38
0-D Simulation of NBI Plasma Start-Up with assistance of 2.45 GHz Microwaves in Heliotron J K . Hada a , K. Nagasaki b , S. Kobayashi b , T. Stange c , K. Masuda b , S. Ohshima b , T. Mizuuchi b , Y. Nakamura a , H. Okada b , T. Minami b , S. Kado b , S. Yamamoto b , S. Konoshima b , H. Kenmochi a , Y. Ohtani a , T. Harada a , M. Kirimoto a , S. Tei a , A. Suzuki a , M. Yasueda a , X. Lu a , M. Motoshima a , N. Asavathavornvanit a , Y. Nakayama a , K. Murakami a , K. Nishikawa a , S. Kitani a , Z. Hong a ,H. Kishikawa a , F. Sano b a Graduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan b Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan c Max Plank Institute fuer Plasmaphysik, Greifswald, Germany Korea-Japan Workshop on Physics and Technology of Heating and Current Drive Daejeon, Korea, February 26-27, 2015

0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

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Page 1: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

0-D Simulation of NBI Plasma Start-Up with assistance of 2.45 GHz Microwaves in Heliotron J

K. Hadaa , K. Nagasakib, S. Kobayashib, T. Stangec, K. Masudab, S. Ohshimab, T. Mizuuchib, Y. Nakamuraa, H. Okadab, T. Minamib, S. Kadob, S. Yamamotob, S. Konoshimab, H. Kenmochia, Y. Ohtania, T. Haradaa, M. Kirimotoa, S. Teia, A. Suzukia, M. Yasuedaa, X. Lua, M. Motoshimaa, N. Asavathavornvanita, Y. Nakayamaa, K. Murakamia, K. Nishikawaa, S. Kitania, Z. Honga,H. Kishikawaa, F. Sanob

aGraduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto 611-0011, JapanbInstitute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 611-0011, JapancMax Plank Institute fuer Plasmaphysik, Greifswald, Germany

Korea-Japan Workshop on Physics and Technology of Heating and Current DriveDaejeon, Korea, February 26-27, 2015

Page 2: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Background & Objective

• In stellarator/heliotron devices, plasma is conventionally produced by the electron cyclotron resonance heating, which limits the operating magnetic field.

• Plasma start-up using neutral beam injection (NBI) has been proposed to extend the operational range of magnetic field.

• In Heliotron J device, this scheme has been successfully applied with the assistance of non-resonant 2.45 GHz microwaves [1].

• Threshold of seed plasma density has been observed.

• The main purposes of this study are to investigate the threshold density and to clarify the dominant physical processes in the initial start-up phase.

[1] S. Kobayashi et al., Nucl Fusion 51, 062002 (2011).

0 1 2 3 4 5 60.0

0.5

1.0

1.5

2.0

n e (@af

ter G

as P

uff t

= 2

30 m

s) [1

019 m

−3]

Seed electron density, ne (@before NBI t = 190 ms) [1017 m−3]

Exp (#56749-56755) 2.45 GHz 12 kW

2

Page 3: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Outline

• Background & Objective• Heliotron J device• Experimental results

Typical waveform of NBI plasma start-up using 2.45 GHz microwaves• 0-D model

Equation for fast hydrogen ion Equation for bulk ion density (hydrogen and deuterium) Energy density equation for electron and ion

• Comparison of simulate results with experiment Time evolution of plasma parameters Threshold density of seed plasma

• Dominant physical processes Comparison between unsuccessful and successful plasma start-up

• Summary

3

Page 4: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Heliotron J device

• Specifications: Plasma major radius 𝑅𝑅 = 1.2 m Plasma minor radius 𝑎𝑎 = 0.1 − 0.2 m Vacuum chamber volume 𝑉𝑉v = 2 m3

Magnetic field 𝐵𝐵 < 1.5 T Electron density 𝑛𝑛e < 1 × 1020 m−3

Electron temperature 𝑇𝑇e < 3 keV Ion temperature 𝑇𝑇i < 0.3 keV

• Heating methods and heating power ECH 70 GHz, < 0.4 MW NBI < 𝟑𝟑𝟑𝟑 𝐤𝐤𝐤𝐤, 𝟑𝟑.𝟖𝟖 𝐌𝐌𝐌𝐌 × 𝟐𝟐(Interaction length about 𝟏𝟏.𝟔𝟔𝐦𝐦) ICRF19 − 23 MHz, 0.4 MW × 2 𝟐𝟐.𝟒𝟒𝟒𝟒 𝐆𝐆𝐆𝐆𝐆𝐆Magnetron < 𝟐𝟐𝟑𝟑 𝐤𝐤𝐌𝐌

• Fueling systems• Gas Puff (D2, H2, He)

NBI (BL1)

2.45 GHz ECR/DC

ECE

Gas Puff

2 mm Interferometer

RogowskiCoils

4

Page 5: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

0

1

2

-200 -100 0 100 200 3000

5

NBI

Gas Puff2.45 GHz

I ECE

[a.u

.]n e [

1017

m−3

]

t [ms]

Typical waveform of NBI plasma start-up using 2.45 GHz microwaves assist in Heliotron J

• Non-resonant 2.45 GHz microwaves apply for the production of seed plasma before switching on the NBI.

• Heating process of non-resonant 2.45 GHz is not clear yet.

• After gas puff, electron density drastically increases and reaches approximately 2 ×1019 m−3. Stored energy reaches 2 kJ.

• OV emission is peaked at 𝑡𝑡 =225 ms. This implies that electron temperature is approximately 50 − 60 eV at this peak.

• In this scheme, we need sufficient seed electron density for ionizing the neutral beams.

0.0

0.5

1.0

150 200 250 3000.00.51.01.52.0

Gas Puff2.45 GHz

NBI#56749

W

ne

OV

ECECIII

I EC

E, C

III, O

V [a

.u.]

n e [10

19 m

−3],

W [k

J]

t [ms]

Seed Plasma

5

Page 6: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

0-D model analysis & Parameters for simulation

• 0-D model Equation for fast hydrogen ion density Equation for bulk ion density (hydrogen and deuterium) Energy density equation for electron and ion Equation for neutral atom density (hydrogen and deuterium)

Vacuum chamber volume: 𝑉𝑉v

Plasma volume: 𝑉𝑉p

Neutral volume in plasma: 𝑉𝑉n

Neutral volume: 𝛾𝛾n𝑉𝑉v = 𝑉𝑉v − (𝑉𝑉p − 𝑉𝑉n)

NBI𝑛𝑛HB, 𝑛𝑛DB, 𝑇𝑇i

Bulk ion

Bulk electron

𝑛𝑛e, 𝑇𝑇eFast ion

𝑛𝑛Hf

𝑛𝑛Hn, 𝑛𝑛DnNeutral atom

Impurity

𝑛𝑛Imp, 𝑇𝑇i

6

Page 7: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Equation for fast hydrogen ion density

• Beam energy components in Heliotron J (positive NBI)𝑃𝑃FULL 25 keV ∶ 𝑃𝑃half 12.5 keV ∶ 𝑃𝑃third 8.3 keV = 6 ∶ 3 ∶ 1• Fast hydrogen ion density 𝑗𝑗 = FULL, half, third energyd𝑛𝑛Hf𝑗𝑗

d𝑡𝑡=

𝑃𝑃𝑗𝑗𝐸𝐸Hf𝑗𝑗𝑉𝑉p

1 − exp −𝐿𝐿 �𝑘𝑘=H,D

𝑛𝑛𝑘𝑘n𝜎𝜎IB𝑗𝑗G + 𝑛𝑛𝑘𝑘B 𝜎𝜎IB𝑗𝑗P + 𝜎𝜎XB𝑗𝑗P +𝑛𝑛e 𝜎𝜎ie𝑣𝑣r𝑣𝑣Hf𝑗𝑗

− �𝑘𝑘=H,D

𝑉𝑉𝑘𝑘n𝑉𝑉p

𝑛𝑛Hf𝑗𝑗𝑛𝑛𝑗𝑗n𝜎𝜎XF𝑗𝑗G𝑣𝑣Hf𝑗𝑗 −𝑛𝑛Hf𝑗𝑗𝜏𝜏slf𝑗𝑗

−𝑛𝑛Hf𝑗𝑗𝜏𝜏pfast

Beam ionization (ioniz)①②③④

Charge exchange (CX) ⑤ Confinement lossSlowing down

Source terms Beam ionization①Hbeam + H → Hf

+ + e + H②Hbeam + H+ → Hf

+ + e + H+

③Hbeam + H+ → Hf+ + H

④Hbeam + e → Hf+ + e + e

Sink terms Charge exchange⑤Hf

+ + H → Hf + H+

Slowing down Confinement loss

7

Page 8: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Bulk ion density equation

• Bulk hydrogen ion densityd𝑛𝑛HB

d𝑡𝑡= �

𝑗𝑗=1,2,3

𝑉𝑉Hn𝑉𝑉p

𝑛𝑛Hf𝑗𝑗𝑛𝑛Hn 𝜎𝜎XF𝑗𝑗G + 𝜎𝜎IF𝑗𝑗G 𝑣𝑣Hf𝑗𝑗 + �𝑗𝑗=1,2,3

𝑛𝑛Hf𝑗𝑗𝜏𝜏slf𝑗𝑗

+𝑉𝑉Hn𝑉𝑉p

𝑛𝑛e𝑛𝑛Hn 𝜎𝜎ie𝑣𝑣e

−𝛼𝛼𝑛𝑛e𝑛𝑛HB −𝑛𝑛HB𝜏𝜏HB

• Bulk deuterium ion densityd𝑛𝑛DB

d𝑡𝑡 = �𝑗𝑗=1,2,3

𝑉𝑉Vn𝑉𝑉p

𝑛𝑛Hf𝑗𝑗𝑛𝑛Dn 𝜎𝜎XF𝑗𝑗G + 𝜎𝜎IF𝑗𝑗G 𝑣𝑣Hf𝑗𝑗 +𝑉𝑉Vn𝑉𝑉p

𝑛𝑛e𝑛𝑛Dn 𝜎𝜎ie𝑣𝑣e − 𝛼𝛼𝑛𝑛e𝑛𝑛DB −𝑛𝑛DB𝜏𝜏DB

Ioniz by electron⑦

Recombination⑧ Confinement loss

CX and Ioniz by fast ion⑤⑥ Slowing down

Sink terms Recombination⑧e + H+ → H Confinement loss

Source terms Charge exchange⑤Hf

+ + H → Hf + H+

Ionization by fast ion⑥ Hf

+ + H → Hf+ + H+ + e

Slowing down Ionization by electron⑦ e + H → e + H+ + e 8

Page 9: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Energy density equation for electron and ion

• Bulk electrond𝑈𝑈ed𝑡𝑡

= �𝑗𝑗=1,2,3

𝑛𝑛f𝑝𝑝f𝑗𝑗→e −32𝑛𝑛e𝑇𝑇e − 𝑇𝑇i𝜏𝜏ei

−𝑉𝑉n𝑉𝑉p𝑛𝑛e 𝑛𝑛Hn + 𝑛𝑛Dn �

𝑙𝑙

𝜎𝜎𝑙𝑙𝑒𝑒𝑣𝑣e∆𝐸𝐸𝑘𝑘

−∑𝑗𝑗 𝑛𝑛e𝑛𝑛𝑗𝑗𝐿𝐿𝑍𝑍𝑗𝑗 𝑇𝑇e

𝑒𝑒−𝑈𝑈e𝜏𝜏e

• Bulk iond𝑈𝑈id𝑡𝑡 = �

𝑗𝑗=1,2,3

𝑛𝑛f𝑝𝑝f𝑗𝑗→i +32𝑛𝑛e

𝑇𝑇e − 𝑇𝑇i𝜏𝜏ei

−𝑉𝑉n𝑉𝑉p

32𝑛𝑛i 𝑛𝑛Hn + 𝑛𝑛Dn 𝜎𝜎CX𝑣𝑣i 𝑇𝑇i −

𝑈𝑈i𝜏𝜏i

Energy gain from fast ion

Equipartition e→i Hydrogen and deuterium atom ionization power loss

Impurity radiation Confinement loss

Energy gain from fast ion Equipartition e→i Confinement lossCX loss

Energy density of electron: 𝑈𝑈e = 32𝑛𝑛e𝑇𝑇e

Energy density of ion: 𝑈𝑈i = 32𝑛𝑛i𝑇𝑇i

9

Page 10: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

• Without slowing down of fast ion Electron heating

𝑝𝑝f→e = 𝑚𝑚f𝑣𝑣f2

𝜏𝜏se=

𝑚𝑚f𝑣𝑣f 1+𝑚𝑚f𝑚𝑚e

𝐴𝐴D𝜓𝜓𝑣𝑣f𝑣𝑣Te

𝑣𝑣Te2

Ion heating 𝑣𝑣Ti ≪ 𝑣𝑣f𝑝𝑝f→i = 𝑚𝑚f𝑣𝑣f

2

𝜏𝜏si− 1

2𝑚𝑚f

Δ𝑣𝑣f⊥2

iΔ𝑡𝑡

≈𝑚𝑚f5/2𝐴𝐴D

23/2𝑚𝑚i𝜀𝜀f1/2

𝐴𝐴D = 𝑛𝑛e𝑒𝑒4 ln Λ2𝜋𝜋𝜀𝜀02𝑚𝑚f

2

• With slowing down of fast ion [2] Electron heating

𝑝𝑝f→e =

𝜀𝜀f0−𝜀𝜀ft𝜏𝜏s II

+ 𝜀𝜀ft𝜏𝜏s I′

1 − 𝜂𝜂 𝜀𝜀ft𝜀𝜀c

𝑇𝑇e ≤4

3 𝜋𝜋

2/3 𝑚𝑚e𝑚𝑚f𝜀𝜀f0

𝜀𝜀f0𝜏𝜏s I

1 − 𝜂𝜂 𝜀𝜀f0𝜀𝜀c

𝑇𝑇e > 43 𝜋𝜋

2/3 𝑚𝑚e𝑚𝑚f𝜀𝜀f0

Ion heating

𝑝𝑝f→i =

𝜀𝜀ft𝜏𝜏s I′

𝜂𝜂 𝜀𝜀ft𝜀𝜀c

𝑇𝑇e ≤4

3 𝜋𝜋

2/3 𝑚𝑚e𝑚𝑚f𝜀𝜀f0

𝜀𝜀f0𝜏𝜏s I

𝜂𝜂 𝜀𝜀f0𝜀𝜀c

𝑇𝑇e > 43 𝜋𝜋

2/3 𝑚𝑚e𝑚𝑚f𝜀𝜀f0

Fraction of ion heating: 𝜂𝜂 𝑥𝑥 = 1𝑥𝑥

13

ln 1− 𝑥𝑥+𝑥𝑥

1+ 𝑥𝑥2 + 2

3tan−1 2 𝑥𝑥−1

3+ 𝜋𝜋

6

Heating power for electron and ion by fast ion

0 1 2 3 4 50.0

0.5

1.0

x

𝜓𝜓 𝑥𝑥 ≈2𝑥𝑥

3 𝜋𝜋

𝜓𝜓 𝑥𝑥 ≈1

2𝑥𝑥2

𝜓𝜓 𝑥𝑥 =𝜙𝜙 𝑥𝑥 − 𝑥𝑥𝜙𝜙′ 𝑥𝑥

2𝑥𝑥2

𝜙𝜙 𝑥𝑥 =2𝜋𝜋�0

𝑥𝑥e−𝜉𝜉2d𝜉𝜉

I II

[2] J. Wesson, Tokamaks, 4th edition, OUP (2011) pp. 246-250 10

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Comparison of simulation results with experimentTime evolution of 𝑛𝑛e, 𝑊𝑊, OV, 𝑇𝑇e, and 𝑇𝑇i,

• We choose the parameters so that the time evolution of electron density and OV intensity agree with the experimental results.

• The stored energy agrees with the experimental results by a factor of 2.

• OV peak is correspond to the experiment.

• This means that the time evolution of electron temperature is reasonable around the peak.

Exp (#56836)

0.0

0.5

0.00.51.01.5

0.0

0.5

1.0

0.00.20.40.60.8

190 200 210 220 230 2400

50

100

PN

BI [

MW

],

QG

P [P

a⋅m

3 s−1]

PNBI QGP

n e [10

19 m

−3]

ne, exp ne, sim

W [k

J] Wexp Wsim

OV

[a.u

.] OVexp OVsim

T [e

V]

t [ms]

Te, sim Ti, sim

11

Page 12: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Comparison of simulation results with experimentThreshold density of seed plasma

• The 0-D model simulation results reproduce the threshold density of seed plasma and agree well with the experimental results.

0 1 2 3 4 5 60.0

0.5

1.0

1.5

2.0 Exp (#56749-56755) 2.45 GHz 12 kW Sim

n e (@af

ter G

as P

uff t

= 2

30 m

s) [1

019 m

−3]

Seed electron density, ne (@before NBI t = 190 ms) [1017 m−3]

① ②

12

Page 13: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Dominant physical process in the initial start-up phase①Determined by particle balance

• For low seed plasma case (𝑛𝑛e 𝑡𝑡 = 194 ms = 2.0 × 1017 m−3), fast hydrogen ion density remains low due to insufficient beam ionization, resulting in unsuccessful plasma start-up.

𝒏𝒏𝐞𝐞 𝒕𝒕 = 𝟏𝟏𝟏𝟏𝟒𝟒𝐦𝐦𝐦𝐦 = 𝟐𝟐.𝟑𝟑 × 𝟏𝟏𝟑𝟑𝟏𝟏𝟏𝟏 𝐦𝐦−𝟑𝟑

𝒏𝒏𝐞𝐞 𝒕𝒕 = 𝟏𝟏𝟏𝟏𝟒𝟒𝐦𝐦𝐦𝐦 = 𝟒𝟒.𝟑𝟑 × 𝟏𝟏𝟑𝟑𝟏𝟏𝟏𝟏 𝐦𝐦−𝟑𝟑

NBI NBIGas puff

Gas puff

1013

1014

1015

1016

1017

10-4

10-3

10-2

10-1

190 200 210 220 23010151016101710181019

190 200 210 220 230 240

n Hf [

m−3

]

Beam ionization

1. Hbeam+H → H+f +e+H

2. Hbeam+H → H+f +e+H+

3. Hbeam+H+ → H+f +H

Successful start-up

nσ [m

−1]

Unsuccessful start-up

4. Hbeam+e→H+f +e+e

Confinement lossSlowing down

Charge exchange

S [m

−3⋅s

−1]

t [ms] t [ms]

Particle balance

13

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Dominant physical process in the initial start-up phase②Determined by energy balance

𝒏𝒏𝐞𝐞 𝒕𝒕 = 𝟏𝟏𝟏𝟏𝟒𝟒𝐦𝐦𝐦𝐦 = 𝟑𝟑.𝟐𝟐 × 𝟏𝟏𝟑𝟑𝟏𝟏𝟏𝟏 𝐦𝐦−𝟑𝟑 𝒏𝒏𝐞𝐞 𝒕𝒕 = 𝟏𝟏𝟏𝟏𝟒𝟒𝐦𝐦𝐦𝐦 = 𝟒𝟒.𝟑𝟑 × 𝟏𝟏𝟑𝟑𝟏𝟏𝟏𝟏 𝐦𝐦−𝟑𝟑

• In this case (𝑛𝑛e 𝑡𝑡 = 194 ms = 3.2 × 1017 m−3), a certain amount of fast hydrogen ions are produced, and then electrons participate in the ionization process. However, electron heating cannot overcome a radiation barrier.

• In order for successful start-up, electron temperature needs to be high to ionize the neutral background gas.

NBI NBIGas puff

Gas puff

0

50

100

10-1

100

101

102

190 200 210 220 23010-1

100

101

102

190 200 210 220 230 240

T [e

V]

Pf→e

PCXPequ

Pirad

Pf→i

Pequ

Pe, con

PionizP [k

W]

TiTe

Pi, con

Successful start-up

P [k

W]

t [ms]

Unsuccessful start-up

t [ms]

Electron energy balance

Ion energy balance

14

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Summary & Future Issue

• Plasma start-up by NBI with assistance of 2.45 GHz microwaves has been successfully demonstrated in Heliotron J.

• We observe a threshold density of seed electron. • In order to simulate the plasma start-up by NBI, we have developed

the 0-D model. • The 0-D model reproduces the threshold in seed plasma density for

successful start-up. • Dominant physical process in the initial start-up phase

Particle balance Energy balance

• Scanning of NBI power• Compare the plasma discharge for hydrogen, deuterium, and helium

15

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補助スライド

16

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Time evolution of gas pressure (D2)

-300 -200 -100 0 100 200 300 40010-6

10-5

10-4

10-3

Pres

sure

[Pa]

t [ms]

56749 56750 56751 no build 56752 56753 no build 56754 56755

2014.11.05 Wed.2.45 GHz 12 kW

17

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Without slowing down

18

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Neutral volume

• Include neutral screening into the previous model Neutral volume

𝑉𝑉n = �𝑉𝑉p if 𝜆𝜆i > 𝑎𝑎

2𝜋𝜋2𝑅𝑅𝜆𝜆i 2𝑎𝑎 − 𝜆𝜆i if 𝜆𝜆i ≤ 𝑎𝑎

where 𝜆𝜆i is the mean free path of a neutral for ionization by electron,

𝜆𝜆i = 𝑣𝑣0𝑛𝑛e 𝜎𝜎i

e𝑣𝑣e

where 𝑣𝑣0 is the velocity of hydrogen atom.We assume that the neutral volume of deuterium is same as that of hydrogen.

Vacuum chamber volume: 𝑉𝑉vPlasma volume: 𝑉𝑉p

Neutral volume: 𝑉𝑉n

19

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Temperature and density in the neutral volume

𝑟𝑟

𝑇𝑇 𝑟𝑟 = 2𝑇𝑇 1 −𝑟𝑟𝑎𝑎

2

𝑥𝑥𝑦𝑦

𝑎𝑎

𝑇𝑇neut = 𝑇𝑇 1 −𝑦𝑦𝑎𝑎

2

𝑇𝑇 and 𝑛𝑛 are temperature and density which are calculated by 0-D model.𝑇𝑇 𝑟𝑟 and 𝑛𝑛 𝑟𝑟 are the radial profile of temperature and density assumed here. 𝑇𝑇neut and 𝑛𝑛neut are temperature and density on the neutral region.

𝑟𝑟

𝑛𝑛 𝑟𝑟 =43𝑛𝑛 1 −

𝑟𝑟𝑎𝑎

6

𝑥𝑥𝑦𝑦

𝑎𝑎

𝑛𝑛neut = 𝑛𝑛 1 −𝑦𝑦𝑎𝑎

21 +

23𝑦𝑦𝑎𝑎

2+

13𝑦𝑦𝑎𝑎

4

Vacuum chamber volume: 𝑉𝑉vPlasma volume: 𝑉𝑉p

Neutral volume: 𝑉𝑉n𝑥𝑥

𝑦𝑦 = 𝑎𝑎 − 𝑥𝑥 = 𝑎𝑎2 −𝑉𝑉n

2𝜋𝜋2𝑅𝑅

𝑦𝑦

𝑎𝑎

20

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Oxygen impurity density equations

d𝑛𝑛0d𝑡𝑡

=𝑉𝑉p

𝛾𝛾On𝑉𝑉v𝑛𝑛e𝑛𝑛1 𝑅𝑅1→0 −

𝑉𝑉On𝛾𝛾On𝑉𝑉v

𝑛𝑛e𝑛𝑛0𝑆𝑆0→1 +𝑉𝑉p

𝛾𝛾On𝑉𝑉v�𝑘𝑘=1

8𝑛𝑛𝑘𝑘𝜏𝜏𝐼𝐼

d𝑛𝑛1d𝑡𝑡

=𝑉𝑉On𝑉𝑉p

𝑛𝑛e𝑛𝑛0𝑆𝑆0→1 + 𝑛𝑛e𝑛𝑛2𝑅𝑅2→1 − 𝑛𝑛e𝑛𝑛1𝑆𝑆1→2 − 𝑛𝑛e𝑛𝑛1𝑅𝑅1→0 −𝑛𝑛1𝜏𝜏𝐼𝐼

d𝑛𝑛𝑗𝑗d𝑡𝑡

= 𝑛𝑛𝑒𝑒𝑛𝑛𝑗𝑗−1𝑆𝑆𝑗𝑗−1→𝑗𝑗 + 𝑛𝑛𝑒𝑒𝑛𝑛𝑗𝑗+1𝑅𝑅𝑗𝑗+1→𝑗𝑗 − 𝑛𝑛𝑒𝑒𝑛𝑛𝑗𝑗𝑆𝑆𝑗𝑗→𝑗𝑗+1 − 𝑛𝑛𝑒𝑒𝑛𝑛𝑗𝑗𝑅𝑅𝑗𝑗→𝑗𝑗−1 −𝑛𝑛𝑗𝑗𝜏𝜏𝐼𝐼

𝑗𝑗 = 2, 3, 4,⋯ , 7d𝑛𝑛8d𝑡𝑡 = 𝑛𝑛e𝑛𝑛7𝑆𝑆7→8 − 𝑛𝑛e𝑛𝑛8𝑅𝑅8→7 −

𝑛𝑛8𝜏𝜏𝐼𝐼

𝑗𝑗 − 1

𝑗𝑗 + 1

𝑗𝑗𝑆𝑆𝑗𝑗+1→𝑗𝑗

𝑆𝑆𝑗𝑗→𝑗𝑗−1 𝑅𝑅𝑗𝑗−1→𝑗𝑗

𝑅𝑅𝑗𝑗→𝑗𝑗+1

Confinement loss

Vacuum chamber volume: 𝑉𝑉v

Plasma volume: 𝑉𝑉p

Neutral volume: 𝑉𝑉On

𝛾𝛾On𝑉𝑉v = 𝑉𝑉v − (𝑉𝑉p − 𝑉𝑉On)21

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Time evolution of charge states of oxygen

22

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• Electron heating by fast ion

𝑝𝑝f→e = 𝑚𝑚f𝑣𝑣f2

𝜏𝜏se=

𝑚𝑚f𝑣𝑣f 1+𝑚𝑚f𝑚𝑚e

𝐴𝐴D𝜓𝜓𝑣𝑣f𝑣𝑣Te

𝑣𝑣Te2

• Ion heating by fast ion 𝑣𝑣Ti ≪ 𝑣𝑣f𝑝𝑝f→i = 𝑚𝑚f𝑣𝑣f

2

𝜏𝜏si− 1

2𝑚𝑚f

Δ𝑣𝑣f⊥2

iΔ𝑡𝑡

≈ 𝑚𝑚f5/2𝐴𝐴D

23/2𝑚𝑚i𝜀𝜀f1/2

𝐴𝐴D = 𝑛𝑛e𝑒𝑒4 ln Λ2𝜋𝜋𝜀𝜀02𝑚𝑚f

2

Neutral beam heating without slowing down of fast ions

0 1 2 3 4 50.0

0.5

1.0

x

𝜓𝜓 𝑥𝑥 ≈2𝑥𝑥

3 𝜋𝜋

𝜓𝜓 𝑥𝑥 ≈1

2𝑥𝑥2

𝜓𝜓 𝑥𝑥 =𝜙𝜙 𝑥𝑥 − 𝑥𝑥𝜙𝜙′ 𝑥𝑥

2𝑥𝑥2

𝜙𝜙 𝑥𝑥 =2𝜋𝜋�0

𝑥𝑥e−𝜉𝜉2d𝜉𝜉

I II

23

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Neutral beam heating with slowing down of fast ions [2]High temperature case

• High temperature case: 𝑇𝑇e > 43 𝜋𝜋

2/3 𝑚𝑚e𝑚𝑚f𝜀𝜀f0

𝑝𝑝f→e =𝑚𝑚f𝑣𝑣f 1+

𝑚𝑚f𝑚𝑚e

𝐴𝐴D𝜓𝜓𝑣𝑣f𝑣𝑣Te

𝑣𝑣Te2 ≈ 2 𝑚𝑚e𝑚𝑚f𝐴𝐴D𝜀𝜀f

3 2𝜋𝜋𝑇𝑇𝑒𝑒3/2

𝑝𝑝f→e + 𝑝𝑝f→i = −d𝜀𝜀fd𝑡𝑡⇒ 𝜀𝜀f 𝑡𝑡 = 𝜀𝜀f0 e

− 3𝑡𝑡𝜏𝜏se I − 𝜀𝜀c

𝜀𝜀f0

3/21 − e

− 3𝑡𝑡𝜏𝜏se I

2/3

• Slowing down time

𝜏𝜏s I =ln 1+

𝜀𝜀f0𝜀𝜀c

3/2

3𝜏𝜏se I

• Heating power by fast ion with slowing down

𝑝𝑝f→e =∫0𝜏𝜏s I 𝑝𝑝f→ed𝑡𝑡

𝜏𝜏s I= 𝜀𝜀f0

𝜏𝜏s I1 − 𝜂𝜂 𝜀𝜀f0

𝜀𝜀c

𝑝𝑝f→i =∫0𝜏𝜏s I 𝑝𝑝f→id𝑡𝑡

𝜏𝜏s I= 𝜀𝜀f0

𝜏𝜏s I𝜂𝜂 𝜀𝜀f0

𝜀𝜀c

𝜂𝜂 𝑥𝑥 = 1𝑥𝑥

13

ln 1− 𝑥𝑥+𝑥𝑥

1+ 𝑥𝑥2 + 2

3tan−1 2 𝑥𝑥−1

3+ 𝜋𝜋

6

[2] J. Wesson, Tokamaks, 4th edition, OUP (2011) pp. 246-250

𝜏𝜏se I = 3 2𝜋𝜋𝑇𝑇e3/2

𝑚𝑚e𝑚𝑚f𝐴𝐴D

𝜀𝜀c = 3 𝜋𝜋4

2/3 𝑚𝑚i𝑚𝑚e

1/3 𝑚𝑚f𝑚𝑚i𝑇𝑇e

0 1 2 3 4 50.0

0.1

0.2

0.3

0.4

0.5

x

𝜀𝜀f0

𝜀𝜀f

𝜏𝜏s I𝑡𝑡

𝜀𝜀𝑐𝑐

𝑝𝑝f→e = 𝑝𝑝f→i

24

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• Low temperature case: 𝑇𝑇e ≤4

3 𝜋𝜋

2/3 𝑚𝑚e𝑚𝑚f𝜀𝜀f0

𝑝𝑝f→e =𝑚𝑚f𝑣𝑣f 1+

𝑚𝑚f𝑚𝑚e

𝐴𝐴D𝜓𝜓𝑣𝑣f𝑣𝑣Te

𝑣𝑣Te2 ≈ 𝑚𝑚f

5/2𝐴𝐴D23/2𝑚𝑚e𝜀𝜀f

1/2

𝑝𝑝f→e + 𝑝𝑝f→i = −d𝜀𝜀fd𝑡𝑡

• Slowing down time

𝜏𝜏s II =1−

𝜀𝜀ft𝜀𝜀f0

3/2

3𝜏𝜏se II , 𝜏𝜏s I′ =

ln 1+𝜀𝜀ft𝜀𝜀c

3/2

3𝜏𝜏se I

• Heating power by fast ion with slowing down

𝑝𝑝f→e =∫0𝜏𝜏s II 𝑝𝑝f→ed𝑡𝑡

𝜏𝜏s II+

∫0𝜏𝜏s I′ 𝑝𝑝f→ed𝑡𝑡

𝜏𝜏s I′

= 𝜀𝜀f0−𝜀𝜀ft𝜏𝜏s II

+ 𝜀𝜀ft𝜏𝜏s I′

1 − 𝜂𝜂 𝜀𝜀ft𝜀𝜀c

𝑝𝑝f→i =∫0𝜏𝜏s II 𝑝𝑝f→id𝑡𝑡

𝜏𝜏s II+

∫0𝜏𝜏s I′ 𝑝𝑝f→id𝑡𝑡

𝜏𝜏s I′= 𝜀𝜀ft

𝜏𝜏s I′𝜂𝜂 𝜀𝜀ft

𝜀𝜀c

Neutral beam heating with slowing down of fast ionsLow temperature case

𝜀𝜀f 𝑡𝑡 = 𝜀𝜀f0 1 − 3𝜏𝜏se II

𝑡𝑡2/3

𝜏𝜏se II =4 2𝑚𝑚𝑒𝑒𝜀𝜀f0

3/2

𝑚𝑚f5/2𝐴𝐴D

𝜀𝜀ft = 3 𝜋𝜋4

2/3 𝑚𝑚f𝑚𝑚e𝑇𝑇e

𝜀𝜀f0 1 2 3 4 5

0.0

0.1

0.2

0.3

0.4

0.5

x

𝜀𝜀f0

𝜏𝜏s II𝑡𝑡

𝜏𝜏s I′

𝜀𝜀ft𝜀𝜀𝑐𝑐

25

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Equipartition energy loss

• Total transfer of energy from field particle to test particle is give by

𝑝𝑝equ,𝑏𝑏→𝑎𝑎 = �0

∞∆𝐸𝐸 𝑏𝑏→𝑎𝑎

∆𝑡𝑡𝑓𝑓𝑎𝑎4𝜋𝜋𝑣𝑣𝑎𝑎2d𝑣𝑣𝑎𝑎

= 𝑛𝑛𝑎𝑎𝑛𝑛𝑏𝑏e3.5𝑍𝑍𝑎𝑎2𝑍𝑍𝑏𝑏2 ln Λ

2𝜋𝜋 3/2𝜀𝜀02𝑚𝑚𝑎𝑎𝑚𝑚𝑏𝑏

𝑇𝑇𝑏𝑏 eV −𝑇𝑇𝑎𝑎 eV𝑇𝑇𝑏𝑏 eV𝑚𝑚𝑏𝑏

+𝑇𝑇𝑎𝑎 eV𝑚𝑚𝑎𝑎

3/2

• Energy loss by electron due to electron-ion collision is given by

𝑝𝑝equ,e→i ≈ 7.61 × 10−34 𝑇𝑇e eV − 𝑇𝑇i eV𝑛𝑛e lnΛ𝑇𝑇e3/2 eV

𝑍𝑍i2𝑛𝑛i𝐴𝐴i

W � m−3

𝐴𝐴i is atomic number of ion.

26

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Hydrogen atom density equation

• Hydrogen atom density in plasmad𝑛𝑛Hn

d𝑡𝑡=

𝑉𝑉p𝛾𝛾Hn𝑉𝑉v

𝛼𝛼𝑛𝑛e𝑛𝑛HB + �𝑗𝑗=1,2,3

𝛼𝛼beam𝑃𝑃𝑗𝑗𝐸𝐸HF𝑗𝑗𝛾𝛾Hn𝑉𝑉v

exp −𝐿𝐿𝑛𝑛𝜎𝜎 +𝛼𝛼plasma𝑉𝑉p𝛾𝛾Hn𝑉𝑉v

�𝑗𝑗=1,2,3

𝑛𝑛Hf𝑗𝑗𝜏𝜏Hf

+𝑛𝑛HB𝜏𝜏HB

+𝐶𝐶d 𝑛𝑛Hb − 𝑛𝑛Hv

𝛾𝛾Hn𝑉𝑉v− �

𝑗𝑗=1,2,3

𝑉𝑉n𝛾𝛾Hn𝑉𝑉v

𝑛𝑛Hf𝑗𝑗𝑛𝑛Hn𝜎𝜎IF𝑗𝑗G𝑣𝑣Hf𝑗𝑗 −𝑉𝑉n

𝛾𝛾Hn𝑉𝑉v𝑛𝑛Hn𝑛𝑛e 𝜎𝜎ie𝑣𝑣e −

𝑛𝑛Hn𝑃𝑃s𝛾𝛾Hn𝑉𝑉v

Vacuum chamber volume: 𝑉𝑉vPlasma volume: 𝑉𝑉p

Neutral volume: 𝑉𝑉Hn𝛾𝛾Hn𝑉𝑉v = 𝑉𝑉v − (𝑉𝑉p − 𝑉𝑉Hn)

Ioniz by fast ion

From plasma region

Influx from beam line Pumping

Fueling by NBI beamRecombination

Ioniz by electron

27

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Deuterium atom density equation

• Deuterium atom density in plasmad𝑛𝑛Dn

d𝑡𝑡=

𝑉𝑉p𝛾𝛾Dn𝑉𝑉v

𝛼𝛼𝑛𝑛e𝑛𝑛DB +𝛼𝛼plasma𝑉𝑉p𝛾𝛾Dn𝑉𝑉v

𝑛𝑛DB𝜏𝜏DB

+𝑄𝑄DGP𝛾𝛾Dn𝑉𝑉v

− �𝑗𝑗=1,2,3

𝑉𝑉Dn𝛾𝛾Dn𝑉𝑉v

𝑛𝑛Hf𝑗𝑗𝑛𝑛Dn 𝜎𝜎XF𝑗𝑗G + 𝜎𝜎IF𝑗𝑗G 𝑣𝑣Hf𝑗𝑗 −𝑉𝑉Dn𝛾𝛾Dn𝑉𝑉v

𝑛𝑛Dn𝑛𝑛e 𝜎𝜎ie𝑣𝑣e −𝐶𝐶d𝑛𝑛Dn𝛾𝛾Dn𝑉𝑉v

−𝑛𝑛Dn𝑃𝑃s𝛾𝛾Dn𝑉𝑉v

Vacuum chamber volume: 𝑉𝑉vPlasma volume: 𝑉𝑉p

Neutral volume: 𝑉𝑉Dn𝛾𝛾Dn𝑉𝑉v = 𝑉𝑉v − (𝑉𝑉p − 𝑉𝑉Dn)

CX and Ioniz by fast ion

From plasma region

Outflux to beam line Pumping

Gas puffRecombination

Ioniz by electron

28

Page 29: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Simulation error

10-7 10-6 10-5 10-410-4

10-3

10-2

10-1

Num

eric

al e

rror [

%]

∆t [s]

Numerical error of ne

10-7 10-6 10-5 10-410-4

10-3

10-2

10-1

Num

eric

al e

rror [

%]

∆t [s]

Numerical error of Te

10-7 10-6 10-5 10-410-4

10-3

10-2

10-1

Num

eric

al e

rror [

%]

∆t [s]

Numerical error of nHf1

29

Page 30: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Parameters used for 0-D model

• Confinement time 𝜏𝜏pfast = 100 ms,

𝜏𝜏pbulk,H = 𝜏𝜏p

bulk,D = 𝜏𝜏Imp = 15 ms, 𝜏𝜏e = 10 ms, 𝜏𝜏i = 100 ms

• Pumping speed 𝑃𝑃s = 500 m3s−1

0.0

0.5

0.00.51.01.5

0.0

0.5

1.0

0.00.20.40.60.8

190 200 210 220 230 2400

50

100P

NB

I [M

W],

QG

P [P

a⋅m

3 s−1]

PNBI QGP

n e [10

19 m

−3]

ne, exp ne, sim

W [k

J] Wexp Wsim

OV

[a.u

.] OVexp OVsim

T [e

V]

t [ms]

Te, sim Ti, sim

30

Page 31: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Parameter dependence of 𝑛𝑛e, 𝑇𝑇e, and 𝑊𝑊 on 𝜏𝜏pfast

0 50 100 150 2000.0

0.5

1.0

1.5

2.0

n e(t =

240

ms)

[1019

m−3

]

τfastp [ms]

0 50 100 150 2000.0

0.2

0.4

0.6

W(t

= 24

0 m

s) [k

J]

τfastp [ms]

0 50 100 150 2000

50

100

150

T e(t =

240

ms)

[eV]

τfastp [ms]

31

Page 32: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Parameter dependence of 𝑛𝑛e, 𝑇𝑇e, and 𝑊𝑊 on 𝜏𝜏p

0 10 20 300.0

0.5

1.0

1.5

2.0

n e(t =

240

ms)

[1019

m−3

]

τp [ms]

0 10 20 300

50

100

150

T e(t =

240

ms)

[eV]

τp [ms]

0 10 20 300.0

0.2

0.4

0.6

W(t

= 24

0 m

s) [k

J]

τp [ms] 32

Page 33: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Parameter dependence of 𝑛𝑛e, 𝑇𝑇e, and 𝑊𝑊 on 𝜏𝜏e

0 10 200.0

0.5

1.0

1.5

2.0

n e(t =

240

ms)

[1019

m−3

]

τe [ms]

0 10 200

50

100

150

T e(t =

240

ms)

[eV]

τe [ms]

0 10 200.0

0.2

0.4

0.6

W(t

= 24

0 m

s) [k

J]

τe [ms] 33

Page 34: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Parameter dependence of 𝑛𝑛e, 𝑇𝑇e, and 𝑊𝑊 on 𝑃𝑃s

0 500 10000.0

0.5

1.0

1.5

2.0

n e(t =

240

ms)

[1019

m−3

]

Ps [m3s−1]

0 500 10000

50

100

150

T e(t =

240

ms)

[eV]

Ps [m3s−1]

0 500 10000.0

0.2

0.4

0.6

W(t

= 24

0 m

s) [k

J]

Ps [m3s−1] 34

Page 35: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Parameter dependence of 𝑛𝑛e, 𝑇𝑇e, and 𝑊𝑊 on 𝑛𝑛C/𝑛𝑛e

10-2 10-1 100 1010.0

0.5

1.0

1.5

2.0

n e(t =

240

ms)

[1019

m−3

]

nC/ne [%]10-2 10-1 100 1010

50

100

150

T e(t =

240

ms)

[eV]

nC/ne [%]

10-2 10-1 100 1010.0

0.2

0.4

0.6

W(t

= 24

0 m

s) [k

J]

nC/ne [%] 35

Page 36: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Parameter dependence of 𝑛𝑛e, 𝑇𝑇e, and 𝑊𝑊 on 𝑛𝑛O/𝑛𝑛e

10-2 10-1 100 1010.0

0.5

1.0

1.5

2.0

n e(t =

240

ms)

[1019

m−3

]

nO/ne [%]10-2 10-1 100 1010

50

100

150

T e(t =

240

ms)

[eV]

nO/ne [%]

10-2 10-1 100 1010.0

0.2

0.4

0.6

W(t

= 24

0 m

s) [k

J]

nO/ne [%] 36

Page 37: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

Parameter dependence of 𝑛𝑛e, 𝑇𝑇e, and 𝑊𝑊 on 𝑛𝑛Fe/𝑛𝑛e

10-3 10-2 10-1 1000.0

0.5

1.0

1.5

2.0

n e(t =

240

ms)

[1019

m−3

]

nFe/ne [%]10-3 10-2 10-1 1000

50

100

150

T e(t =

240

ms)

[eV]

nFe/ne [%]

10-3 10-2 10-1 1000.0

0.2

0.4

0.6

W(t

= 24

0 m

s) [k

J]

nFe/ne [%] 37

Page 38: 0-D Simulation of NBI Plasma Start-Up with assistance of 2 ...psl.postech.ac.kr/kjw15/talks/Hada.pdf · 0 1 2-200 -100 0 100 200 300 0 5 NBI 2.45 GHz Gas Puff. I. ECE [a.u.] n. e

0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

Thre

shol

d de

nsity

of s

eed

elec

tron

[1017

m−3

]

PNBI [MW]

38