Alfvén eigenmodes in RFX-mod

1. 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. 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 ( B2) 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 VDrift is of the order of VA • 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. The Alfvén continuum In inhomogeneous plasmas: Sheared phase velocity Waves at different radii have different velocities, so the pulse rapidly disperses Continuum damping, resonant absorption of wave energy

4. 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. B measurements: Diagnostic tool: the U-probe in RFX-mod Diagnostic: U-probe, a complex probe equipped with triple probes (n, Te, p) and magnetic probes (Br, 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

6. High frequency “coherent” modes • The spectrogram (i.e. freq. vs time) of dBp/dt signals reveals a high frequency activity (~ MHz) strongly dependent on the time behavior of Ip and ne • Two distinct peaks are present

7. Transverse (?) mode 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 • Bt is so largely fluctuating in RFX-mod because of various instabilities (resistive kink, resistive g-modes, …) that Alfvénic coherent modes might be hidden AE

8. The Alfvénic nature of the eigenmodes • The observed peaks have a frequency linearly depending on the Alfvén velocity, vA • Large variation of: Ip = 0.4 ÷ 1.8 MA • ne = 0.5 ÷ 10 x 1019 m-3 ~25% H & He discharges have also been considered H He Critical density: ne 2 x 1019 m-3

9. 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=1/n=0 Alfvén Eigenmodes in tokamaks TFTR • Its frequency scales with the Alfvén velocity. • Its frequency is in the same range as, although consistently above, the expected TAE frequency. • Its frequencycorrelates 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. • The toroidal mode number is n = 0, while the poloidal structure typically shows a standing wave structure with m = 1, 2 main poloidal components. • 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). • There are one or two modes, separated in frequency by about 25% L. Villard (LION code): Global Alfvén Eigenmodes (near the continuum minimum) CHANG, Z., et al., Nucl. Fusion 35 (1995) 1469 L. Villard, J. Vaclavik, Nucl.Fusion, Vol. 37, (1997) 351

11. 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. 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. 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. GAE Alfvén Eigenmodes in SHAx states MH 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 SHAx The Alfvénic nature of this peak is confirmed: frequency  vA

15. Gap: Helical AE or (H)RSAE ? • A minimum in the Alfvén continuum is found at the spatial position (r) 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. 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 Bt 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, …