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We investigate the finite Larmor radius (FLR) effects that are associated with an external heat source or a sink in the full-f formulation of plasma dynamics. Specifically, we show that a gyrocenter or an additional vorticity source due to the FLR effect should be replenished in full-f turbulence simulations. A quantitative energetics analysis in particle phase space demonstrates that an additional vorticity source is required to satisfy the total energy conservation. A physics picture is presented to elucidate the mechanism of the vorticity source generation from the FLR effects of a heat source or a sink, which reproduces the main result obtained from the quantitative analysis. The additional vorticity source is expected to considerably enhance the generation of the radial electric field and subsequent E × B flow shear in the off-axis heating case.

This work presents a nonlinear gyrokinetic analysis, which addresses one of the long-lived conundrums in Ohmically heated fusion plasmas. The widely observed linear Ohmic confinement (LOC) to saturated Ohmic confinement (SOC) transition of the energy confinement time $\tau_E$ with increasing density is successfully reproduced from nonlinear gyrokinetic simulations for the first time. Suppression of trapped electron turbulence by collisional detrapping due to increasing density is found to be responsible for the transition. Microturbulence transition from TEM to ITG is found to coincide, but not a necessary condition for the LOC-SOC transition. Damping of nonlinearly generated zonal flow by increasing collisionality with density can be responsible for the energy confinement degradation in SOC regime.

We perform a computational study of characteristics of coupled drift wave (DW)-parallel velocity gradient (PVG) driven turbulence. The three-dimensional Hasegawa–Mima equation combined with ion parallel flow dynamics is used for this study. Energetic analyses, both analytic and computational, show the energy equipartition of the parallel Reynolds power (i.e. the free energy due to a gradient in equilibrium parallel velocity) in parallel and perpendicular directions. A considerable portion of the perpendicular energy that is transferred through the parallel coupling generates the perpendicular zonal flow (ZF), implying the increase of the ZF level when an equilibrium PVG is present. A careful analysis of parallel-perpendicular coupling dynamics shows that the vortex stretching-like term in this system plays a significant role in the ZF generation. This is in contrast to the neutral fluid turbulence where it hinders the inverse cascade process. However, the ZF generation from PVG turbulence is found to be less effective in comparison with that of DW turbulence.

From global gyrokinetic simulations of toroidal ion temperature gradient-driven turbulence, we show that the ion parallel compression has a strong influence on the generation and radial profile formation of zonal flows. The kinetic potential vorticity (PV) flux and its fluid expression are used to elucidate the zonal flow generation mechanism. In the absence of sheared equilibrium flow, the dominant contributions to the net PV flux are shown to come from the parallel compression and the grad-B drift, and to largely cancel out each other. With a finite parallel rotation shear, however, the parallel compression-driven flux becomes dominant over the grad-B drift-driven one, leading to a change in the radial zonal flow profile. The imbalance between the parallel compression and the grad-B drifts results in a considerable amplification of the zonal flow and a reduction of turbulence fluctuation levels as compared to the non-rotating plasma. These findings demonstrate an essential role of the parallel compression in the zonal flow generation and confinement improvement for rotating tokamak plasmas.

In cold pulse experiments in J-TEXT, not only are rapid electron temperature increases in the core observed, but also steep rises in the inner density are found. Moreover, some evidence of acceleration of the core toroidal rotation is also observed during the non-local transport process of electron temperature. These new findings of cold pulse experiments in J-TEXT suggest that turbulence spreading is a possible mechanism for the non-local transport dynamics.

We study the impact of impurities on turbulence driven intrinsic rotation (via residual stress) in the context of the quasi-linear theory. A two-fluid formulation for main and impurity ions is employed to study ion temperature gradient modes in sheared slab geometry modified by the presence of impurities. An effective form of the parallel Reynolds stress is derived in the center of mass frame of a coupled main ion-impurity system. Analyses show that the contents and the radial profile of impurities have a strong influence on the residual stress. In particular, an impurity profile aligned with that of main ions is shown to cause a considerable reduction of the residual stress, which may lead to the reduction of turbulence driven intrinsic rotation.

© 2015 AIP Publishing LLC. Using three-dimensional nonlinear simulations of tokamak turbulence, we show that an edge transport barrier (ETB) forms naturally once input power exceeds a threshold value. Profiles, turbulence-driven flows, and neoclassical coefficients are evolved self-consistently. A slow power ramp-up simulation shows that ETB transition is triggered by the turbulence-driven flows via an intermediate phase which involves coherent oscillation of turbulence intensity and E × B flow shear. A novel observation of the evolution is that the turbulence collapses and the ETB transition begins when RT> 1 at t = tR(RT: normalized Reynolds power), while the conventional transition criterion (ω E × B > γ l i n where ω E × B denotes mean flow shear) is satisfied only after t = tC( >tR), when the mean flow shear grows due to positive feedback.

From the nonlinear simulations of the two-dimensional forced-damped Hasegawa–Mima equation, we show that a Reynolds number-like parameter, Rew, can represent a power law exponent of the energy spectrum in Hasegawa–Mima turbulence. Rew is defined as the ratio of nonlinear convection to dissipation. For a same value of Rew, the power law exponent in the inertial range is shown to be uniquely determined regardless of the forcing and dissipation conditions. At high Rew, the power law exponent asymptotically converges to −7.2, consistent with a recent theoretical prediction based on the shell model [Gurcan et al., Plasma Phys. Controlled Fusion 52, 045002 (2010)].

We present a semi-analytic model for low (L) to high (H) mode transition power threshold (Pth). Two main assumptions are made in our study. First, high poloidal mode number drift resistive ballooning modes (high-m DRBM) are assumed to be the dominant turbulence driver in a narrow edge region near to last closed flux surface. Second, the pre-transition edge profile and turbulent diffusivity at the narrow edge region pertain to turbulent equipartition. An edge power balance relation is derived by calculating the dissipated power flux through both turbulent conduction and convection, and radiation in the edge region. Pth is obtained by imposing the turbulence quench rule due to sheared E × B rotation. Evaluation of Pth shows a good agreement with experimental results in existing machines. Increase of P th at low density (i.e., the existence of roll-over density in P th vs. density) is shown to originate from the longer scale length of the density profile than that of the temperature profile. © 2014 AIP Publishing LLC.

We present an analytic study of momentum transport of tokamak plasmas in the vicinity of minimum safety factor (q) position in reversed magnetic shear configuration. Slab ion temperature gradient modes with an equilibrium flow profile are considered in this study. Quasi-linear calculations of momentum flux clearly show the novel effects of q-curvature on the generation of intrinsic rotation and mean poloidal flow without invoking reflectional symmetry breaking of parallel wavenumber (k∥). This q-curvature effect originates from the inherent asymmetry in k∥ populations with respect to a rational surface due to the quadratic proportionality of k∥ when q-curvature is taken into account. Discussions are made of possible implications of q-curvature induced plasma flows on internal transport barrier formation in reversed shear tokamaks.

We present a model for turbulent electron thermal transport at the edge pedestal in high (H)-mode plasmas based on electron temperature gradient (ETG) turbulence. A quasi-linear analysis of electrostatic toroidal ETG modes shows that both turbulent electron thermal diffusivity and hyper-resistivity exhibits the Ohkawa scaling in which the radial correlation length of turbulence becomes the order of electron skin depth. Combination of the Ohkawa scales and the plasma current dependence results in a novel confinement scaling inside the pedestal region. It is also shown that ETG turbulence induces a thermoelectric pinch, which may accelerate the density pedestal formation. © 2013 AIP Publishing LLC.

We report the results of a gyrokinetic simulation study elucidating the characteristics of the current driven by electron temperature gradient (ETG) turbulence in toroidal geometry. We examined the amount of the ETG turbulence-driven current for different turbulence levels, which were obtained by varying the relative electron gyroradius ρ* = ρe/a. Simulations show that the amount of the ETG turbulence-driven current increases with ρ* due to the gyro-Bohm scaling of turbulence intensity. A perturbation of the equilibrium q-profile by the ETG turbulence-driven current becomes noticeable when ρ* > 1/4000. Even in a small ρ* case, the proportional relation between the ETG turbulence-driven current and turbulence intensity suggests that a considerable intrinsic current can be driven inside an edge pedestal where a steep gradient of the electron temperature profile can excite ETG turbulence in a narrow region.

We perform an analytic study of the tertiary instability driven by a strong excitation of zonal flows during high density low to high (LH) mode transition. The drift resistive ballooning mode is assumed to be a dominant edge turbulence driver. The analysis reproduces main qualitative features of early computational results [Rogers and Drake, Phys. Rev. Lett. 81, 4396 (1998); Guzdar et al., Phys. Plasmas 14, 020701 (2007)], as well as new characteristics of the maximum edge density due to the onset of the tertiary instability. An analytical scaling indicates that the density scaling of LH transition power may be determined by the onset condition of the tertiary instability when the operating density approaches to the Greenwald density.

A study is conducted on the impact of electromagnetic (EM) fluctuations on residual Reynolds stress in the context of the quasi-linear theory. We employ a fluid formulation describing EM ion temperature gradient turbulence. Analyses show that finite plasma β (=plasma thermal energy/magnetic energy) significantly increases the residual stress, potentially leading to the strong enhancement of flow generation in high β plasmas. We identify that this strong increase of residual stress originates from the reinforcement of radial ⟨k∥⟩ (=spectrally averaged parallel wavenumber) asymmetry due to the deformation of eigenfunctions near a rational surface.

PHYSICS OF PLASMAS 21, 012302 (2014) Momentum transport in the vicinity of q min in reverse shear tokamaks due to ion temperature gradient turbulence Rameswar Singh, 1,2,a) R Singh, 1,3 Hogun Jhang, 3 and P. H. Diamond 3,4,5 Institute for Plasma Research, Bhat, Gandhinagar 382 428, India Laboratoire de Physique des Plasmas, Ecole Polytechnique route de Saclay, 91128 Palaiseau Cedex, France WCI Center for Fusion Theory, National Fusion Research Institute, Daejeon 305-333, South Korea Center for Momentum Transport and Flow Organization, University of California, San Diego, California 92093, USA Center for Astrophysics and Space Sciences, University of California San Diego, 9500 Gilman Dr., La Jolla, California 92093-0424, USA (Received 23 October 2013; accepted 20 December 2013; published online 13 January 2014; publisher error corrected 3 March 2014) We present an analytic study of momentum transport of tokamak plasmas in the vicinity of minimum safety factor (q) position in reversed magnetic shear configuration. Slab ion temperature gradient modes with an equilibrium flow profile are considered in this study. Quasi-linear calculations of momentum flux clearly show the novel effects of q-curvature on the generation of intrinsic rotation and mean poloidal flow without invoking reflectional symmetry breaking of parallel wavenumber (k k ). This q-curvature effect originates from the inherent asymmetry in k k populations with respect to a rational surface due to the quadratic proportionality of k k when q-curvature is taken into account. Discussions are made of possible implications of q-curvature C 2014 induced plasma flows on internal transport barrier formation in reversed shear tokamaks. V AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4861625] I. INTRODUCTION Understanding of turbulent momentum transport in toka- mak plasmas has been a key research topic over the past dec- ades. This is because of the profound influence of plasma flows (both toroidal and poloidal) on confinement properties of tokamak plasmas. Radial transport of toroidal flow deter- mines the flow profile which has an influence on confinement enhancement by providing the E ! B shear driven by the ra- dial flow gradient. 1,2 Plasma rotation can also stabilize dan- gerous, magnetohydrodynamics (MHD) instabilities such as resistive wall modes (RWM), which is essential to realize high performance advanced tokamak operation. 3,4 Either external sources, such as neutral beam injection (NBI), or background turbulence (via turbulent Reynolds stress 5,6 ) can drive plasma flows in tokamaks. The latter, known as intrinsic rotation, 7 has been a focus in confinement physics research for many years because of its potential impact on reactor scale experiments where neutral beams cannot penetrate into the core region. One of the mechanisms of intrinsic rotation generation is by conversion of radial inhomogeneity into hk k i (¼spectrally averaged wavenumber in parallel direction) asymmetry driving residual stress. 8 Since background turbulence also gives rise to turbulent mo- mentum diffusivity (viscosity), momentum convection/ pinch, as well as playing as a source of intrinsic torque, the final flow profile will be determined by a “balance” between external and intrinsic torques and turbulent momentum con- duction and pinch. Momentum pinch itself cannot drive intrinsic rotation; however, it is important for flow profile a) rameswar@ipr.res.in 1070-664X/2014/21(1)/012302/12/$30.00 shaping. Symmetry breaking due to magnetic field curvature and gradient results in momentum pinch in tokamaks. 9–14 Conversion of radial inhomogeneity into hk k i asymme- try requires some symmetry breaking mechanisms. 7,8,15–19 Role of mean E ! B shearing in symmetry breaking, hence in off-diagonal momentum flux, was identified by many authors. 16,18 Recently, G€ urcan et al. showed how the mean E ! B shear can lead to the reflectional symmetry breaking of hk k i in ion temperature gradient (ITG) turbulence, result- ing in finite parallel residual stress. 18 Reflectional symmetry breaking of k jj here means generation of eigenmode averaged wave number hk jj i 6 ¼ 0 by symmetry breaking of eigenmode about a rational surface, i.e., by j/j 2 ðxÞ 6 ¼ j/jð%xÞ. Turbulence intensity gradient can also induce hk k i symmetry breaking, 19 which may be an important driver of the intrinsic torque near the top of a transport barrier where a strong fluc- tuation intensity gradient is present. The process of hk k i sym- metry breaking by E ! B shear and/or intensity gradient implies a coupling between intrinsic rotation and transport barrier dynamics, such as internal transport barrier (ITB) for- mation, which involves steep temperature and/or density gra- dients (i.e., strong radial inhomogeneity) and the strong E ! B shear and/or the fluctuation intensity gradient (i.e., hk k i symmetry breaking). Gyrokinetic simulations have shown the generation of intrinsic rotation from the hk k i sym- metry breaking by mean E ! B shear 20–23 and turbulence in- tensity gradient 20 and up-down asymmetry of equilibrium magnetic topology. 24,25 Gyrokinetic simulations have also shown residual stress from profile shearing effects. 26,27 Apart from the symmetry breaking driven by mean E ! B shear, turbulence can also generate mean poloidal and parallel flows via various other mechanisms. Weiland et al. 28 showed toroidal residual stress generation form by C 2014 AIP Publishing LLC V This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 132.239.66.163 On: Tue, 20 May 2014 19:20:05

We show that strong edge magnetic shear, which is generic to divertor plasmas, makes the E × B shearing of turbulence eddys in toroidal geometry more effective. From calculations of the E × B shearing rates for KSTAR edge parameters, we conclude that the enhanced magnetic shear at the diverted KSTAR plasma edge facilitates E × B shear suppression of turbulence and ensuing H-mode transition. (Some figures may appear in colour only in the online journal)

We present a statistical analysis of heat transport in stationary enhanced confinement regimes obtained from flux-driven gyrofluid simulations. The probability density functions of heat flux in improved confinement regimes, characterized by the Nusselt number, show significant deviation from Gaussian, with a markedly fat tail, implying the existence of heat avalanches. Two types of avalanching transport are found to be relevant to stationary states, depending on the degree of turbulence suppression. In the weakly suppressed regime, heat avalanches occur in the form of quasi-periodic (QP) heat pulses. Collisional relaxation of zonal flow is likely to be the origin of these QP heat pulses. This phenomenon is similar to transient limit cycle oscillations observed prior to edge pedestal formation in recent experiments. On the other hand, a spectral analysis of heat flux in the strongly suppressed regime shows the emergence of a 1/f (f is the frequency) band, suggesting the presence of self-organized criticality (SOC)-like episodic heat avalanches. This episodic 1/f heat avalanches have a long temporal correlation and constitute the dominant transport process in this regime. © 2012 American Institute of Physics.

We study the interplay between intrinsic rotation and internal transport barrier (ITB) dynamics through the dynamic change of the parallel Reynolds stress. Global flux-driven gyrofluid simulations are used for this study. In particular, we investigate the role of parallel velocity gradient instability (PVGI) in the ITB formation and the back transition. It is found that the excitation of PVGI is followed by a change in the Reynolds stress which drives a momentum redistribution. This significantly influences E × B shear evolution and subsequent ITB dynamics. Nonlocal interactions among fluctuations are also observed during the PVGI excitation, resulting in turbulence suppression at the ITB. © 2012 American Institute of Physics.