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
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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
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]
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
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
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
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
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
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
• 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
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
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
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
Dominant physical process in the initial start-up phase②Determined by energy balance
• 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
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
補助スライド
16
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
Without slowing down
18
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
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.