S. da Graca

Interaction of energetic particles with large and small scale instabilities

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.

Fast-ion transport induced by Alfvén eigenmodes in the ASDEX Upgrade tokamak

A comprehensive suite of diagnostics has allowed detailed measurements of the Alfven eigenmode (AE) spatial structure and subsequent fast-ion transport in the ASDEX Upgrade (AUG) tokamak [1]. Reversed shear Alfven eigenmodes (RSAEs) and toroidal induced Alfven eigenmodes (TAEs) have been driven unstable by fast ions from ICRH as well as NBI origin. In ICRF heated plasmas, diffusive and convective fast-ion losses induced by AEs have been characterized in fast-ion phase space. While single RSAEs and TAEs eject resonant fast ions in a convective process directly proportional to the fluctuation amplitude, δB/B, the overlapping of multiple RSAE and TAE spatial structures and wave–particle resonances leads to a large diffusive loss, scaling as (δB/B)2. In beam heated discharges, coherent fast-ion losses have been observed primarily due to TAEs. Core localized, low amplitude NBI driven RSAEs have not been observed to cause significant coherent fast-ion losses. The temporal evolution of the confined fast-ion profile in the presence of RSAEs and TAEs has been monitored with high spatial and temporal resolution. A large drop in the central fast-ion density due to many RSAEs has been observed as qmin passes through an integer. The AE radial and poloidal structures have been obtained with unprecedented details using a fast SXR as well as 1D and 2D ECE radiometers. GOURDON and HAGIS simulations have been performed to identify the orbit topology of the escaping ions and study the transport mechanisms. Both passing and trapped ions are strongly redistributed by AEs.

Localization of MHD and fast particle modes using reflectometry in ASDEX Upgrade

The radial structure of toroidal Alfven eigenmodes (TAEs) is of great importance for comparison with theoretical predictions. A dual-channel fast frequency hopping millimeter-wave reflectometer installed on the ASDEX Upgrade tokamak is capable of measuring density fluctuations from the plasma edge to core, allowing the radial eigenfunction of n = 4 TAE and edge MHD modes to be obtained using phase perturbation and coherence data analysis techniques. The two techniques reveal similar results, and in particular the radial structure of the n = 4 TAE is found to be in good agreement with numerical predictions from linear gyrokinetic simulations. The first results of the radial localization of Alfven cascades are also presented.

Low-frequency Alfvén eigenmodes during the sawtooth cycle at ASDEX Upgrade

The confinement of fast particles, present in tokamak plasmas as nuclear fusion products and through external heating, will be essential for any future reactor. Fast particles can be expelled from the plasma through their interaction with Alfven eigenmode (AE) instabilities. AEs can exist in gaps in the Alfven continuum created by plasma equilibrium non-uniformities. In ASDEX Upgrade low-frequency modes in the Alfven-acoustic frequency regime, including beta-induced Alfven eigenmodes (BAEs) and lower frequency modes with mixed Alfven and acoustic polarizations, have been observed. They exist in gaps in the Alfven continuum opened up by geodesic curvature and finite plasma compressibility. In this paper a kinetic dispersion relation (Lauber et al 2009 Plasma Phys. Control. Fusion 51 124009) is solved numerically to investigate the influence of diamagnetic effects on the evolution of these low-frequency modes during the sawtooth cycle. Other distinct but potentially related modes which sweep significantly upwards in frequency towards the end of the sawtooth cycle are also considered. Using information gained from soft x-ray measurements (Igochine et al 2010 IPP Report 1/338) and electron temperature information from electron cyclotron emission to constrain the safety factor profiles, realistic equilibrium reconstructions for the analysis are obtained using the CLISTE code (Mc Carthy 2012 Plasma Phys. Control. Fusion 54 015010). The results for the mode frequency evolution are then compared with experimental results from ASDEX Upgrade.

Dynamics of flows and confinement in the TJ-II stellarator

This work deals with the results on flow dynamics in TJ-II plasmas under Li-coated wall conditions, which produces low recycling and facilitates the density control and access to improved confinement transitions. The low-density transition, characterized by the emergence of the shear flow layer, is described from first principles and within the framework of neoclassical theory. The vanishing of the neoclassical viscosity when approaching the transition from below explains the observation of a number of turbulent phenomena reported in TJ-II in recent years; a unifying picture is provided in which zonal, i.e. large scale, radially structured, perturbations are observable when the neoclassical damping is sufficiently small. Preliminary linear, collisionless gyrokinetic simulations are carried out to assess that the measured time scale of relaxation of such perturbations is reasonably understood theoretically. In higher density regimes, the physical mechanisms behind the L–H transition have been experimentally studied. The spatial, temporal and spectral structure of the interaction between turbulence and flows has been studied close to the L–H transition threshold conditions. The temporal dynamics of the turbulence-flow interaction displays a predator–prey relationship and both radial outward and inward propagation velocities of the turbulence-flow front have been measured. Finally, a non-linear relation between turbulent fluxes and gradients is observed.

Characterization of Alfvén eigenmodes using NBI during current ramp-up in the ASDEX Upgrade tokamak

Alfv?n cascades (ACs) and beta-induced Alfv?n eigenmodes (BAEs) have been studied in the ASDEX Upgrade tokamak during the current ramp-up phase of neutral beam heated (NBI) discharges using principally reflectometry, but also soft x-ray (SXR) and electron cyclotron emission imaging (ECEI). ACs have been observed on the tokamak high-field side and low-field side in reflectometer signals even in the absence of a cutoff. Under this condition it is shown that the response is not due to an interferometry effect but due to backscatter. The radial structure of BAEs and ACs has been obtained by cross-correlating the reflectometer with SXR, ECEI and magnetic signals. The reflectometer signals reveal a variety of Alfv?n eigenmodes with different characteristics depending on the plasma heating scheme. Here, discharges with similar plasma parameters but varying NBI sources and/or additional electron cyclotron resonance heating were performed. It is shown that the bursting behaviour of ACs for qmin?<?2 depends on the NBI beam geometry. Also, a discrepancy in the n?=?2 AC minimum frequency of a Grand Cascade is explained by the linear gyro-kinetic code LIGKA simulations which include energetic particle effects.

Shear-flow susceptibility near the low-density transition in TJ-II

The emergence of the plasma edge shear-flow layer has been recently shown to be consistent with second-order transition model coupling shear amplification by Reynolds stress and turbulence reduction by shear. A fundamental feature of second-order transitions in equilibrium thermodynamics is the divergence of the susceptibility near the critical point. In this paper, an experimental investigation is carried out to find out whether an analogous phenomenon takes place in the transition leading to the formation of the shear-flow layer in the TJ-II stellarator.

Stability of toroidicity induced shear Alfvén eigenmodes in ASDEX Upgrade

In a tokamak plasma, toroidicity induced Alfven eigenmodes (TAEs) are excited by and alter the orbits of resonant fast ions with the character of these modes defined by both thermal and supra-thermal fast ion populations. To explore the stability of TAEs in ASDEX Upgrade, the effects of magnetic shear and density on TAEs, the decay and growth rate of individual TAEs and fast ion drive rates have been studied. In particular, the mode structure of TAEs, the dependence of the ICRF power-density threshold on the toroidal mode number n, the effect of magnetic shear at the plasma edge on low-n TAEs (n ≤ 2) and a comparison of measured decay rates of TAEs with predictions made by the LIGKA code are discussed. In addition, fast ion pressure profiles generated by the ICRF power deposition codes PION and TORIC and the equilibrium code CLISTE have been examined to see if they lead to a sufficient fast ion drive rate for the observed TAEs, and to benchmark a formula for volume averaged βfast using measurable quantities in ICRH-only plasmas.

I-mode studies at ASDEX Upgrade: L-I and I-H transitions, pedestal and confinement properties

The I-mode is a plasma regime obtained when the usual L-H power threshold is high, e.g. with unfavourable ion direction. It is characterised by the development of a temperature pedestal while the density remains roughly as in the L-mode. This leads to a confinement improvement above the L-mode level which can sometimes reach H-mode values. This regime, already obtained in the ASDEX Upgrade tokamak about two decades ago, has been studied again since 2009 taking advantage of the development of new diagnostics and heating possibilities. The I-mode in ASDEX Upgrade has been achieved with different heating methods such as NBI, ECRH and ICRF. The I-mode properties, power threshold, pedestal characteristics and confinement, are independent of the heating method. The power required at the L-I transition exhibits an offset linear density dependence but, in contrast to the L-H threshold, depends weakly on the magnetic field. The L-I transition seems to be mainly determined by the edge pressure gradient and the comparison between ECRH and NBI induced L-I transitions suggests that the ion channel plays a key role. The I-mode often evolves gradually over a few confinement times until the transition to H-mode which offers a very interesting situation to study the transport reduction and its link with the pedestal formation. Exploratory discharges in which n = 2 magnetic perturbations have been applied indicate that these can lead to an increase of the I-mode power threshold by flattening the edge pressure at fixed heating input power: more heating power is necessary to restore the required edge pressure gradient. Finally, the confinement properties of the I-mode are discussed in detail.

Improved time-frequency analysis of ASDEX Upgrade reflectometry data using the reassigned spectrogram technique.

The spectrogram is one of the best-known time-frequency distributions suitable to analyze signals whose energy varies both in time and frequency. In reflectometry, it has been used to obtain the frequency content of FM-CW signals for density profile inversion and also to study plasma density fluctuations from swept and fixed frequency data. Being implemented via the short-time Fourier transform, the spectrogram is limited in resolution, and for that reason several methods have been developed to overcome this problem. Among those, we focus on the reassigned spectrogram technique that is both easily automated and computationally efficient requiring only the calculation of two additional spectrograms. In each time-frequency window, the technique reallocates the spectrogram coordinates to the region that most contributes to the signal energy. The application to ASDEX Upgrade reflectometry data results in better energy concentration and improved localization of the spectral content of the reflected signals. When combined with the automatic (data driven) window length spectrogram, this technique provides improved profile accuracy, in particular, in regions where frequency content varies most rapidly such as the edge pedestal shoulder.