be measured in the CSS spectrogram, because the fluctuations in the vicinity of the measurement position are carried in the scattered beam like the interferometry. This interferometric signals are characterized by being symmetric on the CSS spectrogram. Therefore, when analyzing CSS data, it is necessary to perform comparative analysis with data from other diagnostics to prevent misinterpretation.
In conclusion, the CSS will make a great contribution to small scale turbulence studies such as its physical properties and suppression mechanism. Furthermore, we expect to make the contribution to the field of turbulence simulation of trapped electron mode (TEM) and ETG mode, which was difficult to prove experimentally. In the future, more intensive analyses of CSS data will be carried out for studies of physics associated with small scale turbulence such as characteristics of ETG or trapped electron mode (TEM) in KSTAR H-mode or hybrid mode edge and their contribution to the plasma performance *This work was supported by the Ministry of Science and ICT of Korea under the KSTAR project and the NRF of Korea under contract Nos. NRF-2014M1A7A1A03029865 and NRF- 2015M1A7A02002627.
Appendix
A.
1. Fourier transform and inverse Fourier transform:
πποΏ½πποΏ½β,πποΏ½= οΏ½ πππ‘π‘+β
ββ οΏ½ ππ+β 3ππ
ββ ππ(ππβ,π‘π‘)ππβπποΏ½πποΏ½βΒ·ππββπππ‘π‘οΏ½ (A. 1) ππ(ππβ,π‘π‘) = οΏ½ ππππ
2ππ
+β
ββ οΏ½ ππ3ππ
(2ππ)3
+β
ββ πποΏ½πποΏ½β,πποΏ½πππποΏ½πποΏ½βΒ·ππββπππ‘π‘οΏ½ (A. 2) 2. Parsevalβs Theorem:
οΏ½ πππ‘π‘+β
ββ |ππ(π‘π‘)|2= οΏ½ ππππ
2ππ
+β
ββ |ππ(ππ)|2 (A. 3) 3. Delta function:
οΏ½ πππ‘π‘ +β πππππππ‘π‘
ββ = 2πππΏπΏ(ππ) (A. 4)
οΏ½ ππ+β 3ππ πππππποΏ½βΒ·ππβ
ββ = (2ππ)3πΏπΏοΏ½πποΏ½βοΏ½ (A. 5) 4. Integral formula I:
οΏ½ ππππ ππβπ₯π₯
2 ππ2 +β
ββ =ππβππ (A. 6) 5. Integral formula II:
οΏ½ ππππ+β
ββ ππβπ₯π₯
2
ππ2βπππππ₯π₯ = οΏ½ ππππ+β
ββ ππβ 1ππ2(π₯π₯2+ππππ2π₯π₯βππ
4ππ2 4 +ππ4ππ2
4 )
= οΏ½ ππππ+β
ββ ππβ 1ππ2(π₯π₯+ππππ
2ππ
2 )2ππβππ24ππ2
= ππππππβππ24ππ2 (A. 7) 6. Integral formula III:
οΏ½+πΏπΏ ππππ πππππππ₯π₯
2π§π§
βπΏπΏ2π§π§
=οΏ½πππππππ₯π₯ ππππ οΏ½
βπΏπΏπ§π§/2 +πΏπΏπ§π§/2
= πππππππΏπΏ2π§π§β ππβπππππΏπΏ2 π§π§ ππππ
= 2ππsin(πππΏπΏπ§π§
ππππ 2 )= πΏπΏπ§π§
sin(πππΏπΏπ§π§ πππΏπΏ2 )π§π§
2
=πΏπΏπ§π§ sincοΏ½πππΏπΏπ§π§
2 οΏ½ (A. 8)
B.
1. Product rule with del operator:
βοΏ½π΄π΄βΒ·π΅π΅οΏ½βοΏ½=οΏ½π΄π΄βΒ·βοΏ½π΅π΅οΏ½β+οΏ½π΅π΅οΏ½βΒ·βοΏ½π΄π΄β+π΄π΄βΓοΏ½βΓπ΅π΅οΏ½βοΏ½+π΅π΅οΏ½βΓοΏ½βΓπ΄π΄βοΏ½ (B. 1.1)
π΄π΄βΓ (π΅π΅οΏ½βΓπΆπΆβ) = π΅π΅οΏ½β(π΄π΄βΒ·πΆπΆ)οΏ½οΏ½οΏ½οΏ½β β πΆπΆβ(π΄π΄βΒ·π΅π΅)οΏ½οΏ½οΏ½οΏ½β (π΅π΅. 1.2) 2. First term of Eq. (2.23 (a)):
οΏ½π π οΏ½βΒ·βοΏ½π£π£β= οΏ½π π π₯π₯ ππ
ππππ+π π π¦π¦ ππ
ππππ+π π π§π§ ππ
πππποΏ½ π£π£β(π‘π‘β²)
= π π π₯π₯πππ£π£β
πππ‘π‘
πππ‘π‘β²
ππππ +π π π¦π¦πππ£π£β
πππ‘π‘
πππ‘π‘β²
ππππ +π π π§π§πππ£π£β
πππ‘π‘
πππ‘π‘β²
ππππ
=π£π£βΜοΏ½π π οΏ½βΒ·βπ‘π‘β²οΏ½ (B. 2) 3. Second term of Eq. (2.23 (a)):
(π£π£βΒ·β)π π οΏ½β= (π£π£βΒ·β)ππβ β(π£π£βΒ·β)πποΏ½οΏ½οΏ½ββ² (B. 3.1)
=π£π£β β π£π£β(π£π£βΒ·βπ‘π‘β²) (B. 3.2) 4. Similar to Eq. (B.2), Eq. (B.3.1) becomes:
(π£π£βΒ·β)ππβ=οΏ½π£π£π₯π₯ ππ
ππππ+π£π£π¦π¦ ππ
ππππ+π£π£π§π§ ππ
πππποΏ½(πππποΏ½+πππποΏ½+ππππΜ) =π£π£β (B. 4) (π£π£βΒ·β)πποΏ½οΏ½οΏ½ββ² =π£π£β(π£π£βΒ·βπ‘π‘β²) (B. 5) 5. Third term of Eq. (2.23 (a)):
βΓπ£π£β= οΏ½πππ£π£π§π§
ππππ β
πππ£π£π¦π¦
ππππ οΏ½ πποΏ½+οΏ½πππ£π£π₯π₯
ππππ β
πππ£π£π§π§
πππποΏ½ πποΏ½+οΏ½πππ£π£π¦π¦
ππππ β
πππ£π£π₯π₯
ππππ οΏ½ ππΜ
= οΏ½πππ£π£π§π§ πππ‘π‘β²
πππ‘π‘β²
ππππ β πππ£π£π¦π¦
πππ‘π‘β²
πππ‘π‘β²
ππππ οΏ½ πποΏ½+οΏ½πππ£π£π₯π₯ πππ‘π‘β²
πππ‘π‘β²
ππππ β πππ£π£π§π§
πππ‘π‘β²
πππ‘π‘β²
ππππ οΏ½ πποΏ½+οΏ½πππ£π£π¦π¦
πππ‘π‘β²
πππ‘π‘β²
ππππ β πππ£π£π₯π₯
πππ‘π‘β²
πππ‘π‘β²
πππποΏ½ ππΜ
=βππβΓβπ‘π‘β² (B. 6)
6. In the same way as Eq. (B.6), Fourth term of Eq. (2.23 (a)) becomes:
βΓπ π οΏ½β= βΓππβ β βΓπποΏ½οΏ½οΏ½ββ²
= βπ£π£βΓβπ‘π‘β² (B. 7) where βΓππβ= 0
7. Calculation required for Eq. (2.30):
From Fig. 2.3,
ππ(π‘π‘ β π‘π‘β²) =π π => ππ2(π‘π‘ β π‘π‘β²)2=π π =π π οΏ½βΒ·π π οΏ½β (B. 8) Differentiate with respect to π‘π‘:
2ππ2(π‘π‘ β π‘π‘β²)οΏ½1βπππ‘π‘β²
πππ‘π‘ οΏ½= 2π π οΏ½βΒ·πππ π οΏ½β
πππ‘π‘ => πππ π οΏ½1βπππ‘π‘β²
πππ‘π‘ οΏ½=π π οΏ½βΒ·πππ π οΏ½β
πππ‘π‘ (B. 9)
πππ π οΏ½β
πππ‘π‘ =βπππποΏ½οΏ½οΏ½ββ²
πππ‘π‘ =βπππποΏ½οΏ½οΏ½ββ²
πππ‘π‘β²
πππ‘π‘β²
πππ‘π‘ =βπ£π£βπππ‘π‘β²
πππ‘π‘ => πππ π οΏ½1βπππ‘π‘β²
πππ‘π‘ οΏ½=βπ π οΏ½βΒ·π£π£βπππ‘π‘β²
πππ‘π‘
=> πππ π =πππ‘π‘β²
πππ‘π‘ οΏ½π π οΏ½βΒ·οΏ½πππ π οΏ½ β π£π£βοΏ½οΏ½ (B. 10)
πππ‘π‘β²
πππ‘π‘ = πππ π
οΏ½πππ π β π π οΏ½βΒ·π£π£βοΏ½ (π΅π΅. 11)
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Acknowledgement
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Curriculum Vitae
Name : Dong Jae Lee
Date of Birth : January 24, 1986 E-mail : [email protected]
Education
2014. 3. - 2020. 8. Ph.D. in Department of Physics, UNIST
2005. 3. - 2014. 2. B.S in Department of Physics, Kyungbuk National University 2002. 3. - 2005. 2. Daegu High School
Experience
2018. 9. 1. - 2019. 6. 31. Student Researcher : Development, Installation and operation of the Microwave Imaging Reflectometry, Collective Scattering system, Nuclear Fusion Research Institute
2016. 9. 1. - 2018. 9. 01. Participating Researcher : Development of scattering system for turbulence study on KSTAR, Nuclear Fusion Research Institute
2013. 7. - 2013. 8. Intern : Density measurements in KSTAR from emission spectroscopy , Nuclear Fusion Research Institute
Research Interests
1. Development and installation of advanced microwave diagnostics in KSTAR (Electron Cyclotron Emission Imaging, Microwave Imaging Reflectometry, Collective Scattering System)
2. Maintenance and operation of Microwave Imaging Reflectometry, Collective Scattering system in KSTAR
3. Optics design of millimeter wave and sub THz system
4. Laboratory experiments with W-band millimeter wave, sub THz wave and RF components
Publication
1. W. Lee, D.J. Lee, H.K. Park, Y.U. Nam, T.G. Lee, M.J. Choi, H.J Ahn, H.K. Park, Y.S. Na, M.S.
Park, βDevelopment of a collective scattering system and its application to the measurement of multiscale fluctuations in KSTAR plasmasβ, Plasma Phys. Control. Fusion 63, 035003 (2021)
2. W. Lee, J. Lee, D.J. Lee, H.K. Park, βStudy of the origin of quasi-coherent modes in low-density KSTAR ECH plasmasβ Nuclear Fusion, 61, 016008 (2020)
3. M. Joung, M. Woo, J.W. Han, S.J. Wang, S.G. Kim, S.H, Hahn, D.J. Lee, J.G. Kwak, R. Ellis,
βDesign of ECH launcher for KSTAR advanced Tokamak operationβ, Fusion Engineering and Design, 151, 111395 (2020)
4. D.J. Lee, W. Lee, H.K. Park and T.G. Kim, βA large-aperture strip-grid beam splitter for partially combined two millimeter-wave diagnostics on Korea Superconducting Tokamak Advanced Researchβ, Rev. Sci. Instrum. 90, 014703 (2019)
5. W. Lee, J. Leem, D.J. Lee, M.J. Choi, H.K. Park, J.A. Lee, G.S. Yun, T.G. Kim, H. Park, K.W. Kim,
βQuasi-coherent fluctuation measurement with the upgraded microwave imaging reflectometer in KSTAR, Plasma Phys. Control. Fusion 60 (2018)
6. Y.B. Nam, D.J. Lee, J. Lee, C. Kim, G.S. Yun, W. Lee and H.K. Park, βNew compact and efficient local oscillator optics system for the KSTAR electron cyclotron emission imaging systemβ, Rev. Sci.
Instrum. 87 (2016)
7. W. Lee, H.K. Park, D.J. Lee, Y.U. Nam, J. Leem and T.K. Kim, βDesign of a collective scattering system for small scale turbulence study in Korea Superconducting Tokamak Advanced Researchβ, Rev. Sci. Instrum. 87 (2016)
Academic Activities
1. D.J. Lee, W. Lee, T.G. Lee, M.J. Choi, Y.U. Nam and H.K. Park, βCollective scattering system developed for high-k turbulence study in KSTARβ, 14th International Reflectometry Workshop,
Lausanne, Swiss, May 22 β 24, 2019
2. D.J. Lee, W. Lee, T.G. Lee, M.J. Choi, Y.U. Nam and H.K. Park, βCommissioning of the collective scattering system developed for high-k turbulence studyβ, 5th UNIST-kyoto Univ. Workshop, Pusan, Korea, April. 22 β 23, 2019
3. D.J. Lee, W. Lee, T.G. Lee, M.J. Choi, Y.U. Nam and H.K. Park, βCommissioning of the collective scattering system developed for electron gyroscale turbulence studyβ, 2019 KSTAR conference, Seoul, Korea, Feb. 20 β 22, 2019
4. D.J. Lee, W. Lee, H.K. Park, J. Leem and Y.U. Nam, βCollective scattering system for high-k turbulence measurement and the modified MIR in KSTARβ, 9th Japan-Korea Seminar on Advanced Diagnostics for Steady-state Fusion Plasmas, Toki-Nagoya, Japan, Aug. 7 β 10, 2018
5. D.J. Lee, W. Lee, H.K. Park, J. Leem and Y.U. Nam, βCollective Thomson scattering System and the modified MIR system in KSTARβ, 2018 KSTAR conference, Muju, Korea, Feb. 21 β 23, 2018 6. D.J. Lee, W. Lee, H.K. Park, J. Leem and Y.U. Nam, βCollective Thomson Scattering System
combined with the MIR system in KSTARβ, 2017 KPS Fall Meeting, Kyungju, Korea, Oct. 25 β 27, 2017
7. D.J. Lee, W. Lee, H.K. Park, J. Leem, Y.U. Nam, T.K. Kim and H. Park, βDesign characteristics of a microwave collective scattering system for KSTARβ, 8th Korea-Japan Workshop on Advanced Diagnostics for Steady-State Fusion Plasmas, Pusan, Korea, Aug. 24 β 27, 2016
8. D.J. Lee, W. Lee, H.K. Park, J. Leem, Y.U. Nam, T.K. Kim and H. Park, βDesign characteristics of a microwave collective scattering system for KSTARβ, High-Temperature Plasma Diagnostics, Wisconsin-Madison, US, June 5 β 9, 2016
9. D.J. Lee, W. Lee, H.K. Park, J. Leem, Y.U. Nam, T.K. Kim and H. Park, βDesign of a collective scattering system for small scale turbulence study on KSTARβ, KPS 2016 spring meeting, Dageon, Korea, April 20 β 22, 2016
10. D.J. Lee, W. Lee, H.K. Park, J. Leem, Y.U. Nam, T.K. Kim and H. Park, βDesign characteristics of the KSTAR collective scattering system for small scale turbulence studyβ, 2016 KSTAR conference, Dageon, Korea, Jan. 24- 26, 2016