The Shoelace Antenna: Measurements of DrivenTransport and Prospects for Active Edge Control

T. GolfinopoulosB. LaBombard, D. Brunner, J.L. Terry, S.G. Baek, P. Ennever,

E. Edlund, W. Han, W.M. Burke, S.M. Wolfe, J.H. Irby,J.W. Hughes, E.W. Fitzgerald, R.S. Granetz, M.J. Greenwald,

R. Leccacorvi, E.S. Marmar, S.Z. Pierson, M. Porkolab,R.F. Vieira, S.J. Wukitch, and the Alcator C-Mod Team

PSFC@MIT

American Physical SocietyDivision of Plasma Physics

Fall Meeting, San Jose, CA, USA1161102

1

Shoelace antenna: an actuator to mimic coherent edgemodes that regulate the pedestal

4.2 cm

Figure: 2016 configuration

2

Enhanced Dα (EDA) H-mode: a steady-state, ELM-lessconfinement regime with continuous edge fluctuation

f [k

Hz]

t [s]

PCI

PCI_171110201015

0.6 0.8 1 1.2 1.4

50

100

150

0

2

4

n

[10

m

]20 -3

e

_

0

2

4

D

�

[a.u

.]

3

Enhanced Dα (EDA) H-mode: a steady-state, ELM-lessconfinement regime with continuous edge fluctuation

◮ Quasi-Coherent Mode (QCM): continuous edge fluctuationthat exhausts impurities

◮ Regulates pedestal without ELMs

4

Outline

◮ Antenna relocated, greatly improving diagnostic coverage &allowing operation in favorable regimes

◮ Peak in driven response localized by MLP, reflectometer, andGPI; FWHM ∼1-4 mm, peak ∼ 1 mm outside LCFS

◮ ne/ne,0 ∼ 2.5% in ELM-free H-mode, 7.5% in EDA H-mode(0% in L-Mode)

◮ Correlated radial flow, Γne/ne,0 .7 m/s in EDA, . 2.5 m/s inELM-free H-mode

5

Why move? Before, Shoelace didn’t map to GPI,reflectometer, barely mapped to MLP...

A B C D E F G H J K A B

- φ [port]

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

z [

m]

1150902025

0.960 s

q95=5.01

Mirnov coils

GPI

Figure: 2012-15, q95 ∼ 5.

6

...but now, it does...

F G H J K A B C D E F

- φ [port]

-0.4

-0.2

0

0.2

0.4

z [

m]

1160607010

0.830 s

q95=3.30

Figure: 2016 q95 ∼ 3. Antenna translated 107.5° CW toroidally.

7

...and maps for 2.5 . q95 . 5.5 ⇒improved ohmic H-modeaccess...

00.5

1

-Ip

[MA

] 1160607010

01234

-BT

,0[T

]

2.55

q95

0

2

4

ne

[x1

020m

-3]

0 0.5 1 1.5t [s]

0

1

2

Pra

d

[MW

]

_

Figure: 3 ohmic H-modes: 1st ELM-free, 2nd ELM-free with incipientQCM, 3rd EDA.

8

...creating plasmas in which antenna response is strong

1160607010

|R75GHZ_ANG| 0.25

Reflectometer

6080

100120140

f [k

Hz]

1160607010

|GPI_4_8| 0.25

GPI

6080

100120140

f [k

Hz]

1160607010

|BP1T_ABK|0.25

Mirnov coil

6080

100120140

f [k

Hz]

0.8 1 1.2

t [s]

123

ne

[×10

20

m-3

]

1160607010

Density from NL04

divided by chord length

Shoelace off

ELM-free

H-mode L ELM-free H-mode L

EDA

H-mode

MLP scan

Figure: Spectrograms: Mirnov coil, GPI chord, & 75 GHz reflectometerchannel.

9

...and giving answers to the following questions...

◮ ...where is the driven fluctuation located?

◮ ...what is its width?

◮ ...is it correlated with any net radial particle flow?

10

Gas Puff Imaging:

F G H J K A B C D E F

- φ [port]

-0.4

-0.2

0

0.2

0.4

z [

m]

1160607015

1.140 s

q95=2.76

FSP

Mirnov coils

GPI

PCI

0.5 1

R [m]

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

z [

m]

1160607015

Mapping to GPI

φ=-18.0 o

◮ Toroidally localized by D2 puff

◮ Gives poloidal slice of fluctuating emission= f (n, T ), 1 MHzbandwidth

11

New antenna location enabled 2D image of driven modelayer via GPI

1160607015

Magnitude Squared Coherence

1.140 s

-4

-2

z [cm

]

0

0.5

1

86 88 90 92R [cm]

-4

-2

z [cm

]

1160607015

Magnitude Squared Coherence

1.140 s

-100

0

100

Mag

. S

q.

Coh

.P

hase

�

[d

eg

]

Figure: Mag.-squared coherence & cross-phase, GPI and Iant .

12

New antenna location enabled 2D image of driven modelayer via GPI

1160607015

Magnitude Squared Coherence

1.140 s

-4

-2

z [cm

]

0

0.5

1

86 88 90 92R [cm]

-4

-2

z [cm

]

1160607015

Magnitude Squared Coherence

1.140 s

-100

0

100

Mag

. S

q.

Coh

.P

hase∠

[d

eg

]

Figure: Mag.-squared coherence & cross-phase, GPI and Iant .

For additional GPI analysis, please see BP10.00032 : W. Han et al . “Gas-Puff

Imaging Observations of the Edge Mode Driven by the ‘Shoelace’ Antenna”

13

Mirror Langmuir Probe: high-fidelity, simultaneousmeasurement of ne , Te , and Φ at 1.1 MHz

0

1

2

ne

[×10

20m

-3]

-

R [m]0.5 1

-0.6

-0.4

-0.2

0

0.2

0.4

0.61160607010

Mapping to ASP

φ=-3.1 o

z [

m]

Edge profiles and fluctuations from MLP1160607010

Probe Ind=4, NW

0.8060-0.8305 s

0

50

Te

[eV

]

0

50

100

Φ[V

]

-2 0 2 4

ρ [mm]

50 eVsurface

◮ 50 eV surface used to locate LCFS (ρ = 0) via power balance

◮ High sampling rate & reciprocating probe head ⇒ fluctuation& profile quantities obtained in each scan from same data.

14

Driven mode profile in ELM-free H-mode: Narrow peakoffset just outside and spanning LCFS

0 5 10

ρ [mm]

0

1

2

3

4

5

ne,driven[m

�

3]

×10 18

1160607010

0.806-0.872 s

Peaks:

MLP: 0.7 mm

Reflect.: 0.3 mm

+implies inward scan

x implies outward scan

MLP

Gaussian fit

15

In EDA H-mode...

1160607027

|R75GHZ_ANG| 0.25

Reflectometer

6080

100120140

f [k

Hz]

1160607027

|GPI_4_8| 0.25

GPI

6080

100120140

f [k

Hz]

1160607027

|BP1T_ABK|0.25

Mirnov coil

6080

100120140

f [k

Hz]

0.8 0.9 1 1.1 1.2 1.3

t [s]

123

ne

[×1

02

0m

-3]

ELM-free

H-mode L

EDA

H-mode

Shoelace off

scanscan

1160607027

Density from NL04

divided by chord length

-

Shoelace

off

16

...fluctuation component correlated with antenna current is2-5 times larger

-2 0 2 4 6 8 10

ρ [mm]

0

0.5

1

1.5

2ne,driven[m

−3]

×10 19

1160607027

1.119-1.189 s

Peaks:

MLP: 0.4 mm

Reflect.: 0.9 mm

+implies inward scan

x implies outward scan

MLPGaussian fit

17

Transport inferred from correlated fluctuation is ∼3-10×greater in EDA

0

2.5

5

7.5

10

Γn,e

[m-2

s-1

]

×10 20

1160607010

NW,0.806-0.872 s

Inward Scan

1160607027

NW,1.119-1.189 s

Outward Scan

Tolias SEEC

τsmooth

=1.0 ms

-2 0 2 4 6 8 10

ρ [mm]

ELM-free H-mode

EDA H-mode

Figure: Radial electron flux from MLP measurements. Peaks correspondto VR = Γne/ne,0 = 7 m/s in EDA, 2.5 m/s in ELM-free. Compare to∼10 m/s for intrinsic mode.

18

Lessons Learned

◮ Possible to drive edge fluctuations resembling the intrinsicmodes that sustain steady-state H-modes

◮ Driven perturbation exhibits resonant behavior & is localizedto mapped flux tube

◮ Success in driving resonance when antenna ω, k are matchedto range of intrinsic flucts.

19

Lessons Learned

◮ When intrinsic modes are present, large fraction of radialparticle flow is correlated with antenna drive

◮ In transient H-mode with quiescent edge, antenna still drivesradial flow, but less so than in EDA H-mode

◮ Antenna drives local transport on mapped flux tube, but doesnot cause obvious change in global plasma parameters

◮ Coherent driven fluctuation can be used to align multiplefluctuation diagnostics

20

Open Questions

◮ Driven transport in ELM-free H-mode ∼ 10× < intrinsic flowin EDA

◮ Would 10× increase in power change this?

◮ Does mode-locking occur?

21

Additional Slides

22

Shoelace on the move

Shoelace Antenna

Original Configuration

(a)

4.2 cm

Shoelace Antenna

New Winding

(b)

4.2 cm

(c)

Figure: (a) 2012, (b) 2015, (c) 2016 – Shoelace translated 107.5°CWtoroidally.

23

Transport inferred from correlated fluctuation is ∼3-10×greater in EDA

0

2.5

5

7.5

10

Γn

,e[m

-2s

-1]

×10 20

1160607010

NW,0.806-0.872 s

Inward Scan

1160607027

NW,1.119-1.189 s

Outward Scan

Tolias SEEC

τsmooth

=1.0 ms

-2 0 2 4 6 8 10

ρ [mm]

0

3

6

9

12

Γt,

e[k

W m

-2] 1160607010

NW,0.806-0.872 s

Inward Scan

1160607027

Outward Scan

NW,1.119-1.189 s

Tolias SEEC

τsmooth

=1.0 ms

ELM-free H-mode

EDA H-mode

Figure: Radial electron and heat flux from MLP measurements. Peakscorrespond to VR = Γne/ne,0 = 7 m/s in EDA, 2.5 m/s in ELM-free.Compare to ∼10 m/s for intrinsic mode.

24

Merged MLP and Thomson Profiles: ELM-free H-mode

0

1

2

3

ne

[m-3

]

×10 20

50 GHz60 GHz

75 GHz

88 GHz

112 GHz

132 GHz

140 GHz

1160607010

ASP: 0.806-0.872 s

Thomson: 0.810-0.850 s

∆ ρ=-11.5 mm

[0.63 ×10 20 m -3 ,0.81 mm,2.13 mm,

0.79 ×10 20 m -3 ,-0.31 ×10 18 m -3 /mm]

-40 -20 0 20

ρ [mm]

0

200

400

Te

[eV

]

50 eV

1160607010

ASP: 0.806-0.872 s

Thomson: 0.810-0.850 s

∆ ρ=-11.5 mm

[82.7 eV,-1.33 mm,4.69 mm,

88.8 eV,-3.45 eV/mm]

MLP & Thomson, shifted

Thomson, no shift

Fit

Figure: Thomson data windowed to time bin of MLP scan.25

Merged MLP and Thomson Profiles: EDA H-mode

0

1

2

3

ne

[m-3

]

×10 20

50 GHz60 GHz

75 GHz

88 GHz

112 GHz

132 GHz

140 GHz

1160607027

ASP: 1.119-1.189 s

Thomson: 1.130-1.170 s

∆ ρ=-12.4 mm

[0.80 ×10 20 m -3 ,0.81 mm,2.41 mm,

0.98 ×10 20 m -3 ,-0.63 ×10 18 m -3 /mm]

-40 -20 0 20

ρ [mm]

0

200

400

600

Te

[eV

]

50 eV

1160607027

ASP: 1.119-1.189 s

Thomson: 1.130-1.170 s

∆ ρ=-12.4 mm

[56.2 eV,-1.14 mm,4.70 mm,

66.7 eV,-7.12 eV/mm]

MLP & Thomson, shifted

Thomson, no shift

Fit

Figure: Thomson data windowed to time bin of MLP scan.26

Driven mode profile in ELM-free H-mode: Narrow peakoffset just outside and spanning LCFS

0 5 10

ρ [mm]

0

1

2

3

4

5

ne,driven[m

−3]

×10 18

1160607010

0.806-0.872 s

Peaks:

MLP: 0.7 mm

Reflect.: 0.3 mm

+implies inward scan

x implies outward scan

MLP

Reflectometer

Gaussian fit

◮ Caveat: ne from reflectometer amplitude not known precisely

27

...fluctuation component correlated with antenna current is2-5 times larger

-2 0 2 4 6 8 10

ρ [mm]

0

0.5

1

1.5

2

ne,driven[m

−3]

×10 19

1160607027

1.119-1.189 s

Peaks:

MLP: 0.4 mm

Reflect.: 0.9 mm

+implies inward scan

x implies outward scan

MLP

Reflectometer

Gaussian fit

◮ Caveat: ne from reflectometer amplitude not known precisely

28

Dependence of driven transport on antenna currentobfuscated by...

1160607010

Spectrogram

Mirnov Coil,BP1T_ABK

50

100

150f [k

Hz]

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15

t [s]

0

0.2

0.4

0.6

0.8

1

|Hxy

| [A

U]

1160607010

|Hxy

|,|Cxy

| 2 at fant

,

Mirnov Coil,BP1T_ABK

Figure: Spectrogram & transfer function magnitude for Mirnov coil...

◮ ...strong resonant response◮ ...variable resonant frequency◮ ...short-time nature of MLP measurement

29

Dependence of driven transport on antenna currentobfuscated by...

1160607010

Spectrogram

\CMOD::TOP.MHD.MAGNETICS.SHOELACE.TRANS\_FUN:R75GHZ\_ANG:RAW

60

80

100

120

140

160

180

f [k

Hz]

0.8 0.85 0.9 0.95 1 1.05 1.1

t [s]

0

1

2

3

|Hxy

| [A

U]

10-3

1160607010

Trans. Fun. Mag.

Figure: ...and reflectometer 75 GHz channel.

◮ ...strong resonant response◮ ...variable resonant frequency◮ ...short-time nature of MLP measurement

30

Field-aligned coord. sys. reveals driven mode rests on fluxsurface, mild radial shear in phase ang. across flux surf.’s

1160607015

|Cxy

| 2

1.142 s

-42-40-38-36-34-32

φm

ap

[de

g]

0

0.5

1

1160607015

∠Cxy

, Cxy

2 |thresh

=0.10

1.142 s

|

0.9 1 1.1(Ψ- Ψ

0)/( Ψ

a

- Ψ0)

LCFS

-42-40-38-36-34-32

�

map

[de

g]

-100

0

100

1160607015

gpi_4_8 Spectrogram

1.142 s

60100

f [k

Hz]

0.9 1 1.1 1.2 1.3

t [s]

321

ne

[10

20

m

�

3]

0100200

I ant

[A]

Shoelace

rung

Shoelace

rung

Mag

. S

q.

Coh

.P

hase

�

[d

eg

]

31

Source power quadrupled from original experiments...

0

50

100

150

200New max. current: 181 A

Old max.

current

I an

t[A

]

0

200

400

600

800V

an

t[V

]

0.5 1 1.5

100

120

f vco

[kH

z]

t [s]

1150904019Shoelace Performance

}}Dynamic

matching

network

Expanded

source

power,

2 8 kW

32

Shoelace antenna dynamic match power system operatedat highest-ever currents

050

100150200

I an

t [A

]

0

500

Va

nt [

V]

80

100

120

f vco [

kH

z]

0

0.5

1

1−

|Γ|2

0.7 0.8 0.9 1 1.1 1.2 1.30

2000

4000

t [s]

Psrc

/am

pl [W

]

1160607031Shoelace Performance

Figure: ∼ 7400 W source power(∼ 4× level in 2012 campaign); recoveredvariable frequency capability with ∼ 50 kHz bandwidth (did not have atthis power level in 2015).

33

...and phase lock achieved (not explored further in thistalk)

0

50

100

I an

t[A

]

0.5 1 1.5

100

120

f vco

[kH

z]

t [s]

1150904010Shoelace Performance

−200

−100

0

100

200

1150904010

Phase between I and PCI_31ant

Real-time relative phase control, ~5 stepso

Phase lock

ne

,PC

I~_

~R

el. P

ha

se

, <

-<

I an

t[d

eg

]

34

With old winding pitch, antenna does not map toMirror Langmuir Probe in optimal q95 range

0 72 216 288 360 432−0.4

−0.2

0

0.2

0.4

z [

m]

1120814025 - 1.00 s

35

Shoelace antenna response guided by field lines

A B C D E F G H J K A B

- φ [port]

-0.4

-0.2

0

0.2

0.4

z [

m]

1150724015

1.220 s

q95=2.81

0.5 1

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

1150724015

1.220 s, q95

=2.81

PCI, φ=-144.0o

36

Shoelace antenna response guided by field lines

f [k

Hz]

t [s]0.8 1 1.2 1.4

50

100

150

0

2

4

ne[1

020/m3]

0

0.5Dα

1150724017

PCI_31

ELM-free H-modeL-mode EDA H-mode

Shoelace feature

QCM

37

Shoelace antenna response may spread into gap...

t [s]

Rp

ci ch

ord

[m]

0.9 1 1.1 1.2 1.3 1.4

0.66

0.68

0.7

0.72

1

2

3

ne

[10

20

m−

3]

0

1

2

Dα

0

0.5

1

|C |xy2

Mag. Squared. Coherence, PCI (n ) with antenna currente~_

Shoelace rungs

mapped to PCI

plane on LCFS

ELM-free H-modeL-mode EDA H-mode

_

Phase

velocity

Spreading

into gap?

38

...though apparent spreading counter to phase velocity...

-2

-1

0

1

2

k⊥

cm

1150724015

PCI_26-32

t [s]0.9 1 1.1 1.2 1.3 1.4

-1]

[ o� ���� �luct.

m� ����� �� o�ter PCI

chords indicat�� � ���� m� f� �� velocity

directed radially outward

���ob m�f� �� ��electron diamag. ����direction).

Shoelace antenna k⊥

k⊥

Shoelace antenna k⊥

39

How radial transport is calculated:moving average

Γr = 〈nevr 〉 = 〈ne(t)vE×B(t)〉 = −

⟨

k⊥H{Φ}neB

⟩

(1)

vE×B =E× B

B2=

−∇Φ× B

B2(2)

and H{u(t)} is the Hilbert transform of u(t).

◮ Filter ne(t) and Φ(t) around bands of interest

40

How radial transport is calculated:synchronous detection

Γr = 〈nevr 〉 =1

2ℜ{ne(jω)vr (jω)

∗}

=1

2Bℜ{

ne(jω)[

jk⊥Φ(jω)]∗}

=k⊥

2Bℑ{

ne(jω)Φ∗(jω)

}

=k⊥

2Bℑ{

Hne (jω)HΦ(jω)∗

} ∣

∣

∣IA

∣

∣

∣

2

(3)

◮ Hy (jω) =transfer fun. wrt. to antenna current, y(jω)/I (jω)◮ Calculated by synchronous detection,

Hy =LP

{

y(t)(

I (t)− jhilb{I (t)})}

LP{

I 2(t)} , (4)

where the overbar denotes band-pass filtering in the frequencyrange of interest, and LP{} indicates low-pass filtering

41