1. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 Alfvén eigenmodes in RFX-mod M. Zuin, S. Spagnolo, E. Martines, B. Momo, R. Cavazzana, M. Spolaore, N. Vianello Consorzio RFX, Padova, Italy In collaboration with: L. Villard Ecole Polytechnique Federale de Lausanne (EFPL), Switzerland

2. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 Introduction: the shear Alfvén wave Shear Alfvén waves are transverse low frequency electromagnetic waves that propagate along the magnetic field B. Shear Alfvén waves are analogous to transverse waves on a plucked string, with the tension (  B 2 ) being supplied by the magnetic field and the mass density being supplied by the ions. Transverse polarization: Alfvén instabilities can be destabilized by Energetic Particles (inverse Landau damping), when V Drift is of the order of V A Alfvén instabilities are of practical importance as they can be responsible for radial transport of energetic particles (alpha), causing damages to the walls of confinement devices (venting).

3. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 The Alfvén continuum Continuum damping, resonant absorption of wave energy In inhomogeneous plasmas: Waves at different radii have different velocities, so the pulse rapidly disperses Sheared phase velocity

4. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 The Alfvén “zoo”: discrete mode *AE A large variety of Alfvén eigenmodes (gaps in the continuum) can be destabilized in a non-uniform plasma Gaps are created by any periodic variation of the Alfvén velocity At spatial locations where ∂ω/∂t vanishes, weakly damped discrete modes can appear Two types of AE: 1) associated with frequency crossings of counter-propagating waves (e.g. TAE, EAE, HAE, NAE…) 2) associated with an extremum of the continuous spectrum (e.g. RSAE, GAE,…) TAE in a RFP - Regnoli et al PoP 2005, T2R: high n (~ 30), high freq. ~300 kHz

5. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 Diagnostic tool: the U-probe in RFX-mod Diagnostic: U-probe, a complex probe equipped with triple probes (n, T e,  p ) and magnetic probes (B r, B , B  ). 2 radial arrays of 7 probes Frequency bandwidth: 1 kHz – 5 MHz Toroidal mode numbers: |n|  85 Radial insertion: r/a  0.9 B measurements:

6. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 High frequency “coherent” modes The spectrogram (i.e. freq. vs time) of dB p /dt signals reveals a high frequency activity (~ MHz) strongly dependent on the time behavior of I p and n e Two distinct peaks are present

7. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 Transverse (?) mode AE Tearing, Interchange instabilities, drift-kinetic Alfvén vortices, microtearing (?)…. The polarization condition is (apparently) not satisfied for the two peaks Peaks are present on the parallel component B t is so largely fluctuating in RFX-mod because of various instabilities (resistive kink, resistive g- modes, …) that Alfvénic coherent modes might be hidden

8. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 The Alfvénic nature of the eigenmodes The observed peaks have a frequency linearly depending on the Alfvén velocity, v A Large variation of:I p = 0.4 ÷ 1.8 MA n e = 0.5 ÷ 10 x 10 19 m -3 H & He discharges have also been considered H He ~25% Critical density: n e  2 x 10 19 m -3

9. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 Toroidal & poloidal mode numbers The toroidal mode number associated to the AE mode is: n = 0 m = 1 They are not TAE: the “first” TAE in RFX-mod should have |n|>4

10. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 m=1/n=0 Alfvén Eigenmodes in tokamaks CHANG, Z., et al., Nucl. Fusion 35 (1995) 1469 TFTR a)Its frequency scales with the Alfvén velocity. b)Its frequency is in the same range as, although consistently above, the expected TAE frequency. c)Its frequency correlates with variations in the edge density. More precisely, it is related to the Alfvén frequency for n = 0, m = 1 near r/a = 0.9. d)The toroidal mode number is n = 0, while the poloidal structure typically shows a standing wave structure with m = 1, 2 main poloidal components. e)The mode has maximal amplitude where the plasma touches the limiter (‘antiballooning’ if it is the inside limiter, ‘ballooning’ if it is the outside limiter). f)There are one or two modes, separated in frequency by about 25% L. Villard (LION code): Global Alfvén Eigenmodes (near the continuum minimum) L. Villard, J. Vaclavik, Nucl. Fusion, Vol. 37, (1997) 351

11. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 m/n = 1/0 Global Alfvén Eigenmode (GAE) The Alfvén continuum for m/n=1/0 is found to have a minimum around the reversal surface, at a frequency close to those of the two peaks GAE frequency 2 peaks In the next future: LION code adaptation to RFP configuration for numerical wavefields solutions

12. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 Alfvén Eigenmodes at high Ip Ip = 1.8 MA GAE High plasma current spectrograms are characterized by a richer “coherent” modes population A new mode is found to appear intermittently at a frequency around 400 kHz

13. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 Alfvén Eigenmodes in SHAx states The formation of SHAx states is associated to the appearance in the spectrogram of the “new” coherent (intermittent) activity Driving mechanism: Fast ion population, Drift-Alfvén waves coupling,...?

14. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 Alfvén Eigenmodes in SHAx states GAE The Alfvénic nature of this peak is confirmed: frequency  v A SHAx While “GAE”s are present both during MH and SHAx states, the peak at 400 kHz disappears during the crashes of the n=7 dominant mode MH

15. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 Gap: Helical AE or (H)RSAE ? A minimum in the Alfvén continuum is found at the spatial position (  ) of the maximum of the q profile in Single Helical Axis states. The observed frequency is in (potential) agreement with the m=1, |n|=7 combination

16. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010 Conclusions and open questions A variety of high frequency (~ MHz) Alfvén eigenmodes has been recognized in RFX-mod for the first time by means of magnetic insertable edge probes They seem to be associated to the existence of an extremum in the Alfvén continuum Coherent activity is observed to emerge (intermittently) within the turbulent spectra during SHAx states The polarization of the fluctuation is not the expected one for shear Alfvén waves, probably due to a largely fluctuating B t in RFP’s Further (numerical) analysis is needed to correctly interpret the observed magnetic fluctuation (LION code) Which is the driving mechanism: fast particles, coupling to drift wave, …. ?  NPA diagnostics, edge drift-Alfvénic wave measurements, …

17. M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010