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The radial size convergence of the E × B staircase pattern is addressed in local gradient-driven flux tube simulations of ion temperature gradient (ITG)-driven turbulence. It is shown that a mesoscale pattern size of ∼ 57 – 76 ρ is inherent to ITG-driven turbulence with Cyclone Base Case parameters in the local limit. [ABSTRACT FROM AUTHOR]

Electromagnetic microturbulence at finite normalized plasma pressure β = n 0 T 0 / (B 0 2 / 2 μ 0) (n0 is the equilibrium density, T0 the equilibrium temperature, B0 the equilibrium magnetic field, and μ0 the permeability of free space) is investigated within a local gradient-driven gyrokinetic framework. The focus lies on the well-known high β turbulence runaways [R. E. Waltz, Phys. Plasmas 17, 072501 (2010)] that have been proposed to set a nonlinear upper threshold β c , also known as the nonzonal transition [M. J. Pueschel, Phys. Rev. Lett. 110, 155005 (2013)]. In this paper, it is shown that persistent mesoscale zonal flow patterns, developing self-consistently on long time scales, mitigate high β turbulence runaways. The application of such mesoscale zonal flow states as initial conditions allows for the access of an improved β-regime, that is, β > β c , in which no turbulence runaway occurs. Various aspects of those mesoscale zonal flow-dominated improved states are investigated, such as (i) the stability constraints with respect to the mesoscale zonal flow level for the triggering of turbulence runaways, (ii) the influence of mesoscale zonal flows on magnetic stochasticity [W. M. Nevins, Phys. Rev. Lett. 106, 065003 (2010)], and (iii) the transfer processes connected to the drive and damping of mesoscale zonal flows. This work implies that β c does not set the upper limit in the normalized plasma pressure for stationary operation, provided persistent mesoscale zonal flow patterns can develop. Since variations of β occur on the energy confinement time, which is large compared to the time required for mesoscale zonal flows to develop, the reported mesoscale zonal flow-dominated improved β-regime is expected to be the experimentally relevant branch. Furthermore, this work highlights the need for sufficiently long simulation time traces of at least a few ∼ 10 3 R 0 / v th , i (R0 is the major radius, and v th , i is the ion thermal velocity), also within kinetic electron frameworks, to capture non-negligible long-term dynamics. [ABSTRACT FROM AUTHOR]

Microturbulence close to marginality with inclusion of electron dynamics and in the electrostatic limit [A. Weikl et al., Phys. Plasmas 25, 072305 (2018)] is revisited. In such states the E × B shearing rate ω E × B , i.e., the second radial derivative of the zonal electrostatic potential, a quantity often applied to study zonal flow structure formation, has been found to be dominated by radial fine scale features. Those features are significantly different from the mesoscale E × B staircase structures [G. Dif-Pradalier et al., Phys. Rev. E 82, 025401(R) (2010)] normally occurring close to the threshold. Instead of the E × B shearing rate, here, zonal flow structure formation is studied through the zonal flow shear induced tilt of turbulent structures, which is measured by director field methods. In contrast to dominant fine scale features in ω E × B , mesoscale zonal flow pattern formation on two disparate scales is identified: (i) A zonal flow with radial scale of the boxsize develops, (ii) superposed by zonal flow corrugations in form of shear layers emerging in the vicinity of lowest order rational layers. This mesoscale zonal flow pattern exhibits properties of E × B staircases: (i) A shearing rate of ∼ 10 − 1 v th , i / R 0 ( v th , i is the ion thermal velocity and R0 is the major radius), comparable to typical growth rates, can be attributed to both components of the mesoscale pattern. (ii) Avalanche-like turbulent transport events organize spatially on the same mesoscales. (iii) Shear stabilization by a background E × B shear flow requires values of the background shearing rate exceeding those connected to the mesoscale pattern. In conclusion, this work demonstrates that E × B staircases do develop, even when the E × B shearing rate ω E × B is dominated by radial fine scale features. The E × B shearing rate ω E × B , therefore, fails to estimate the shear provided by zonal flows when fine scale structures dominate its radial profile. [ABSTRACT FROM AUTHOR]

The interplay between an external torque and spontaneously occurring mesoscale structures, known as staircases, is investigated. Gyrokinetic simulations show that the E × B shear connected with the external torque does not simply add to the shear of the mesoscale structures. A positive (negative) externally forced E × B shear leads to a broadening of the positive (negative) region of the staircase but does not significantly change the plateau value or the narrow zero shear layer. In consequence, while the space and time averaged shearing rate is enhanced by the external torque, there is little or no effect on the turbulent transport. This raises doubts about the importance of driven or intrinsic rotation as a means to improve plasma confinement close to the stability threshold. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of turbulent dynamics on the neo-classical equilibrium in a tokamak, with an emphasis on the turbulence driven stationary electric current. The neo-classical solution is evaluated using the Hirschmann-Sigmar formalism, in which the turbulent dynamics enter as a forcing term. The latter forcing terms are evaluated through time averages of gyro-kinetic turbulence simulations and are linked with the velocity non-linearity in the gyro-kinetic equation. The time averaged turbulent forcing terms connected with the velocity non-linearity provide a non-negligible current drive, despite being a correction of second order in the normalized Larmor radius. For ITG turbulence, the force exerted due to the heat flux balance is the dominant contribution to the current. The parallel fluctuations of electron density/temperature and the electrostatic potential drive the majority of the current, which is in magnitude comparable to the bootstrap current in the kinetic cyclone base case and increases the total current by a few percent in cases with an experimentally relevant heat flux. An up-down symmetry breaking mechanism is required for turbulent current drive, which is provided in this study by a background rotation or rotation gradient. Consequently, the current is nearly linear in the plasma rotation or its gradient. [ABSTRACT FROM AUTHOR]

Large scale structures in the E × B shearing rate, known as staircases, are shown to form in nonlinear gyro-kinetic turbulence simulations with kinetic electrons. However, in many cases, a small scale structure in the shearing rate is observed that appears to prevent the formation of staircases. The small scale structures are interpreted to be linked to the self-interaction of turbulent modes connected with the double periodic boundary conditions on the torus. The self-interaction is a newly discovered mechanism for zonal flow generation and is shown to scale proportional to the normalized Larmor radius. The mechanism is also affected by magnetic shear, being weaker at larger values. [ABSTRACT FROM AUTHOR]

This paper investigates the so-called tertiary instabilities driven by the zonal flow in gyro-kinetic tokamak core turbulence. The Kelvin Helmholtz instability is first considered within a 2D fluid model and a threshold in the zonal flow wave vector k ZF > k ZF , c for instability is found. This critical scale is related to the breaking of the rotational symmetry by flux-surfaces, which is incorporated into the modified adiabatic electron response. The stability of undamped Rosenbluth-Hinton zonal flows is then investigated in gyro-kinetic simulations. Absolute instability, in the sense that the threshold zonal flow amplitude tends towards zero, is found above a zonal flow wave vector k ZF , c ρ i ≈ 1.3 ( ρ i is the ion thermal Larmor radius), which is comparable to the 2D fluid results. Large scale zonal flows with k ZF < k ZF , c are unstable for sufficiently large amplitudes with increasing trend for an increasing radial scale. However, the critical E × B-shearing rate associated with the stability boundary ω E×B , c exceeds typical values connected to the pure flow state at marginal stability by more than an order of magnitude, which therefore lies deeply in the stable parameter region. Furthermore, the impact of zonal temperature perturbations on the tertiary instability is examined. Although temperature perturbations favor instability, the realistic values of gradient-driven gyro-kinetic simulations still lie deeply in the stable parameter regime. Therefore, the relevance of the tertiary instability as a saturation mechanism to the zonal flow amplitude is questioned, as most of the zonal flow intensity is concentrated in modes satisfying k ZF ≪ k ZF , c as well as ω E×B ≪ ω E×B , c . [ABSTRACT FROM AUTHOR]

The dependence of the heat flux on the temperature gradient length in collisionless ion temperature gradient turbulence has recently been revisited. It has been found that the heat flux is discontinuous at a finite heat flux threshold larger than the (Dimits) interpolated threshold. In this paper, the influence of collisions on the heat flux close to the threshold is investigated. It is found that up to relatively high collision frequencies, relevant to the modern day experiments, a discontinuous behaviour of the heat flux as a function of the gradient length persists. Collisions, however, do lead to a reduction in the gradient length at which the discontinuity is observed. Below the finite heat flux threshold, a state of low turbulence with a vanishing small heat flux persists, which can drive the zonal flow against the collisional dissipation. This state is characterised by the fully developed staircases in the radial ExB shearing profile. Increasing the collision frequency at a fixed gradient length leads to the loss of the fully developed staircase structure with the ExB shearing profile having the form of a sawtooth that allows for avalanche formation and a finite heat flux. At very high collision frequencies or gradient lengths well above the threshold the staircase structure is lost. The simulations indicate that the long wave length zonal flow saturates through a mechanism that directly involves the turbulence intensity. [ABSTRACT FROM AUTHOR]

Flux and gradient driven ion temperature gradient turbulence in tokamak geometry and for Cyclone base case parameters are compared in the local limit using the same underlying gyrokinetic turbulence model. The gradient driven turbulence described using the flux tube model with periodic boundary conditions has a finite ion heat flux Qi ≈ 10n0T0ρ2* vth, where n0 (T0) is the background density (temperature), ρ* = q/R is the normalized Larmor radius, R is the major radius of the device, and vth is the ion thermal velocity at the nonlinear threshold of the temperature gradient length for turbulence generation. Consequently, the gradient driven local transport model is unable to accurately describe heat fluxes below Qi < 10n0T0q2*vth, since no stationary fully developed turbulent state can be obtained. The turbulence in the flux driven case shows intermittent behaviour and avalanches for Qi < 10n0T0ρ2* vth. Isolated avalanches disappear for Qi > 10n0T0ρ2* vth, and at higher heat fluxes, the statistics of the turbulence is the same for the flux and gradient driven case. The nonlinear upshift of the temperature gradient length threshold for turbulence generation (known as the Dimits shift) is larger in the case of flux driven turbulence. This higher nonlinear upshift is attributed to the generation of structures in the radial temperature profile, known as staircases [Dif-Pradalier, Phys. Rev. E 82, 025401 (2010)]. Avalanches are initiated at specific locations and have roughly the same radial extent of 50-70 ion Larmor radii. The staircases are obtained at low heating rates, and become unstable and break up at higher heating rates. At the heat fluxes for which staircase formation is observed, no stationary gradient driven simulations can be obtained. [ABSTRACT FROM AUTHOR]

Verification is the fundamental step that any turbulence simulation code has to be submitted in order to assess the proper implementation of the underlying equations. We have carried out a cross comparison of three flux tube gyrokinetic codes, GENE [F. Jenko et al., Phys. Plasmas 7, 1904 (2000)], GKW [A. G. Peeters et al., Comput. Phys. Commun. 180, 2650 (2009)], and GS2 [W. Dorland et al., Phys. Rev. Lett. 85, 5579 (2000)], focusing our attention on the effect of realistic geometries described by a series of MHD equilibria with increasing shaping complexity. To simplify the effort, the benchmark has been limited to the electrostatic collisionless linear behaviour of the system. A fully gyrokinetic model has been used to describe the dynamics of both ions and electrons. Several tests have been carried out looking at linear stability at ion and electron scales, where for the assumed profiles Ion Temperature Gradient (ITG)/Trapped Electron Modes and Electron Temperature Gradient modes are unstable. The capability of the codes to handle a non-zero ballooning angle has been successfully benchmarked in the ITG regime. Finally, the standard Rosenbluth-Hinton test has been successfully carried out looking at the effect of shaping on Zonal Flows (ZFs) and Geodesic Acoustic Modes (GAMs). Inter-code comparison as well as validation of simulation results against analytical estimates has been accomplished. All the performed tests confirm that plasma elongation strongly stabilizes plasma instabilities as well as leads to a strong increase in ZF residual and GAM damping. [ABSTRACT FROM AUTHOR]

The interplay between toroidal rotation u, parallel flow shear u', and perpendicular flow shear cE in the stabilisation of tokamak turbulence is investigated in non-linear flux-tube gyrokinetic simulations. The simulations are performed for a reference L-mode DIII-D plasma (the so-called shortfall case) at r=a = 0:8, varying the flow parameters around their nominal values. Depending on the respective signs of u, u', and λE, turbulence is found to be enhanced, reduced, or unchanged. When the coupling is favorable, the overall effect on the non-linear heat fluxes can be very large, even at moderate flow values. The ion heat flux is, for instance, decreased by a factor of 3 when the direction of the parallel flow shear is reversed with respect to its nominal value. Even more surprising, keeping u' and λE at their nominal values, the ion heat flux decreases by more than 50% when the toroidal flow is reversed. The relevance of this mechanism in the experiments which depends on the ability to decouple u, u', and cE is discussed. The interplay between u and u0 observed in the non-linear simulations qualitatively follows the linear stability results and is interpreted in the frame of a simple fluid model. [ABSTRACT FROM AUTHOR]

This paper studies the effect of rotation on microinstabilities under experimentally relevant conditions in the spherical tokamak National Spherical Torus Experiment (NSTX). The focus is specifically on the centrifugal force effects on the impurity and momentum transport in the core (r/a = 0:7) of an H-mode plasma. Due to relatively high beta, the linear simulations predict the presence of both microtearing mode (MTM) and hybrid ion temperature gradient-kinetic ballooning mode (ITG-KBM) electromagnetic instabilities. Rotation effects on both MTM and ITG-KBM growth rates and mode frequencies are found to be small for the experimental values. However, they do influence the quasi-linear particle and momentum fluxes predicted by ITG-KBM (MTM contributes only to electron heat flux). The gradient of the intrinsic carbon impurity in the sourcefree core region is predicted to be locally hollow, strengthened by centrifugal effects. This result is consistent with experimental measurements and contradicts neoclassical theory that typically provides a reasonable explanation of the impurity profiles in NSTX. The diffusive and Coriolis pinch contributions to momentum transport are found to be relatively weak. Surprisingly, the strongest contribution derives from a centrifugal effect proportional to the product of rotation and rotation shear, which predicts an inward momentum flux roughly three times bigger than the Coriolis pinch, suggesting it should be considered when interpreting previous experimental pinch measurements. [ABSTRACT FROM AUTHOR]

The collisional stabilisation via energy scattering and pitch-angle scattering of micro-instabilities in tokamak plasmas is investigated by means of gyrokinetic simulations with a special emphasis on the often neglected energy scattering operator. It is shown that in the linear regime energy scattering has a negligible effect on Ion Temperature Gradient (ITG) modes but enhances the stabilisation of Trapped Electron Modes (TEM) in presence of nonzero ion temperature and density gradients. This stabilisation is sensitive to the model used for the energy restoring term in the collision operator. The contributions of parallel and drift motion to the total growth rate in velocity space are used to characterize the complex stabilisation mechanisms behind pitch-angle and energy scattering for a range of relevant parameters such as the magnetic shear, the collisionality, the logarithmic density gradient, and the logarithmic ion temperature gradient. It is shown that depending on these parameters, energy scattering stabilisation of TEM can be either due to a decrease of the contribution from drifting trapped electrons or to an increase of the contribution from the parallel motion of passing electrons. Finally, for a standard ITG/TEM case, the effect of energy scattering on the nonlinear heat and particle fluxes is investigated. [ABSTRACT FROM AUTHOR]

A rotating magnetic island is imposed in the gyrokinetic code GKW, when finite differences are used for the radial direction, in order to develop the predictions of analytic tearing mode theory and understand its limitations. The implementation is verified against analytics in sheared slab geometry with three numerical tests that are suggested as benchmark cases for every code that imposes a magnetic island. The convergence requirements to properly resolve physics around the island separatrix are investigated. In the slab geometry, at low magnetic shear, binormal flows inside the island can drive Kelvin-Helmholtz instabilities which prevent the formation of the steady state for which the analytic theory is formulated. [ABSTRACT FROM AUTHOR]

Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro-kinetic turbulence code, GKW. The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate, and frequency of the mode were investigated by varying the current profile, collisionality, and the pressure gradients. Both collisionless and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absence of a pressure gradient is observed, which is attributed to toroidal finite Larmor-radius effects. When a pressure gradient is present at low collisionality, the mode rotates at the expected electron diamagnetic frequency. However, the island rotation reverses direction at high collisionality. The growth rate is found to follow a η1/7 scaling with collisional resistivity in the semi-collisional regime, closely following the semi-collisional scaling found by Fitzpatrick. The stability of the mode closely follows the stability analysis as performed by Hastie et al. using the same current and safety factor profiles but for cylindrical geometry, however, here a modification due to toroidal coupling and pressure effects is seen. [ABSTRACT FROM AUTHOR]

The effect of profile shearing on toroidal momentum transport is studied in linear and non-linear gyro-kinetic simulations. Retaining the radial dependence of both plasma and geometry parameters leads to a momentum flux that has contributions both linear in the logarithmic gradients of density and temperature, as well as contributions linear in the derivatives of the logarithmic gradients. The effect of the turbulence intensity gradient on momentum transport is found to be small for the studied parameters. Linear simulations at fixed normalized toroidal wave number predict a weak dependence of the momentum flux on the normalized Larmor radius ρ= ρ/R. Non-linear simulations, however, at sufficiently small ρ* show a linear scaling of the momentum flux with ρ*. The obtained stationary rotation gradients are in the range of, although perhaps smaller than, current experiments. For a reactor plasma, however, a rather small rotation gradient should result from profile shearing. [ABSTRACT FROM AUTHOR]

Recent work investigating the interaction of magnetic islands with micro-turbulence has uncovered the striking observation of large scale vortex modes forming within the island structure [W. A. Hornsby et al., Phys. Plasmas 17, 092301 (2010)]. These electrostatic vortices are found to be the size of the island and are oscillatory. It is this oscillatory behaviour and the presence of turbulence that leads us to believe that the dynamics are related to the geodesic acoustic mode (GAM), and it is this link that is investigated in this paper. Here, we derive an equation for the GAM in the MHD limit, in the presence of a magnetic island modified three-dimensional axisymmetric geometry. The eigenvalues and eigenfunctions are calculated numerically and then utilised to analyse the dynamics of oscillatory large-scale electrostatic potential structures seen in both linear and non-linear gyro-kinetic simulations. [ABSTRACT FROM AUTHOR]

The electrostatic potential related to a magnetic island structure with imposed width and rotation frequency is studied by means of gyrokinetic simulations, which allow its self-consistent determination via the Poisson equation. An adiabatic response of the trapped ions at the island separatrix leads to a significant smoothing of the potential with respect to analytic calculations based on a complete flattening of the pressure profile inside the island. As a consequence, the magnitude of the polarization current is drastically reduced. When the island size is comparable to the ion banana width, the adiabatic response covers the whole island region, leading to a reduced density flattening for islands rotating in the electron diamagnetic direction. This confirms previous results based on drift-kinetic simulations. [ABSTRACT FROM AUTHOR]

The effect of a finite βe = 8πneTe/B2 on the turbulent transport of toroidal momentum in tokamak plasmas is discussed. From an analytical gyrokinetic model as well as local linear gyrokinetic simulations, it is shown that the modification of the parallel mode structure due to the nonadiabatic response of passing electrons, which changes the parallel wave vector k∥ with increasing βe, leads to a decrease in size of both the diagonal momentum transport as well as the Coriolis pinch under ion temperature gradient turbulence conditions, while for trapped electron modes, practically no modification is found. The decrease is particularly strong close to the onset of the kinetic ballooning modes. There, the Coriolis pinch even reverses its direction. [ABSTRACT FROM AUTHOR]

Two symmetries of the local nonlinear δf gyrokinetic system of equations in tokamaks in the high flow regime are presented. The turbulent transport of toroidal angular momentum changes sign under an up-down reflection of the tokamak and a sign change of both the rotation and the rotation shear. Thus, the turbulent transport of toroidal angular momentum must vanish for up-down symmetric tokamaks in the absence of both rotation and rotation shear. This has important implications for the modeling of spontaneous rotation. [ABSTRACT FROM AUTHOR]

Tokamak experiments operate with a rotating plasma, with toroidal velocity which can be driven externally but can also arise spontaneously. In the frame that corotates with the plasma, the effects of the centrifugal force are felt through a centrifugal drift and an enhanced mirror force [Peeters et al., Phys. Plasmas 16, 042310 (2009)]. These inertial terms become important in the case of strong rotation, as is common in spherical devices, and are also important for heavy impurity ions even at small toroidal velocities. In this work, the first gyrokinetic simulations including the centrifugal force in a strongly rotating plasma are presented. The enhanced mirror force redistributes density over a flux surface and modifies the trapping condition, destabilizing trapped electron modes. At intermediate scales this can result in promotion of the trapped electron mode over the ion temperature gradient (ITG) mode as the dominant instability, which under marginal conditions could result in an enhanced electron heat flux. The centrifugal drift acts to damp the residual zonal flow of the geoacoustic mode, while its frequency is increased. For nonlinear ITG dominated turbulence, increased trapped electron drive and reduced zonal flow lead to an increase in ion heat diffusivity if the increased rotation is not accompanied by rotational shear stabilization. An increased fraction of slow trapped electrons enhances the convective particle pinch, leading to an increase in the steady state density gradient with strong rotation. Linear ITG mode results show an increased pinch of heavy trace impurities due to their strong centrifugal trapping. [ABSTRACT FROM AUTHOR]

The interaction between small scale turbulence (of the order of the ion Larmor radius) and mesoscale magnetic islands is investigated within the gyrokinetic framework. Turbulence, driven by background temperature and density gradients, over nonlinear mode coupling, pumps energy into long wavelength modes, and can result in an electrostatic vortex mode that coincides with the magnetic island. The strength of the vortex is strongly enhanced by the modified plasma flow response connected with the change in topology, and the transport it generates can compete with the parallel motion along the perturbed magnetic field. Despite the stabilizing effect of sheared plasma flows in and around the island, the net effect of the island is a degradation of the confinement. When density and temperature gradients inside the island are below the threshold for turbulence generation, turbulent fluctuations still persist through turbulence convection and spreading. The latter mechanisms then generate a finite transport flux and, consequently, a finite pressure gradient in the island. A finite radial temperature gradient inside the island is also shown to persist due to the trapped particles, which do not move along the field around the island. In the low collisionality regime, the finite gradient in the trapped population leads to the generation of a bootstrap current, which reduces the neoclassical drive. [ABSTRACT FROM AUTHOR]

Perturbative experiments have been carried out in the Joint European Torus [Fusion Sci. Technol. 53(4) (2008)] in order to identify the diffusive and convective components of toroidal momentum transport. The torque source was modulated either by modulating tangential neutral beam power or by modulating in antiphase tangential and normal beams to produce a torque perturbation in the absence of a power perturbation. The resulting periodic perturbation in the toroidal rotation velocity was modeled using time-dependent transport simulations in order to extract empirical profiles of momentum diffusivity and pinch. Details of the experimental technique, data analysis, and modeling are provided. The momentum diffusivity in the core region (0.2<ρ<0.8) was found to be close to the ion heat diffusivity (χ[lowercase_phi_synonym]/χi∼0.7-1.7) and a significant inward momentum convection term, up to 20 m/s, was found, leading to an effective momentum diffusivity significantly lower than the ion heat diffusivity (χ[lowercase_phi_synonym]eff/χieff∼0.4). These results have significant implications on the prediction of toroidal rotation velocities in future tokamaks and are qualitatively consistent with recent developments in momentum transport theory. Detailed quantitative comparisons with the theoretical predictions of the linear gyrokinetic code GKW [A. G. Peeters et al., Comput. Phys. Commun. 180, 2650 (2009)] and of the quasilinear fluid Weiland model [J. Weiland, Collective Modes in Inhomogeneous Plasmas (IOP, Bristol, 2000)] are presented for two analyzed discharges. [ABSTRACT FROM AUTHOR]

The toroidal momentum transport in the presence of trapped electron mode microinstabilities in tokamak plasmas is studied by means of quasilinear gyrokinetic calculations. In particular, the role of the Coriolis drift in producing an inward convection of toroidal momentum is investigated. The Coriolis drift term has been implemented in the gyrokinetic code GS2 [W. Dorland et al., Phys. Rev. Lett. 85, 5579 (2000)] specifically for the completion of this work. A benchmark between the GS2 implementation of the Coriolis drift and the implementations included in two other gyrokinetic codes is presented. The numerical calculations show that in the presence of trapped electron modes, despite of a weaker symmetry breaking of the eigenfunctions with respect to the case of ion temperature gradient modes, a pinch of toroidal momentum is produced in most conditions. The toroidal momentum viscosity is also computed, and found to be small as compared with the electron heat conductivity, but significantly larger than the ion heat conductivity. In addition, interesting differences are found in the dependence of the toroidal momentum pinch as a function of collisionality between trapped electron modes and ion temperature gradient modes. The results identify also parameter domains in which the pinch is predicted to be small, which are also of interest for comparisons with the experiments. [ABSTRACT FROM AUTHOR]

The effect of edge turbulence on the electron-cyclotron wave propagation in ITER is investigated with emphasis on wave scattering, beam broadening, and its influence on localized heating and current drive. A wave used for electron-cyclotron current drive (ECCD) must cross the edge of the plasma, where density fluctuations can be large enough to bring on wave scattering. The scattering angle due to the density fluctuations is small, but the beam propagates over a distance of several meters up to the resonance layer and even small angle scattering leads to a deviation of several centimeters at the deposition location. Since the localization of ECCD is crucial for the control of neoclassical tearing modes, this issue is of great importance to the ITER design. The wave scattering process is described on the basis of a Fokker–Planck equation, where the diffusion coefficient is calculated analytically as well as computed numerically using a ray tracing code. [ABSTRACT FROM AUTHOR]

Nondiffusive anomalous momentum transport in toroidal plasmas occurs through symmetry breaking mechanisms. In this paper the contribution of sheared E×B flows to parallel momentum transport [R. R. Dominguez and G. M. Staebler, Phys Fluids B 5, 3876 (1993)] is investigated with nonlinear gyrokinetic simulations in toroidal geometry. The background perpendicular shear is treated independently from the parallel velocity shear to isolate a nondiffusive, nonpinch contribution to the parallel momentum flux. It is found that the size of the term depends strongly on the magnetic shear, with the sign reversing for negative magnetic shear. Perpendicular shear flows are responsible for both symmetry breaking and suppression of turbulence, resulting in a shearing rate at which there is a maximum contribution to the momentum transport. The E×B momentum transport is shown to be quenched by increasing flow shear more strongly than the standard linear quench rule for turbulent heat diffusivity. [ABSTRACT FROM AUTHOR]

The bootstrap current in small magnetic islands of neoclassical tearing modes is studied with guiding center particle simulations including pitch angle scattering. A model for a rotating island and its electric field is used and a new approximation to the electric potential in small islands is derived. Islands with sizes of the order of the ion banana orbit width are studied by means of a two-step model, which allows to treat both ions and electrons kinetically. The bootstrap current in such small islands is found to depend strongly on the direction of rotation of the island. The bootstrap current in small islands rotating in the ion diamagnetic direction is strongly diminished, similarly to what happens in big islands. In small islands rotating in the electron diamagnetic direction, on the contrary, the bootstrap current is almost completely preserved, implying a reduced neoclassical drive of the island growth. [ABSTRACT FROM AUTHOR]

The transport of parallel momentum by small scale fluctuations is intrinsically linked to symmetry breaking in the direction of the magnetic field. In tokamaks, an up-down asymmetry in the equilibrium proves to be an efficient parallel symmetry breaking mechanism leading to the generation of a net radial flux of parallel momentum by the electrostatic turbulence [Y. Camenen et al., Phys. Rev. Lett. 102, 125001 (2009)]. This flux is neither proportional to the toroidal rotation nor to its gradient and arises from an incomplete cancellation of the local contributions to the parallel momentum flux under the flux surface average. The flux of parallel momentum then depends on the asymmetry of the curvature drift and on the extension of the fluctuations around the low field side midplane. In this paper, the mechanisms underlying the generation of the flux of parallel momentum are highlighted and the main dependences on plasma parameters investigated using linear gyrokinetic simulations. [ABSTRACT FROM AUTHOR]

This paper discusses the effect of the mode structure on the Coriolis pinch effect [A. G. Peeters, C. Angioni, and D. Strintzi, Phys. Rev. Lett. 98, 265003 (2007)]. It is shown that the Coriolis drift effect can be compensated for by a finite parallel wave vector, resulting in a reduced momentum pinch velocity. Gyrokinetic simulations in full toroidal geometry reveal that parallel dynamics effectively removes the Coriolis pinch for the case of adiabatic electrons, while the compensation due to the parallel dynamics is incomplete for the case of kinetic electrons, resulting in a finite pinch velocity. The finite flux in the case of kinetic electrons is interpreted to be related to the electron trapping, which prevents a strong asymmetry in the electrostatic potential with respect to the low field side position. The physics picture developed here leads to the discovery and explanation of two unexpected effects: First the pinch velocity scales with the trapped particle fraction (root of the inverse aspect ratio), and second there is no strong collisionality dependence. The latter is related to the role of the trapped electrons, which retain some symmetry in the eigenmode, but play no role in the perturbed parallel velocity. [ABSTRACT FROM AUTHOR]

The generic problem of how, in a turbulent plasma, the experimentally relevant conditions of a particle flux very close to the null are achieved, despite the presence of strong heat fluxes, is addressed. Nonlinear gyrokinetic simulations of plasma turbulence in tokamaks reveal a complex dependence of the particle flux as a function of the turbulent spatial scale and of the velocity space as collisionality is increased. At experimental values of collisionality, the particle flux is found close to the null, in agreement with the experiment, due to the balance between inward and outward contributions at small and large scales, respectively. These simulations provide full theoretical support to the prediction of a peaked density profile in a future nuclear fusion reactor. [ABSTRACT FROM AUTHOR]

The paper derives the gyro-kinetic equation in the comoving frame of a toroidally rotating plasma, including both the Coriolis drift effect [A. G. Peeters et al., Phys. Rev. Lett. 98, 265003 (2007)] as well as the centrifugal force. The relation with the laboratory frame is discussed. A low field side gyro-fluid model is derived from the gyro-kinetic equation and applied to the description of parallel momentum transport. The model includes the effects of the Coriolis and centrifugal force as well as the parallel dynamics. The latter physics effect allows for a consistent description of both the Coriolis drift effect as well as the ExB shear effect [R. R. Dominguez and G. M. Staebler, Phys. Fluids B 5, 3876 (1993)] on the momentum transport. Strong plasma rotation as well as parallel dynamics reduce the Coriolis (inward) pinch of momentum and can lead to a sign reversal generating an outward pinch velocity. Also, the ExB shear effect is, in a similar manner, reduced by the parallel dynamics and stronger rotation. [ABSTRACT FROM AUTHOR]

The comment addresses questions raised on the derivation of the momentum pinch velocity due to the Coriolis drift effect [A. G. Peeters et al., Phys. Rev. Lett. 98, 265003 (2007)]. These concern the definition of the gradient, and the scaling with the density gradient length. It will be shown that the turbulent equipartition mechanism is included within the derivation using the Coriolis drift, with the density gradient scaling being the consequence of drift terms not considered in [T. S. Hahm et al., Phys. Plasmas 15, 055902 (2008)]. Finally the accuracy of the analytic models is assessed through a comparison with the full gyrokinetic solution. [ABSTRACT FROM AUTHOR]

Recent developments in the gyrokinetic theory have shown that, in a toroidal device, the Coriolis drift associated with the background plasma rotation significantly affects the small scale instabilities [A. G. Peeters et al., Phys. Rev. Lett. 98, 265003 (2007)]. The later study, which focuses on the effect of the Coriolis drift on toroidal momentum transport is extended in the present paper to heat and particle transport. It is shown numerically using the gyrokinetic flux-tube code GKW [A. G. Peeters and D. Strintzi, Phys. Plasmas 11, 3748 (2004)], and supported analytically, that the Coriolis drift and the parallel dynamics play a similar role in the coupling of density, temperature, and velocity perturbations. The effect on particle and heat fluxes increases with the toroidal rotation (directly) and with the toroidal rotation gradient (through the parallel mode structure), depends on the direction of propagation of the perturbation, increases with the impurity charge number and with the impurity mass to charge number ratio. The case of very high toroidal rotation, relevant to spherical tokamaks, is investigated by including the effect of the centrifugal force in a fluid model. The main effect of the centrifugal force is to decrease the local density gradient at the low field side midplane and to add an extra contribution to the fluxes. The conditions for which the inertial terms significantly affect the heat and particle fluxes are evidenced. [ABSTRACT FROM AUTHOR]

Quasilinear gyrokinetic calculations of the transport of fast α particles with a slowing-down equilibrium distribution function in the trace limit are presented. Diffusive and convective contributions to the total flux are separated and their dependence on the ratio of the fast particle energy to the background plasma temperature is investigated. The results are compared with those obtained in the case an equivalent Maxwellian distribution function is assumed for the fast particles. On the basis of the gyrokinetic results, simple models for α particle transport are proposed for transport modeling purposes. [ABSTRACT FROM AUTHOR]

Fluid and gyrokinetic calculations of the toroidal momentum diffusivity in a tokamak are compared. The four-moment gyrofluid model predicts the Prandtl number connected with the ion temperature gradient mode reasonably well provided the drift term is kept in the momentum balance. Without the drift term in the momentum balance, some previous gyrofluid models predicted small values of the Prandtl number in the range of experimental observations. It is shown that the drift term enters in the fluid equations through the gyroviscosity. Gyrokinetic calculations of the ion temperature gradient mode with kinetic electrons, and for experimentally relevant parameters yield a Prandtl number in the range 0.7–1.2. [ABSTRACT FROM AUTHOR]

Experimental observations on core particle and impurity transport from the Axial Symmetric Divertor Experiment Upgrade [O. Gruber, H.-S. Bosch, S. Günter et al., Nucl Fusion 39, 1321 (1999)] and the Joint European Torus [J. Pamela, E. R. Solano, and JET EFDA Contributors, Nucl. Fusion 43, 1540 (2003)] tokamaks are reviewed and compared. Robust general experimental behaviors observed in both the devices and related parametric dependences are identified. The experimental observations are compared with the most recent theoretical results in the field of core particle transport. [ABSTRACT FROM AUTHOR]

In this Letter, it is shown that global, nonlinear, particle-in-cell (PIC) simulations of electron temperature driven turbulence recover the same level of transport as flux-tube codes when the level of statistical noise, associated with the PIC discretization, is sufficiently small. An efficient measure of the signal-to-noise ratio, applicable to every PIC code, is introduced. This diagnostic provides a direct measure of the quality of PIC simulations and allows for the validation of analytical estimates of the numerical noise. Global simulations for values of ρe*<1/450 (normalized electron gyroradius) show no evidence of a gyro-Bohm scaling. [ABSTRACT FROM AUTHOR]

Linear gyrokinetic calculations and a quasilinear model are applied to compute the radial particle fluxes and investigate the properties of the particle transport in a tokamak plasma induced by ion temperature gradient and trapped electron mode instabilities. The paper focuses on the specific problem of the dependence of anomalous pinch and density peaking on collisionality. [ABSTRACT FROM AUTHOR]

It is shown from a symmetry in the gyrokinetic equation that for up–down symmetric tokamak equilibria and for u[lowercase_phi_synonym]>ρυthi/r (where u[lowercase_phi_synonym] is the toroidal velocity, υthi is the thermal ion velocity, ρ is the Larmor radius, and r is the radius of the flux surface), the transport of parallel momentum can be written as the sum of a diffusive and a pinch contribution with no off-diagonal terms due to temperature and pressure gradients. The measured parallel velocity gradient in ASDEX Upgrade [O. Gruber, H.-S. Bosch, S. Günter et al., Nucl. Fusion 39, 1321 (1999)] is insufficient to drive the parallel velocity shear instability. The parallel velocity is then transported by the ion temperature gradient mode. The diffusive contribution to the transport flux is investigated using a linear gyrokinetic approach, and it is found that the diffusion coefficient for parallel velocity transport divided by the ion heat conductivity coefficient is close to 1, and only weakly dependent on plasma parameters. [ABSTRACT FROM AUTHOR]

The effect of collisions on the polarization current caused by a rotating island in a Tokamak plasma is studied with guiding center particle simulations. The simulations are performed with a δf code which includes a Monte Carlo model for Coulomb collisions. The transition between the two limiting cases of low and high collision frequency ν (compared to the island rotation frequency ω) is found to occur at ν≈ω in agreement with a recent analytic theory. [ABSTRACT FROM AUTHOR]

New experimental results obtained in ASDEX Upgrade [O. Gruber, H.-S. Bosch, S. Günter et al., Nucl. Fusion 39, 1321 (1999)] plasmas in low confinement mode with central electron cyclotron heating are presented in which transitions in both the particle and electron heat transport properties have been observed. A comprehensive albeit qualitative explanation for both the transport channels is provided in the framework of the theory of ion temperature gradient and trapped electron mode microinstabilities. The different transport behaviors are related to the dominant instability at play and to the collisionality regime. In particular, central electron heating induces a flattening of the density profile when the dominant instability is a trapped electron mode, and density peaking is observed to increase with decreasing collisionality. [ABSTRACT FROM AUTHOR]

Linear gyrokinetic calculations of low density electron heat dominated plasmas in ASDEX Upgrade [O. Gruber, H.-S. Bosch, S. Günter et al., Nucl. Fusion 39, 1321 (1999)] are presented. It is found that the dominant mode is a trapped electron mode, which under the experimental conditions is sensitive to the density gradient, collisions, and magnetic shear. The quasilinear heat flux scales in good agreement with the experimental observed heat conductivity. Many experimentally observed phenomena can be explained on the basis of the presented calculations: the existence of a threshold, the fast propagation of the heat wave, and the moderate stiffness of the electron channel. The implications of the calculations for the empirical investigations are discussed. [ABSTRACT FROM AUTHOR]

It has been shown [Maccio, Phys. Plasmas 8, 895 (2001)] that a uniform radial electric field can stabilize the toroidal ion temperature gradient mode in tokamak plasmas. In this paper, using the ballooning transform, the mechanism leading to stabilization is further clarified. However, the stabilizing effect depends on the choice of the background distribution function. It is shown that if the electric field is connected with a toroidal plasma rotation the stabilizing effect becomes ineffective. Consequently, in many current experiments this effect should not play a role. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The theoretical prediction of density profiles in tokamak plasmas plays a major role for the prediction of the plasma performance in a fusion reactor. The density peaking measured in plasmas in high confinement mode of the ASDEX Upgrade tokamak [O. Gruber, H.-S. Bosch, S. Günter et al., Nucl. Fusion 39, 1321 (1999)] is shown to decrease with increasing collisionality. This experimental behavior is explained with a theoretical fluid transport model for ion temperature gradient and trapped electron modes, GLF23, which includes a valid description of the effects of collisions on these instabilities. Collisionless reactive models, like the Weiland model, are in disagreement with the experimental observations. The difference between the predictions of the two models must be ascribed to collisionality. This has been ascertained by a detailed comparison of the physics content of the two models and by the implementation of modified, collisionless versions of the GLF23 model, which yield results analogous to those of the Weiland model and in disagreement with the experiment. It is shown that the anomalous particle pinch decreases with collisionality and the relative role of the neoclassical Ware pinch becomes important at high collisionality, that is close to the density limit in present large tokamak experiments, while it is practically negligible at low collisionality. The present results reconciliate apparently contradictory observations on the existence of an anomalous particle pinch collected so far in tokamaks. [ABSTRACT FROM AUTHOR]

The neoclassical ion transport in a tokamak plasma with circular cross section is studied with guiding center particle simulations. A Monte Carlo model of pitch-angle scattering which includes momentum conservation is employed. The model includes the whole plasma inside closed flux surfaces, but the focus is on the near-axis transport due to particles with wide orbits which lead to a different heat flux than in the standard theory. Neither of two recent theories of banana regime transport near the axis is confirmed by the simulations, nor do the numerical results for the plateau regime agree with a recent theory of wide-orbit transport in this regime. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]