Comparison study of the measured ELM by ECEI and synthetic image - - PowerPoint PPT Presentation

• M. Kim1, M. J. Choi1, J. Lee1, G. S. Yun1, W. Lee1, H. K. Park2,
• X. Xu3, C. W. Domier4, N. C. Luhmann, Jr.4 and KSTAR team

Comparison study of the measured ELM by ECEI and synthetic image from BOUT++ in KSTAR H-mode plasma

KSTAR conference 2014

• Feb. 24-26, 2014, Jeongseon, Gangwon-do, Korea

Supported by In collaboration with Y. S. Park and S. Sabbagh (Columbia Univ./ PPPL)

1Pohang University of Science and Technology, Pohang, Korea 2Ulsan National Institute of Science Technology, Ulsan, Korea 3Lawrence Livermore National Laboratory, Livermore, USA 4University of California at Davis, Davis, USA

ABSTRACT

Edge Localized Mode (ELM) is a class of edge instabilities leading to quasi-periodic bursts of the pedestal region in typical H-mode plasmas. The ELM dynamics have been studied using an Electron Cyclotron Emission Imaging (ECEI) system on the KSTAR [1]. At the plasma edge, interpretation of ECE signal is complicated due to the rapid change of the optical

• thickness. To provide confidence on the observation, the observed ELM filamentary structure

is compared with the synthetic image deduced from the BOUT++ simulations based on 3-field fluid equations [2, 3]. In the synthetic diagnostic process, spatial resolution of the KSTAR ECEI system, the intrinsic broadening of ECE and the background system noise are taken into

• account. The observed image is successfully reproduced by synthetic process, providing a

high confidence on the observed ELM dynamics. [1] G. S. Yun et al, Physics Review Letter 107, 045004 (2011). [2] B. D. Dudson et al, Computer Physics Communications 180, 1467 (2009). [3] X. Q. Xu et al, Nuclear Fusion 51, 103040 (2011).

This research was supported by NRF of Korea under contract no. 2009-0082507 and US DoE by LLNL under contract no. DE-AC52-07NA27344 and by UC Davis under contract no. DE-FG02-99ER54531

1

2

Introduction

Motivation: ECEI observations at the plasma edge should be carefully

interpreted due to complexity of ECE signal interpretation.

• B. Dudson, Computer Phys. Comm. (2009)
• X. Xu, Phys. Rev. Lett. (2010)
• 3D two-fluid ELM simulation code.
• Generating ELM mode structure.

BOUT++

• G. S. Yun, Rev. Sci. Instrum. (2010)
• Electron Cyclotron Emission Imaging
• Based on principles of conventional ECE

radiometry.

• Local Te fluctuation measurement in 2D.

ECEI

• Considering instrumental effect of

diagnostic system and characteristics of EC emission.

Synthetic diagnostic

• B. J. Tobias, Rev. Sci. Instrum. (2012)

ECEI at t~4.36 EFIT at t = 4.36 (s)

ELM observation by ECEI system

𝑪𝐔 = 𝟑. 𝟑𝟔 𝐔, 𝑱𝐪 = 𝟖𝟔𝟏 𝐥𝐁 , 𝒓𝟘𝟔~𝟔. 𝟏, 𝑸𝐎𝐂𝐉~𝟒. 𝟏 𝐍𝐗

KSTAR #7328

• Coherent mode structures were observed prior to the ELM crash.

Da intensity Spectrogram of ECEI Ch. 13-4

.3643 4.36 60 120 180 240 300 360

f (degree) time (s) 4.3643 4.3648 360 300 240 180 120 60 9 (1) 8 7 6 5 4 3 2 1

• The toroidal mode number of the observed structure was n = 8

Band-pass filtered signals of the toroidal Mirnov coil array

3

Question

At the plasma edge, the interpretation of ECE signal is complex;

• Rapidly changing optical thickness
• Relativistic downshifted ECE signal.

 The observed mode structure represents the ELM filamentary structure?

• J. Lee submitted to Nuclear Fusion (2013)
• J. E. Lee’s poster

BOUT++ simulation for the ELMs in KSTAR

𝜖𝜕 𝜖𝑢 = − 1 𝐶0 𝑐0 × 𝛼𝜚0 ∙ 𝛼𝜕 + 𝑐0 × 𝜆0 ∙ 𝛼𝑞 + 𝐶0

2

𝑐0 ∙ 𝛼 𝐾∥ 𝐶0 𝜖𝐵∥ 𝜖𝑢 = − 𝑐0 ∙ 𝛼Φ + 𝜃 𝜈0 𝛼⊥

2𝐵∥

𝜖𝑞 𝜖𝑢 = − 1 𝐶0 𝑐0 × 𝛼𝜚 ∙ 𝛼𝑞0 − 1 𝐶0 𝑐0 × 𝛼𝜚0 ∙ 𝛼𝑞 𝐾∥ = 𝐾∥0 + 𝑘∥ = 𝐾∥0 − 1

𝜈0 𝛼⊥ 2𝐵∥.

• BOUT++ is 3D edge simulation code in two-fluid frame
• 3-field (pressure 𝑞, magnetic potential 𝐵∥, vorticity 𝜕) simulation was used in this

comparison study

• B. Dudson, Computer Physics Comm. (2009), X. Q. Xu, PRL (2010)

𝜕 = 𝑜0𝑁𝑗

𝐶0

𝛼⊥

2𝜚 + 1 𝑜0𝑎𝑗𝑓 𝛼⊥ 2𝑞𝑗 ,

Pressure Magnetic potential Vorticity

• Here, only linear simulation results are considered because mode stability can

be determined by linear simulation only where

4

• Plasma equilibrium is from EFIT reconstruction except for pressure profile
• Pressure profile reconstruction
• 𝑞(𝑠) =

𝑞ped,top 2

1 − tanh 𝑞s 𝜔(𝑠) − 𝜔0

• The measured Te (ECE) & an assumed ne (constrained by interferometry)  pped,top
• Linear growth rate analysis  ps (related to 𝛽 = −

2𝜈0𝑆𝑟2 𝐶2 𝑒𝑞 𝑒𝑠)

• Finally, amax = 16.0 (ps = 50) was chosen to pressure profile.

Initial condition for ELM simulation

5

0.86 0.88 0.9 0.92 0.94 0.96 2 4 6 8 amax=12.8 amax=16.0 amax=19.2

Pressure (kPa) Normalized radius 𝐬/𝐛

4 5 6 7 8 9 10 11 12 0.02 0.04 0.06 amax=12.8 amax=16.0 amax=19.2

g/wA Toroidal mode number 𝒐

(a) 𝛽max = 12.8 (b) 𝛽max = 16.0

𝜀𝑄(𝐵. 𝑉. ) 1

• 1

20 15 10 5

• 5
• 10
• 15

z (cm)

• 20

215 225

R (cm)

20 15 10 5

• 5
• 10
• 15
• 20

215 225

R (cm) (c) 𝛽max = 19.2

20 15 10 5

• 5
• 10
• 15
• 20

215 225

R (cm)

Difference in simulation & observation

6 𝜀𝑈

𝑓𝑑𝑓/ 𝑈 𝑓𝑑𝑓

0.1 0.05

• 0.05

20 15 10 5

• 5
• 10
• 15
• 20

215 225

R (cm) (d) ECEI observation

• As the pressure gradient was relaxed, the radial width of the mode increased.
• However, this change was too small to reconcile the difference with the
• bservation.
• For comparison, it is necessary to consider ECE characteristic at the plasma edge

and instrumental effect of the ECEI system.  synthetic diagnostic process

𝑈

syn(𝑆𝑑ℎ, 𝑨𝑑ℎ) = Δ𝑆 Δ𝑨 𝑈 𝑆, 𝑨 𝑔 R 𝑕(z) dRd𝑨 Δ𝑆 Δ𝑨 𝑔 R 𝑕 z dRd𝑨

• Synthetic electron temperature Tsyn at specific channel position (Rch, zch)

Synthetic image reconstruction

• 𝑈 𝑆, 𝑨 : Te from simulation
• 𝑔 𝑆 : radial response function including
• ECEI instrumental broadening due to IF bandwidth
• Intrinsic ECE broadening due to relativistic effect

[M. Bornatici, Nucl. Fus. (1983)]

• 𝑕(𝑨): vertical response function
• Gaussian-like antenna response function

(a)

20 15 10 5

• 5
• 10
• 15

z (cm)

• 20

215 225

R (cm) (b)

20 15 10 5

• 5
• 10
• 15
• 20

215 225

R (cm)

𝜀𝑈

𝑓𝑑𝑓

𝑈

𝑓𝑑𝑓

0.04 0.02

• 0.02

7

LCFS

R (cm) Emission Intensity (A.U.)

214 226 218 222 216 228 220 224 1.0 0.8 0.6 0.4 0.2

Radial response function at mid-plane

• Each curve is normalized by its

maximum value.

• Dotted lines: only considering effect of

IF bandwidth

• Solid lines: including relativistic

broadening (a) From dotted curve

• Interpolation between channels 

radial width increase. (b) From solid curve

• Interpolation and channel overlap

between adjacent channels radial width is comparable to the observed

• ne.
• Mirror image outside the separatrix is

due to downshifted signal.

(a) (b) (c) (d)

20 15 10 5

• 5
• 10
• 15

z (cm)

• 20

215 225

R (cm)

𝜀𝑄(𝐵. 𝑉. )

1

• 1

𝜀𝑈

𝑓𝑑𝑓

𝑈

𝑓𝑑𝑓

0.04 0.02

• 0.02

20 15 10 5

• 5
• 10
• 15

z (cm)

• 20

215 225

R (cm)

20 15 10 5

• 5
• 10
• 15
• 20

215 225

R (cm) LCFS

20 15 10 5

• 5
• 10
• 15
• 20

215 225

R (cm)

Comparison with the measured image

• To make more realistic image, the system background noise (mostly instrumental

noise of electronics) was considered.

• 𝜀𝑈

syn,mirror ~ 𝜀𝑈 syn,noise  It is difficult to interpret signal outside the LCFS.

 Only focus on signal inside LCFS.

• The measured ELM image was successfully reproduced by synthetic reconstruction

based on BOUT++ simulation.

(a) BOUT++ simulation (b) synthetic image w/o system noise (c) synthetic image w/ system noise (d) ECEI observation at t ~ 4.36

8

𝛽 = − 2𝜈0𝑆𝑟2

𝐶2 𝑒𝑞 𝑒𝑠

#: most unstable toroidal mode number at given pedestal condition

Future work: P-B stability diagram

9

• Mapping of experimental points on P-B stability diagram

unstable unstable, 𝛿/𝜕𝐵 < 0.02 stable # #

• Future plan: comparing simulation results with the measured pedestal

condition and mode number of ELM

KSTAR #7328 t = 4.36 s

• Bootstrap current was introduced using Sauter’s formula
• CORSICA: reconstruction of new equilibrium with fixed Ipconstraint

5 10 15 20 20 40 60 80 100

7 9 7 12 11 13 13 9

a

J// (A/cm2)

14 12 9

Summary

• ECEI system on KSTAR observed coherent mode structure at the plasma edge

during inter-ELM phase.

• Because interpretation of the ECE signal has intrinsic complexity at the plasma

edge, the observed ECE images should be carefully interpreted.

• For consistency, the results of 3-field version BOUT++ simulation was converted

to synthetic image.

• The synthetic process takes into account the instrumental effect of ECEI, intrinsic

broadening of ECE and system noise.

• The observed image was successfully reconstructed through the synthetic

diagnostic process.

• Mapping of the measured points with various n-numbers on P-B stability

diagram is under study.

10

Back Up

ECEI: 2D imaging diagnostics system

Schematics of ECEI system

Diode detector

• Vertical 24 channels
• Each vertical Ch. split into 8 freq. Ch.
• 24 X 8 channels in each system
• Electron Cyclotron (EC) frequency

𝑔

𝐹𝐷𝐹 ∝ 1/𝑆

• Optically thick plasma, EC emission is like

a blackbody 𝐽𝐹𝐷𝐹(𝑆) ∼ 𝑈

𝑓 𝑆 𝑔 𝐹𝐷𝐹 2

(𝑆) 𝑔

𝑓𝑑𝑓

𝑆

Large aperture optics

… … … … Electron Cyclotron Emission Image (ECEI)

• Based on principles of conventional

ECE radiometry.

• High temporal (1 ~ 2 ms) and spatial

(1 X 1 ~ 2 X 3 cm2) resolution.

• Measuring local Te fluctuation in 2D.

Toroidal mode number estimation

5 10 15 20

20 10

• Ch. #

Band-passed signal of toroidal Mirnov coil array

H-port 1st ECEI G-port 2nd ECEI 0° f

1 6 11 16

.3643 4.36 60 120 180 240 300 360

f (degree) time (s) 4.3643 4.3648 360 300 240 180 120 60

Contour plot of band-passed signal Schematics of toroidal Mirnov coil array

• S. G. Lee, Rev. Sci. Instrum.

(2001)