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Abstract. Alfvén eigenmodes (AEs) and energetic particle modes (EPMs) are often excited by energetic particles (EPs) in tokamak plasmas. One of the main open questions concerning EP driven instabilities is the non-linear evolution of the mode structure. The aim of the present paper is to investigate the properties of betainduced AEs (BAEs) and EP driven geodesic acoustic modes (EGAMs) observed in the ramp-up phase of off-axis NBI heated ASDEX Upgrade (AUG) discharges. This paper focuses on the changes in the mode structure of BAEs/EGAMs during the nonlinear chirping phase. Our investigation has shown that in case of the observed downchirping BAEs the changes in the radial structure are smaller than the uncertainty of our measurement. This behaviour is most probably the consequence of that BAEs are normal modes, thus their radial structure strongly depends on the background plasma parameters rather than on the EP distribution. In the case of rapidly upward chirping EGAMs the analysis consistently shows shrinkage of the mode structure. The proposed explanation is that the resonance in the velocity space moves towards more passing particles which have narrower orbit widths.
Integrating the plasma core performance with an edge and scrape-off layer (SOL) that leads to tolerable heat and particle loads on the wall is a major challenge. The new European medium size tokamak task force (EU-MST) coordinates research on ASDEX Upgrade (AUG), MAST and TCV. This multi-machine approach within EU-MST, covering a wide parameter range, is instrumental to progress in the field, as ITER and DEMO core/pedestal and SOL parameters are not achievable simultaneously in present day devices. A two prong approach is adopted. On the one hand, scenarios with tolerable transient heat and particle loads, including active edge localised mode (ELM) control are developed. On the other hand, divertor solutions including advanced magnetic configurations are studied. Considerable progress has been made on both approaches, in particular in the fields of: ELM control with resonant magnetic perturbations (RMP), small ELM regimes, detachment onset and control, as well as filamentary scrape-off-layer transport. For example full ELM suppression has now been achieved on AUG at low collisionality with n = 2 RMP maintaining good confinement . Advances have been made with respect to detachment onset and control. Studies in advanced divertor configurations (Snowflake, Super-X and X-point target divertor) shed new light on SOL physics. Cross field filamentary transport has been characterised in a wide parameter regime on AUG, MAST and TCV progressing the theoretical and experimental understanding crucial for predicting first wall loads in ITER and DEMO. Conditions in the SOL also play a crucial role for ELM stability and access to small ELM regimes.
Magnetic perturbations directly driven by pellets were studied in three different plasma scenarios in the ASDEX Upgrade tokamak to gain a deeper insight into the triggering process of type-I ELMs. In the type-I ELMy H-mode, promptly after the ELM, a mode with toroidal mode number n = −6 (the negative sign denoting the ion drift direction) was detected in the 100-150 kHz frequency range, for both spontaneous and triggered ELMs. For triggered ELMs with pellets ablating longer than the ELM crash, this mode was observed for a longer time-therefore this could be identified as the pellet-driven perturbation. However, pellets promptly trigger ELMs after entering the plasma, and the large-amplitude ELM footprint masks the pellet-driven perturbation at the instance of the trigger event, i.e. the pellet-driven mode can only be studied after the ELM in a type-I ELMy H-mode. In L-mode plasmas the pellet was observed to drive broadband Alfvén waves, detected in the 80-300 kHz frequency range with a toroidal mode number of n = −6, similar to the mode after type-I ELMs, confirming that the mode seen in the H-mode after ELMs is indeed the pellet-driven perturbation. The magnitude of the pellet-driven perturbation was observed to increase monotonically with pellet penetration, and showed an exponential decay after pellet burn-out. Similarities and differences are discussed for the type-III ELMy H-mode scenario, which resulted in the finding that the pellet only drives and/or triggers modes which can be naturally present in the target plasma. Concerning type-I ELM triggering, the pellet-driven magnetic perturbation is unlikely to be the trigger for ELMs, since the structure of the pellet-driven modes is completely different from that of the observed pre-ELM modes (coherent modes with toroidal mode number n = 3 and 4, similar to Washboard modes) or type-I ELMs themselves (also n = 3 and 4).
Time delay estimation methods (TDE) are well-known techniques to investigate poloidal flows in hot magnetized plasmas through the propagation properties of turbulent structures in the medium. One of these methods is based on the estimation of the time lag at which the cross-correlation function (CCF) estimation reaches its maximum value. The uncertainty of the peak location refers to the smallest determinable flow velocity modulation, and therefore the standard deviation of the time delay imposes important limitation to the measurements. In this article, the relative standard deviation of the CCF estimation and the standard deviation of its peak location are calculated analytically using a simple model of turbulent signals. This model assumes independent (non interacting) overlapping events (coherent structures) with randomly distributed spatio-temporal origins moving with background flow. The result of our calculations is the derivation of a general formula for the CCF variance, which is valid not exclusively in the high event density limit, but also for arbitrary event densities. Our formula reproduces the well known expression for high event densities previously published in the literature. In this paper we also present a derivation of the variance of time delay estimation that turns out to be inversely proportional to the applied time window. The derived formulas were tested in real plasma measurements. The calculations are an extension of the earlier work of Bencze and Zoletnik [Phys. Plasmas 12, 052323 (2005)] where the autocorrelation-width technique was developed. Additionally, we show that velocities calculated by a TDE method possess a broadband noise which originates from this variance, its power spectral density cannot be decreased by worsening the time resolution and can be coherent with noises of other velocity measurements where the same turbulent structures are used. This noise should not be confused with the impact of zero mean frequency zonal flow modulations and can be the explanation for the TEXTOR velocity spectra measured by beam emission spectroscopy.
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