Investigation of ICR heating efficiency in the spherical tokamak Globus-M
V.V.Dyachenko1, F.V.Chernyshev1, V.K.Gusev1, Yu.V.Petrov1, N.V.Sakharov1,
1. A.F.Ioffe Physico-Technical Institute, RAS, 194021, St.-Petersburg, Russia
2. NFI RRC “Kurchatov Institute”, Moskow, Russia
Abstract. The ICRH experiments and numerical modeling are performed on the low aspect ratio tokamak Globus-
M (R=0.36 m, a=0.24 m, B0=0.3-0.4 T, Ip=0.15-0.25 MA, vertical elongation 1.2-2) at RF power input level up to
200 kW at frequencies 7.5 – 9.2 MHz. A 12-channel neutral particle analyzer measured simultaneously hydrogen
and deuterium fluxes and relative concentration of ion components. In spite of specific features and essential
limitations of the method applied to small aspect ratio tokamaks in the experiment the ion temperature increases
more then 2 times, but the ion heating efficiency depends on the location of the second hydrogen cyclotron
harmonic and on the concentration of the light ion component. It is shown, that position of the second hydrogen
harmonic in front of antenna decreases efficiency of on-axis ion heating approximately 20-30% probably due to
worse confinement and thermalization fast ion population, part of which is created on plasma periphery in this
case. Variation of H-concentration in a range 10–70% does not influence ion heating efficiency essentially. The
expected electron heating was not detected in the experiment, probably because the RF power absorbed by
electrons is much less than the ohmic power. Experimental results are in a good agreement with modeling by the
1.5 D transport ASTRA code and 1 D wave code and demonstrate well ability to effective plasma heating.
Ion cyclotron resonance (ICR) heating (in minority scenario) has demonstrated very
high efficiency in conventional type tokamaks. It allows consider this method of heating as one
of the candidates for the ITER project. In spherical tokamaks this scenario of plasma heating
has a number of specific features and such investigation is for the first time. The most
important point consists in simultaneous existence of several IC harmonics in the plasma crosssection,
in which RF power absorption is possible with different efficiency. The other feature
consists in the fact, that due to steep magnetic field gradient the width of resonance absorption
layers is much smaller than excited wavelength and consequently the efficiency of one-pass
absorption is not high. The same refers to efficiency of cut-off barriers. And at last, there is an
intrinsic property of the Globus-M tokamak: the amount of hydrogen in deuterium plasma can
vary in the range 10-50% in different experimental conditions. Also necessarily to note that the
shadow of the limiter in the Globus-M chamber is too shallow to place there a multi-element
RF antenna to create a well shaped wave spectrum.
All these reasons require additional investigations of possibility and efficiency ICR
heating in small aspect ratio tokamaks. For this aim the modeling of wave spectra, exited by an
antenna, wave propagation and absorption was performed by the 1D wave code , developed
in the Ioffe institute. Plasma heating was simulated by 1.5 D transport code ASTRA.
The ICRH experiments were performed on the low aspect ratio tokamak Globus-M
(R=0.36 m, a=0.24 m) at B0 = 0.4 T . Plasma currents in various shots differed from 150 kA
up to 240 kA, axial plasma density changed from 2⋅1019 m-3 to 5⋅1019 m-3 and operating
frequency changed in the range 7.5 MHz – 9.2 MHz. A single-loop antenna installed in the
equatorial chamber port was used for fast magnetosonic (FMS) wave excitation. Faraday shield
was covered by boron nitride or titanium nitride.
Because one-pass absorption is small, the character of wave propagation is like to a
resonator kind, when the whole tokamak chamber with plasma plays the role of a multimode
resonator of low quality. The typical wave spectrum calculated for the single-loop Globus
antenna is shown in Fig.1. The peaks seen in the spectrum correspond to resonator modes
excited in the chamber. It should be reminded that they were calculated in the cylindrical
geometry. They exist in the real toroidal geometry also, but their exact value should be
somewhat different. The wave absorption efficiency was examined by using the wave code
which describes the propagation of FMS waves with allowance for cyclotron absorption,
Landau damping and magnetic pumping in FLR approximation.
Calculations were performed in cylindrical geometry, which corresponded to a tokamak with
an infinite elongation, but the radial dependences of all parameters were taken as they are in
the equatorial plane of the real Globus-M tokamak.
Calculations were made for typical Globus-M parameters: Bt0 = 0.4 T, Ip = 200-250 kA,
ne (0) = 5·1019 m-3, Te0 = 600 eV, Ti0 = 300 eV, position of current axis – 2.1 cm., ellipticity –
1.6, triangularity – 4. Operating frequency was taken variable from 7.5 MHz to 9.2 MHz. Fig.2
shows position of resonance layers in the Globus cross-section for f = 9 MHz. Black ovals –
magnetic flux surfaces ψ = 0.2, 0.6, 1.0; 1 – deuterium second harmonic and hydrogen
fundamental resonance; 2 – third harmonic for deuterium; 3 – second harmonic for hydrogen
and fourth harmonic for deuterium; 4 – ion-ion hybrid resonance for 50%H+50%D. The
fundamental resonance for deuterium is just outside of the magnetic surface ψ = 1.0. Position
of the second harmonic resonance of hydrogen is sensitive to plasma parameters. Small
decrease of frequency or increase of full magnetic field can allow to the 2nd hydrogen
harmonic to disappear from the plasma.
The profiles of RF energy absorption by various plasma species calculated for the case
of single-loop antenna ( f = 7.5 MHz, the 2nd hydrogen harmonic is absent) are shown in Fig.3.
Green lines present the absorption by electrons (Landau damping and magnetic pumping
mechanism), red lines – by hydrogen (cyclotron and Bernstein wave absorption) and blue lines
– by deuterium. Fig.4 shows the distribution of total absorbed RF energy between plasma
species in dependence on hydrogen concentration CH after integration over plasma diameter.
Profiles of RF energy absorption by ions are determined by localization of resonance zones.
The energy absorption occurring on the left from ion-ion hybrid resonance position (at r≈ -10 –
-15 cm) is accounted for by Bernstein wave born in this resonance. The energy release at r ≈ 10
– 15 cm (in the third harmonic vicinity) can be associated with absorption of weak Bernstein
wave excited directly by the antenna. This absorption of Bernstein wave was introduced in the
code artificially since the third cyclotron harmonic can not be taken into account correctly in
FLR approximation. The most striking result is large FMS wave absorption around
fundamental hydrogen resonance (at r ≈ -5 cm) in cases of high hydrogen concentration The
detailed analysis showed that this absorption is connected with short wave part of the spectrum
excited by the single-loop antenna.
In the experiments the main attention was paid to the plasma temperature
measurements. The ion temperature behavior was observed by a 12-channel NPA analyzer,
which measured simultaneously hydrogen and deuterium fluxes and relative concentration of
ion components . The line of observation was perpendicular to the plasma boundary, in the
equatorial plane of the vessel. The electron temperature was evaluated by the SXR technique
and Thomson scattering diagnostics. After procedure of conditioning and wall boronization in
typical regimes of the tokamak the doubling of ion temperature was observed at RF power
input up to 150 kW (Fig.5). RF power was absorbed mainly by hydrogen as it was proved by
fast hydrogen “tails” appearance in ion energetic spectra (Fig.6). Then both ion components
reached thermal equilibrium. The characteristic time of temperature rise at the beginning of the
RF pulse and its decay after the pulse corresponded to the plasma energy confinement time for
both ion components. The experimental results indicate good energy exchange between
deuterium and hydrogen populations in a case of on-axis power absorption.
In Fig 8, 9 – Bt0 = 0.4 T, Ip = 190 – 210 kA, f = 7.5 MHz, Pinp = 120 kW. Reliable electron
heating was not observed in these experiments, probably because the RF power absorbed by
electrons (about 100 kW) is much less than the ohmic heating power. Temperature behavior
simulation during the RF heating pulse
was performed by the ASTRA 1.5D
transport code (Fig.10), when the 2nd
cyclotron hydrogen harmonic was present
at plasma periphery. RF power profiles
absorbed by ions (80 kW) and by
electrons (40kW) derived from RF code
were accepted for transport simulations.
ITER-89P L-mode scaling for the electron
and neo-classical Chang-Hinton scaling
for ion heat diffusivities were assumed.
The loop voltage was used as a fitting
parameter to the experimental data. The
satisfactory agreement between simulated
ion temperature waveform and
experimentally measured ones was
obtained at ion heat diffusivity value χi
Conclusions: 1. In spite of specific features and essential limitations ICRF method applied to
small aspect ratio tokamak demonstrates increasing of the ion temperature more then 2 times
in the Globus-M conditions.
2. The ion heating efficiency does not practically depend of concentration of light ion
component but increases slightly with rise of CH.
3. The appearance of the 2nd H-harmonic in front of the antenna decreases efficiency of ion
heating in the plasma center.
4. Experimental results are in agreement with numerical modeling by 1D wave code and 1.5D
transport code ASTRA.
This work was partly supported by the Russian Foundation for Basic Research as
1.. M.A.Irzak, E.N.Tregubova, O.N.Shcherbinin, Plasma Physics Reports, 25(8), 1999, p.659.
2. V.K.Gusev, V.V.Dyachenko, F.V.Chernyshev et al, Tech.Phys.Lett., 30(8), 2004, p.690.
3. A.B.Izvozchikov, M.P.Petrov, S.Ya.Petrov et al., Technical Physics, 37(2), 1992, p.201.
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