D. Strintzi

Overview of toroidal momentum transport

Toroidal momentum transport mechanisms are reviewed and put in a broader perspective. The generation of a finite momentum flux is closely related to the breaking of symmetry (parity) along the field. The symmetry argument allows for the systematic identification of possible transport mechanisms. Those that appear to lowest order in the normalized Larmor radius (the diagonal part, Coriolis pinch, E x B shearing, particle flux, and up-down asymmetric equilibria) are reasonably well understood. At higher order, expected to be of importance in the plasma edge, the theory is still under development.

Intrinsic rotation driven by the electrostatic turbulence in up-down asymmetric toroidal plasmas

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.

The influence of the self-consistent mode structure on the Coriolis pinch effect

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.

Electron-cyclotron wave scattering by edge density fluctuations in ITER

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.

The toroidal momentum diffusivity in a tokamak plasma: A comparison of fluid and kinetic calculations

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.

The correlation of fractal structures in the photospheric and the coronal magnetic field

Context. This work examines the relation between the fractal properties of the photospheric magnetic patterns and those of the coronal magnetic fields in solar active regions. Aims. We investigate whether there is any correlation between the fractal dimensions of the photospheric structures and the magnetic discontinuities formed in the corona. Methods. To investigate the connection between the photospheric and coronal complexity, we used a nonlinear force-free extrapolation method that reconstructs the 3d magnetic fields using 2d observed vector magnetograms as boundary conditions. We then located the magnetic discontinuities, which are considered as spatial proxies of reconnection-related instabilities. These discontinuities form well-defined volumes, called here unstable volumes. We calculated the fractal dimensions of these unstable volumes and compared them to the fractal dimensions of the boundary vector magnetograms. Results. Our results show no correlation between the fractal dimensions of the observed 2d photospheric structures and the extrapolated unstable volumes in the corona, when nonlinear force-free extrapolation is used. This result is independent of efforts to (1) bring the photospheric magnetic fields closer to a nonlinear force-free equilibrium and (2) omit the lower part of the modeled magnetic field volume that is almost completely filled by unstable volumes. A significant correlation between the fractal dimensions of the photospheric and coronal magnetic features is only observed at the zero level (lower limit) of approximation of a current-free (potential) magnetic field extrapolation. Conclusions. We conclude that the complicated transition from photospheric non-force-free fields to coronal force-free ones hampers any direct correlation between the fractal dimensions of the 2d photospheric patterns and their 3d counterparts in the corona at the nonlinear force-free limit, which can be considered as a second level of approximation in this study. Correspondingly, in the zero and first levels of approximation, namely, the potential and linear force-free extrapolation, respectively, we reveal a significant correlation between the fractal dimensions of the photospheric and coronal structures, which can be attributed to the lack of electric currents or to their purely field-aligned orientation.

Ion heat transport studies in JET

Detailed experimental studies of ion heat transport have been carried out in JET exploiting the upgrade of active charge exchange spectroscopy and the availability of multi-frequency ion cyclotron resonance heating with (3)He minority. The determination of ion temperature gradient (ITG) threshold and ion stiffness offers unique opportunities for validation of the well-established theory of ITG driven modes. Ion stiffness is observed to decrease strongly in the presence of toroidal rotation when the magnetic shear is sufficiently low. This effect is dominant with respect to the well-known omega(ExB) threshold up-shift and plays a major role in enhancing core confinement in hybrid regimes and ion internal transport barriers. The effects of T(e)/T(i) and s/q on ion threshold are found rather weak in the domain explored. Quasi-linear fluid/gyro-fluid and linear/non-linear gyro-kinetic simulations have been carried out. Whilst threshold predictions show good match with experimental observations, some significant discrepancies are found on the stiffness behaviour.

Comment on “Turbulent equipartition theory of toroidal momentum pinch” [Phys. Plasmas 15, 055902 (2008)]

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.

Perturbative studies of toroidal momentum transport using neutral beam injection modulation in the Joint European Torus: Experimental results, analysis methodology, and first principles modeling

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 (χϕ/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 (χϕeff/χieff∼0.4). These resu...

Comparison of gradient and flux driven gyro-kinetic turbulent transport

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 gyro-kinetic turbulence model. The gradient driven turbulence described using the flux tube model with periodic boundary conditions has a finite ion heat flux Qi≈10n0T0ρ*2vth, where n0 (T0) is the background density (temperature), ρ*=ρ/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 10n0T0ρ*2vth, and at higher heat fluxes, the statistics of the turbulence is ...