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A nonlinear unified fluid model that describes the Equatorial Electrojet, including the Farley-Buneman and gradient-drift plasma instabilities, is defined and shown to be a noncanonical Hamiltonian system. Two geometric constants of motion for the model are obtained and shown to be Casimir invariants. A reformulation of the model shows the roles of the density-gradient scale-length (Ln) and the cross-field drift-velocity (vE) in controlling the dynamics of unstable modes in the growing, transition and saturation phases of a simulation. [ABSTRACT FROM AUTHOR]

The electron temperature gradient (ETG) mode, which is a universal mechanism for turbulent electron thermal transport in plasmas, is produced and verified in steady-state, collisionless hydrogen plasma of the Columbia Linear Machine. Electron temperature profiles with strong gradients are produced by DC acceleration in a remote biased mesh and subsequent thermalization. Finite amplitude ∼5%, steady-state oscillations at ∼0.3-0.5MHz (in the plasma frame), with azimuthal wave numbers m∼14-16 and parallel wave number k∥∼0.01cm-1 are measured. The massively parallel gyrokinetic toroidal code is used to study these modes. The results show that in the linear phase, the dispersion relation is consistent with kinetic theory. In the nonlinear stage, very strong nonlinear wave coupling gives rise to an inverse cascade of the energy from the fastest growing high-m modes to low-m nonlinear oscillations, which are consistent with the measured azimuthal mode spectrum. The radial structure of the fluctuation also agrees with the experiment. An inward radial shift of the peak of the potential fluctuation occurs during the nonlinear saturation and fluctuation fingers extend radially out to the edge plasma. Three-wave coupling mechanism is involved in the saturation of ETG modes. The simulations show a power law spectrum of the turbulence which suggests that the renormalization theory is appropriate to interpret the turbulent thermal flux. [ABSTRACT FROM AUTHOR]

Vortex structures and related heat transport properties in slab electron temperature gradient (ETG) driven turbulence are comprehensively investigated by means of nonlinear gyrokinetic Vlasov simulations, with the aim of elucidating the underlying physical mechanisms of the transition from turbulent to coherent states. Numerical results show three different types of vortex structures, i.e., coherent vortex streets accompanied with the transport reduction, turbulent vortices with steady transport, and a zonal-flow-dominated state, depending on the relative magnitude of the parallel compression to the diamagnetic drift. In particular, the formation of coherent vortex streets is correlated with the strong generation of zonal flows for the cases with weak parallel compression, even though the maximum growth rate of linear ETG modes is relatively large. The zonal flow generation in the ETG turbulence is investigated by the modulational instability analysis with a truncated fluid model, where the parallel dynamics such as acoustic modes for electrons is incorporated. The modulational instability for zonal flows is found to be stabilized by the effect of the finite parallel compression. The theoretical analysis qualitatively agrees with secondary growth of zonal flows found in the slab ETG turbulence simulations, where the transition of vortex structures is observed. [ABSTRACT FROM AUTHOR]

Vortex structures in slab electron temperature gradient (ETG) driven turbulence are investigated by means of a gyrokinetic simulation with high phase-space resolution. Depending on parameters that determine the eigenfrequency of the linear ETG modes, two different flow structures, i.e., statistically steady turbulence with a weak zonal flow and coherent vortex streets along a strong zonal flow, are observed. The former involves many isolated vortices and their mergers with complicated motion and leads to steady electron heat transport. When the latter is formed, phase difference and high wavenumber components of potential and temperature fluctuations are reduced, and the electron heat transport decreases significantly. It is also found that the phase matching with the potential fluctuation is correlated with the reduction in the imaginary part of the perturbed distribution function, and it occurs not only for the temperature fluctuation but also for any nth velocity moments. A traveling wave solution of a Hasegawa–Mima type equation derived from the gyrokinetic equation with the ETG agrees well with the coherent vortex streets found in the slab ETG turbulence. [ABSTRACT FROM AUTHOR]

According to recent experiments, magnetically confined fusion plasmas with “drift wave–zonal flow turbulence” (DW-ZF) give rise to broadband electromagnetic waves. Sharapov et al. [Europhysics Conference Abstracts, 35th EPS Conference on Plasma Physics, Hersonissos, 2008, edited by P. Lalousis and S. Moustaizis (European Physical Society, Switzerland, 2008), Vol. 32D, p. 4.071] reported an abrupt change in the magnetic turbulence during L-H transitions in Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)] plasmas. A broad spectrum of Alfvénic-like (electromagnetic) fluctuations appears from E×B flow driven turbulence in experiments on the large plasma device (LAPD) [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] facility at UCLA. Evidence of the existence of magnetic fluctuations in the shear flow region in the experiments is shown. We present one possible theoretical explanation of the generation of electromagnetic fluctuations in DW-ZF systems for an example of LAPD experiments. The method used is based on generalizing results on shear flow phenomena from the hydrodynamics community. In the 1990s, it was realized that fluctuation modes of spectrally stable nonuniform (sheared) flows are non-normal. That is, the linear operators of the flows modal analysis are non-normal and the corresponding eigenmodes are not orthogonal. The non-normality results in linear transient growth with bursts of the perturbations and the mode coupling, which causes the generation of electromagnetic waves from the drift wave–shear flow system. We consider shear flow that mimics tokamak zonal flow. We show that the transient growth substantially exceeds the growth of the classical dissipative trapped-particle instability of the system. [ABSTRACT FROM AUTHOR]

The controlled formation of an internal transport barrier (ITB) is observed in GAMMA 10 [T. Cho et al., Nucl. Fusion 45, 1650 (2005)]. The barrier is localized within a layer of a strongly sheared Er×B plasma rotation (5.5c≤10 cm). This high-vorticity layer is formed and maintained by off-axis electron-cyclotron heating, which generates a cylindrical layer (4c<7 cm) with a high-energy electron population that modifies the initial Gaussian radial potential profile into a nonmonotonic one with a hump structure. The local gradients of Ti and Te are appreciably enhanced in the ITB layer, similarly to those of the ITB in tokamaks and stellarators. Reductions in the effective ion and electron thermal diffusivities are obtained in the barrier layer. A reduction of the observed low-frequency turbulence in the ITB layer and a partial decoupling of the turbulent structures localized on either side of the layer are demonstrated by two-dimensional x-ray diagnostics. [ABSTRACT FROM AUTHOR]

The interaction between turbulence and a nonlinear tearing mode is investigated numerically using a 2D electrostatic model. Turbulence is found to cause transitions between the different roots for the propagation velocity of the mode. The transitions take the mode towards roots with slower propagation that are characterized by a locally flattened density profile. For sufficiently large islands the transition reduces the drive for the tearing mode. [ABSTRACT FROM AUTHOR]

The nonlinear dynamics of coherent circular/elliptical cyclonic and anticyclonic vortices in plane flow with constant shear is investigated numerically using a dealiased Fourier pseudospectral code. The flow is asymptotically linearly stable, but is highly non-normal, allowing perturbations to gain energy transiently from the background shear flow. This linear transient growth interplays with nonlinear processes. In certain cases it is shown that the nonlinear feedback is positive, leading to self-sustaining coherent vortices. Self-sustaining coherent vortices exist where the vorticity is parallel to the mean flow vorticity (cyclonic rotation). The required nonlinear feedback is absent for small amplitude anticyclonic vortices. However, elliptical anticyclonic vortices become self-sustaining if the amplitude exceeds a threshold value. The self-sustaining of coherent vortices is similar to the subcritical, so-called bypass, transition to turbulence in shear flows. The common features are: transient linear growth; positive nonlinear feedback; and anisotropy of the linear and nonlinear phenomena (in contrast to isotropic Kolmogorov turbulence). A plasma laboratory experiment is suggested based on the results of this investigation. [ABSTRACT FROM AUTHOR]

A novel closure model is presented to give a set of fluid equations which describe a collisionless kinetic system. In order to take account of the time reversal symmetry of the collisionless kinetic equation, the new closure model relates the parallel heat flux to the temperature and the parallel flow in terms of the real-valued coefficients in the unstable wave number space. Effects of the closure model on turbulence saturation and anomalous transport are investigated based on kinetic and fluid entropy balances. When the closure model is applied to the three-mode ion temperature gradient (ITG) driven system, the fluid system of equations reproduces the exact nonlinear kinetic solution found by Watanabe, Sugama, and Sato [Phys. Plasmas 7, 984 (2000)]. Oscillatory behaviors and initial amplitude dependence of other numerical kinetic solutions of the three-mode ITG problem can also be accurately described by the fluid system. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Models of ion temperature gradient-driven turbulence are reexamined in terms of the structure of the turbulent spectrum for radially localized modes to explain the significant difference between the radial profiles of ion heat conductivity inferred from local turbulence models and those observed in experiments. The strong radial inhomogeneity of the effective density of the turbulence spectrum in k is shown to produce a significant increase of the fluctuation level and ion thermal diffusion toward the plasma edge as compared with the local models under certain conditions. The conditions required are stated and should be tested with numerical simulations. [ABSTRACT FROM AUTHOR]

Previous studies of the ion-temperature-gradient (ITG) driven turbulence are expanded to include the effect of sheared E×B flows in sheared magnetic fields. The radial eigenmodes are shown to substantially change character by shifting the modes off the rational surface. The new mode structure and growth rate directly affects the transport of both thermal energy and momentum in the sheared flows. The growth rate first increases with small shear flow and then decreases. The theoretical correlation of the shear flow with the thermal transport is important with respect to the transitions observed in tokamaks of a low (L mode) to a high (H mode) thermal confinement state as a function of the poloidal rotation velocity in the shear flow layer. The three-dimensional nonlinear simulations show that the anomalous ion thermal diffusivity is reduced significantly when dvE/dx[bar_over_tilde:_approx._equal_to]2(cs/Ls) ((1+ηi)Ti/Te)1/2. This condition is thought to be satisfied in a boundary layer in tokamaks with shear flow. [ABSTRACT FROM AUTHOR]

A new approach to the calculation of turbulent transport coefficients for radially localized modes is presented. The theory takes into account the nonuniformity of the distribution of rational (resonant) magnetic surfaces in minor radius. This distribution function is proportional to the density of available states of excitation. The resulting density of states correction qualitatively changes the radial profile of the transport coefficients, as compared to the usual local diffusivity formulas. The correction factor calculated for the ηi -mode turbulence increases toward the plasma edge and allows a better qualitative agreement of the radial χi profile with experimental data than the conventional approach. [ABSTRACT FROM AUTHOR]

By an electromagnetic incompressible two-fluid model describing both ion temperature gradient drift modes (ηi modes) and resistive interchange modes (g modes), a new type of ηi mode is studied in cylindrical geometry including magnetic shear and an averaged curvature of Heliotron/Torsatron. This ηi mode is destabilized by the coupling to the unstable g mode. Finite plasma pressure beta increases the growth rate of this mode and the radial mode width also increases with plasma pressure beta indicating large anomalous transport in the Heliotron/Torsatron configuration. The transport from ηi mode exceeds that from resistive g when the mean-free-path exceeds the machine circumference. For plasma beta above two to three times the Suydam limit, the m=1/n=1 growth rate increases from the ηi mode value to the magnetohydrodynamic (MHD) value. [ABSTRACT FROM AUTHOR]

Discusses the use of low-order mode coupling equations to describe computer simulations of resistive-g turbulent convection that show bifurcations for the onset of steady and pulsating sheared mass flows. Convective transport states identified with tokamak confinement regimes; Time scale expansion required to drive the Markovian close formula.

Studies the low-frequency turbulence driven by the shear in the mass flow velocity parallel to the magnetic field. Use of the fluid theory in a slab configuration with magnetic shear; Ion temperature gradient effects; Eigenfunctions of the linear instability; Quasilinear Reynolds stress induced by asymmetric fluctuations.

Focuses on turbulent momentum transport given by the Reynolds stress as a candidate for explaining the production and sustainment of the mean shear flow in the high confinement mode. Fluctuation mechanism for the shear flow generation and transport reduction in the three-dimensional multihelicity system.

Demonstrates and analyzes suppression of resistive g-mode turbulence by background shear flow generated from a small external flow source and amplified by the fluctuation-induced Reynolds stress. Paradigm for the low-to-high (L-H) confinement mode transition; Properties used in the sheared slab configuration to demonstrate the L-H transition model.

From the nonlinear gyrokinetic equation we formulate the renormalized turbulence equation for the η[sub i]-mode drift wave instability. The study shows that the dominant nonlinear damping mechanism is from the E X B convection of the pressure fluctuation and that the kinetic modifications to the fluid E X B mode coupling, studied earlier, shift the spectrum toward the shorter wavelengths. Balancing the linear growth rate with the nonlinear damping rate at the linearly most unstable region, we calculate the anomalous ion thermal conductivity, which exceeds the neoclassical plateau formula and gives a value of the same order as that previously computed by Horton, Choi, and Tang [Phys. Fluids 26, 1077 ( 1981 ) ], but with a kinetic enhancement factor. Also, the thermal conductivity formula remains finite for vanishing density gradient. [ABSTRACT FROM AUTHOR]

Studies the turbulence driven by the ion temperature gradient, the mass shear flow parallel to the magnetic field, and the impurity ion density gradient in confined plasma, in a sheared slab magnetic configuration. Enhancement of the turbulence drive by the shear flow and the negative density gradient of the impurity ions.

Focuses on transport processes and resultant entropy production in magnetically confined plasmas for toroidal systems with gyrokinetic electromagnetic turbulence. Derivation of the entropy balance equation from the double-averaged kinetic equation; Validity of the Onsager symmetry for the anomalous transport equations within the quasilinear framework.

Investigates self-consistent shear flow generation from the interaction of neoclassical and drift wave turbulence effects. Competition of the neoclassical poloidal flow damping with the plasma flow generation driven through the divergence of the Reynolds stress; Need for external torques to maintain fluctuation levels.

The universal drift instability and other drift instabilities driven by density and temperature gradients in a toroidal system are investigated in both linear and nonlinear regimes via particle simulation. Runs in toroidal and cylindrical geometry show dramatic differences in plasma behavior, primarily due to the toroidicity-induced coupling of rational surfaces through the poloidal mode number m. In the toroidal system studied, the eigenmodes are seen to possess (i) an elongated, nearly global radial extent, (ii) a higher growth rate than in the corresponding cylindrical system, (iii) an eigenfrequency nearly constant with radius, and (iv) a global temperature relaxation and enhancement of thermal heat conduction. Most importantly, the measured χi shows an increase with radius and an absolute value on the order of that observed in experiment. On the basis of the present observations, it is argued that the increase in χi with radius observed in experiment is caused by the global nature of heat convection in the presence of toroidicity-induced mode coupling. [ABSTRACT FROM AUTHOR]

The properties of the internal transport barriers are developed using theory and radial transport simulations that evolve local turbulent energy density with the temperature profiles. Standard ion temperature gradient models for the nonlinear radial fluxes driven by drift wave turbulence and stabilized by flow shear are implemented in a new high resolution multiple space-time transport code. A dimensionless parameterization of the input power is introduced and shown to characterize the bifurcation to an internal transport barrier. Examples of the interaction and feedback loops of the turbulence with the transport profiles are given for transport barriers as in the Tokamak Fusion Test Reactor [D. J. Grove et al. Nucl. Fusion 25, 1167 (1985)] and the Japan Atomic Energy Research Institute Tokamak-60 Upgrade (JT-60U) [Ninomiya et al., Phys. Fluids B 4, 2070 (1992)]. For the JT-60U the high performance discharge E 27969, which reached an equivalent Q[sub DT] of unity, is modeled with an appropriate set of turbulent thermal, angular momentum and particle diffusivities. The bifurcation analysis suggests a scaling law for the critical power for the onset of internal transport barriers. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We find and investigate via numerical simulations self-sustained two-dimensional turbulence in a magnetohy-drodynamic flow with a maximally simple configuration: plane, noninflectional (with a constant shear of velocity), and threaded by a parallel uniform background magnetic field. This flow is spectrally stable, so the turbulence is subcriticai by nature and hence it can be energetically supported just by a transient growth mechanism due to shear flow non-normality. This mechanism appears to be essentially anisotropic in the spectral (wave-number) plane and operates mainly for spatial Fourier harmonics with streamwise wave numbers less than the ratio of flow shear to Alfvén speed, ky < S/uA (i.e., the Alfvén frequency is lower than the shear rate). We focus on analysis of the character of nonlinear processes and the underlying self-sustaining scheme of the turbulence, i.e., on the interplay between linear transient growth and nonlinear processes, in the spectral plane. Our study, being concerned with a new type of energy-injecting process for turbulence--the transient growth--represents an alternative to the main trends of magnetohydrodynamic (MHD) turbulence research. We find similarity of the nonlinear dynamics to the related dynamics in hydrodynamic flows: to the bypass concept of subcriticai turbulence. The essence of the analyzed nonlinear MHD processes appears to be a transverse redistribution of kinetic and magnetic spectral energies in the wave-number plane [as occurs in the related hydrodynamic flow; see Horton et al., Phys. Rev. E 81, 066304 (2010)] and differs fundamentally from the existing concepts of (anisotropic direct and inverse) cascade processes in MHD shear flows. [ABSTRACT FROM AUTHOR]