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Context. Multiple mechanisms are known to give rise to turbulence in protoplanetary disks, which facilitates the accretion onto the central star. Small dust particles that are well coupled to the gas undergo diffusion due to this turbulent motion. Aims. This paper investigates the influence of turbulence induced dust diffusion on the equilibrium of protoplanetary disks. Methods. The model accounts for dust sublimation, radiative transfer with the flux-limited diffusion approximation and dust diffusion. It predicts the density and temperature profiles as well as the dust-to-gas ratio of the disk. Results. It is shown that dust diffusion can have a large impact: assuming the dust survives for 104 seconds or longer before it can be evaporated, leads the dust diffusion to widen the inner disk considerably. The latter effect is generated through a feedback mechanism as the diffusion length is much smaller than the disk width. With increasing dust diffusion, the inclination of the inner rim towards the stellar radiation becomes steeper until it is almost vertical. The temperature range of evaporation and condensation, which is linked to the dust composition, has no influence on this effect. Conclusions. For realistic parameters dust diffusion can not be neglected when determining the equilibrium of the disk. Stronger turbulence inside the disk induces more dust diffusion. Therefore, the dust density grows more gradually over a greater distance and less radiation reaches the disk surface. The new equilibrium shape of the disk is more inclined towards the star. This effect is universal and independent of the specific dust composition.

The paper investigates the influence of accretion heating and turbulent heat conduction on the equilibrium of protoplanetary disks, extending the 2D axis-symmetric passive disk model of Flock (Flock et al. 2016, ApJ 827, 144). The model includes dust sublimation and radiative transfer with the flux-limited diffusion approximation, and predicts the density and temperature profiles as well as the dust to gas ratio of the disk. It is shown that the accretion heating can have a large impact: For accretion rates above 5*10^(-8) M_solar /yr a zone forms behind the silicate condensation front with sufficiently high temperature to sublimate the dust and form a gaseous cavity. Assuming a Prandtl number ~ 0.7, it is furthermore shown that the turbulent heat conduction cannot be neglected in the evaluation of the temperature profile. While the inner rim position is not affected by viscous heating, the dead zone edge shifts radially outward for higher accretion rates.

Non-linear, radially global, turbulence simulations of ASDEX Upgrade (AUG) plasmas are performed and the nonlinear generated intrinsic flow shows agreement with the intrinsic flow gradients measured in the core of Ohmic L-mode plasmas at nominal parameters. Simulations utilising the kinetic electron model show hollow intrinsic flow profiles as seen in a predominant number of experiments performed at similar plasma parameters. In addition, significantly larger flow gradients are seen than in a previous flux-tube analysis (Hornsby et al {\it Nucl. Fusion} (2017)). Adiabatic electron model simulations can show a flow profile with opposing sign in the gradient with respect to a kinetic electron simulation, implying a reversal in the sign of the residual stress due to kinetic electrons. The shaping of the intrinsic flow is strongly determined by the density gradient profile. The sensitivity of the residual stress to variations in density profile curvature is calculated and seen to be significantly stronger than to neoclassical flows (Hornsby et al {\it Nucl. Fusion} (2017)). This variation is strong enough on its own to explain the large variations in the intrinsic flow gradients seen in some AUG experiments. Analysis of the symmetry breaking properties of the turbulence shows that profile shearing is the dominant mechanism in producing a finite parallel wave-number, with turbulence gradient effects contributing a smaller portion of the parallel wave-vector.

The progress made in understanding spontaneous toroidal rotation reversals in tokamaks is reviewed and current ideas to solve this ten-year-old puzzle are explored. The paper includes a summarial synthesis of the experimental observations in AUG, C-Mod, KSTAR, MAST and TCV tokamaks, reasons why turbulent momentum transport is thought to be responsible for the reversals, a review of the theory of turbulent momentum transport and suggestions for future investigations.

The non-linear evolution of a magnetic island is studied using the Vlasov gyro-kinetic code GKW. The interaction of electromagnetic turbulence with a self-consistently growing magnetic island, generated by a tearing unstable $\Delta' > 0$ current profile, is considered. The turbulence is able to seed the magnetic island and bypass the linear growth phase by generating structures that are approximately an ion gyro-radius in width. The non-linear evolution of the island width and its rotation frequency, after this seeding phase, is found to be modified and is dependent on the value of the plasma beta and equilibrium pressure gradients. At low values of beta the island evolves largely independent of the turbulence, while at higher values the interaction has a dramatic effect on island growth, causing the island to grow exponentially at the growth rate of its linear phase, even though the island is larger than linear theory validity. The turbulence forces the island to rotate in the ion-diamagnetic direction as opposed to the electron diamagnetic direction in which it rotates when no turbulence is present. In addition, it is found that the mode rotation slows as the island grows in size.

In this paper a conservation equation is derived for the radially dependent entropy in toroidal geometry using the local approximation of the gyro-kinetic framework. This equation naturally leads to an operative definition for the turbulence intensity. It is shown that the conservation equation can be split in two separate conservation equations, one describing the dynamics of the zonal modes and one for the non-zonal modes. In essence the paper provides an operative tool for both analytic as well as numeric studies of the radial propagation of turbulence in tokamak plasmas.

Non-linear local electromagnetic gyrokinetic turbulence simulations of the ITER standard scenario H-mode are presented for the q=3/2 and q=2 surfaces. The turbulent transport is examined in regions of velocity space characteristic of electrons heated by electron cyclotron waves. Electromagnetic fluctuations and sub-dominant micro-tearing modes are found to contribute significantly to the transport of the accelerated electrons, even though they have only a small impact on the transport of the bulk species. The particle diffusivity for resonant passing electrons is found to be less than 0.15 m^2/s, and their heat conductivity is found to be less than 2 m^2/s. Implications for the broadening of the current drive and energy deposition in ITER are discussed., Comment: Letter, 5 pages, 5 figures, for submission to Nuclear Fusion

The impact of lithium impurities on the microstability and turbulent transport characteristics in the core of a typical FTU Liquid Lithium Limiter (LLL)(Mazzitelli et al., Nucl. Fusion, 2011) discharge during the density ramp-up phase is studied. A non-linear gyrokinetic analysis performed with GKW (Peeters et al.,Comp. Phys. Comm., 2009) accompanied by a quasi-linear fluid analysis is presented. We show that a centrally peaked, high concentration lithium profile contributes to the electron peaking by reducing the outward electron flux, and that it leads to inward turbulent deuterium transport through ion flux separation., Comment: 23 pages, 12 figures

A new mechanism for toroidal momentum transport in a tokamak is investigated using the gyro-kinetic model. First, an analytic model is developed through the use of the ballooning transform. The terms that generate the momentum transport are then connected with the poloidal derivative of the ballooning envelope, which are one order smaller in the normalised Larmor radius, compared with the derivative of the eikonal. The mechanism, therefore, does not introduce an inhomogeneity in the radial direction, in contrast with the effect of profile shearing. Numerical simulations of the linear ion temperature gradient mode with adiabatic electrons, retaining the finite rho* effects in the ExB velocity, the drift, and the gyro-average, are presented. The momentum flux is found to be linear in the normalised Larmor radius (\rho*) but is, nevertheless, generating a sizeable counter-current rotation. The total momentum flux scales linear with the aspect ratio of the considered magnetic surface, and increases with increasing magnetic shear, safety factor, and density and temperature gradients.

Two symmetries of the local nonlinear delta-f 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., Comment: 15 pages, 2 figures

An expression for the extrapolated fusion gain G = Pfusion /5 Pheat (Pfusion being the total fusion power and Pheat the total heating power) of ITER in terms of the confinement improvement factor (H) and the normalised beta (betaN) is derived in this paper. It is shown that an increase in normalised beta can be expected to have a negative or neutral influence on G depending on the chosen confinement scaling law. Figures of merit like H betaN / q95^2 should be used with care, since large values of this quantity do not guarantee high values of G, and might not be attainable with the heating power installed on ITER., Comment: 6 Pages, 3 figures, Submitted to Nuclear Fusion on the 29th of November 2006

In this letter a pinch velocity of toroidal momentum is shown to exist for the first time. Using the gyro-kinetic equations in the frame moving with the equilibrium toroidal velocity, it is shown that the physics effect can be elegantly formulated through the ``Coriolis'' drift. A fluid model is used to highlight the main coupling mechanisms between the density and temperature perturbations on the one hand and the perturbed parallel flow on the other. Gyro-kinetic calculations are used to accurately asses the magnitude of the pinch. The pinch velocity leads to a radial gradient of the toroidal velocity profile even in the absence of a torque on the plasma. It is shown to be sizeable in the plasmas of the International Thermonuclear Experimental Reactor (ITER) leading to a moderately peaked rotation profile. Finally, the pinch also affects the interpretation of current experiments., Comment: 4 Pages, 2 Figures. Submitted to Phys. Rev. Letters on the 17th of Nov. 2006