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The current status and the progress of research and development (R&D) activities for a Fusion DEMO reactor in the National Institutes for Quantum and Radiological Science and Technology (QST) Rokka...

A particle flux induced by a source in the gyro-center phase space is investigated through push-forward representations of the particle flux. The difference between the particle and gyro-center density sources is represented by the divergence of the particle flux due to the source in the gyro-center space. A gradient of a gyro-center perpendicular heat source causes a particle flux that may modify the particle density profile even when the source does not change positions of gyro-centers. The whole particle flux including the flux by the source is explicitly represented in terms of gyro-center fluid moments (gyrofluid moments) in the long wavelength limit of the standard electrostatic gyrokinetic model. Continuity equations for particle density with finite Larmor radius terms and the term related to the perpendicular heat source in the gyro-center space are derived from these representations by transforming gyrofluid moments to particle fluid moments. Finally, a vorticity equation with a source term stemming from a perpendicular heat source is derived from one of the continuity equations.

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.

Oscillatory zonal flows called geodesic acoustic modes (GAMs) appearing in a high safety factor region of tokamak plasmas show nonlocal behaviour in their frequency. The frequency of the GAMs is unchanged over a certain radial region and the radial variation of the frequency is step-like. The effects of ρ* = ρi/a on the nonlocal behaviour of the GAMs are investigated by global ion temperature gradient driven turbulence simulations, where ρi is an ion Larmor radius and a is a minor radius of a torus. It is found that the radial width in which the GAMs have the same frequency is almost proportional to , while the radial wavelength of the GAMs is proportional to ρi. As for turbulent transport, the boundary between a high transport region where the GAMs are dominant and a low transport region becomes clearer for smaller ρ*.

The dynamics of secondary large-scale structures in electron-temperature-gradient (ETG) turbulence is investigated based on gyrofluid simulations in sheared slab geometry. It is found that structural bifurcation to zonal flow dominated or streamer-like states depends on the spectral anisotropy of turbulent ETG fluctuation, which is governed by the magnetic shear. The turbulent electron transport is suppressed by enhanced zonal flows. However, it is still low even if the streamer is formed in ETG turbulence with strong shears. It is shown that the low transport may be related to the secondary excitation of poloidal long-wavelength mode due to the beat wave of the most unstable components or a modulation instability. This large-scale structure with a low frequency and a long wavelength may saturate, or at least contribute to the saturation of ETG fluctuations through a poloidal mode coupling. The result suggests a low fluctuation level in ETG turbulence.

The important issue of whether zonal flows or streamers are preferentially formed in plasma turbulence with electron gyroradius scale is studied based on a gyrofluid model of electron temperature gradient (ETG) driven turbulence. Results from three approaches are presented. It is analytically derived first that the secondary generation of different large-scale structures is determined by the spectral anisotropy of turbulent fluctuation in two-dimensional Charney–Hasegawa–Mima turbulence. This is verified subsequently using three-dimensional simulations of sheared slab ETG turbulence, which show that the magnetic shear governs the pattern selection. It is found that a weak shear favours the enhancement of zonal flows so that the electron transport is strongly suppressed. In contrast, radially elongated streamers are formed nonlinearly in stronger-shear ETG turbulence. Finally, three-dimensional toroidal ETG simulations show that streamers are excited in the linearly stable region along the field (i.e. good curvature region) through a modulation instability after initial saturation of ETG modes. Although the electron transport at the quasi-steady state becomes higher than the initial saturation level, which is dominated by fluctuations with a peaked spectrum, the averaged value is still low at around the gyro-Bohm level. Furthermore, it is shown that the enhanced zonal flows in weak shear ETG turbulence may be limited by a Kelvin–Helmholtz instability. Also, it is found that the electromagnetic effects reduce the generation of zonal flows and reverse the so-called Okawa-scaling of electron transport on the β dependence.

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.

Global characteristics of the coupled system of zonal flows and electromagnetic ion temperature gradient driven turbulence in tokamak plasmas are investigated using a global electromagnetic Landau fluid code. Zonal flow behavior changes with the safety factor q. In a low q region stationary zonal flows are excited and they suppress the turbulence effectively. Coupling between zonal flows and poloidally asymmetric pressure perturbations due to a geodesic curvature makes the zonal flows oscillatory in a high q region. Energy transfer from the oscillatory zonal flows to the turbulence via the poloidally asymmetric pressure perturbations is identified. Therefore in the high q region where the zonal flows are oscillatory, the zonal flows cannot quench the turbulence and turbulent transport is not suppressed completely. As for the zonal flow behavior, it is favorable for confinement improvement to make the low q region where the stationary zonal flows are dominant in tokamak plasmas.

Two representations of fluid moments in terms of a gyro-center distribution function and gyro-center coordinates, which are called push-forward representations, are compared in the standard electrostatic gyrokinetic model. In the representation conventionally used to derive the gyrokinetic Poisson equation, the pull-back transformation of the gyro-center distribution function contains effects of the gyro-center transformation and therefore electrostatic potential fluctuations, which is described by the Poisson brackets between the distribution function and scalar functions generating the gyro-center transformation. Usually, only the lowest order solution of the generating function at first order is considered to explicitly derive the gyrokinetic Poisson equation. This is true in explicitly deriving representations of scalar fluid moments with polarization terms. One also recovers the particle diamagnetic flux at this order because it is associated with the guiding-center transformation. However, higher-order solutions are needed to derive finite Larmor radius terms of particle flux including the polarization drift flux from the conventional representation. On the other hand, the lowest order solution is sufficient for the other representation, in which the gyro-center transformation part is combined with the guiding-center one and the pull-back transformation of the distribution function does not appear.

Shear flow is the most important ingredient governing nonlinear behaviour of many types of plasma instability. Electromagnetic effects on shear flow generation have been studied for an electromagnetic drift wave called resistive drift-Alfven mode (RDAM) and a global MHD mode called resistive wall mode (RWM). For RDAM it is found that the generated shear flow stabilizes the dominant modes; however, other modes are destabilized. For RWM Maxwell stress due to magnetic fluctuations has a tendency to suppress the poloidal flow near the plasma surface, which gives almost the same saturation level for different initial poloidal flows, since the shear flow stabilization disappears.

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.

Toroidal rotation effects are self-consistently taken into account not only in the linear magnetohydrodynamic (MHD) stability analysis but also in the equilibrium calculation. The MHD equilibrium computation is affected by centrifugal force due to the toroidal rotation. To study the toroidal rotation effects on resistive wall modes (RWMs), a new code has been developed. The RWMaC modules, which solve the electromagnetic dynamics in vacuum and the resistive wall, have been implemented in the MINERVA code, which solves the Frieman?Rotenberg equation that describes the linear ideal MHD dynamics in a rotating plasma. It is shown that modification of MHD equilibrium by the centrifugal force significantly reduces growth rates of RWMs with fast rotation in the order of M2?=?0.1 where M is the Mach number. Moreover, it can open a stable window which does not exist under the assumption that the rotation affects only the linear dynamics. The rotation modifies the equilibrium pressure gradient and current density profiles, which results in the change of potential energy including rotational effects.

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 kinetic ballooning mode (KBM) turbulence in Tokamak plasma is investigated by electromagnetic gyrokinetic simulations. From the entropy balance analysis, it is revealed that the field-particle interactions transfer a significant fraction of the ion entropy produced by the instability to electrons. Then, the produced ion entropy balances to the sum of the ion and electron dissipations at the saturation of the KBM instability growth, in contrast to ITG turbulence where ion entropy production mostly balances to ion dissipation.

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 gyrokinetic quasi-neutrality equation is considered from the point of view of the push-forward representation of particle density associated with the guiding-center transformation and the gyro-center transformation involved in the standard gyrokinetic formulation. It is clearly shown that the higher order displacement vector of the guiding-center transformation as well as the gyro-center displacement vector should be taken into account in the long wavelength regime. The higher order displacement vector of the guiding-center transformation yields additional higher order terms related to nonuniformity of magnetic field in the gyrokinetic quasi-neutrality equation. These additional terms may be important when the gradient scale length of electric field can be comparable to that of the magnetic field as in low aspect ratio tokamaks. Also the gyrokinetic Hamiltonian should be modified for consistency.

The first detailed measurements of ion-impurity dynamics for NBI-heated ELMy H-modes at the edge of the JT-60U tokamak are reported. We investigated the ability of external momentum/power input to modify and control the radial electric field, E r , and pedestal structures. The relationship between E r and pedestal structures of ion-impurity density, n i, and temperature, T i, during the ELMing H-mode phase for various momentum input directions (i.e. co-, balanced- and counter-NBI) and input powers from perpendicular NBI are compared with the ELM-free phase. The observed trend is that the edge E r -well width increases in the co-NBI discharge, while the E r value at the base of the E r -well becomes more negative in the counter-NBI discharge. The scale length for both n i and T i in the pedestal is ∼2 cm and values are ∼1 for both ELM-free and ELMing phases with different magnitudes of E r (and/or E r shear). Characteristics of the turbulent density fluctuation, in addition to a uniform toroidal MHD oscillation (i.e. n = 0), during both ELM-free and ELMing phases are also reported.

Representation of particle fluid moments in terms of fluid moments in the modified guiding-centre model for flowing plasmas with large E × B velocity [N. Miyato et al., J. Phys. Soc. Jpn. 78, 104501 (2009)] is derived from the formal exact representation by a perturbative expansion in the subsonic flow case. It is similar to that in the standard gyrokinetic model in the long wavelength limit, except it has an additional flow term. The flow term has no effect on the representation for particle density, leading to the same representation as the standard one formally. In the conventional guiding-centre models for flowing plasmas, on the other hand, the representation for particle density is different from the standard one. This is due to the difference in the transformation for the guiding-centre position. Although the exact representation usually used in the standard gyrokinetic model has a different form from that in the modified guiding-centre case, correspondence between the two models is shown by considering the alternative form of exact representation in the standard gyrokinetic case. The representation for particle density is also obtained from the single particle Lagrangian by a variational method which is used to derive the representation in the transonic case.

The nonlinear excitation and saturation mechanism of geodesic acoustic mode (GAM), as well as its radial structure, in tokamak plasmas are investigated by applying a newly well-benchmarked gyrofluid model. At first, an empirical closure relation for the conventional three-field gyrofluid modeling is presented for ion temperature gradient (ITG) fluctuations and the GAMs. The zonal flow damping is precisely examined by comparing with theoretical predictions and other kinetic calculations. Then, a local code and the global version are advanced to simulate the nonlinear excitation of the GAMs by ITG fluctuations through the Reynolds stress. It is found that the GAM instability can be nonlinearly excited under the competition between the nonlinear driving and the collisionless damping. The pump amplitude threshold of the GAM instability is higher than that of the zonal flow instability. Meanwhile, the unstable GAMs are mainly saturated by the intrinsic Landau damping, which is different from the stationary zonal flow counterpart. It is testified that the sound waves are damped fluctuations in ITG turbulence. Furthermore, the radial structure of the GAMs is shown as krρi ≤ 1.0, which is shorter than that of the pure zonal flows.

We have constructed a four-field minimal model that describes the growing intermittency of turbulence associated with the geodesic acoustic mode (GAM) observed in our toroidal Landau-fluid simulations [K Miki et al. 2007 Phys. Rev. Lett. 99, 145003]. The intermittent dynamics are well reproduced by the model for the reference parameters used in the simulation. The model can also reproduce characteristics of turbulent transport associated with the GAM, such as a single burst leading to a full quench of turbulence and also a steady state turbulence mixed with steady zonal flows and GAMs. Investigating the behaviour of the solution trajectories around the fixed points in four-dimensional phase space, we study the comprehensive properties of the model and identify the bifurcation property between Dimits shift and steady state turbulence regimes, which correspond to different eigen-states.

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...

Zonal flow behaviour and its effect on turbulent transport in reversed magnetic shear tokamaks are investigated by global simulations of electrostatic ion temperature gradient driven turbulence. When the safety factor q is reduced. zonal flows in a minimum q region change from oscillatory to stationary and suppress the turbulent transport effectively This result indicates that the change of zonal flow behaviour in the minimum q region may trigger the formation of ion transport barriers.

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.

The dynamics of secondary fluctuations with poloidal long wavelength and low frequency in electron-temperature-gradient (ETG) turbulence saturation is considered in sheared slab geometry. A simplified modeling analysis shows that this kind of large-scale structure including streamers may saturate primary ETG instability through poloidal mode coupling. Spectral analyses in three-dimensional ETG simulations clearly exhibit the secondary excitation and the probable relevancy to KTG saturation. The result may implicate a lower fluctuation level in ETG turbulence.