable mode and leads to saturation of the nonlinear resistive drift-Alfven modes. It is noted that some harmonics are destabilized by this flow. The level of magnetic fluctuations is much smaller than that due to density and electrostatic potential fluctuations. Particle flux due to the magnetic fluctuations is also extremely small compared to that due to electrostatic fluctuations. However, it is shown that the effect of magnetic fluctuations on the poloidal flow is significant. The magnetic fluctuations play a role of suppressing the poloidal flow drive by convective nonlinearity.

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.

Turbulent transport near the critical gradient in toroidal plasmas is studied based on global Landau-fluid simulations and an extended predator-prey theoretical model of ion temperature gradient turbulence. A new type of intermittent transport associated with the emission and propagation of a geodesic acoustic mode (GAM) is found near the critical gradient regime, which is referred to as GAM intermittency. The intermittency is characterized by new time scales of trigger, damping, and recursion due to GAM damping. During the recursion of intermittent bursts, stationary zonal flow increases with a slow time scale due to the accumulation of undamped residues and eventually quenches the turbulence, suggesting that a nonlinear upshift of the critical gradient, i.e., Dimits shift, is established through such a dynamical process.

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.

The temporal and spatial responses of electron channels (the electron density, ne, and the electron temperature, Te) and ion channels (the ion temperature, Ti, and the toroidal rotation velocity, V) to central electron cyclotron heating (ECH) have been investigated in positive shear H-mode plasmas with a relatively peaked Ti profile and internal transport barrier (ITB) plasmas on JT-60U. Ion temperature decreases with ECH after the increase in the electron temperature in the core region. The time scale of the change in Ti is ≈30–60 ms in H-mode plasmas and almost constant in radius. In ITB plasmas, the time scale is shorter around the ITB foot and becomes longer inside the ITB foot. The experimentally measured causality indicates that the decrease in Ti is consistent with the ion temperature gradient critical gradient reduction. This is also verified through a comparison with linear gyrokinetic stability analyses. The electron heat diffusivity increases with ECH in both H-mode and ITB plasmas, correlating to the increase in the ion heat diffusivity. Electron density with a relatively flat ne profile does not decrease with ECH. On the other hand, the electron density with a peaked ne profile decreases with ECH. The flattening of the ne profile is observed after the increase in the electron temperature in the core region. The time scale of the change in ne is about 200–350 ms. Linear gyrokinetic stability analyses imply that the growth rate of the trapped electron modes, which increase outward particle flux, becomes more pronounced during ECH. The counter intrinsic rotation with ECH is identified on H-mode plasmas with a small torque input (BAL-NBI). The counter intrinsic rotation is generated after the increase in the electron temperature and correlates to the change in the electron temperature with ECH around the EC deposition. The radial region where the counter intrinsic rotation is observed is wider than the radial region where the electron temperature varies with ECH. The time scale of the change in the toroidal rotation velocity is about 90–200 ms around the ECH deposition and longer than the time scale of the change in Te and Ti.

The effects of geodesic acoustic modes (GAMs) on the toroidal ion temperature gradient turbulence and associated transport near the critical gradient regime in tokamak plasma are investigated based on global Landau-fluid simulations and extended predator-prey modeling analyses. A new type of intermittent dynamics of transport accompanied with the emission and propagation of the GAMs, i.e., GAM intermittency [K. Miki et al., Phys. Rev. Lett. 99, 145003 (2007)], has been found. The intermittent bursts are triggered by the onset of spatially propagating GAMs when the turbulent energy exceeds a critical value. The GAMs suffer collisionless damping during the propagation and nonlocally transfer local turbulence energy to wide radial region. The stationary zonal flows gradually increase due to the accumulation of non-damped residual part over many periods of quasi-periodic intermittent bursts and eventually quench the turbulence, leading to a nonlinear upshift of the linear critical gradient; namely, the Dimits...

In order to better understand tlie feature of turbulent transport in tokamak plasmas dominated by zonal flows and nonlinearly excited tertiary (Kelvin-Helmholtz-like) waves, the radial dependency of the turbulent structure in the back of steady-state zonal flows was analyzed based on gyrofluid simulation of the electron temperature gradient turbulence in a sheared-slab configuration. The zonal flows change the characteristics of plasma turbulence from homogeneous to inhomogeneous. Thus. it is found that turbulent vortices are regulated by a radially alternative potential pattern where the spatiotemporal characteristic scales with respect to local fluctuations change radially. From the cross spectrum analysis between tlie poioidal electric field and the pressure perturbation, it was found that. in plasmas dominated by zonal flows, the restriction of heat flux is conducted by two mechanisms, i.e. the reduction of coherence and the phase synchronization.