1

Pedestal Magnetic Turbulence Measurements

in ELMy H-mode Plasmas in DIII-D Tokamak

𝒕 [s]

Broadband magnetic

fluctuations

𝑾𝑴𝑯𝑫 [MJ]

𝒑𝒆𝒑𝒆𝒅

[kpa]

[kH

z]

175816

Broadband magnetic fluctuations

correlate with confinement

J. Chen/FEC2020/May 2021 ID: 682

by

Jie Chen1

with

D. L. Brower1, W. X. Ding1, Z. Yan2, T. Osborne3,

E. Strait3, X. Jian4, M. Curie5, D.R. Hatch5,

M. Kotschenreuther5, M.R. Halfmoon5, S. M. Mahajan5

1, University of California, Los Angeles

2, University of Wisconsin - Madison

3, General Atomics

4, University of California, San Diego

5, University of Texas, Austin

Presented at the

28th IAEA Fusion Energy Conference

May 10-15, 2021

2

Motivation: experimental pedestal turbulence study

is critical to validate physics models

• Models predict electromagnetic instability, in

particular Kinetic Ballooning Mode (KBM) and

Micro-Tearing Modes (MTM), are important in H-

mode pedestal transport

Main results: Internal magnetic fluctuation

measurements support presence of MTM in ELMy H-

mode pedestal

• Faraday-effect polarimetry observes internal

broadband magnetic fluctuations originate in the

pedestal of ELMy H-mode plasmas

• Magnetic fluctuations are characterized and

identified as micro-tearing mode

• Magnetic fluctuations correlate with confinement

degradation in H-mode

Motivation and Main Results

𝒕 [s]

Broadband magnetic

fluctuations

𝑾𝑴𝑯𝑫 [MJ]

𝒑𝒆𝒑𝒆𝒅

[kpa]

[kH

z]

175816

Broadband magnetic fluctuations

correlate with confinement

Chen et al., Phys. Plasmas 27, 120701 (2020)

Chen et al., Phys. Plasmas 28, 022506 (2021)

3

• Faraday polarimetry for internal magnetic fluctuation measurement

• Fundamental observations of internal magnetic fluctuations

• Internal magnetic fluctuations identified as micro-tearing modes

• Correlation between internal magnetic fluctuations and confinement

Outline

4

Three-wave Polarimetry-Interferometry Measures Faraday

Rotation and Line-integrated Electron Density Simultaneously

• Launch right (R, 𝝎𝟏) and left (L, 𝝎𝟐)-handed

circularly-polarized electromagnetic waves (𝜔1,2 ≫ 𝜔𝑐𝑒 , 𝜔𝑝) into magnetized plasma

• Use the third wave 𝝎𝟑 as reference

• Measuring phase differences provides Faraday rotation and line-integrated electron density

– 𝝋𝑭𝑹 =𝝋𝑹−𝝋𝑳

𝟐= 𝒄𝒑 𝒏𝒆𝑩∥𝒅𝒍

– 𝝋𝒏𝑳 =𝝋𝑹+𝝋𝑳

𝟐= 𝒄𝒊 𝒏𝒆𝒅𝒍

• Low phase noise (~0.1 Gauss) and high

temporal resolution (~0.1𝜇𝑠, determined by

source frequency differences) allows fluctuation measurements at low-k (𝑘⊥,𝑚𝑎𝑥~1/𝑐𝑚)

Linear-

polarized

𝑬𝟎

𝒌

ne

𝑩∥

𝝋𝑭𝑹 =𝝋𝑹 − 𝝋𝑳

𝟐

𝝋𝒏𝑳 =𝝋𝑹 + 𝝋𝑳

𝟐

𝑬𝟏

Principle of three-wavePolarimetry-Interferometry

Right & left-hand

Circular polarized Reference𝝎𝟑

𝝎𝟏

𝝎𝟐

5

• 3 chords: Z=0 & ±13.5 cm near / at magnetic axis

– 𝑩𝑹 along chords close to zero

– Faraday fluctuation dominated by magnetic

fluctuation: 𝜹𝝋𝑭𝑹 ∝ 𝒏𝒆𝜹𝑩𝑹𝒅𝑹 + 𝑩𝑹𝜹𝒏𝒆 𝒅𝑹

• Low-k (𝒌𝜽 ≤ 𝟏/𝒄𝒎), 𝟏 𝑴𝑯𝒛, ~𝟎. 𝟏 𝑮𝒂𝒖𝒔𝒔/ 𝒌𝑯𝒛

• Measures density fluctuation 𝜹𝒏𝒆𝒅𝑹 simultaneously

• Other fluctuation diagnostics

– Beam-emission-spectroscopy (BES): localized, low-k (𝒌𝜽 ≤2/cm) density fluctuation at the edge, 500 kHz

– Mirnov coil on wall: external, low-k (𝒌𝜽 ≤1/cm)

magnetic fluctuation, 1 MHz

DIII-D Faraday-effect Radial-Interferometer-Polarimeter (RIP) is

Developed to Measure Internal Magnetic Fluctuation

R

Z

175823

Poloidal cross-section of DIII-D

Faraday

Polarimeter

Limiter

Mirnov

coil

BES13.5cm

0cm

-13.5cm

6

179431

𝒛𝟎 [𝒎]

𝒕 [𝒔]

Faraday-effect Provides Absolute Amplitude of Magnetic Field

• Polarimeter-measured ഥ𝑩𝑹 agrees quantitatively with EFIT calculation

• Faraday fluctuation provides absolute 𝜹𝑩𝑹

Measured ഥ𝑩𝑹 [Tesla]

EFIT

ഥ 𝑩𝑹

[Te

sla

]

Faraday

ഥ𝑩𝑹 ≡ 𝒏𝒆𝑩𝑹𝒅𝑹

𝒏𝒆𝒅𝑹[Tesla]

𝒕 = 𝟑. 𝟐 𝒔

Z=-13.5cm

Z=-13.5cm

Z=0cm

7

Faraday Fluctuation is Dominated by Magnetic Fluctuation

• Faraday fluctuation

• 𝜹𝝋𝑭𝑹 = 𝒏𝒆𝜹𝑩𝑹𝒅𝑹 + 𝑩𝑹𝜹𝒏𝒆𝒅𝑹

• Estimated 𝑩𝑹𝜹𝒏𝒆𝒅𝑹 ~𝑩𝑹,𝒎𝒂𝒙 𝜹𝒏𝒆𝒅𝑹

• 𝑩𝑹,𝒎𝒂𝒙 from EFIT

• 𝜹𝒏𝒆𝒅𝑹 from interferometer

• Compared to 𝑩𝑹,𝒎𝒂𝒙 𝜹𝒏𝒆𝒅𝑹, 𝜹𝝋𝑭𝑹 is two

orders Larger & has different spectral shape

• 𝑩𝑹𝜹𝒏𝒆𝒅𝑹 ≪ 𝒏𝒆𝜹𝑩𝑹𝒅𝑹

• 𝜹𝝋𝑭𝑹 ≈ 𝒏𝒆𝜹𝑩𝑹𝒅𝑹

𝒇 [𝒌𝑯𝒛]

[𝑫𝒆

𝒈./

𝒌𝑯

𝒛] Measured Faraday

Fluctuation 𝜹𝝋𝑭𝑹

Estimated density term

𝑩𝑹,𝒎𝒂𝒙 𝜹𝒏𝒆𝒅𝑹

175823: 3-4 s

Density fluctuation term is negligible in Faraday fluctuation

8

• Faraday polarimetry for internal magnetic fluctuation measurement

• Fundamental observations of internal magnetic fluctuations

• Internal magnetic fluctuations identified as micro-tearing modes

• Correlation between internal magnetic fluctuations and confinement

Outline

9

𝒕 [𝒔]

𝑯𝟗𝟖,𝒚𝟐

P_total [MW]

𝑫𝜶 [a.u.]

175823

Type-I ELM, ~𝟏𝟎𝟎 𝑯𝒛

Faraday Polarimeter Observes Broadband (150-500 kHz)

Magnetic Fluctuations in the Edge of ELMy H-mode Plasmas

𝒇[𝒌𝑯𝒛]

Faraday 𝒏𝒆𝜹𝑩𝑹𝒅𝒍, 𝒁 = 𝟎

𝒇[𝒌𝑯𝒛]

𝒕 [𝒔]

Magnetic fluctuation amplitude varies between ELMs

10

Mirnov coil

Faraday 𝒏𝒆𝜹𝑩𝑹𝒅𝒍

𝒕𝑬𝑳𝑴 [𝒎𝒔]

Ensemble averaged

Spectrogram

Faraday 𝒏𝒆𝜹𝑩𝑹𝒅𝒍

Mirnov coil

𝒇[𝒌𝑯𝒛]

𝒇[𝒌𝑯𝒛]

𝒕 [𝒔]

175823: raw spectrogram

Internal and external differences (spectral width & temporal

evolution) associate with spatial decay of magnetic fluctuation

Internal Measurement Provides New Magnetic Fluctuation

Information

Amplitude evolution

Faraday

Mirnov

Faraday

Mirnov

[a.u

.] [a.u

.]

𝒇 [𝒌𝑯𝒛]

[a.u

.]

[a.u

.]

𝒇 ∈ [𝟏𝟓𝟎, 𝟓𝟎𝟎]

Spectra: tELM=7 ms

𝒕𝑬𝑳𝑴 [𝒎𝒔]

11

Interferometer and BES observe the same density fluctuations

Interferometer and BES Observe Broadband (100-500 kHz)

Pedestal-localized Density Fluctuations Simultaneously

BES@𝝆~𝟎. 𝟗𝟖

Interf. 𝜹𝒏𝒆𝒅𝑹

𝒕𝑬𝑳𝑴 [𝒎𝒔]

𝒏𝒆

[𝟏𝟎

𝟏𝟗

𝒎−

𝟑]

|𝒅𝒏

/𝒏|

[%]

𝝆

𝒇 ∈ [𝟏𝟓𝟎, 𝟑𝟓𝟎]

𝒇[𝒌𝑯𝒛]

𝒇[𝒌𝑯𝒛]

Ensemble averaged

Spectrogram

𝒕𝑬𝑳𝑴 [𝒎𝒔]

[a.u

.][a

.u.]

Interf.

BES

𝒇 [𝒌𝑯𝒛]

[a.u

.][a

.u.]

Amplitude evolution𝒇 ∈ [𝟏𝟓𝟎, 𝟓𝟎𝟎]

Spectra: tELM=7 ms

Interf.

BES

Wave number measured

by BES• 𝒌𝜽 ≈ 𝟎. 𝟑/𝒄𝒎• 𝒌𝜽𝝆𝒔 ≈ 𝟎. 𝟎𝟔

12

Density and Magnetic Fluctuations Have Finite Coherence

[a.u

.][a

.u.]

Faraday

Interf.

𝒇 [𝒌𝑯𝒛]

[a.u

.] [a.u

.]

𝒕𝑬𝑳𝑴 [𝒎𝒔]

Amplitude evolution𝒇 ∈ [𝟏𝟓𝟎, 𝟓𝟎𝟎]

Spectra: tELM=7 ms

Faraday

Interf.

𝒇 [𝒌𝑯𝒛]

Coherence (𝜸𝟐)

between Faraday

and interf. at Z=0

Interf. 𝜹𝒏𝒆𝒅𝑹

𝒕𝑬𝑳𝑴 [𝒎𝒔]

𝒇[𝒌𝑯𝒛]

𝒇[𝒌𝑯𝒛]

Ensemble averaged

Spectrogram

Faraday 𝒏𝒆𝜹𝑩𝑹𝒅𝒍

Finite Coherence Indicates the Magnetic and Density Fluctuations

Have Same (𝝎, 𝒌) and Result From the Same Perturbation

13

• Faraday polarimetry as internal magnetic fluctuation diagnostic

• Fundamental observations of internal magnetic fluctuations

• Internal magnetic fluctuations identified as micro-tearing modes

• Correlation between internal magnetic fluctuations and confinement

Outline

14

• low-k (𝒌𝜽𝝆𝒔 < 𝟏), 𝝎𝑴𝑻𝑴 = 𝝎𝒆∗ = 𝒌𝜽𝝆𝒔𝒄𝒔(

𝟏

𝑳𝒕𝒆+

𝟏

𝑳𝒏𝒆), electron diamagnetic direction

• Electromagnetic: 𝜹𝒃

𝑩~

𝝆𝒆

𝑳𝑻𝒆> 𝟎. 𝟏% in pedestal,

𝜹𝒃

𝑩/|

𝜹𝒏

𝒏|~𝑶(𝟏)

• Destabilized by electron temperature gradient

• Minimum amplitude near mid-plane and peak near top and bottom of plasma

• Growth rate depends on collision frequency (𝝂𝒆𝒊) non-monotonically

Features of Micro-Tearing Modes (MTM)1-6

1: Drake, Phys. Fluids, 1977

2: Drake, Phys. Rev. Lett., 1980

3: Hatch, Nucl. Fusion, 2016

4: Guttenfelder, Phys. Plasmas, 2012

5: Hillesheim, Plasma Phys. Control. Fusion, 2016

6: Kotschenruether, Nucl. Fusion, 2019

15

Propagation Direction, Wave Number and Frequency of

Observed Magnetic Fluctuations are Consistent with MTM

• In poloidal direction of lab frame

– BES measures mode velocity: 𝑽𝒍𝒂𝒃𝒑𝒐𝒍

= 𝟒𝟓 −

𝟓𝟎 𝒌𝒎/𝒔, electron direction

– Charge-Exchange-Recombination (CER)

diagnostic measures 𝑬 × 𝑩 velocity:

𝑽𝑬×𝑩𝒑𝒐𝒍

≤ 𝟏𝟎 𝒌𝒎/𝒔, electron direction

• Poloidal mode velocity in plasma frame

– 𝑽𝒎𝒐𝒅𝒆𝒑𝒐𝒍

= 𝑽𝒍𝒂𝒃𝒑𝒐𝒍

− 𝑽𝑬×𝑩𝒑𝒐𝒍

in electron direction

• GENE simulation identifies MTM as most

unstable mode in the pedestal

𝝆

𝑽𝒍𝒂𝒃𝒑𝒐𝒍

(BES)

𝑽𝑬×𝑩𝒑𝒐𝒍

(CER)

[𝒄𝒔/𝒂

][𝒌

𝒎/𝒔

]

[𝒌𝑯

𝒛]

175823

Electron

Direct.

Ion

Direct.

Pedestal Top Steep gradient

𝒇𝑴𝑻𝑴𝜸𝑴𝑻𝑴

GENE calculation

Frequency 𝒌𝜽𝝆𝒔

Linear GENE 100-250 kHz, plasma 0.05-0.2

Observation 150-500 kHz, Lab 0.06

16

• Line-averaged radial magnetic fluctuation by Faraday polarimeter

–𝜹ഥ𝑩𝑹 ≡ 𝒏𝒆𝜹𝑩𝑹𝒅𝑹

𝒏𝒆𝒅𝑹, averaged in 1.2m

– Serves as lower-bound of local magnetic fluctuation amplitude

Lower-bound Magnetic Fluctuation Amplitude Indicates

Electromagnetic Instability1-2, Same as MTM

𝒇 [𝒌𝑯𝒛]

At 250 kHz:𝜹ഥ𝑩𝑹~𝟎. 𝟖 𝑮

150-500 kHz:𝜹ഥ𝑩𝑹~𝟏𝟓 𝑮

175823: 3-4 s

Faraday 𝜹ഥ𝑩𝑹

[𝑮𝒂𝒖𝒔𝒔/ 𝒌𝑯𝒛]

1: Guttenfelder, Phys. Rev. Lett., 2011; Phys. Plasmas, 2012

2: Hillesheim, Plasma Phys. Control. Fusion, 2016

Quantities 250 kHz 150-500 kHz

𝜹ഥ𝑩𝒓 ~𝟎. 𝟖 Gauss ~𝟏𝟓 Gauss

|𝜹ഥ𝑩𝒓/𝑩| ~𝟒 × 𝟏𝟎−𝟓 ~𝟖 × 𝟏𝟎−𝟒

𝜹ഥ𝑩𝒓

𝑩/

𝜹𝒏

𝒏~𝟎. 𝟎𝟖 ~𝟎. 𝟏𝟓

17

For the observed fluctuations at 250 kHz

• Lower-bound 𝜹𝑩𝒓 estimated using RIP data and

plasma diameter 120 cm as path length: 0.8 Gauss

• Upper-bound 𝜹𝑩𝒓 estimated using RIP data and

pedestal width 3 cm as path length: 16 Gauss

• Estimate using 𝒌𝜽 = 𝟎. 𝟑 ± 𝟎. 𝟎𝟓/𝒄𝒎 from BES and

model profile 𝛅𝐁𝐫 ∝ 𝐞−𝐤𝛉𝐫 (cylindrical geometry,

poloidal mode number 𝑚 ≫ 1 and field point close

to resonant surface (𝑟 − 𝑟𝑟𝑠 ≪ 𝑟𝑟𝑠))

– RIP & model: peak 𝛿𝐵𝑟 = 7.2 ± 1.2 Gauss

– Mirnov & model: peak 𝛿𝐵𝑟 = 7 − 581 Gauss

– RIP & model provides most realistic estimate

• Further understanding awaits comparison with

gyro-kinetic simulation

𝜹𝑩𝒓 profile of the High-Frequency Fluctuations is estimated

[

]

[ ]

Estimated 𝜹𝑩𝒓 profile using

different methods

18

• Three phases between ELMs

– 0 – 2 ms: ELM crash

– 2 – 4 ms: 𝛁𝑻𝒆𝒑𝒆𝒅

, 𝛁𝒏𝒆𝒑𝒆𝒅

and fluctuation

amplitude recover

– After 4-5 ms: fluctuation amplitude and gradients saturated

• Fluctuation amplitude evolution

correlates with 𝛁𝐓𝐞,

– 𝛁𝐧𝐞𝐩𝐞𝐝

not decoupled

Magnetic Fluctuation Amplitude Correlates with Pedestal

Temperature Gradient Between ELMs, as Expected for MTM*

𝒕𝑬𝑳𝑴 [𝒎𝒔]

𝛁𝐧𝐞𝐩𝐞𝐝

[𝟏𝟎𝟐𝟏𝒎−𝟒]

𝛁𝐓𝐞𝐩𝐞𝐝

[𝒌𝒆𝑽/𝒎]

ഥ𝑩𝒓 [𝑮𝒂𝒖𝒔𝒔]

*: Drake, Phys. Fluids, 1977

Crash Recovery Saturation175921

19

Magnetic Fluctuation Amplitude Always Peaks off Mid-plane,

Similar to Predicted Global Structure of MTM

• Poloidal variation of fluctuation

amplitude is measured by moving

ELMy H-mode plasma rigidly in

vertical direction

• Magnetic fluctuation peaks furthest

below mid-plane, and close to

minimum near mid-plane

• Off mid-plane peak similar to MTM*

Faraday 𝜹ഥ𝒃𝑹 [𝑮𝒂𝒖𝒔𝒔]

Mid-plane

of plasma𝚫𝒁𝒎𝒂𝒈

[𝒄𝒎]

179431

*: Hatch, Nucl. Fusion, 2016

𝒕=2,3,4 s

20

• In plasmas with same shape, 𝒛𝟎 ≈ −𝟗 cm, 𝒒𝟗𝟓 ≈ 𝟒. 𝟕 and NBI power≈4 MW, magnetic

fluctuation amplitude exhibits non-monotonic

dependence on 𝝂𝒆𝒊

𝝎, peaking at

𝝂𝒆𝒊

𝝎~0.3

– 𝝂𝒆𝒊 evaluated in steep gradient region

– 𝝎 is estimated mode frequency in plasma

frame

• Linear GENE* shows MTM growth rate with

similar dependence and peak at 𝝂𝒆𝒊

𝝎~0.4

𝝂𝒆𝒊𝒑𝒆𝒅

/𝝎

Faraday

𝜹ഥ𝒃𝑹

[𝑮𝒂𝒖𝒔𝒔]

1: Guttenfelder, Phys. Plasmas, 2012

2: Kotschenruether, Nucl. Fusion, 2019

𝜸𝑴𝑻𝑴/(𝒄𝒔

𝒂)

from GENE

Magnetic Fluctuation Amplitude Correlates with 𝝂𝒆𝒊 Non-

monotonically, Consistent with MTM growth Rate Dependence1,2

21

Observations of broadband fluctuations

electromagnetic

Propagates in electron direction

𝐟~𝟏𝟓𝟎 − 𝟓𝟎𝟎 𝐤𝐇𝐳, 𝐤𝛉𝝆𝒔~𝟎. 𝟎𝟔

Correlation with 𝛁𝐓𝐞𝐩𝐞𝐝

Peak off mid-plane

Non-monotonic dependence with 𝛎𝐞𝐢𝐩𝐞𝐝

Summary: Comparison of Magnetic Fluctuations with MTM

Consistent with

MTM

Inconsistent with

KBM

Inconsistent with

electrostatic

modes

22

• Faraday polarimetry as internal magnetic fluctuation diagnostic

• Fundamental observations of internal magnetic fluctuations

• Internal magnetic fluctuations identified as micro-tearing modes

• Correlation between internal magnetic fluctuations and confinement

Outline

23

Magnetic Fluctuations Correlate with Confinement Degradation

• Density ramp leads to 20-30% degradation of pedestal and

global confinement

• Broadband magnetic

fluctuation amplitude

correlates with confinement

change

• Magnetic fluctuations likely play a role in thermal

transport, as expected for MTM

175816

P_total [MW]ഥ𝒏𝒆 [𝟏𝟎𝟏𝟗/𝒎𝟑]

𝒑𝒆𝒑𝒆𝒅

[𝒌𝒑𝒂]

𝑾𝑴𝑯𝑫 [MJ]

Faraday𝒇

[𝒌𝑯𝒛]

𝒕 [𝒔]

Faraday 𝜹ഥ𝒃𝑹

[𝑮𝒂𝒖𝒔𝒔] 𝒇 ∈ [𝟏𝟓𝟎, 𝟓𝟎𝟎]

24

• Broadband magnetic fluctuations in the pedestal are observed internally

in ELMy H-mode plasmas in DIII-D using Faraday-effect polarimeter

• Characteristics of broadband magnetic fluctuations agree with MTM

– 𝐟~𝟏𝟎𝟎 − 𝟓𝟎𝟎 𝒌𝑯𝒛, 𝒌𝜽~𝟎. 𝟑/𝒄𝒎 and propagate in electron direction

– Lower-bound 𝜹𝒃𝒓~𝟏𝟓 𝑮,𝜹𝒃𝒓

𝑩/

𝜹𝒏

𝒏~𝟎. 𝟏𝟓 integrated from 150 to 500 kHz

–Amplitude correlates with 𝜵𝑻𝒆𝒑𝒆𝒅, peaks off mid-plane, and depends

non-monotonically on 𝝂𝒆𝒊𝒑𝒆𝒅

• Magnetic fluctuations correlate with H-mode confinement degradation

Summary

Thanks for your attention