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

Fast-ion transport induced by Alfvén eigenmodes in the ASDEX Upgrade tokamak To cite this article: M. Garcia-Munoz et al 2011 Nucl. Fusion 51 103013 View the article online for updates and enhancements. Related content Fast-ion losses induced by ACs and TAEs in the ASDEX Upgrade tokamak M. García-Muñoz, N. Hicks, R. van Voornveld et al. - MHD induced fast-ion losses on ASDEX Upgrade M. García-Muñoz, H.-U. Fahrbach, S.D. Pinches et al. - Energetic particle physics in fusion research in preparation for burning plasma experiments N.N. Gorelenkov, S.D. Pinches and K. Toi - Recent citations Tomography of the positive-pitch fast-ion velocity distribution in DIII-D plasmas with Alfvén eigenmodes and neoclassical tearing modes B. Madsen et al - A fast model to resolve the velocity-space of fast-ion losses detected in ASDEX Upgrade and MAST Upgrade J.F. Rivero-Rodriguez et al - Theoretical studies and simulations of mode structure symmetry breaking in tokamak plasmas in the presence of energetic particles Z X Lu et al - This content was downloaded from IP address 87.218.223.151 on 18/08/2020 at 11:10 IOP PUBLISHING and INTERNATIONAL ATOMIC ENERGY AGENCY NUCLEAR FUSION Nucl. Fusion 51 (2011) 103013 (14pp) doi:10.1088/0029-5515/51/10/103013 Fast-ion transport induced by Alfv´ en eigenmodes in the ASDEX Upgrade tokamak M. Garcia-Munoz1, I.G.J. Classen2, B. Geiger1, W.W. Heidbrink3, M.A. Van Zeeland4,S. ¨ Ak¨ aslompolo5, R. Bilato1, V. Bobkov1, M. Brambilla1, G.D. Conway1, S. da Grac¸a6, V. Igochine1, Ph. Lauber1, N. Luhmann7, M. Maraschek1,F.Meo 8,H.Park 9, M. Schneller1, G. Tardini1and the ASDEX Upgrade Team 1Max-Planck-Institut f¨ ur Plasmaphysik, EURATOM Association, Garching, Germany 2FOM-Institute for Plasma Physics Rijnhuizen, EURATOM Association, The Netherlands 3University of California-Irvine, Irvine, CA 92697, USA 4General Atomics, San Diego, CA 92186-5608, USA 5Helsinki University of Technology, Association EURATOM-TEKES, Finland 6Associacao EURATOM/IST, Instituto de Plasmas e Fosao Nuclear – Laboratorio Associado, IST, Lisbon, Portugal 7University of California at Davis, Davis, CA 95616, USA 8Association Euratom-Risø National Laboratory for Sustainable Energy, Technical University of Denmark, DK-4000 Roskilde, Denmark 9POSTECH, Pohang, Gyeongbuk, 790-784, Korea E-mail: [email protected] Received 2 February 2011, accepted for publication 21 July 2011 Published 19 August 2011 Online at stacks.iop.org/NF/51/103013 Abstract A comprehensive suite of diagnostics has allowed detailed measurements of the Alfv´ en eigenmode (AE) spatial structure and subsequent fast-ion transport in the ASDEX Upgrade (AUG) tokamak [1]. Reversed shear Alfv´ en eigenmodes (RSAEs) and toroidal induced Alfv´ en 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. (Some figures in this article are in colour only in the electronic version) 1. Introduction Future burning plasma experiments such as ITER may be subject to the excitation of Alfv´ en eigenmode (AE) instabilities [2] by 3.5 MeV fusion born alpha particles as well as fast ions created by auxiliary heating systems [3,4]. If allowed to grow unabated, these instabilities have the potential to cause fast-ion redistribution and loss leading to a degradation of the fusion performance, heating and current drive efficiencies [5,6]as well as to possible serious damage of first wall components [7]. Of special importance to magnetically confined fusion plasmas are toroidal Alfv´ en eigenmodes (TAEs) [8,9] and reverse shear Alfv´ en eigenmodes (RSAEs) [10–15] because of their potential to eject fast ions before their thermalization [6,16]. On the road to address these issues, significant progress in fast-ion physics has been made recently on ASDEX Upgrade 0029-5515/11/103013+14$33.00 1© 2011 IAEA, Vienna Printed in the UK & the USA Nucl. Fusion 51 (2011) 103013 M. Garcia-Munoz et al (AUG). An extended suite of diagnostics now allows detailed measurements of AE spatial structure and the subsequent fast-ion transport. Fast 1D and 2D imaging [17] electron cyclotron emission (ECE) measurements of the temperature fluctuations induced by the AEs have delivered unprecedented details on eigenmode radial and poloidal structure. Apart from the recently installed ECE-imaging (ECEI) system, the upgraded fluctuation diagnostics, used in these studies, include 1D ECE [18], soft x-ray (SXR) [19] and reflectometry [20]. The main systems utilized to diagnose the fast-ion internal redistribution and eventual loss are the neutron rates [21], the fast-ion D-alpha (FIDA) spectroscopy [22] and the scintillator based fast-ion loss detectors (FILDs) [23]. An overview of the AUG diagnostics utilized in this work is shown in figure 1. FIDA spectroscopy has recently been developed at AUG [24] following the technique employed for the first time at DIII-D [22] and more recently at TEXTOR [25], NSTX [26] and LHD [27]. The upgraded AUG FILDs provide energy and pitch-angle resolved measurements of fast-ion losses with a bandwidth of 1 MHz at two different toroidal positions and ≈30 cm above the midplane. The AUG FILD design is based on the concept of the α-particle detector used for the first time on the TFTR tokamak [28,29] and more recently on several fusion devices such as CHS [30], W7-AS [31,32], LHD [33], JET [34], NSTX [35], TJ-II [36] and DIII-D [37,38]. Over the past two years, experiments have been conducted in AUG to study the fast-ion transport due to AEs in plasmas heated purely by ICRH or NBI. In ICRH heated plasmas, strong fast-ion losses induced by RSAEs and TAEs have been observed correlated with a neutron rate drop of ≈50% [39,40]. Time-resolved energy and pitch-angle measurements of fastion losses correlated in frequency and phase with RSAEs and TAEs have allowed clear identification of the loss mechanisms. In NBI heated plasmas, RSAEs and TAEs have been driven unstable during the current ramp-up phase when incomplete current penetration results in a high central safety factor and strong drive due to multiple higher order resonances [41]. Core localized, low amplitude NBI driven RSAEs have not been observed to cause significant coherent fast-ion losses. The fastion redistribution due to RSAEs and TAEs has been measured using the recently developed in AUG FIDA spectroscopy. This paper is divided into two sections devoted to the study of the AE induced fast-ion transport in ICRH (section 2) and NBI (section 3) heated discharges. In section 2.1,an overview of the main plasma parameters is presented together with the observed AE activity in ICRH heated discharges. The nature and radial structures of the AEs are analysed by means of the AUG magnetic pick-up coils, SXR and 1D ECE diagnostics together with simulations performed with the NOVA code. Section 2.2 is dedicated to the fast-ion losses observed in the presence of these AEs. Time-resolved fast-ion loss measurements show a linear and quadratic dependence on the AE fluctuation amplitude which indicate the convective and diffusive character of the loss mechanisms. Preliminary modelling results are presented to identify the topology of the measured escaping ions and the possible wave–particle resonances that may be causing the fast-ion losses. Section 3.1 is dedicated to the AE activity measured with the AUG 2D ECE imaging and reflectometer systems in NBI heated discharges. The neutron rate during the first phase of the discharges is FIDA NBI 3 ++ ++++++ + +++++++ 1D ECE 1.85 1.9 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 -4 -2 0 2 4 6 8 10 12 14 x 10-3 R ( m ) RSAE mode amplitude z (m) 2D ECE FILD ECEI Magnetics SXR Reflectometry Figure 1. AUG poloidal cross section showing an overview of the relevant diagnostics for AE studies. On the right, the typical radial structure of a RSAE measured by the 2D ECE-imaging system is shown. shown to give the reader an idea of the global impact that AEs have on the fast-ion confinement. In section 3.2, the AE induced fast-ion redistribution and loss measured by the FIDA system and FILD detectors, respectively, are presented. The weighting function of the new FIDA diagnostic at AUG is also briefly introduced in order to make a direct comparison between FIDA and FILD measurements. 2. Alfv´ en eigenmodes and associated fast-ion transport in ICRF heated discharges An important difference between present experiments and ITER will be the presence of fusion born α-particles as main heating source. These MeV α-particles with relatively small characteristic orbit lengths (compared with plasma minor radius), velocities well above the Alfv´ en velocity, and an isotropic distribution function will likely excite meso-scale fluctuations. In contrast, in present experiments, fast ions are mainly generated by external heating systems with highly anisotropic distribution functions that typically excite macroscale collective modes (e.g. AEs). While RF heating systems mostly populate the fast-ion phase space corresponding to deeply trapped supra-Alfv´ enic ions, NBI systems, depending on their injection geometries, mainly create a large population of supra-thermal (in some cases even supra-Alfv´ enic) passing ions. In general, minority and high-harmonic RF heating constitute a unique tool to achieve some burning-relevant dynamical regimes with ions in the MeV range. 2.1. Alfv´ en eigenmodes In AUG, on-axis minority RF heating in low density deuterium plasmas create a large population of supra-Alfv´ enic ions that usually drive a rich variety of Alfv´ en/Alfv´ en-acoustic eigenmodes [42]. The experiments discussed here have been performed in plasmas with plasma current Ip≈0.8MA, 2 Nucl. Fusion 51 (2011) 103013 M. Garcia-Munoz et al 40 40 60 80 100 120 140 160 Frequency (kHz) 1.05 1.15 1.25 1.35 Time ( s ) SXR core n=3 n=3 n=4 n=4 TAEs RSAEs n=3 fRSAE min #23824 60 80 100 120 140 160 Frequency (kHz) Magnetics #23824 n=3 n=3 n=4 n=4 n=5 n=5 TAEs RSAEs 1.05 1.15 1.25 1.35 Time (s) fRSAE min (c) (b) 2.5 3.5 4.5 5.5 P (MW) ICRH n (10 m ) e 19 -3 1 2 3 4 ~ 50% Neutron rate (10 n/s) 12 (a) Figure 2. AUG discharge #23824. (a) Core line integrated electron density, ne, neutron rate and ICRH power (dashed line), PICRH.(b) Spectrogram of an in-vessel magnetic pick-up coil. (c) Spectrogram of a core SXR channel. toroidal field Bt=2.0 T, safety factor at the edge q95 ≈4.0 and ion cyclotron resonance heating (ICRH) as main heating and fast-particle source. 4.5 MW of on-axis ICRF hydrogen minority heating was applied to a deuterium plasma (nH/nD≈ 5%). In figure 2(a), the core line integrated electron density, ne, applied ICRH power and neutron rate of the baseline discharge, #23824, are presented. Figures 2(b) and (c) show, respectively, the Fourier spectrograms for a magnetic fluctuation signal and for a SXR signal corresponding to a line of sight passing through the plasma core. Several coherent MHD fluctuations are visible around 110 kHz up to 170 kHz. They correspond to TAEs with different toroidal mode numbers, n=3,4,5, as obtained from Mirnov coils, whose presence is confirmed also by comparison with ideal MHD calculations carried out with the NOVA code [43]. Magnetic fluctuations chirping in frequency from ≈50 kHz up to the TAE frequencies (barely visible in the magnetics spectrogram) have been identified as RSAEs by means of the SXR emission from the plasma core as figure 2(c) shows. The lowest RSAE frequency, fmin RSAE, in figure 2(b) and (c) is mainly given by the geodesic compressibility and the toroidal coupling to the acoustic waves, as expected by the theory [44]. Pressure effects modify the local dispersion relation for shear Alfv´ enwavesinlow-β plasmas: ωRSAE ≈| m qmin−n|·VA R0, with mthe poloidal mode number. The modified minimum of the local dispersion relation is then given by the geodesic acoustic frequency: ωmin geo ≈√2 R0·Cs=√2 R0·Ti mi1/2 ·7 4+Te Ti1/2 .(1) An excellent agreement between the experimental lowest RSAE frequency (fmin RSAE) and the modified dispersion relation is clearly visible in figures 2(b) and (c) (superimposed in white). The estimated fmin RSAE has been calculated assuming Te=Tiand taking Tefrom an ECE channel near the RSAE localization and assuming a negligible plasma rotation. Fluctuations in the electron temperature profile caused by the RSAEs and TAEs [45] have been measured with the 1D ECE radiometer. The RSAE and TAE radial structures have been reconstructed by means of ECE-FILD cross-correlation techniques to improve signal-to-noise ratios. Figures 3(a)–(c) show the normalized crosspower spectral densities (coherence) asa function ofρpol and frequencyfor 50 mstime intervals. The RSAE and TAE radial structures were obtained by selecting and averaging a certain frequency band of the coherence. The selected RSAE and TAE frequency bands are given in figures 3(a)–(c). Figure 3(a) shows global TAEs extended from ρpol ≈0.23 up to the edge with broad RSAEs localized at ρpol ≈0.4. A complete overlapping of RSAE–TAE radial structures is clearly visible (highlighted in yellow). Figure 3(b) shows the RSAE–TAE radial structures for a later time interval. TAEs shift outwards becoming more localized while RSAEs shift inwards becoming also more localized at ρpol ≈0.3. The overlapping region becomes smaller. Finally, figure 3(c) shows a negligible RSAE–TAE spatial overlapping with RSAEs and TAEs well localized at ρpol ≈0.3 and ρpol ≈0.6, respectively. The largest RSAEs and TAEs presented here caused a normalized Teperturbation of δTe/Te≈0.009. NOVA simulations have been performed to identify the AEs as well as their spatial structures and radial shifts. In figures 3(d)–(f) the displacements predicted by NOVA for three different AEs are presented. NOVA calculations used experimental profiles of electron density and electron temperature combined with the assumption of Te=Tito obtain the equilibrium pressure information. The q-profile for the NOVA simulations has been inferred from the MHD activity evolution during the plasma discharge, i.e. RSAE, TAE and later sawtooth spatial location and occurrence. Figures 3(d)–(f) show the radial structures of n=3 RSAE at qmin =1.58, and both n=3 TAEs at qmin =1.46. The different curves in figures 3(d)–(f) represent the different poloidal harmonics. The timing corresponding to this qmin evolution can be identified in figure 4. A Fourier analysis of the total losses measured by FILD in the presence of the AEs reveals details of the RSAEs, TAEs and RSAE–TAE-transition that are not visible either on the magnetic or on the SXR spectrogram (figures 2(b) and (c)). The FILD spectrogram of figure 4(a) shows the frequency evolution of the RSAEs from the geodesic acoustic frequency up to the TAE frequency with a clear frequency gap at the RSAE–TAE transition between the RSAE and its associated TAE. This apparent frequency-gap has been 3 Nucl. Fusion 51 (2011) 103013 M. Garcia-Munoz et al Figure 3. AUG discharge #23824. RSAEs and TAEs radial structures obtained by means of ECE-FILD cross-correlation. The fast-ion losses used for the cross-correlation technique have energies (E) and pitch angles () ≈(600 keV,70◦). RSAE radial structures are reconstructed at the RSAE lowest frequency. Different time intervals are displayed; (a) for (1.08–1.13) s, (b) for (1.24–1.29) s and (c) for (1.32, 1.37) s. In yellow are highlighted the regions with overlapping TAE–RSAE internal structures well before the RSAE–TAE transition. (d)–(f)n=3 RSAEs and TAE spatial profiles calculated with the NOVA code. (g) and (h) show the Alfv´ en spectra for the RSAEs and TAEs n=3 at two different time points. The corresponding q-profiles are plotted in dashed lines. studied using the ideal MHD eigenvalue solver NOVA. The minimum qwas successively reduced and the eigenfrequency of modes identified as RSAEs as well as the TAEs resulting from the typical RSAE to TAE transition were recorded for n=3–6. An effect not typically described in the literature, but important here to explain the frequency gap during the RSAE–TAE transition visible on the FILD spectrogram (inset in figure 4(a)), is that it is possible as qmin changes from m/n to (m −1/2)/n, for the RSAE to transition to two separate TAEs each one centred near the q≈(m−1/2)/n surface (one on either side of qmin) and being composed of the mand m−1 poloidal harmonics. The inset in figure 4(b) shows a zoom of this eigenmode splitting at the transition for the RSAE n=5. The yellow points predicted by NOVA are stable in the plasma 4 Nucl. Fusion 51 (2011) 103013 M. Garcia-Munoz et al 1.60 1.55 1.50 1.45 1.40 1.35 1.30 qmin 0 50 100 150 Frequency (kHz) n=3 n=4 n=5 n=6 AUG#23824 NOVA simulations (b) 50 100 150 Frequency (kHz) 1.16 1.20 1.24 Time(s) RSAEs TAEs n=5 n=3 n=5 n=4 n=6 n=5 n=5 AUG#23824 (a) FILD spectrogram n=5 fgap trans fgap trans Figure 4. AUG discharge #23824. (a) Fourier analysis of the total fast-ion losses with energies (E) and pitch angles (), (E,)≈ (600 keV, 70◦), during the time window (1.14,126) s. The inset shows a zoom of the RSAE–TAE transition frequency gap. (b) NOVA simulations of AE activity during the same time window (1.14,126) s. The inset shows the RSAE splitting into two TAEs with different frequencies at transition. and therefore not visible in the FILD spectrogram. Whether these modes are eigenmodes of the plasma itself is determined by the actual equilibrium pressure gradients, magnetic shear, etc and that observed experimentally is, in a perturbative sense, due to the details of the fast-ion population that provides drive for the eigenmodes. The NOVA calculations reproduce well both the experimentally measured frequency sweeping as well as the actual magnitudes. Note, the effective gamma used in these simulations was γ=(Te+7/4Ti)/(Te+ Ti)=1.375, which affects the minimum RSAE frequency obtained. The frequency splitting due to the appearance of two separate TAEs (relatively constant frequency modes) from each RSAE frequency sweep also looks similar to that measured experimentally with the difference being that experimentally, only one of the two TAEs from each RSAE transition is observed. Experimentally, the RSAE appears to jump to the lower frequency TAE near qmin ≈(m −1/2)/n, which corresponds to the mode at larger minor radius, creating the frequency gap visible on the FILD spectrogram. As mentioned, this is probably due to the details of the fast-ion profile driving the modes and a change in stability from one mode to the other. This stability analysis using a realistic ICRH fast-ion distribution function and a MSE constrained q-profile will be the subject of a future study. However, although the mode stability as well as radial extension depend strongly on the details of the q-profile, the frequency gap observed experimentally during the RSAE–TAE transition, and explained using NOVA simulations follow the basics of the RSAE–TAE general theory for a reversed shear magnetic configuration. 2.2. Fast-ion transport A minimum RF power of ≈3 MW for on-axis minority heating is typically necessary in AUG to drive AEs unstable with energetic ions [46,47]. In the presence of ICRH driven RSAEs and TAEs strong fast-ion losses are detected by the FILD system [23] correlated with a neutron rate drop of ≈50%, see figure 2(a). According to ICRH simulations performed with the TORIC full-wave code [48], about 10% of the ICRH power is absorbed in this discharge directly by deuterium ions at the second harmonic (ω=2cD =cH). The deuterium distribution function presents a clear fast-ion tail, which is responsible for a substantial increase in the neutron rate. Indeed, the neutron rate synthetic diagnostic built in SSFPQL [49] estimates a neutron rate four times higher due to the ICRH than due to the deuterium background alone. This may explain the neutron rate drop as a redistribution of the energetic deuterium ions created by ICRH second-harmonic heating. In order to fully characterize the orbits of the lost ions and identify the wave–particle resonances responsible for the losses, the phase space (energy and pitch angle at the FILD position) of the fast-ion losses is shown in figure 5. The energy of the lost ions is given by their gyroradius (ρ) and the pitch angle by angle between the ion velocity and the local magnetic field (=arcos(v/v)). In the presence of multiple AEs, i.e. t=1.36 s, fast ions are ejected within a broad energy range with gyroradius from ≈35 mm up to ≈105 mm, see figure 5(a). For the magnetic field at the probe, ≈1.6 T, this gyroradii range corresponds to hydrogen ions with energies between ≈0.2 MeV and ≈1.4 MeV (note that at very large gyroradius (⩾80 mm) the FILD collimator efficiency is rather limited making virtually impossible the identification of different energies). As expected from ICRF heated plasmas the fast-ion losses appear at high pitch angles between 67◦ and 80◦. The velocity space of lost fast ions changes strongly during the evolution of the AE activity, showing a completely different pattern within the next 200 ms. Figure 5(b) presents fast-ion losses well localized at high pitch angles (≈71◦) and energies (gyroradius ≈60 mm). The topology of the escaping ions detected by the FILD system has been investigated using the full orbit code GOURDON. The trajectory of the escaping ions has been calculated backwards in time from the detector to the plasma. 5 Nucl. Fusion 51 (2011) 103013 M. Garcia-Munoz et al Figure 5. AUG discharge #23824. Phase space of escaping ions. (a) Velocity space of escaping ions in the presence of (a) many AEs and (b) a single n=5 AE. (c) Typical trajectory of a lost hydrogen ion with E=200 keV calculated backward in time from detector collimator position to plasma. The vertical black line indicates the position of the ICRH resonance layer. The particles have been started at the FILD collimator position with the right gyro-phase and the detected energy and pitch angle and followed until they close a full poloidal transit in the absence of AE wave fields. Figure 5(c) shows a typical trajectory of an escaping ion. A Fourier analysis of the fast-ion loss signal allows us to identify the MHD fluctuations responsible for the losses during the entire time window with AE activity, figure 6(a). A clear correlation between the TAE frequency pattern and the fastion loss frequencies is observed in both magnetics, figure 2(b), and FILD, figure 6(a), spectrograms during the whole time window. Although all TAEs eject resonant ions, the relative amplitude of the measured losses with respect to the fluctuation amplitude does not depend only on the magnetic fluctuation amplitude e.g. the losses measured at the n=4 TAE frequency are not as strong as one could expect from its large fluctuation amplitude in figure 2(b). Changes in the spatial distribution of the losses could explain this observation as the measurements are performed at a single poloidal position. In addition, fast-ion losses chirping in frequency from approximately the geodesic frequency, fmin RSAE, up to the TAE frequency, fTAE , emerge following the typical RSAE frequency pattern. The RSAE induced resonant losses appear stronger (≈10% of the total resonant losses) in the frequency range where the RSAEs interact with the Alfv´ en-acoustic branch near the fmin RSAE and during the RSAE–TAE transition. The raw data of the Fourier-analysed fast-ion loss signal shown in figure 6(a) is presented in figure 6(b) to investigate the diffusive and convective character of the losses. The signal consists of a modulated (coherent) signal sitting on an incoherent background (see the inset in figure 6(b)) whose amplitude varies with time. The coherent component of the fast-ion losses is correlated in frequency and phase with the corresponding magnetic fluctuation, giving rise to the spectrogram shown in figure 6(a). The incoherent component is dominant, up to 80% of the total losses, in the presence of multiple frequency chirping AEs, t≈(1.1–1.3)s, and decreases when the number of modes decreases. However, it should be noted that it is not zero when only one mode is ejecting ions with a relatively large amplitude, t≈ (1.42–1.52)s, as discussed later. During the time window t≈(1.52–1.65)s only coherent losses induced by a single TAE, n=5, are visible. Going backwards in time, the incoherent losses of ions with gyroradius ≈60–70 mm appear, for t⩽1.52 s, when the local maximum radial displacement of the magnetic field lines is larger than ≈2 mm as measured by its fluctuation induced on the SXR emission. This threshold in the fluctuation amplitude is depicted in figure 6(b) with a vertical dashed line. The basic properties of the coherent and incoherent losses are investigated through their dependence on the magnetic fluctuation amplitude. Tracking the frequencies of the individual fluctuations in both, magnetics and FILD spectrograms, we get the relationship between the coherent fast-ion losses and the corresponding magnetic fluctuation amplitude. Figure 6(c) shows this exercise for the TAE n=3 between t=1.24 s and t=1.32 s. A clear linear dependence is visible during the whole time window, showing the convective character of the underlying loss mechanism. A similar analysis has been done for the incoherent losses shown in figure 6(d). The envelope of the incoherent losses, black curve in figure 6(b), is plotted in figure 6(d) as a function of the amplitude of the TAE n=5 for a time interval close to the onset of the incoherent losses, inset in figure 6(d), t=(1.42,1.50)s. 6 Nucl. Fusion 51 (2011) 103013 M. Garcia-Munoz et al FILD (10 V) -2 B (10 T) -4 1.42 1.44 1.46 1.48 1.50 Time (s) 3 4 5 6 2 3 4 5 6 #23824 70mm TAE n=5 (d) δB (10 T) -4 2345 3 4 5 6 FILD (10 V) -2 0.0 0.5 1.0 1.5 δB (10 T) -3 0246810 0.0 0.5 1.0 1.26 1.24 1.28 1.30 1.32 0 1 2 Time (s) FILD (10 V) -2 B (10 T) -2 #23824 ρ∼70mm TAE n=3 (c) FILD (10 V) -2 0.1 0.2 0.3 0.4 coherent FIL incoherent FIL 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Time ( s ) FIL (V) FILD raw signal ( = 70 mm)ρ(b) threshold 200 150 100 50 Frequency (kHz) 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Time (s) FILD spectrogram ( = 70 mm)ρ(a) fRSAE min PICRH n=3 n=5 RSAEs TAEs Figure 6. AUG discharge #23824. (a) Power spectrogram of the fast-ion loss signal with gyroradius ≈70 mm. The lowest RSAE frequency, fmin RSAE, is superimposed in white while the total ICRH power (PICRH) is superimposed in red. The inset shows the single TAE responsible for the onset of the incoherent losses. (b) Fast-ion loss signal. The coherent and incoherent components of the losses are highlighted. The vertical dashed line depicts the threshold for the incoherent losses. (c) Linear dependence of the coherent losses at the TAE n=3 frequency on the MHD fluctuation amplitude. (d) Quadratic dependence of the incoherent losses on the TAE n=5 fluctuation amplitude. A clear quadratic dependence has been obtained, strongly suggesting a diffusive mechanism involving several resonances in phase space. This is supported by the fact that the losses cover a larger domain in velocity space when the incoherent signal is not zero. It should also be underlined that, as shown in figure 6(b), the incoherent component is even larger in the presence of several modes, which is also expected to induce a stochastic fast-ion transport. The experimental results presented here are in agreement with previous works carried out at other large fusion devices with similar diagnostics and MHD fluctuations of diverse nature. Indeed, the linear and non-linear fast-ion transport in the presence of various MHD fluctuations have been observed in tokamaks [50–52] as well as stellerators [16,53,54] highlighting the importance of a detailed understanding of the underlying physics towards the realization of commercial fusion. Simulations with the guiding centre drift orbit code HAGIS [55] have been performed to better understand the loss mechanisms. A wave–particle exchange of canonical momentum, Pφ, and energy, E, takes place if the resonant condition n,p=nωφ−pωθ−ω≈0 is fulfilled. Here, ωφ is the fast-ion precession frequency, ωθthe fast-ion poloidal frequency, ωthe mode frequency and n,pthe resonance width. The fast-ion orbital frequencies, ωφand ωθ, are easily calculated using the ion constants of motion; energy, magnetic moment and toroidal canonical momentum, (E,µ,Pφ) and taking advantage of the characteristics of the ICRH fast-ion distribution function. For on-axis RF heated discharges, fastions are mostly on banana orbits with their turning points (banana tips) within the ICRH resonance layer (a vertical line passing through the magnetic axis). A simplified RF particle distribution function for the on-axis ICRF minority heating can be simulated by taking pitch angle =(µB0/E) =1. In this especial case, the use of zand Pφas the phase-space variable is equivalent at the turning points (v=0), where Pφ=Rmiv− Zep(z) =−Zep(z), with R, the magnetic axis radius, mi, the fast-ion mass, Z, the atomic number, e, the electron charge and pthe poloidal flux. By plotting, log(1/n,p) in the energy range of the fast-ions measured by FILD, we can identify the regions of phase space where a resonant interaction could occur [56,57]. Figures 7(a)–(f) show the possible wave–particle resonances between the trapped fastions generated by the on-axis ICRF heating, i.e. with the banana tips along a vertical line at the magnetic axis, and the single AE fluctuations present in the plasma at t=1.16 s. One can easily see that the low-energy region of the fast-ion phase space is virtually covered by wave–particle resonances even in the presence of single fluctuations while the high energy region (E⩾0.5–0.6 MeV) presents some resonances only with certain AE fluctuation frequencies at ≈100 kHz (panels (c) and (d)). The last panel (g) shows all possible wave– particle resonances with the AEs causing coherent fast-ion 7 Nucl. Fusion 51 (2011) 103013 M. Garcia-Munoz et al Figure 7. AUG discharge #23824. Possible wave–particle resonances between the ICRH generated fast-ions and the AEs causing coherent fast-ion losses at t=1.16 s. The colour table represents the resonance width given by log(1/n,p)with n,p=nωφ−pωθ−ω. Panels (a)–(f) show the possible wave–particle resonances due to single AEs while panel (g) present all possible AE-particle resonances in plasma at t=1.16 s. losses at t=1.16 s. The resulting high density of resonances suggests a stochastic transport though detailed non-linear HAGIS simulations with different q-profiles are underway to estimate the convective and stochastic contribution to the total ion loss. 3. Alfv´ en eigenmodes and associated fast-ion transport in NBI heated discharges NBI is a standard heating system in present magnetically confined fusion devices. Indeed, in many machines, it is the primary source of auxiliary heating, particles and torque. A thorough understanding of the beam behaviour (deposition profile, steady state fast-particle distribution function, injection energy, etc) is crucial for plasma operation and it is therefore typically available. This information makes the NBI system a reliable tool for quantitative analysis of MHD stability and fast-ion transport to for instance benchmark numerical tools. 3.1. Alfv´ en eigenmodes In AUG, AEs are driven unstable by sub-Alfv´ enic NBI ions during the current ramp-up phase with relative high off-axis minimum of the safety factor. The plasma density is kept at a relatively low value of ≈(2–3)×1019 m−3, so the fast-ion pressure is a significant fraction of the total plasma pressure. The discharge is initially in limiter configuration and switches to divertor configuration at t≈0.5 s. Throughout the period of interest, the NBI system is injecting deuterium neutrals with a main energy of 60 keV thus producing sub-Alfv´ enic deuterium 8