The robustness and the effect of zonal flows in trapped electron mode (TEM) turbulence and Ion Temperature Gradient (ITG) turbulence in the reversed-field pinch (RFP) are investigated from numerical solutions of the gyrokinetic equations with and without magnetic external perturbations introduced to model tearing modes. For simulations without external magnetic field perturbations, zonal flows produce a much larger reduction of transport for the density-gradient-driven TEM turbulence than they do for the ITG turbulence. Zonal flows are studied in detail to understand the nature of their strong excitation in the RFP and to gain insight into the key differences between the TEM- and ITG-driven regimes. The zonal flow residuals are significantly larger in the RFP than in tokamak geometry due to the low safety factor. Collisionality is seen to play a significant role in the TEM zonal flow regulation through the different responses of the linear growth rate and the size of the Dimits shift to collisionality, while affecting the ITG only minimally. A secondary instability analysis reveals that the TEM turbulence drives zonal flows at a rate that is twice that of the ITG turbulence. In addition to interfering with zonal flows, the magnetic perturbations are found to obviate an energy scaling relation for fast particles.

Recent experiments on the ASDEX Upgrade tokamak aim at improving the physics base for ITER and DEMO to aid the machine design and prepare efficient operation. Type I edge localized mode (ELM) mitigation using resonant magnetic perturbations (RMPs) has been shown at low pedestal collisionality . In contrast to the previous high ν* regime, suppression only occurs in a narrow RMP spectral window, indicating a resonant process, and a concomitant confinement drop is observed due to a reduction of pedestal top density and electron temperature. Strong evidence is found for the ion heat flux to be the decisive element for the L–H power threshold. A physics based scaling of the density at which the minimum PLH occurs indicates that ITER could take advantage of it to initiate H-mode at lower density than that of the final Q = 10 operational point. Core density fluctuation measurements resolved in radius and wave number show that an increase of R/LTe introduced by off-axis electron cyclotron resonance heating (ECRH) mainly increases the large scale fluctuations. The radial variation of the fluctuation level is in agreement with simulations using the GENE code. Fast particles are shown to undergo classical slowing down in the absence of large scale magnetohydrodynamic (MHD) events and for low heating power, but show signs of anomalous radial redistribution at large heating power, consistent with a broadened off-axis neutral beam current drive current profile under these conditions. Neoclassical tearing mode (NTM) suppression experiments using electron cyclotron current drive (ECCD) with feedback controlled deposition have allowed to test several control strategies for ITER, including automated control of (3,2) and (2,1) NTMs during a single discharge. Disruption mitigation studies using massive gas injection (MGI) can show an increased fuelling efficiency with high field side injection, but a saturation of the fuelling efficiency is observed at high injected mass as needed for runaway electron suppression. Large locked modes can significantly decrease the fuelling efficiency and increase the asymmetry of radiated power during MGI mitigation. Concerning power exhaust, the partially detached ITER divertor scenario has been demonstrated at Psep/R = 10 MW m−1 in ASDEX Upgrade, with a peak time averaged target load around 5 MW m−2, well consistent with the component limits for ITER. Developing this towards DEMO, full detachment was achieved at Psep/R = 7 MW m−1 and stationary discharges with core radiation fraction of the order of DEMO requirements (70% instead of the 30% needed for ITER) were demonstrated. Finally, it remains difficult to establish the standard ITER Q = 10 scenario at low q95 = 3 in the all-tungsten (all-W) ASDEX Upgrade due to the observed poor confinement at low βN. This is mainly due to a degraded pedestal performance and hence investigations at shifting the operational point to higher βN by lowering the current have been started. At higher q95, pedestal performance can be recovered by seeding N2 as well as CD4, which is interpreted as improved pedestal stability due to the decrease of bootstrap current with increasing Zeff. Concerning advanced scenarios, the upgrade of ECRH power has allowed experiments with central ctr-ECCD to modify the q-profile in improved H-mode scenarios, showing an increase in confinement at still good MHD stability with flat elevated q-profiles at values between 1.5 and 2.

Recent experimental and theoretical studies highlight the need to predict the turbulence-induced radial diffusion of energetic particles quantitatively in present-day and future fusion devices. Gyrokinetic simulations with passive fast ion species in realistic tokamak equilibria are used to investigate the influence of the particle energy on diffusion due to electrostatic and electromagnetic turbulence. To facilitate more straightforward comparisons between theory and experiments, scaling relations are derived that allow for writing the relevant diffusivities as functions of experimentally readily accessible quantities. In this context, an improved method for estimating the magnetic fluctuation level is described. (Some figures may appear in colour only in the online journal)

Recent experimental and theoretical studies highlight the need to predict the turbulence-induced radial diffusion of energetic particles quantitatively in present-day and future fusion devices. Gyrokinetic simulations with passive fast ion species in realistic tokamak equilibria are used to investigate the influence of the particle energy on diffusion due to electrostatic and electromagnetic turbulence. To facilitate more straightforward comparisons between theory and experiments, scaling relations are derived that allow for writing the relevant diffusivities as functions of experimentally readily accessible quantities. In this context, an improved method for estimating the magnetic fluctuation level is described.

The level and distribution of the wall power flux of energetic ions in ITER have to be known accurately in order to ensure the integrity of the first wall. Until now, most quantitative estimates have been based on the assumption that fast ion transport is dictated by neoclassical effects only. However, in ITER, the fast ion distribution is likely to be affected by various MHD effects and probably also by microturbulence. We have now upgraded our orbit-following Monte Carlo code ASCOT so that it has simple, theory-based models for neoclassical tearing mode (NTM)-type islands as well as for turbulent diffusion. ASCOT also allows for full-orbit following, which is important close to the material surfaces and, possibly, also when strong toroidal inhomogeneities are present in the magnetic field. Here we introduce the new models, preliminary results obtained with them, and how these models could be made more realistic in the future. The simulations are carried out for thermonuclear alpha particles in ITER scenario 2 plasma, because we consider this combination to be most critical for the successful operation of ITER. Neither the turbulent transport nor NTM-type islands are found to introduce alarming changes in the wall loads. However, at this stage it was not possible to combine the island structures with the non-axisymmetric magnetic field of ITER, and it remains to be seen what the combined effect of drift islands together with the toroidal ripple and local field aberrations, such as those due to test blanket modules and resonant magnetic perturbations will be.

A Reply to the Comment by W. Zhang, Z. Lin, and L. Chen.Received 11 October 2011DOI:https://doi.org/10.1103/PhysRevLett.107.239502© 2011 American Physical Society

The transport of charged particles (e. g., cosmic rays) in astrophysically relevant, turbulent magnetic fields (like they exist, e. g., in the solar wind) is investigated. Generic theoretical models-using concepts and insights developed recently in the context of magnetic confinement fusion research-are applied to the present problem and confirmed by means of numerical simulations. At high energies, a novel transport regime is found, in which the particles decorrelate on a gyro-orbit timescale. Explicit scaling laws for the cross-field diffusivities in various limits are derived.

Analytical and numerical work is used in tandem to address the problem of turbulent transport of energetic ions in magnetized plasmas. It is shown that orbit averaging is not valid under rather generic conditions, and that perpendicular decorrelation effects lead to a slow $1/E$ decay of the electrostatic particle diffusivity of beam ions, while the respective magnetic quantity is even independent of the particle energy $E$.

The question if and how streamers (i.e., radially elongated vortices) can lead to an enhancement of the electron heat transport in electron temperature gradient turbulence is addressed. To this aim, the electrons are treated as passive tracers, and their decorrelation mechanisms with respect to the advecting electrostatic potential are studied. A substantial transport enhancement is found in a wide region of parameter space.

The mechanisms found for the magnetic transport of fast ions in the work of Hauff et al. [Phys. Rev. Lett. 102, 075004 (2009)] are extended to the diffusion of runaway electrons. Due to their smaller mass and larger energy, they behave strongly relativistically, for which reason the scaling laws defined previously have to be modified. It is found that due to these changes, the regime of constant magnetic transport does not exist anymore, but diffusivity scales with E−1 for magnetic transport, or even with E−2 in the case that finite gyroradius effects become important. It is shown that the modified analytical approaches are able to explain the surprisingly small values found in experiments, although it cannot be excluded that possibly other reduction mechanisms are present at the same time.

The turbulent E×B advection of energetic ions in three-dimensional tokamak geometry is investigated both analytically and numerically. It is shown that orbit averaging (leading to a significant reduction of the diffusivity) is only valid for low magnetic shear. At moderate or high magnetic shear, a rather slow decrease of the diffusivity is found, proportional to (E∕Te)−1 or (E∕Te)−1.5 for particles with a large or small parallel velocity component, respectively. The decorrelation mechanisms responsible for this behavior are studied and explained in detail. Moreover, it is found that resonances between the toroidal drift of the particles and the diamagnetic drift of the turbulence can lead to an enhancement of the fast ion transport.

The radial redistribution of energetic ions by background turbulence is investigated by means of linear and nonlinear gyrokinetic simulations with the GENE code [T. Dannert and F. Jenko, Phys. Plasmas 12, 072309 (2005)]. The fast particles are described by an asymmetric and anisotropic Maxwellian distribution function, and they are treated as passive tracers. It is found that there can be a significant fast ion diffusivity for particle energies up to about 10 times the thermal energy, with details depending on the properties of the magnetic geometry and of the microinstabilities driving the turbulence. This finding provides a possible explanation of experimental results concerning the efficiency of neutral beam current drive reported recently from ASDEX Upgrade [S. Gunter et al., Nucl. Fusion 47, 920 (2007)].

Test particle transport in realistic plasma core turbulence (as described by nonlinear gyrokinetics) is investigated, focusing on the question whether and under what conditions the transport may become “anomalous”; i.e. super- or subdiffusive. While in the presence of stochastic fluctuations, the transport always becomes diffusive for large times, coherent flow components such as zonal flows or poloidal drifts can induce non-Gaussian transport over large intermediate time spans. In order to understand the origin of these phenomena, a simple model employing stochastic potentials is used to complement the analysis based on gyrokinetic turbulence simulations.

Beyond a certain heating power, measured and predicted distributions of NBI driven currents deviate from each other, in a form that can be explained by the assumption of a modest diffusion of fast particles. Direct numerical simulation of fast test particles in a given field of electrostatic turbulence indicates that for reasonable parameters fast and thermal particle diffusion indeed are similar. High quality plasma edge plasma profiles on ASDEX Upgrade, used in the linear, gyrokinetic, global stability code LIGKA give excellent agreement with the eigenfunction measured by a newly extended reflectometry system for ICRH-excited TAE-modes. They support the hypothesis of TAE-frequency crossing of the continuum in the edge region as explanation of the high TAE-damping rates measured on JET.A new fast ion loss detector with 1MHz time resolution allows frequency and phase resolved correlation between low frequency magnetic perturbation, giving, together with modelling of the particle orbits, new insights into the mechanism of fast particle losses during NBI and ICRH due to helical perturbations.

Beyond a certain heating power, measured and predicted distributions of neutral beam injection (NBI) driven currents deviate from each other even in the absence of MHD instabilities. The most reasonable explanation is a redistribution of fast NBI ions on a time scale smaller than the current redistribution time. The hypothesis of a redistribution of fast ions by background turbulence is discussed. Direct numerical simulation of fast test particles in a given field of electrostatic turbulence indicates that for reasonable parameters fast and thermal particle diffusion can indeed be similar. High quality plasma edge density profiles on ASDEX Upgrade and the recent extension of the reflectometry system allow for a direct comparison of observed TAE eigenfunctions with theoretical ones as obtained with the linear, gyrokinetic, global stability code LIGKA. These comparisons support the hypothesis of TAE-frequency crossing the continuum at the plasma edge in ASDEX Upgrade H-mode discharges. A new fast ion loss detector with 1 MHz time resolution allows frequency and phase resolved correlation between the observed losses and low frequency magnetic perturbations such as TAE modes and rotating magnetic islands. Whereas losses caused by TAE modes are known to be due to resonances in velocity space, by modelling the particle drift orbits we were able to explain losses caused by magnetic islands as due to island formation and stochasticity in the drift orbits.