Recent GAM studies in ASDEX Upgrade - ULisboa · G.D.Conway, 30-June-2015 : EFTSOMP (Lisbon) 2 GAM...

G.D.Conway, 30-June-2015 : EFTSOMP (Lisbon) 1

EFTSOMP 2015 (Lisbon)

Recent GAM studies in ASDEX Upgrade

P.Simon*#, G.D.Conway, A.Biancalani, T.Happel, P.Manz*$, D.Prisiazhniuk, U.Stroth*$, and the ASDEX Upgrade Team

*Max-Planck-Institut für Plasmaphysik, Garching, Germany#IGVP, Universität Stuttgart, Germany

$Technische Universität München, Garching, Germany

● GAM parameter dependences – freq. & amp. scaling

● GAM structure & propagation

● Magnetic signature

● Impact of non-axisymmetric (resonant) magnetic perturbations MP

● GAM envelope detection – turb. interaction


GAM measurements from Doppler reflectometry on AUG

● Complex spectra from I/Q signal and determine Doppler peak fD & AD (using weighted average CoG or Gaussian fit)

fD = ku/2p AD ~ (dn)2

● Repeat process on sliding window to obtainfD(t) and AD(t) time series

● Power spectrum of fD(t) to find peak at fGAM

● Calculate GAM strength0 2 4 6 t (ms)

-0.6

-0.2

0.2

f D (

MH

z)

1 10 100 f (kHz)0.01

0.10

1.00

Pow

er (

kHz-

1 )

-2 -1 0 1 2 f (MHz)10-5

Pow

er S

f (a.

u.)

fD = Σ(f*Sf)/Σ(Sf)

AD10-4

10-3

10-2

10-1

A[kHz ]=2 f 1

f 2 S f D 4/1.5

f1

AGAM=2 A[ kHz ]/k ┴f2


GAM Frequency Scaling: κb Dependence

● Freq. scale factor G = wGAM Ro/cs : G ~ 2 for “core” (inside ped. circular kb 1) [Windsor, PF 1968]

● Edge GAMs (rpol > 0.95) show strong dependence on boundary elongation kb

● Conway empirical scaling good overall prediction of edge GAMs (especially limiter config.)

● Divertor data deviate more than limiter role of X-point?

f scale=c s

2 Ro4 [ 1

1b− o ]

1.0 1.2 1.4 1.6 1.8 2.0Boundary elongation kb

0

1

2

3

G =

wG

AM

R0/

c s

LimiterDivertor

√2

GConway

LimiterDivertor

Core GAMs

[Conway, PPCF 2008]

0

5

10

15

20

25

f GA

M (

kHz)

0 10 20 30fscale (kHz)

kb<1.2

1.2< kb<1.4

1.4< kb<1.6

kb>1.6

New AUG data

5 15 25


GAM Frequency Scaling: Gao-scaling

● Analytic Gao scaling: Influence of k lessstrong than Conway scaling

● All experimental data lie above Gao

● Gao (linear) gives min. wGAM – non-linearity & X-point etc. may raise GAM frequency

LimiterDivertor

[Gao, PST 2011]

q=4,=0.3, '=0

1.0 1.2 1.4 1.6 1.8 2.0

LimiterDivertor

GConway

Missing AUG data

GGao

fscale (kHz)Boundary elongation kb

kb<1.2

1.2< kb<1.4

1.4< kb<1.6

kb>1.6

0 10 20 305 15 25

f scale∝ 2b21

0

1

2

3

G =

wG

AM

R0/

c s

0

5

10

15

20

25

f GA

M (

kHz)

√2

[Simon, IRW 2015]


GAM Amplitude: Damping dependence on k & q

● GAM amp. generally increases with q, but falls at high q

● Shape / kb dependence also present

● Stronger variation for divertor configuration

● NEMORB simulations in progress

GA

M a

mp.

(km

/s)

Damping coefficient × 10102 3 4 5 6

q_local

0.00

0.01

0.02

0.03

0.04

0.05

0.06LimiterDivertor

kb<1.2

1.2< kb<1.4

1.4< kb<1.6

kb>1.6

0.1 1.0 10.0

GA

M a

mp.

(km

/s)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

● Collisionless damping – w/o krri (Finite Orbit Width) corrections [Gao, PoP 2008]:

Strong freq. dependence

Dominant at low q

Dominant at high q

q5 exp(-q2)


GAM Radial structure

● 2 forms of GAM radial structure:

– low kb: freq. continuum

– high kb: freq. eigenmode

● Stronger GAM at low elongation kb (lim.)

● Collisionality & other dependences under investigation

limiter discharge

Pow

er (

arb.

)

1 10 10010-8

Frequency (kHz)

10-7

10-6

10-5

0.80 0.85 0.90 0.95 1.00

5

10

15

20

25

30

Freq

uenc

y (k

Hz)

-9

-8

-7

-6

-5

kb = 1.675

10

15

20

25

30

0.80 0.85 0.90 0.95 1.00

kb = 1.12

Radius ρpol Radius ρpol

#29722 Time: 1.17-1.37s #29722 Time: 3.51-3.71s

AD

fD

1 10 100Frequency (kHz)

AD

fD


GAM Propagation

● 2 chn. radial corr. fD filtered around fGAM (5 – 25kHz)

● Corr. pattern inclined inward GAM radial prop. (outward prop. also seen: towards GAM peak)

● Inclination falls at high kb, eigenmode vs continuum?

● Local Sl (w,kr) spectra inward kr ~ 0.67 rad/cm-1

Del

ay D

t (m

s)

-1.0

-0.5

0.0

0.5

1.0

Δr ~ 2.3 cmlimiter discharge

#29722 @ 3.51-3.71s

-0.05

0.00

0.05

Dt ~ 15 sμvr ~1.6 km/s

kb = 1.12

0.00

-0.05

0.05

kb = 1.67

0 10 15 20 25 30Frequency (kHz)

-1.0

0

1.0

Wav

enum

ber

k r (

rad/

cm)

5

#29722 @ 1.17-1.37s

17 kHz : 0.67 rad/cmvr ~1.59 km/s

0.80 0.85 0.90 0.95 1.00Radius ρpol

0.80 0.85 0.90 0.95 1.00Radius ρpol

In

war

d

Out

war

d


GAM magnetic signature: Divertor discharge

● Theory indicates m = ±2 magnetic component [Wahlberg, PPCF 2009]

● Doppler: strong eigenmode GAM at 15 kHz

● No Br signal near outer mid-plane, but weak at top

● For GAM expect: Bpol > Br

● Mode analysis: m ~ 2 structureBr coils (LFS, midplane)Bpol coils (poloidal coverage)

0.1

1.0

Pow

er (

arb.

) 15 kHz

0 10 20 30 40 50Frequency (kHz)

0 10 20 30 40 50Frequency (kHz)

0.01

0.10

1.00

Pow

er (

arb.

)

0.01

0.10

Pow

er (

arb.

)

1

10

100

Pow

er (

arb.

)

#29725

15 kHz

15 kHz


GAM magnetic signature: Limiter discharge at low k

● Doppler: GAM freq. continuum: 15 – 20 kHz

● Magnetics: approx. m = 2 mode structure

● Tilt due to choice of reference probe

● Why different fGAM at top & bottom?

0.01

0.10

1.00

Pow

er (

arb.

)

0.001

0.010

0.100

Pow

er (

arb.

)

0 10 20 30 40 50Frequency (kHz)

0.01

0.10

Pow

er (

arb.

) #29722

1.0 1.5 2.0 2.5Radius R (m)

1.0

0.5

0.0

-0.5

-1.0

Hei

ght z

(m

)

0.5

0.0

-0.5

20 kHz

15 kHz


Impact of RMPs on GAM

Radius rpol

0

10

20

30

40

Fre

quen

cy (

kHz)

10-5

10-6

10-7

10-8

10 100 kHz

Pow

er (

arb.

)

Er

ne

14.6 kHz

15.9 kHz

rpol ~ 0.99

1.00 1.050.95

110 1001

GAM

2nd GAM

LFfeature

Peaksplit

#29464MP off

MP off MP on

Er spectrogram

GAM

● Without MP: Strong GAM (flow peak) inside separatrix

● With MP: Flow peak weakens & freq. increases (nb. no Te change)

● Radial max. moves closer to Er min.

● dne increases, dEr decreases

= 45°, D = 180° n = 2, sig. resonantBT = -2.5 T, Ip = 0.8 MA

q95 ~ 5.2, no = 1.5×1019 m-3

10-5

10-6

10-7

10-8

Hole

Axisymmetric GAMs

Flow: n = 0, m = 0

Pres: n = 0, m = ±1

Mag: n = 0, m = ±2 ...

- -- -

[Conway, PPCF 2015]


Impact of RMPs on GAM

neo (1019 m-3)

Te ped (keV)

12

14

16

18

20

Freq

uenc

y (k

Hz)

0

2

4

6

IB

Mirnov coil dbr (B31-14)

2 3 4 5 6Time (s)

-1

1

0

Cur

rent

(kA

)

1.5

0.5

1.0

0.0

● Enhanced edge magnetic “signature” above MP threshold (in both dbr & dbq)

● Non-MP GAM normally only dbq signature

0.90

MP off

MP on(0.90 kA)

AUG #29464q = 4 5 6

0.95 1.00 1.05Radius rpol

-5

0

5

10

Er (

kV/m

)

= 45°, D = 180° n = 2 MP sig. resonantBT = -2.5 T, Ip = 0.8 MA

q95 ~ 5.2, no = 1.5×1019 m-3

“Mode” extent

GAM freq.

● dbr & dbq : Complex toroidal structure

● GAM interacts with MP field non axisymmetric (n 0) GAM

● GAM reduced in stochastic regions

“Mode”(n = 2, m > 7?)

- -- -

[Conway, PPCF 2015]


Impact of RMPs on GAM: Magnetic signature

0 10 20 30 40 50Frequency (kHz)

15 kHz

RMP off RMP on

0.01

0.1019 kHz

19 kHzno peak

AD

fD

15.3 kHz

1 10 100 kHz

19 kHz

#27652

Pow

er (

arb.

)P

ower

(ar

b.)

0.01

0.10

0.01

0.10

Pow

er (

arb.

)P

ower

(ar

b.)

0.01

0.10

0 10 20 30 40 50Frequency (kHz)

10-8

Pow

er (

arb.

)

10-6

10-5

10-4

1 10 100 kHz

Top

Mid

10-7

10-8

10-6

10-5

10-4

10-7

AD

fD

Pow

er (

arb.

)

38 kHz


GAM / turbulence interaction

Coh. g between Env(dn) (PCR) & flow (DR)

● Theory GAM modulates the HF density fluctuations

● Extract flow from envelope of high-pass filtered dne using Env(n) = {nn* + H(n)H*(n)} [Nagashima, PPCF 2007]

● Correlate Env(dne) {PCR} & fD {DR} ~ 0 cross-phase at tok. mid-plane (different tor. sectors)

● Env(A){DR} & fD {DR} ~ 0.0 Expect = p /2 at top?

0.0

0.4

0.8

f D:E

nv(A

) C

oh. g

2

60

0

p

f D:E

nv(A

)

16.5 kHz

AD

fD

Env(F(A))

0 20 40Frequency (kHz)

10-8

10-6

10-5

10-7Pow

er (

arb.

)

-p

p/2

-p/2

AUG #29722

[Prisiazhniuk, IRW 2015]


Conclusions

● GAM frequency > Gao formular (gives min. freq.)

– fGAM raised by non-linear effects and possibly higher shaping orders (X-point)

– Still to include Zeff in scaling

● GAM amplitude

– Scales roughly inversely with damping (drive effects under investigation)

– Different behaviour for divertor config.

– Numerical simulations progressing

● GAM structure & propagation

– Either radial continuum or eigenmode (k dependence – collisionality under investigation)

– Propagates mostly inward: kr ~ 0.7 rad/cm & vr ~ 1.6 km/s (radial acceleration under invest.)

– Roughly m = 2 magnetic structure (eigenmode vs continuum)

● External MPs – strong impact

– non-axisymmetric GAM structure?

– Stochastization weakens & ev. suppresses GAM despite turb. rise

● GAM – turbulence interaction evident


GAM Frequency Scaling: Core vs. Edge

● GAMs contribute to effective shearing rate & reduce turb. correlation length if fGAM < td-1

● Analysis of new limiter and divertor with varying κb line-up with previous results

● Core GAMs (limiter only) follow classic scaling (even with κb scan)

● Edge GAMs deviate from core scaling

Core: ρpol < 0.95 Edge: ρpol > 0.95 f scale=2cs /2 R0

0 5 10 15 20 25fscale (kHz)

0

5

10

15

20

25

f GA

M (

kHz)

kb<1.2

1.2< kb<1.4

1.4< kb<1.6

kb>1.6

LimiterDivertor

0

5

10

15

20

25

f GA

M (

kHz)

0 5 10 15 20 25fscale (kHz)

[Winsor et al., PF 1968]

kb<1.2

1.2< kb<1.4

1.4< kb<1.6

kb>1.6


GAM Amplitude: Dependence on k & q

LimiterDivertor

0.00

0.01

0.02

0.03

0.04

GA

M a

mp.

(km

/s)

3.4 3.6 3.8 4.0 4.2 4.4q95

-20

-15

-10

-5

0

Dam

ping

coe

ffici

ent ×

101

0kb<1.2

1.2< kb<1.4

1.4< kb<1.6

kb>1.6

Divertor

0.06

GA

M p

.t.p.

am

p. (

km/s

)

1.0 1.2 1.4 1.6 1.8

Limiter0.04

0.02

0.00

Boundary elongation kb

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Recent GAM studies in ASDEX Upgrade - ULisboa · G.D.Conway, 30-June-2015 : EFTSOMP (Lisbon) 2 GAM...

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