m. zuin 14th iea rfp workshop, padova, april, 26-28, 2010 alfvén eigenmodes in rfx-mod m. zuin, s....

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


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).


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


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


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:


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


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


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


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=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/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


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


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, ...?


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


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


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 alfvén eigenmodes in rfx-mod m. zuin, s....

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