The dependence of the damping rate of medium-n toroidal Alfvén eigenmodes on the edge plasma elongation in JET*

Abstract

This paper reports the first quantitative analysis of the measurements of the damping rate (γ/ω) for stable Alfvén Eigenmodes (AEs) with toroidal mode number (n) in the range |n|=3÷15 as function of the edge plasma elongation (κ 95 ). We find that the damping rate γ/ω vs. κ 95 for medium-n Toroidal AEs, with n=3 and n=7, increases for increasing elongation, i.e. its scaling vs. κ 95 follows the same trend previously measured and explained theoretically for the n=1 and n=2 TAE modes.Theoretical analysis of the measurements for the n=3 TAEs has been performed using the LEMan code. The results are in excellent agreement for all the magnetic configurations where there is only a very minor up/down asymmetry in the poloidal cross-section of the plasma. These experimental results further confirm the possibility of using the edge shape parameters as a real-time actuator for control of the stability of alpha-particles driven AEs in burning plasma experiments, such as ITER. PACS Classification scheme: D0, Te.

The JET Alfvén Eigenmode Local Manager for the real-time detection and tracking of a frequency-degenerate spectrum of MHD instabilities

“…This simple real time estimate of the mode frequency and damping rate from the centre and width of the driven resonance follows very closely the value obtained from a post-pulse analysis [6][7][8]. One of the first results obtained with the AEAD diagnostic system in the most recent JET experimental campaigns has been that, despite the very low magnetic field driven by the antennae for medium-n AEs (in the plasma core we have |B DRIVEN |~110 -3 G for n=5 compared to |B DRIVEN |~510 -2 G for the n=1and n=2 modes), many modes with |n|~0-12 and very low-damping rate /<0.2% were found to be simultaneously excited in plasmas without populations of resonant fast ions [7,8]. Correct real-time detection and n-number discrimination of these modes is particularly important as their low intrinsic (i.e.…”

“…A Lorentzian model fit of the antenna/plasma transfer function is used to obtain the mode frequency and quality factor in realtime, and the value of the magnetic perturbation at the different probes. This simple real time estimate of the mode frequency and damping rate from the centre and width of the driven resonance follows very closely the value obtained from a post-pulse analysis [6][7][8]. One of the first results obtained with the AEAD diagnostic system in the most recent JET experimental campaigns has been that, despite the very low magnetic field driven by the antennae for medium-n AEs (in the plasma core we have |B DRIVEN |~110 -3 G for n=5 compared to |B DRIVEN |~510 -2 G for the n=1…”

“…This is clearly a much more satisfying situation for machine protection and plasma control. The measurements of the mode frequency, damping rate, amplitude and toroidal mode number are passed to the JET Real Time Signal Server (RTSS), and their real-time estimate has been shown to be in very good agreement with the result obtained with a more detailed post-pulse analysis [6][7][8]. This allows in principle the implementation of a control system and feedback for the modes, so that when the mode's damping rate reduces too much and approaches the marginal stability limit /=0, a control parameter (for instance the edge elongation in the case of AEs [6][7][8][9]) can be changed to bring the plasma back to a situation where it is further away from the marginal stability limit.…”

“…Mode numbers can be directly separated in real-time and individually tracked to measure the changes in the mode frequency and / during the evolution of the plasma background. It is also paramount that the real-time detection matches the results obtained via the more complex and accurate post-pulse analysis method, and this has been discussed and demonstrated in detail in [7,8].Figure7a shows an example of the real-time detection and tracking of individual n=3, n=5 and n=7TAEs for the JET shot #77417, where the excitation system was configured to drive predominantly n-11 odd modes, with max(|B DRIVEN (n)|) in the range |n|<5. For this shot, the AELM tracking algorithm was configured in the "SparSpec-highest" mode, with Amp.Thresh=310 -9 T/s, Speed.Thresh=310 -13 T/A (using the same value for the start and end speed thresholds), Minimum.Twist=2rad,  NORM =0.9 (the normalization value for the L1-norm criterion, see Appendix-A), N MAX =10 (the maximum toroidal mode number to be detected) and detection for modes with n=310 (i.e.…”

“…Post-pulse analysis can obviously still be performed using the much larger set of raw signals (between 32 and 80 additional channels depending on the operational setup) having the required sampling rate (at least 1MHz) via software-based synchronous detection. Further technical details on the active MHD diagnostic system used at JET can be found in [4,7,8,10] and the references therein.One essential and worldwide unique component of the AEAD system is the AELM. The AELM is a digital VME plant control system, used to monitor and control the operation of the AEAD plant in real time, with a 1kHz clock-rate.…”