ST workshop 2005
O.N.Shcherbinin, F.V.Chernyshev, V.V.Dyachenko, V.K.Gusev,
Yu.V.Petrov, N.V.Sakharov
Numerical modeling and experimental
study of ICR heating in the spherical
tokamak Globus-M
A.F.Ioffe Physico-Technical Institute, St.Petersburg, Russia
1
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.
2
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 (510 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 .
3
Cyclotron Harmonics in Globus-M
wcD
2wcD,
wcH
3wcD
1.2
40
BcD
1
0.8
B, T
y, cm
20
0
BcD /2 ,BcH
0.4
-20
BcD /3
BcH /2
-40
0
-20
0
20
4
3
-20
-10
0
10
20
r, cm
x, cm
Magnetic fields in
Cyclotron harmonic positions
in Globus-M cross-section
equatorial plane of Globus-M
for 7.5 MHz at B0=0.4 T
4
Dispersion Curves for 7.5 MHz
10%H+90%D
50%H+50%D
Re(NX), Im(NX)
3000
2000
1000
0
-20
-10
0
r, cm
wii 2wCD
10
20
3wCD
-20
-10
0
r, cm
wii 2wCD
10
20
3wCD
Blue lines – FMS waves, red lines – Bernstein waves
Broken lines – imaginary part of refractive indices
5
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.
RF Energy Absorption Profiles
-20
-10
0
10
20
-20
-10
0
10
20
-20
-10
0
CH=50%
-10
0
10
20
20
80
electrons
60
40
deuterons
20
protons
0
-20
10
100
CH=30%
dP/dr, rel.un.
CH=20%
CH=10%
Energy fraction, %
dP/dr, rel.un.
CH=2%
-20
-10
0
10
20
0
10
20
30
40
50
CH , %
absorption by electrons (TTMP and Landau damping)
absorption by protons and by deuterons (cyclotron absorption and
Bernstein wave absorption)
7
Spectrum excited by a single-loop
antenna
Prad, arb.un
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.
-200
-100
0
100
Nz
8
Prad, arb.un
Spectra excited by various antennas
-200
-100
0
100
Nz
Spectrum of single-loop
antenna
-200
-100
0
100
Nz
Spectrum of a set of 4 oneloop antennas
(in 0π0π mode).
9
RF Energy Absorption Profiles
in case of 4 antennas
CH=10%
dP/dr, rel.un.
CH=2%
-20
-10
0
10
20
-20
-10
0
10
CH=20%
20
-20
-10
0
10
20
CH=50%
dP/dr, rel.un.
CH=30%
Energy fraction, %
100
80
electrons
60
40
deuterons
20
protons
0
-20
-10
0
10
20
-20
-10
0
10
20
0
10
20
30
40
50
C H, %
absorption by electrons (TTMP and Landau damping)
absorption by protons and by deuterons (cyclotron absorption and
Bernstein wave absorption)
10
Comparison of absorption profiles for different
antennas - 1
A single-loop antenna
A set of 4 antennas
dP/dr, rel.un.
CH=10%
-20
-10
0
10
20
-20
-10
0
10
20
-20
-10
0
10
20
-20
-10
0
10
20
dP/dr, rel.un.
CH=20%
r, cm
r, cm
11
Comparison of absorption profiles for different
antennas - 2
A single-loop antenna
A set of 4 antennas
dP/dr, rel.un.
CH=30%
-20
-10
0
10
20
-20
-10
0
10
20
-20
-10
0
10
20
-20
-10
0
10
20
dP/dr, rel.un.
CH=50%
r, cm
r, cm
12
Energy Spectra of Ions
with/without RF pulse
#11360-11363, t =165 ms
11
10
H
TD
183 eV
322 eV
-1
OH
ICRH
nH/(nH+nD) = 20%
10
10
cx / E
IP = 185 kA
ne(0)=3.1019 m-3
Thermalized
particles
Pinp= 120 kW
9
10
ICRH
accelerated
particles
0.5
3/2
2
(eV cm ster s)
D
f = 7.5 MHz
8
10
7
10
0
1
2
3
E (keV)
4
5
13
Evolution of Ion Temperature
with/without RF pulse
Globus-M
NPA ACORD-12
Ioffe Institute
2004.12.27 (#11360 - 11363)
400
OH
#11360,11361
ICRH #11362,11363
IP=185 kA
300
TD (eV)
ne(0)=3.1019 m-3
Pinp= 120 kW
f = 7.5 MHz
200
RF
100
130
140
150
160
t (ms)
170
180
14
Ion heating in dependence on Hconcentration
500
The 2nd H-harmonic is
absent in the plasma
volume.
TD,TH, eV
400
300
200
Bt/Bt0=1
 - TH
100
-
B0 = 0.4 T,
ne(0) ≈ 3.1019 m-3,
IP = 195 – 230 kA,
f = 7.5 MHz,
Pinp = 120 kW.
TD
0
0
20
40
60
80
CH, %
In OH-regime TD=TH=180-200 eV
15
RF energy absorption profiles for CH=20%
calculated for equatorial Globus-M parameters:
Bo = 0.4 T, Ip= 200 kA, Ne(0)= 51013cm-3.
dP/dr, rel.un.
f=9.1MHZ
f=8.5MHz
f=7.5MHz
2wCH
—H
—D
—e

wCH

-20
-10
0
r, cm
10
20
-20
-10
0
r, cm
10
20
-20
-10
0
10
20
r, cm
absorption by electrons (TTMP and Landau damping)
absorption by protons and by deuterons (cyclotron absorption and
16
Bernstein wave absorption)
Ion Temperature Behavior
in dependence on Bt
350
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
TD, eV
300
250
200
150
100
0.8
0.9
Bt/Bt0
1
TH/TD ratio in dependence on Bt
1.4
Bt0=0.4 T
Ip= 190-210 kA
CH=15%
f = 7.5 MHz
Pinp= 120 kW
In OH regime
TD=180-200 eV
a=23 cm
TH/TD
1.3
1.2
1.1
1
0.75
0.8
0.85
0.9
0.95
1
Bt / Bt0
r=17,5 cm
21 cm 23
26 cm
r – position of 2nd Hharmonic in cross-section
at given Bt/Bto
18
500
500
400
400
TD,TH, eV
TD,TH, eV
Ion heating in dependence on Hconcentration with/without
the 2nd H-harmonic
300
200
300
200
Bt/Bt0=1
 - TH
100
-
Bt=0.8Bt0
100
 - TH
-
TD
0
TD
0
0
20
40
CH, %
60
80
0
20
40
60
80
CH, %
In OH-regime TD=TH=180-200 eV
19
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.
20
Globus-M RF antenna
Outside arrangement
21
RF antenna set-up
and voltage distribution in the antenna resonator
40
0
-20
-40
-20
0
20
40
60
80
100
120
140
160
180
200
220
x, cm
6
U, kV
y, cm
20
4
2
0
0
40
80
120
160
x1, cm
22
Globus-M characteristics
Parameter
Designed Achieved
Toroidal magnetic
field
0.62 T
Plasma current
0.5 MA
Major radius
0.36 m
Minor radius
0.24 m
Aspect ratio
1.5
Vertical elongation2.2
Triangularity
0.3
Average density 11020 m-3
Pulse duration
0.2 s
Safety factor, edge4.5
Toroidal beta
25%
0.55 T
0.36 MA
0.36 m
0.24 m
1.5
2.0
0.45
0.71020 m-3
0.085 s
2
~10% OH
ICRF power
1.0 MW 0.5 MW
Frequency 8 -30 MHz 7–30 MHZ
Duration
30 mc
30 mc
NBI power
Energy
Duration
1.0 MW
30 keV
30 mc
0.7 Mw
30 keV
30 mc
23
Dispersion Curves for 9.1 MHz
10%H+90%D
50%H+50%D
3000
3000
2000
2000
1000
1000
0
0
-20
-10

wii 2wCD
10%H
0

3wCD
10
20

2wCH
wCD
-20
-10

wii
50%H

2wCD
0
10

3wCD
20

2wCH
wCD
24
Magnetic Field Distribution
In 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
25