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Abstract: The self-organization is one of the most interesting phenomena in the non-equilibrium complex system, generating ordered structures of different sizes and durations. In tokamak plasmas, various self-organized phenomena have been reported, and two of them, coexisting in the near-marginal (interaction dominant) regime, are avalanches and the E × B staircase. Avalanches mean the ballistic flux propagation event through successive interactions as it propagates, and the E × B staircase means a globally ordered pattern of self-organized zonal flow layers. Various models have been suggested to understand their characteristics and relation, but experimental researches have been mostly limited to the demonstration of their existence. Here we report detailed analyses of their dynamics and statistics and explain their relation. Avalanches influence the formation and the width distribution of the E × B staircase, while the E × B staircase confines avalanches within its mesoscopic width until dissipated or penetrated. Our perspective to consider them the self-organization phenomena enhances our fundamental understanding of them as well as links our findings with the self-organization of mesoscopic structures in various complex systems.

An experimental study is conducted on macro- and microscopic characteristics of low to high (LH) transition acquired by electron cyclotron resonance heating (ECRH) in KSTAR. A scan of pre-transition density demonstrates the existence of the characteristic minimum density, which requires minimum power to make LH transition. The minimum density in KSTAR shows a tendency to be lower than that evaluated from an empirical scaling law proposed by Ryter et al. [Nucl. Fusion 54, 083003 (2014)]. A comprehensive study of the evolution of low wavenumber electron temperature fluctuations is carried out using electron cyclotron emission imaging diagnostics. An analysis of the fluctuation amplitude in L-mode in terms of the electron collisionality and the electron temperature scaling length suggests that the dissipative trapped electron mode is likely to be a dominant instability before the LH transition. The fluctuation amplitude reduces first as the transition starts. A coherent mode that chirps down from 60 to 20 kHz emerges when the transition further develops. This coherent mode is then shown to revive turbulence that has been reduced significantly during the initial stage of the LH transition. The revival of turbulence could be a possible origin of the absence of the large edge localized mode when the coherent mode is persistent in ECRH-induced H-mode plasmas. [ABSTRACT FROM AUTHOR]

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 physical origins of parallel guiding center drift and parallel velocity-dependent effective magnetic field ( B ‖ * ) appearing in the Hamiltonian formulation of a particle motion in a curved magnetic field. The magnetic twist term is shown to be responsible for both of them. The parallel guiding center drift originates from the change in the effective parallel velocity due to the combined effect of the initial perpendicular motion (v⊥0) and the magnetic twist. The effective magnetic field arises from the collated effect of the change in v⊥0 due to its initial parallel guiding center motion and the conservation of magnetic moment. This understanding clearly shows that the appearance of B ‖ * is a consequence of magnetic moment conservation in curved magnetic fields. [ABSTRACT FROM AUTHOR]

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.

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 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 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. © 2013 IAEA, Vienna.

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.

We present an analytic study of the impact of external torque on the formation of ion internal transport barriers (ITBs). A simple analytic relation representing the effect of low external torque on transport bifurcations is derived based on a two field transport model of pressure and toroidal momentum density. It is found that the application of an external torque can either facilitate or hamper bifurcation in heat flux driven plasmas depending on its sign relative to the direction of intrinsic torque. The ratio between radially integrated momentum (i.e., external torque) density to power input is shown to be a key macroscopic control parameter governing the characteristics of bifurcation. © 2012 American Institute of Physics.