pedestal magnetic turbulence measurements in elmy h-mode … · 2021. 4. 8. · 28th iaea fusion...
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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