Carfantan, H.

Fasoli, A.

JET-EFDA, contributors

Klein, A.

Snipes, J.

Testa, D.

Infoscience - École polytechnique fédérale de Lausanne

Toroidal mode number analysis of degenerate Alfvén Eigenmodes in theactive MHD spectroscopy on JETA. Klein1, D. Testa2, J. Snipes1, A. Fasoli2, H. Carfantan3, JET-EFDA contributors*1MIT Plasma Science and Fusion Center, Cambridge, USA2CRPP, Association EURATOM –EPFL, Lausanne, Switzerland3CNRS/Université Paul Sabatier Toulouse 3, Toulouse, FranceThe active MHD spectroscopy program at JET incorporates eight antennas, designedto excite and characterize stable Alfvén Eigenmodes (AE’s) with medium toroidal modenumbers (-10 < n < 10) in a variety of plasma conditions [1,2]. The antennas consist of simplerectangular loops (18 turns per antenna) which cover less than 0.5 m2 of the plasma surface.Due to the compact antenna geometry, the generated magnetic perturbations are composed ofa broad spectrum of mode numbers (in vacuum, -100 < n < 100).  In the presence of a strong,single AE plasma resonance, traditional methods such as straight line phase fitting of signalsfrom an array of Mirnov coils easily  reveals the n-number. Often however, severaldegenerate AE’s with multiple mode numbers may be excited by the antennas, andsubsequent n-number analysis of the plasma response becomes difficult. A new method basedon the SPARSPEC code [3], used in Astronomy, is applied to resolve individual modenumbers in this data.It is easily seen that temporal frequencies in astronomical data can correspond to spatialtoroidal mode numbers in tokamaks, and that unevenly sampled data in time is the analog ofdata from unevenly distributed Mirnov sensors in the toroidal coordinate. As it turns out,SPARSPEC is ideally suited for toroidal mode number analysis because it models data as alarge number (possibly larger than the data size) of pure sinusoidal modes, discretized on afixed, arbitrarily thin, grid, which means that it can be configured to search for only integermode numbers.  Among the many representations fitting the data, SPARSPEC seeks the onewith the fewest non-zero amplitudes, i.e. the sparsest spectrum, by assigning a penalty tosolutions which invoke larger numbers of modes to fit the data. The minimization in SparSpecto detect frequencies and estimate the amplitude of the detected modes is performed on whatis known as the   1-norm, which bypasses the requirement to test every possible combinationof mode vectors as is the case with the   0-norm, and which results in very rapid computation.Many theoretical works have been done to determine conditions of equivalence of bothsettings, one example is found in [4]. We adapted the SPARSPEC code to take complex dataas input, and Monte-Carlo style simulations were run to benchmark the method with the JETstyle data and sensor geometry.Figure 1: SparSpec calculation using simulated data: top: data (points) and model fit (lines).Bottom: input mode amplitudes vs. estimation from SparSpec, along with Lomb periodogram.11 positions (corresponding to JET Mirnov coils), complex data with 4 random modes + 5%Gaussian noise. Mode number grid restricted to –40 < n < 40. Computation time: < 6 msecon a 2.2 GHz processor.The code was then applied to real data consisting of unstable AEs at frequencies up to500 kHz, very good agreement was found with straight line phase fitting methods, andSPARSPEC was found to be much more immune to noise and false n-number detection. Webelieve that this new method of processing fast-fluctuation data from toroidal plasmas will befound useful for all experiments in which spatial harmonic analysis is desireable.Figure 2: Toroidal mode analysis for unstable Alfvén Cascades with straight line phase fitting(left) and SPARSPEC analysis (right) show SPARSPEC is somewhat less sensitive to noiseand errors.detail of SparSpec calculation near t = 31.8 s for JET shot #69586Experimentally, the antenna excitation fields are strongly edge localized, so that AEswith long wavelengths (n ≤ 2) couple much more efficiently to the antennas, because theirradial eigenfunctions tend to be broad and extend all the way to the plasma edge. As aconsequence, data from initial experiments which utilized only one octant of antennas in 2007consist predominantly of low-n damping measurements, which are not the goal of the projectand for which a large data base already exists.  However, despite the tendency for theresonance detection and tracking system to lock onto low-n AEs, many weak medium-nresonances could be extracted from the data using SPARSPEC.Figure 3: Left: . Three modes can be seen to have slightly different resonant frequencies.Middle: normalized amplitude and phase each mode vs. antenna frequency. Right: dampingcalculation the three modes: for n =0: freqres = 123 kHz, γ /ω = 1.96%, for n =-1 : freqres =125 kHz, γ /ω = 2.11%, for n =2 : freqres = 124 kHz, γ /ω = 2.12%.In the 2007 campaigns, the TAE spectroscopy system was active for about 75% of alldischarges in a large variety of plasma conditions, filling a data base with over 56,000damping measurements. Clear scaling and physics trends are not easily extracted however.AEs are ubiquitous in toroidal plasmas, and very often they can be essentially undamped. Theresonance detection algorithm is able to detect modes with damping rates between 0.1% < γ/ω= 10%.Theoretical predictions calculations show that small differences in equilibriumparameters such as the q profile can cause wild variation in the damping rates [5], so thatoverall trends may be obscured by the drastic effect of very subtle differences in the MHDenvironment. Some preliminary results are shown in fig.4.  Figure 4:Left: damping rate γ/ω (in %) vs. edge elongation, κ95, for –5 < n < 5. Medium nmodes (n > 2) semm to be more easily excited at higher elongation. Right: Mean of dampingrates for ~1000 discharges (no aux heating)shows that medium-n modes are consistentlyobserved to be subject to very low damping, in contrast to low-n eigenmodes.In addition to post-pulse analysis, the efficiency of the SparSpec method makes itsuitable for real-time application, allowing for selective targeting of individual AEs in thetracking algorithm which controls the antennas. For the resonance detection and trackingcomputer on JET, looprates of 1 msec are required, which is easily accomplished whenSPARSPEC is applied to synchronously detected signals from eight Mirnov coils. With theability to ignore the strong low-n response in selected Mirnov coils, the range of the activeantenna system can be functionally extended to allow for medium-n specific experiments.New experiments with improved mode selection and detection, are planned in 2008.This work is supported by US DOE Grant  DEFG02-99ER54563.References:                                                 [1] A.Fasoli et al., Phys. Rev. Lett. 75, (1995) 645[2] D.Testa et al., 23rd Symposium on Fusion Technology, Venice (Italy), September 2004[3] S.Bourguignon, H.Carfantan, T.Böhm, Astronomy and Astrophysics 462 (2007) 379[4] D. Donoho, J. Communications on Pure & Applied Math. 59 (2006) 797[5] Snipes J. A., Gorelenkov N. N., Sears J. A.,  Nuclear Fusion 46 (2006) 1036<γ/ω>% toroidal mode number, n1.2          1.3           1.4          1.5           1.6          1.7Edge elongation, κ95Mean of damping rates for ~1000discharges (no aux heating)shows thatmedium-n modes are consistentlyobserved to be subject to very lowdamping, in contrast to low-neigenmodes                                                                                                                                                         

Toroidal mode number analysis of degenerate Alfven eigenmodes in the active MHD spectroscopy on JET

http://infoscience.epfl.ch/record/135164/files/Klein_SparSpecResultsKC1T_PaperEPS08.pdf

Toroidal mode number analysis of degenerate Alfven eigenmodes in the active MHD spectroscopy on JET

Abstract

Similar works

Full text

Available Versions

Infoscience - École polytechnique fédérale de Lausanne