Kinetic Alfvén waves driven by rotating magnetic islands

K. L. Wong, K. Tritz, D. R. Smith, Y. Ren,

E. Mazzucato, R. Bell, S. Kaye, K. C. Lee

NSTX Physics MeetingLSB318, PPPLFeb 1, 2010

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Low freq high-k scattering signals from NSTX#125272 with giant ELMs (K. Tritz - PoP2008)

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• Distinct freq. peaks associated with MHD: f~MHD freq.

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Identification of MHD poloidal mode number m- SVD analysis of USXR data

• SVD analysis: T. Dudok de Wit et al., PoP(1994) – IDL program by D. R. Smith

• Topo shows m=2 eigenfunction – node at r/a~0.5

- for the m=1 eigenfunction, the node is at the magnetic axis

- see K.L. Wong et al., PRL 85(2000)996.

Toroidal Mirnov coil array gives n=1 m/n=2/1 islands

In addition, fmhd= F at q=2 surface.

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Many peaks (~40) in spectra when approaching locked mode#135416 – provided by Yang Ren (has Lithium, ne<4e13 cm-3)

Asymmetric spectrum, f ~ fmhd as rotation freq decreases

islands at R~122-137cm, scatt. vol. at R~123cm

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Thermal quench due to locked mode

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Low freq scattering signal in NSTX is unchartered water

• Avoided by large grad_Te ETG~1-3 MHz by HHFW heating and / or by

Doppler shift due to plasma rotation (large V during NBI + non-zero k)

- see Mazzucato (PRL-2008), Smith (PRL-2009), Yuh (PoP-2008)

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Prevailing explanation: Interferometry effect from stray light (no beam dump)

- can explain some low freq. lines, but NOT those in #135416 @ t>0.5s

• Assumptions: 1. Stray light intensity strong enough ***(cannot quantify)

2. Phase modulation z large enough (z=2L/0.1cm)

L= optical path length, n = index of refraction : n2 = 1 – pe2/2

• Stray light modulated by low freq. density oscillation gives a signal

S = ei z sin(t)= n Jn(z) ei n t - Bessel identity (Stix, p.253)

FFT[S] gives amplitude Jn(z) at harmonic freq n. – Symmetric about =0

• Need z > 15 to get 20 freq. peaks within 30db on each side of =0,

for shot 135416, z~2 – get only 6 peaks – cannot explain our data

Note: low density plasma with Lithium: ne<4e13 all the time.

Moreover, our data have asymmetric spectrum

Asymptotic forms: z<<1, Jn(z)(z/2)n/(n+1); z>>1, Jn(z)[2/(z)]½cos[z-(½n+¼]

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Raw signals modulated by fmhd

– are these scattering signals ?

• Raw signals provided by E. Mazzucato: “ modulation of signal interferometry

effect , not scattering signal ” - I disagree :

Interferometry effect gives modulated signals, but the converse is not

necessarily true, i.e., Scattering signals can also be modulated

• Interferometry effect gives discrete lines in freq. spectrum, so can scattering signals

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Discrete lines in spectrum from coherent wave scattering

- Scattering signals come in many forms- Many ways to modulate scattering signals i.e., : modulate the RF amplitude, frequency,

chop the l.o. beam, move the scatt. vol, etc…

Wurden, Wong & Ono, Phys. Fluids(1985):

CO2 laser scattering of LH Waves

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X-ray scattering in solid state physics (Bragg2-1915 Nobel):Scattering pattern Reciprocal lattice (lattice in k-space)

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Properties of kinetic Alfvén waves (KAW) – Stix p.354-358

• Shear Alfvén waves: no plasma kinetic effects (assume zero me and i )

- dispersion relation from ideal MHD eqns: /k|| = VA - long wavelength (low k)

- many forms of toroidal eigenmodes: TAE, GAE, EAE, NAE, RSAE etc.. . .

- f~1-300 kHz (NSTX), have long wavelengths not observable by high-k scattering

• KAW: include kinetic effects (non-zero me and i );

- dispersion relation: (/k||VA)2 = i / [ 1 – Io(i) exp (-i) + (Ti / Te) i ]

i=(ki)2, VA= Alfvén velocity, Io= modified Bessel function

- Polarization: electrostatic wave, strong E|| sensitive to ELD

- Weak electron Landau damping requires /k||Ve<1/3 which implies ki < 2 for

normal modes (weakly damped – damp<<1) of KAW

- Our exp’t looks at ki ~ 5 – 10, /k||Ve ~ 0.5 – 1, strongly damped quasi-modes

(forced oscillations); can still be excited but cannot

propagate far from where they are generated.

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Quasi-modes not new - were observed long time agoNonlinearly driven: LHW LHW + QM : , ko = k1 + k2

• Ref: Wong & Ono, PRL 47, 842(1981)

• Ref: Skiff, Wong & Ono: Phys. Fluids 27, 2205 (1984)

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KAW quasi-modes excitated by rotating magnetic islands- this mechanism should be more efficient than 3 wave coupling

• Perturbed B of pure m/n=2/1 island near q=2 surface:

b(,,) = b()exp[i( - 2)]

• Include other toroidal harmonics: b(,,) =n bn(,) exp(in)

• Neoclassical tearing mode propagates in the plasma along the direction

with freq. ’f i where f < 1

• The q=2 surface rotates with angular freq in the laboratory frame,

and the 2/1 mode freq. is: ’+k.V= ’+kV+kV =

because i<<at low mode numbers, and V<<V .

• bn(,) has freq n in the laboratory frame.

• The induced Erf =Vxbn , i.e., the rotating island acts like an RF antenna driven at

various harmonic freq n and KAWs at these frequencies are excited.

• Island location: R~122-137 cm, scattering volume at R~123 cm (at island edge)13

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KAW not new - was observed in TFTR 15 years ago, - the excitation mechanism is new & common in tokamaks

• Ref: Wong et al., Phys. Lett. A. 244, 99 (1996) – mode conversion from TAEs- fast ions from ICRF; scattering from 5 Watt 60GHz (5mm) probing beam, no beam dump.

“ghost feature” near f~0

• NSTX data is interesting because of their association with locked mode• Many KAWs appear in plasmas with violent MHD activities shortly

before locking• Can we use this as a locked mode / disruption precursor ?

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Conclusion: Spectrum with 40 peaks is scattering from KAWs driven by rotating 2/1 islands

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Generalized Interferometry effect : n More peaks , but . . . . .

Transition from n=2 to n=1 at 0.48s: flat to peaked ne(r),f(r)