1
ST workshop 2005
Numerical modeling and experimental study of ICR heating in the spherical
tokamak Globus-M
O.N.Shcherbinin, F.V.Chernyshev, V.V.Dyachenko, V.K.Gusev, Yu.V.Petrov, N.V.Sakharov
A.F.Ioffe Physico-Technical Institute, St.Petersburg, Russia
2
Outline
1. Specific features of ICRH experiments on spherical tokamaks.
2. Model for numerical simulation.
3. Effect of light ion content in plasma on RF heating efficiency (simulation and experiment).
4. Effect of the second hydrogen harmonic position on ion heating.
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Specific features of ICR heating at small plasma aspect ratio
• Due to strong variation of toroidal magnetic field along major radius, several ion cyclotron harmonics exist simultaneously in plasma cross- section.
• For typical conditions of spherical tokamaks (low Bt and high ne) it is necessary to use low frequency RF power (5-10 МHZ). So the wavelength is much larger than plasma dimensions and width of resonance and cut-off zones.
• Tokamak Globus-M operates with high hydrogen concentration (10-50)% in deuterium plasma.
• The shadow of the limiter in Globus-M is too shallow to place there a multi-element antenna to excite a well shaped wave spectra .
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Cyclotron Harmonics in Globus-M
Magnetic fields in equatorial plane of Globus-M
-20 0 20x, cm
-40
-20
0
20
40
y, c
m
-20 -10 0 10 20r, cm
0
0.4
0.8
1.2
B,
T
1
3 4
B cD
B cD /2 ,B cH
B cD /3
B cH /2
cD cD,
cH
cD
Cyclotron harmonic positions in Globus-M cross-section
for 7.5 MHz at B0=0.4 T
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Dispersion Curves for 7.5 MHz
Blue lines – FMS waves, red lines – Bernstein waves
Broken lines – imaginary part of refractive indices
-20 -10 0 10 20r, cm
0
1000
2000
3000
Re(
NX),
Im(N
X)
50% H+50% D
-20 -10 0 10 20r, cm
10% H +90% D
C D C DC DC Dii
ii
Model accepted for numerical simulation
Plasma is confined between two cylindrical surfaces.
All plasma parameters change in radial direction only. They follow the
behavior of plasma parameters in the equatorial plane of the real
Globus-M tokamak.
Cyclotron absorption, magnetic pumping and Landau damping are included in the code. The effects related to poloidal inhomogeneity
are absent in the calculations.
Spectra of excited waves are calculated using 3-D antenna model.
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RF Energy Absorption Profiles
absorption by electrons (TTMP and Landau damping)absorption by protons and by deuterons (cyclotron absorption and
Bernstein wave absorption)
-20 -10 0 10 20
dP
/dr,
rel
.un
. C H=2%
-20 -10 0 10 20
dP
/dr,
rel
.un
. C H=30%
-20 -10 0 10 20
C H=10%
-20 -10 0 10 20
C H=20%
-20 -10 0 10 20
C H=50%
0 10 20 30 40 50C H , %
0
20
40
60
80
100
En
erg
y fr
acti
on
, %
pro tons
deu te rons
electrons
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Spectrum excited by a single-loop antenna
-200 -100 0 100N z
Pra
d, a
rb.u
n
The peaks correspond to resonator modes excited in
the chamber (calculated in the cylindrical geometry).
The broken line shows the idealized spectrum if all
excited waves are completely absorbed in the plasma
without any reflection from
inner plasma layers.
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Spectra excited by various antennas
-200 -100 0 100N z
Pra
d,
arb.
un
-200 -100 0 100N z
Spectrum of single-loop antenna
Spectrum of a set of 4 one-loop antennas
(in 0π0π mode).
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RF Energy Absorption Profilesin case of 4 antennas
absorption by electrons (TTMP and Landau damping)absorption by protons and by deuterons (cyclotron absorption and
Bernstein wave absorption)
-20 -10 0 10 20
-20 -10 0 10 20
-20 -10 0 10 20
0 10 20 30 40 50 CH, %
0
20
40
60
80
100
En
erg
y fr
acti
on
, %
-20 -10 0 10 20
dP
/dr,
rel
.un
.
-20 -10 0 10 20
dP
/dr,
rel
.un
.
C H=50%C H=30%electrons
pro tons
C H=20%C H=10%C H=2%
deute rons
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Comparison of absorption profiles for different antennas - 1
-20 -10 0 10 20
-20 -10 0 10 20r, cm
-20 -10 0 10 20r, cm
dP/d
r, r
el.u
n.
-20 -10 0 10 20
dP/d
r, r
el.u
n.
C H=20%
C H=10%
A single-loop antenna A set of 4 antennas
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Comparison of absorption profiles for different antennas - 2
-20 -10 0 10 20r, cm
-20 -10 0 10 20
C H=50%
C H=30%
-20 -10 0 10 20
dP
/dr,
re
l.un.
-20 -10 0 10 20r, cm
dP
/dr,
re
l.un.
A single-loop antenna A set of 4 antennas
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Energy Spectra of Ionswith/without RF pulse
IP = 185 kA
ne(0)=3.1019 m-3
Pinp= 120 kW
f = 7.5 MHz
0 1 2 3 4 5107
108
109
1010
1011
nH/(n
H+n
D) = 20%
ICRHaccelerated
particles
Thermalizedparticles
H D TD
OH 183 eV ICRH 322 eV
cx /
E0.5 (
eV
3/2c
m2 s
ter
s)-1
E (keV)
#11360-11363, t =165 ms
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Evolution of Ion Temperaturewith/without RF pulse
IP=185 kA
ne(0)=3.1019 m-3
Pinp= 120 kW
f = 7.5 MHz
130 140 150 160 170 180100
200
300
400 OH #11360,11361 ICRH #11362,11363
NPA ACORD-12Ioffe Institute
Globus-M2004.12.27 (#11360 - 11363)
TD (
eV
)
t (ms)
RF
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Ion heating in dependence on H-concentration
Bt/Bt0=1
In OH-regime TD=TH=180-200 eV
0 20 40 60 80
C H , %
0
100
200
300
400
500
TD
,TH,
eV
- T H
- T D
The 2nd H-harmonic is absent in the plasma
volume.
B0 = 0.4 T, ne(0) ≈ 3.1019 m-3, IP = 195 – 230 kA, f
= 7.5 MHz, Pinp = 120 kW.
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RF energy absorption profiles for CH=20% calculated for equatorial Globus-M parameters:
Bo = 0.4 T, Ip= 200 kA, Ne(0)= 51013cm-3.
absorption by electrons (TTMP and Landau damping)absorption by protons and by deuterons (cyclotron absorption and
Bernstein wave absorption)
-20 -10 0 10 20r, cm
dP
/dr,
rel
.un
.
f=7.5M H z
-20 -10 0 10 20r, cm
f=8.5M H z
-20 -10 0 10 20r, cm
f=9.1M H Z
C H
C H
— H — D— e
Ion Temperature Behaviorin dependence on Bt
Bt0=0.4 T
Ip= 190-210 kA
CH=15%, 30%
f = 7.5 MHz
Pinp= 120 kW
In OH regime
TD=180-200 eV
0.8 0.9 1Bt/Bt0
100
150
200
250
300
350
TD
, eV
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TH/TD ratio in dependence on Bt
0.75 0.8 0.85 0.9 0.95 1Bt / Bt0
1
1.1
1.2
1.3
1.4
TH
/TD
Bt0=0.4 T
Ip= 190-210 kA
CH=15%
f = 7.5 MHzPinp= 120 kW
In OH regimeTD=180-200 eV
a=23 cmr – position of 2nd H-
harmonic in cross-section at given Bt/Bto
26 cm21 cmr=17,5 cm 23
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Ion heating in dependence on H-concentration with/without
the 2nd H-harmonic
Bt/Bt0=1 Bt=0.8Bt0
In OH-regime TD=TH=180-200 eV
0 20 40 60 80
C H , %
0
100
200
300
400
500
TD
,TH,
eV
- T H
- T D
0 20 40 60 80
C H , %
0
100
200
300
400
500
TD
,TH, e
V - T H
- T D
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Conclusions The ICRF heating experiments were carried out on the
Globus-M spherical tokamak where conditions for several cyclotron harmonics were fulfilled simultaneously.
The experiments with hydrogen-deuterium plasma have shown that the ion heating efficiency does not practically depend of concentration of light ion component but increases slightly with rise of CH from 10% to 70% .
It is shown that presence of 2nd H-harmonic in front of the antenna diminishes efficiency of on-axis ion heating.
Experimental results are in agreement with numerical modeling by 1-D wave code.
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Globus-M RF antennaOutside arrangement
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RF antenna set-upand voltage distribution in the antenna resonator
-2 0 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0x , c m
-4 0
-2 0
0
2 0
4 0
y, c
m
0 4 0 8 0 1 2 0 1 6 0x 1 , c m
0
2
4
6
U, k
V
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Globus-M characteristics
Parameter Designed Achieved
Toroidal magneticfield 0.62 T 0.55 TPlasma current 0.5 MA 0.36 MAMajor radius 0.36 m 0.36 mMinor radius 0.24 m 0.24 mAspect ratio 1.5 1.5Vertical elongation2.2 2.0Triangularity 0.3 0.45Average density 11020 m-3 0.71020 m-
3
Pulse duration 0.2 s 0.085 sSafety factor, edge4.5 2Toroidal beta 25% ~10% OH
ICRF power 1.0 MW 0.5 MW Frequency 8 -30 MHz 7–30 MHZ Duration 30 mc 30 mc
NBI power 1.0 MW 0.7 Mw Energy 30 keV 30 keV Duration 30 mc 30 mc
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Dispersion Curves for 9.1 MHz
-20 -10 0 10 20
0
1000
2000
3000
10% H +90% D
-20 -10 0 10 20
0
1000
2000
3000
50% H +50% D
C D C D C H
C D
i i5 0 % H
C H
C D
C DC Di i
1 0 % H
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Magnetic Field DistributionIn equatorial plane of the Globus-M chamber
R0 = 36 cm, a0 = 23 cm
B0 = 0.4 T, Ip= 250 kA, f=9 MHz
blue line – toroidal vacuum field
green line – poloidal field
violet line – paramagnetic field
red line – full magnetic field
dashed red line – full magnetic
field without paramagnetic
component