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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
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 ( 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).
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
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-propagatingwaves (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
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, 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
B measurements:
M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010
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
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
• Bt is so largely fluctuating in
RFX-mod because of various instabilities (resistive kink, resistive g-modes, …) that Alfvénic coherent modes might be hidden
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, vA
• Large variation of: Ip = 0.4 ÷ 1.8 MA
ne = 0.5 ÷ 10 x 1019 m-3
H & He discharges have also been considered H
He
~25%
Critical density: ne 2 x 1019 m-3
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
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
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
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
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, ...?
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 vA
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
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
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 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, …
M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010
M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010
M. Zuin 14th IEA RFP workshop, Padova, April, 26-28, 2010