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

Comparison study of the measured ELM by ECEI and synthetic image from BOUT++ in KSTAR H-mode plasma M. Kim 1 , M. J. Choi 1 , J. Lee 1 , G. S. Yun 1 , W. Lee 1 , H. K. Park 2 , X. Xu 3 , C. W. Domier 4 , N. C. Luhmann, Jr. 4 and KSTAR team 1 Pohang University of Science and Technology, Pohang, Korea 2 Ulsan National Institute of Science Technology, Ulsan, Korea 3 Lawrence Livermore National Laboratory, Livermore, USA 4 University of California at Davis, Davis, USA In collaboration with Y. S. Park and S. Sabbagh (Columbia Univ./ PPPL) KSTAR conference 2014 Feb. 24-26, 2014, Jeongseon, Gangwon-do, Korea Supported by

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

Introduction Motivation: ECEI observations at the plasma edge should be carefully interpreted due to complexity of ECE signal interpretation. BOUT++ ECEI - Electron Cyclotron Emission Imaging - 3D two-fluid ELM simulation code. - Based on principles of conventional ECE - Generating ELM mode structure. radiometry. B. Dudson, Computer Phys. Comm. (2009) - Local T e fluctuation measurement in 2D. X. Xu, Phys. Rev. Lett. (2010) G. S. Yun, Rev. Sci. Instrum. (2010) Synthetic diagnostic - Considering instrumental effect of diagnostic system and characteristics of EC emission. B. J. Tobias, Rev. Sci. Instrum. (2012) 2

ELM observation by ECEI system KSTAR #7328 𝑪 𝐔 = 𝟑. 𝟑𝟔 𝐔 , 𝑱 𝐪 = 𝟖𝟔𝟏 𝐥𝐁 , 𝒓 𝟘𝟔 ~𝟔. 𝟏 , 𝑸 𝐎𝐂𝐉 ~𝟒. 𝟏 𝐍𝐗 • Coherent mode structures were observed prior to the ELM crash. ECEI at t ~ 4.36 EFIT at t = 4.36 (s) D a intensity Spectrogram of ECEI Ch. 13-4

Band-pass filtered signals of the toroidal Mirnov coil array 360 360 8 9 (1) 7 300 300 6 240 240 f (degree) 5 4 180 180 3 120 120 2 1 60 60 0 0 4.3643 4.3648 .3643 4.36 time (s) J. Lee submitted to Nuclear Fusion (2013) J. E. Lee’s poster • The toroidal mode number of the observed structure was n = 8 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? 3

BOUT++ simulation for the ELMs in KSTAR B. Dudson, Computer Physics Comm. (2009), X. Q. Xu, PRL (2010) • 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 𝜖𝑞 𝜖𝑢 = − 1 𝑐 0 × 𝛼𝜚 ∙ 𝛼𝑞 0 − 1 𝑐 0 × 𝛼𝜚 0 ∙ 𝛼𝑞 Pressure 𝐶 0 𝐶 0 𝜖𝐵 ∥ 𝑐 0 ∙ 𝛼Φ + 𝜃 𝜖𝑢 = − 2 𝐵 ∥ 𝛼 ⊥ Magnetic potential 𝜈 0 𝜖𝜕 𝜖𝑢 = − 1 𝐾 ∥ 𝑐 0 × 𝛼𝜚 0 ∙ 𝛼𝜕 + 2 𝑐 0 × 𝜆 0 ∙ 𝛼𝑞 + 𝐶 0 𝑐 0 ∙ 𝛼 Vorticity 𝐶 0 𝐶 0 𝜕 = 𝑜 0 𝑁 𝑗 1 𝐾 ∥ = 𝐾 ∥0 + 𝑘 ∥ = 𝐾 ∥0 − 1 2 𝜚 + 2 𝑞 𝑗 , 2 𝐵 ∥ . 𝛼 ⊥ 𝑜 0 𝑎 𝑗 𝑓 𝛼 ⊥ 𝜈 0 𝛼 ⊥ where 𝐶 0 • Here, only linear simulation results are considered because mode stability can be determined by linear simulation only 4

Initial condition for ELM simulation • Plasma equilibrium is from EFIT reconstruction except for pressure profile • Pressure profile reconstruction 𝑞 ped,top - 𝑞(𝑠) = 1 − tanh 𝑞 s 𝜔(𝑠) − 𝜔 0 2 The measured T e (ECE) & an assumed n e (constrained by interferometry)  p ped,top - 2𝜈 0 𝑆𝑟 2 𝑒𝑞 Linear growth rate analysis  p s (related to 𝛽 = − - 𝑒𝑠 ) 𝐶 2 • Finally, a max = 16.0 ( p s = 50) was chosen to pressure profile. 8 0.06 a max =12.8 a max =12.8 a max =16.0 a max =16.0 6 Pressure (kPa) a max =19.2 a max =19.2 0.04 g / w A 4 0.02 2 0 0 0.86 0.88 0.9 0.92 0.94 0.96 4 5 6 7 8 9 10 11 12 Normalized radius 𝐬/𝐛 Toroidal mode number 𝒐 5

Difference in simulation & observation (a) 𝛽 max = 12.8 (b) 𝛽 max = 16.0 (c) 𝛽 max = 19.2 (d) ECEI observation 20 20 20 20 𝜀𝑄(𝐵. 𝑉. ) 𝜀𝑈 𝑓𝑑𝑓 / 𝑈 15 15 15 15 𝑓𝑑𝑓 0.1 1 10 10 10 10 5 5 5 5 z (cm) 0.05 0 0 0 0 -5 -5 -5 -5 -10 -10 -10 -10 0 -15 -15 -15 -15 -20 -20 -20 -20 -1 -0.05 215 225 215 225 215 225 215 225 R (cm) R (cm) R (cm) R (cm) • 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 observation. • For comparison, it is necessary to consider ECE characteristic at the plasma edge and instrumental effect of the ECEI system.  synthetic diagnostic process 6

Synthetic image reconstruction • Synthetic electron temperature T syn at specific channel position ( R ch , z ch ) Δ𝑨 𝑈 𝑆, 𝑨 𝑔 R 𝑕(z) dRd𝑨 Δ𝑆 𝑈 syn (𝑆 𝑑ℎ , 𝑨 𝑑ℎ ) = Δ𝑨 𝑔 R 𝑕 z dRd𝑨 Δ𝑆 - 𝑈 𝑆, 𝑨 : T e 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

Radial response function at mid-plane • Each curve is normalized by its 1.0 Intensity (A.U.) maximum value. 0.8 Emission • Dotted lines: only considering effect of 0.6 0.4 IF bandwidth 0.2 • Solid lines: including relativistic 0 214 216 218 220 222 224 226 228 broadening R (cm) (a) (b) (a) From dotted curve 20 20 𝜀𝑈 𝑓𝑑𝑓 - Interpolation between channels  𝑈 15 15 𝑓𝑑𝑓 radial width increase . 10 10 0.04 (b) From solid curve 5 5 z (cm) - Interpolation and channel overlap 0 0 0.02 between adjacent channels  radial -5 -5 width is comparable to the observed -10 -10 0 one. -15 -15 - Mirror image outside the separatrix is LCFS -20 -20 -0.02 due to downshifted signal. 215 225 215 225 R (cm) R (cm) 7

Comparison with the measured image (a) (b) (c) (d) 𝜀𝑈 𝑓𝑑𝑓 20 20 20 20 𝜀𝑄(𝐵. 𝑉. ) 𝑈 𝑓𝑑𝑓 (a) BOUT++ simulation 15 15 15 15 0.04 1 (b) synthetic image 10 10 10 10 w/o system noise 5 5 5 5 0.02 z (cm) z (cm) (c) synthetic image 0 0 0 0 w/ system noise -5 -5 -5 -5 (d) ECEI observation at 0 -10 -10 -10 -10 t ~ 4.36 -15 -15 -15 -15 -1 -0.02 LCFS -20 -20 -20 -20 215 225 215 225 215 225 215 225 R (cm) R (cm) R (cm) R (cm) • 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. 8

Future work: P-B stability diagram • Mapping of experimental points on P-B stability diagram KSTAR #7328 t = 4.36 s 100 # unstable 9 13 9 # unstable, 𝛿/𝜕 𝐵 < 0.02 80 13 11 J // (A/cm 2 ) 12 stable 60 # : most unstable toroidal mode number 14 12 9 7 7 40 at given pedestal condition 20 𝛽 = − 2𝜈 0 𝑆𝑟 2 𝑒𝑞 𝐶 2 𝑒𝑠 0 0 5 10 15 20 a • Bootstrap current was introduced using Sauter’s formula • CORSICA: reconstruction of new equilibrium with fixed I p constraint • Future plan: comparing simulation results with the measured pedestal condition and mode number of ELM 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

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