Quadrupole Antenna and Diagnostic Complex for Ion Cyclotron Plasma Heating and Current Drive at the L-2M Stellarator

— A quadrupole antenna has been designed and produced at the L-2M stellarator for experiments on ion cyclotron plasma heating and current drive. Using a power meter of the incident and reflected waves, the first measurements of the radiation resistance of the antenna have been performed in the ohmic heating regime. The radiation resistance of the antenna has been measured as a function of the mean plasma density. It is shown that the fraction of absorbed power ensured by the coaxial modes is 25%. The created quadrupole antenna can also be used for current drive. The proposed method is based on the conversion of fast magnetosonic waves to slow magnetosonic waves with their subsequent absorption by plasma electrons, which is accompanied by current drive processes.


INTRODUCTION
One of the most common methods for auxiliary plasma heating in toroidal magnetic traps consists in RF heating in the range of ion cyclotron frequencies using fast magnetosonic (FMS) waves. This method is used in many facilities along with the methods of electron cyclotron resonance heating, heating in the lower-hybrid frequency range, and neutral injection.
Loop antennas consisting of one or more current loops are now used to excite waves in the range of ion cyclotron frequencies. These antennas create azimuthal currents inside the vacuum chamber of a toroidal magnetic trap. Quadrupole antennas consisting of four current loops have demonstrated the best results in terms of the efficiency of FMS wave excitation and heating. This is explained by the fact that such antennas are able to excite FMS waves with the necessary toroidal and poloidal wave numbers and to considerably reduce the excitation amplitude of parasitic surface waves and cylindrical modes with low longitudinal wave numbers. At the same time, the heating of the peripheral plasma layers and the scrape-off layer is considerably reduced and, hence, the intake of impurities into the plasma decreases during ion cyclotron heating.
Experiments on the ion cyclotron resonance (ICR) plasma heating using quadrupole antennas were carried out at many tokamaks, e.g., JET, ASDEX, D-IIID, KSTAR, and EAST. The most successful ICR heating experiments in which the maximum power was injected into the plasma were performed at the JET tokamak. The JET tokamak is the largest active tokamak in the world. 16-MW fusion energy has been obtained in experiments at this facility [1]. Four fourloop antennas and eight RF generators were used in the experiments on ICR plasma heating at the JET tokamak. In addition, a special system, including hybrid 3 dB separators, was used for matching individual antenna loops and a generator. This power supply system of the antenna helps to avoid sudden changes in the generator loads in case of ELM events. The maximum power absorbed in a plasma in the experiment on ICR heating of D+H plasma in the JET tokamak was 22 MW [2]. As a result, the electron temperature increased from 2.5 to 8 keV, the ion temperature of the plasma increased from 2 to 7 keV, and the plasma energy content increased from 1.5 to 6 MJ. The power radiated into the plasma, being divided by the area of the antennas in these experiments, was as high as 1 MW/m 2 . The antenna designed to work at the ITER tokamak that is under construction is currently being tested at the JET tokamak [1]. The radiated power, reduced to a unit area of this antenna, is approximately 4 MW/m 2 .
The ICR plasma heating system at the ASDEX-Upgrade tokamak consists of four 2-MW RF generators, each with a power of 2 MW, and four quadrupole antennas, each with an area of 0.8 m 2 . The maximum power absorbed in the plasma in the experiments on the D+H plasma heating reached 7.2 MW (90% of the power of RF generators), and the reduced power emitted by the antenna was 2.25 MW/m 2 [3].
The KSTAR tokamak has been in operation since 2008. It is one of the facilities with fully superconduct-

GENERAL EXPERIMENTAL TECHNIQUES
ing magnetic coils. The ion cyclotron heating system includes an antenna that consists of four current loops enclosed in the vacuum chamber of the tokamak [4]. The power emitted by one antenna loop is 1.5 MW, and the power of the entire ion cyclotron heating system is 6 MW.
The Chinese EAST Tokamak also has a fully superconducting magnetic system. The ICR heating system of the EAST tokamak has been specially designed for experiments with long high-β discharges (β is the ratio of gas kinetic pressure to the magnetic field pressure). The ICR heating system at the EAST tokamak consists of two antennas, each of which has four current loops [5]. The phase of the voltage applied to each current loop may be selected so as to optimize the spectrum of excited waves. The RF generators of the ICR heating system are capable of supplying power P ICRH = 12 MW for two antennas in a pulse with duration t = 1000 s.
The RF methods are also used for current drive in toroidal magnetic traps. The creation of stationary plasma current by the current drive is a key problem for providing uninterruptable cycle of operation of tokamak reactor. An active search for the most efficient current-drive methods is currently being conducted at existing toroidal facilities.
The greatest success in the current drive at tokamaks has been achieved to date by using waves in the lower hybrid (1-10 GHz) frequency range. This method consists in exciting a slow wave in the plasma by means of waveguide grills. This wave propagates towards the center of the plasma column, where it is absorbed by electrons in the region of the lower hybrid resonance. This current drive method is quite efficient; however, it has a fundamental limitation on the plasma density for each specific facility. There is an opacity region for waves in this frequency band at the edge of the plasma column, which prevents the penetration of a slow wave into the central plasma regions. The limitation on the plasma density for this method is determined for each facility by its magnetic field, as well as by the spectrum of waves excited by the used antenna.
The lower hybrid current drive experiments at the JT-60U tokamak were the most successful [6]. The highest current drive efficiency of 3.5 × 10 19 m -2 A/W was achieved at this tokamak, and the obtained drag current of 3.6 MA was the highest for toroidal magnetic traps. These values are record-breaking for all current drive experiments performed using any methods.
One more current drive method is now investigated at toroidal facilities; it uses waves in the electron cyclotron frequency range (20-200 GHz). The current drive process results in these experiments from electron cyclotron resonance absorption of microwaves. Such experiments were carried out at the T-10 [7] and DIII-D tokamaks [8]. Since the wave-absorption mechanism is cyclotronic, the wave energy increases the transverse (relative to the direction of the magnetic field) electron velocity. As a result, the current drive efficiency in the magnetic-field direction turns out to be low. For example, in experiments at the DIII-D tokamak, the current drive efficiency was 0.19 × 10 19 m -2 A/W when the electron temperature increased to approximately 7 keV [8]. Thus, the efficiency of the current drive by waves in the electron-cyclotron frequency range, which was obtained in the experiments at these tokamaks, turned out to be at least an order of magnitude lower than the efficiency obtained when the lowhybrid current drive methods were used.
Tokamaks are also used to study the current drive by waves in the ion-cyclotron frequency range. Experiments on the current drive using FMS waves in the range of 60-83 MHz were carried out at the DIII-D tokamak [9]. Propagation of the FMS wave in the direction of the plasma current or counter to it was achieved in the experiment by phasing three antennas. The FMS wave was absorbed by electrons due to the Landau damping mechanism. The current drive efficiency attained in this experiment was 0.54 × 10 19 m -2 A/W. It can be seen that this current drive method is noticeably inferior in terms of the efficiency to the method of lower hybrid frequency waves.
In this article, we describe a quadrupole antenna, which is intended for experiments on the ICR heating and current drive at the L-2M stellarator. A diagnostic complex designed to investigate the FMS-wave propagation and absorption in plasmas is also described, and the results of the first experiments are presented.

QUADRUPOLE ANTENNA FOR ICR PLASMA HEATING IN THE L-2M STELLARATOR
The quadrupole antenna for ICR plasma heating in the L-2M stellarator consists of four current strips located in two adjacent sections of the vacuum chamber in the stellarator. Two current strips (1, 2) located in the same cross section are shown in Fig. 1. The adjacent cross section with two identical current strips is separated from this cross section by a distance of 22.5 cm along the axis of the plasma column. The width of each current strips is 7.5 cm, and the surface area is 2.5 dm 2 . The surface of each strips facing the plasma duplicates the shape of the separatrix surface and is separated by 1 cm from it (Fig. 1). The current strips are not protected by an electrostatic shield. Each strip is powered from the generator by an individual RF feeder; therefore, depending on the phase shift of the voltage applied to the individual antenna loops, it is possible to excite FMS waves with different toroidal and azimuthal modes. Vacuum ports are based on high-voltage ceramic insulators, which allow an RF voltage of up to 15 kV to be supplied for the antenna. When such a voltage is applied to the quadrupole antenna (taking into account the total area of the antenna system S an ≈ 0.1 m 2 ), it can be expected that the radiated power P ICRH of the quadrupole antenna in experiments on the ICR heating of D+H plasma will exceed 200 kW.
In the cylindrical plasma approximation, the solution to the wave equation for the electric vector components of the FMS wave can be obtained in the following form: where m is the azimuthal wave number, k || is the longitudinal wave number, and E 0 (r) is the radial distribution of the electric-field components of the wave.
Let us consider the spectra of azimuthal and toroidal modes that this quadrupole antenna can excite in the plasma of the L-2M stellarator. These spectra were obtained by expanding the antenna current in a Fourier series in the azimuthal and toroidal modes. Figure 2 shows the simulated azimuthal-mode spectra obtained under conditions when either antiphase (0-π) or inphase (0-0) powers were supplied to the antenna loops 1 and 2 (Fig. 1). According to Fig. 2, when antiphase power was supplied to the loops, the maximum amplitude of the azimuthal modes corresponded to The studies of the excitation and propagation of FMS waves in the plasma of the L-2M stellarator were carried out previously [10]. It was established that only one azimuthal mode m = 1 was excited in the plasma under the experimental conditions of the L-2M stellarator when the plasma density was n e = (1-3) × 10 19 m -3 . Therefore, for efficient excitation of FMS waves in the plasma of the L-2M stellarator, only antiphase power supply should be used for quadrupole antenna loops located in the same cross section.
Let us consider the spectrum of toroidal modes that can be excited using the described quadrupole antenna. Figure 3 shows the simulated spectra of toroidal modes obtained under conditions when either antiphase (0-π) or in-phase (0-0) power was supplied to the antenna loops located in adjacent plasma sections. According to Fig. 3, when antiphase power was supplied to the loops located in adjacent cross sections, the maximum amplitude of the toroidal modes corresponded to k || = 14 m -1 . It was experimentally shown [10] that toroidal modes with k || = 5-15 m -1 could be excited in the operating density range of the L-2M stellarator: 1 × 10 19 ≤ n e ≤ 3 × 10 19 m -3 . Thus, the conditions for the effective excitation of FMS waves were produced when the antiphase power was supplied to the loops located in adjacent cross sections.
We also note that a single-loop antenna is also capable of exciting surface waves and coaxial modes. The longitudinal wave numbers of these waves are close to zero. Therefore, for these waves not to be excited, it is necessary that the spectrum of toroidal modes be cut in the range k || → 0. According to Fig. 3, this can be done by applying an antiphase voltage to the antenna loops located in adjacent toroidal cross sections.   Thus, the analysis of the azimuthal and toroidal mode spectra suggests that, for the efficient excitation of FMS waves in the L-2M stellarator using the quadrupole antenna, it is necessary that antiphase power be supplied for every two adjacent loops (in both toroidal and azimuthal directions). The directions of currents in the quadrupole antenna loops with the power supply optimal for the excitation of FMS waves are schematically shown in Fig. 4.

DIAGNOSTIC COMPLEX OF THE SYSTEM FOR ICR PLASMA HEATING AND CURRENT DRIVE
The diagnostic complex of the ICR plasma heating system in the L-2M stellarator includes a power (amplitude) meter of the incident and reflected waves in an RF feeder and a system of magnetic probes.
The amplitude meter of the incident and reflected waves is a part of a high-frequency feeder, inside which there are two conductors forming two additional distributed lines (Fig. 5). The output signals from the additional lines are proportional to the amplitudes of the incident U in and reflected U ref waves. The ratio of the incident (reflected) wave amplitude in the additional line to the amplitude of the incident (reflected) wave in the main RF feeder U in (U ref ) is [11] where r 0 and R 0 are the radii of the central conductor and the feeder sheath, respectively; r is the distance from the center of the feeder to the additional conductor; k is the wave number of the wave propagating in the feeder; and l is the length of the additional line.
In the used amplitude meter of the incident and reflected waves, this ratio was /U in = /U ref = 1.1 × 10 -2 . Calibration of the amplitude meter of the incident and reflected waves showed that the measurement error of this device was 10%.
This device allows measuring the RF power absorbed in the plasma as well as the radiation resistance of the antenna and the antenna current. The RF power P ab absorbed in the load can be determined from the measured amplitudes of the incident and reflected waves: P ab = /(2ρ) -/(2ρ), where ρ is the wave impedance of the feeder. By measuring the absorbed power with and the without plasma, it is possible to determine the RF power absorbed in the plasma P pl from the difference in the signals.
The RF current in the antenna I an can also be determined from the measured amplitudes of the incident and reflected waves: I an = U an /ρ an , where U an = U in + U ref (in this case, the wave impedance of the load is greater than the wave impedance of the feeder), and ρ an = L an ω is the wave impedance of the antenna.
If the RF power absorbed in the plasma and the antenna current are known, it is possible to determine the radiation resistance of the antenna using the following ratio: No. 5 2022 In the absence of the plasma, R load = 0. The radiation resistance of the antenna depends both on the antenna design and on the heating method used, i.e., on the type of excited waves and the plasma parameters affecting the propagation and damping of these waves. By investigating the radiation resistance of the antenna as a function of the plasma parameters, it is possible to determine the optimal plasma-heating conditions for the heating method in use.
A system of magnetic probes is the second element of the diagnostic complex for the ICR-heating system. Five magnetic probes are placed in five ports outside the vacuum chamber of the stellarator from its inner side (Fig. 6). Each magnetic probe is a 12-loop coil with a diameter of 6 mm. The probes are enclosed in containers with a ceramic cap that separates the probe from the vacuum volume of the chamber. This allows changing the probe polarization without the vacuum deterioration in the chamber. The probes measure the magnetic-field component of the FMS wave in the direction of its propagation (B z component) and in the perpendicular direction (B ϕ component).
The magnetic-probe signal is shaped as a sinusoid with the frequency equal to the generator frequency. The phase and amplitude relations of the signals from the probes located in different chamber sections make it possible to determine the phase velocity and attenuation length of the FMS wave, respectively. The probe signals are recorded using the ADC, which is a 32-channel fast data-acquisition system with a buffer storage capacity of 2 GB (manufactured by the Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk). Signal digitization can be performed at frequencies of ν 0 = 50, 25, and 12.5 Msps. The amplitude resolution is 12 bit. From the phase shift Δϕ of the signals from two probes separated by distance Δl, one can determine the phase velocity of wave propagation along the torus V ϕ and the longitudinal wave number k || = ω/V ϕ . This diagnostic complex is intended for measuring the phase velocities and spectral compositions of excited FMS waves as well as for determining the conditions under which the heating and current drive effects are maximal.

FIRST EXPERIMENTS USING THE QUADRUPOLE ANTENNA
The first experiments were carried out at the L-2M stellarator on testing the described quadrupole antenna in the ohmic heating regime. Figure 7 shows time evolution of the main plasma parameters in this experiment: the ohmic heating current I p (t), the chord-average electron density of the plasma n e (t), the intensity of radiation losses P rad (t), the radiation resistance of the antenna R load (t), and the RF voltage sup- The radiation resistance of the antenna was determined using the amplitude meter of the incident and reflected waves according to the method described above. The RF-generator power in this experiment did not exceed 1 kW. It was fed to one of the four loops of the quadrupole antenna using the feeder. The RFgenerator pulse ended at the 60th ms. Figure 7 allows tracing the dynamics of the radiation resistance of the antenna during a plasma pulse. In the initial stage (30-36 ms), the plasma is heated, and the radiation resistance of the antenna increases rapidly. Coaxial modes and FMS waves contribute to it. After a kink the R load (t) curve (after 36 ms), the plasma temperature reaches its stationary value, and a further slow increase in the radiation resistance of the antenna is associated with the further increase in the plasma density.
Using the data of Fig. 7, it is possible to construct the dependence of the radiation resistance of the antenna on the plasma density, which confirms the above statements about the wave types that contribute to the radiation resistance of the antenna. This dependence is shown in Fig. 8. It can be seen that the radiation resistance of the antenna remains approximately constant (~0.2 Ω) when the density increases from 0.2 × 10 19 to 0.9 × 10 19 m -3 in the initial stage of plasma formation and heating. This level of the antenna radiation resistance corresponds to the contribution of coaxial modes. The coaxial modes exist in the scrape-off layer, i.e., in the region between the wall of the vacuum chamber and the separatrix, where the Antenna plasma density in the L-2M stellarator is 2 × 10 15 m -3 and does not depend on the plasma density inside the plasma column [12]. In the next stage of the ohmic discharge (at a density exceeding 0.9 × 10 19 m -3 ), the plasma heating begins, and conditions appear for the absorption of FMS waves excited by the antenna. This causes a rapid increase in the radiation resistance of the antenna to approximately 0.65 Ω (Fig. 8). After the plasma temperature reaches a stationary value, the radiation resistance of the antenna increases almost linearly to approximately 0.8 Ω due to an increase in the density. Such a linear dependence of the radiation resistance of the antenna on the density was observed in the previous experiments on the ICR heating at the L-2M stellarator [13]. As can be seen, the fraction of "parasitic" coaxial modes excited by the antenna is approximately 25%. Thus, the test measurements of the antenna resistance with a low power showed that the maximum radiation resistance of the antenna that was produced and mounted on the L-2M stellarator was approximately 0.8 Ω. This level of the radiation resistance of the antenna allows expecting that, when an operating voltage of ~12 kV is applied to it and all four antenna loops are used, the power absorbed in the plasma will be 250 kW. In this case, the excitation of the coaxial modes by a quadrupole antenna will be considerably weaker as compared to the single-loop antenna used in this test experiment.

APPLICABILITY OF THE QUADRUPOLE ANTENNA FOR CURRENT DRIVE IN THE L-2M STELLARATOR
The quadrupole antenna created at the L-2M stellarator can also be used for current drive. The proposed method is based on the conversion of FMS waves into slow magnetosonic (SMS) waves with their subsequent absorption by plasma electrons, which is followed by the current drive processes.
Experiments on the ion cyclotron heating of deuterium plasma with the addition of hydrogen by the FMS wave created by the loop antenna were carried out at the L-2M stellarator [14]. These experiments have shown that the FMS wave propagating in one toroidal direction is excited in deuterium plasma with hydrogen addition in the operating range of the L-2M stellarator parameters. Next, the FMS wave is linearly transformed into the SMS wave with the preservation  of the longitudinal wave number. The SMS wave subsequently slows down in the ion−ion hybrid resonance region. Its phase velocity decreases, resulting in its possible absorption by electrons due to the Landau damping mechanism. The Landau mechanism of SMS wave damping by electrons ensures current drive due to the momentum transfer from the wave to the electrons in the direction of wave propagation. Thus, it is possible to create the current drive conditions in deuterium plasma with the addition of hydrogen in the L-2M stellarator using waves in the ion cyclotron frequency range. The use of the quadrupole antenna in these experiments is preferable since it allows exciting more efficiently the FMS wave in the plasma. It is expected that the efficiency of the proposed current drive method will be of the same order as the efficiency of the method for the current drive by waves of the lower hybrid frequency range. A distinctive feature of the stellarator is its operability in the current-free regime (the regime of electron cyclotron resonance plasma heating). It will be possible to measure low drag currents (~100 A) in the current-free regime of the L-2M stellarator using the Rogowski loop. Conducting such experiments at the L-2M stellarator will make it possible to study in detail this new current drive method.

CONCLUSIONS
The quadrupole antenna has been created for future experiments on ion cyclotron plasma heating and current drive at the L-2M stellarator. The spectra of azimuthal and toroidal modes that this quadrupole antenna can excite in the plasma of the L-2M stellarator have been simulated. By analyzing the spectra of the azimuthal and toroidal modes, it has been shown that the antiphase power must be supplied to every two adjacent loops (both in the toroidal and azimuthal directions) to attain efficient excitation of FMS waves by the quadrupole antenna in the L-2M stellarator.
The diagnostic complex has been created; it consists of the power (amplitude) meter of the incident and reflected waves and the system of magnetic probes. The amplitude meter allows studying the radiation resistance of the antenna as a function of the plasma parameters and to optimize the conditions for the plasma heating and current drive. The system of magnetic probes is intended to measure the phase velocities as well as the toroidal and azimuthal wave numbers of excited FMS waves.
The first test experiments were carried out with the antenna in the ohmic heating regime. The dependence of the antenna's radiation resistance on the mean plasma density in one selected pulse has been obtained. Based on this dependence, the fraction of the antenna's radiation resistance attributable to the coaxial modes (25%) has been determined. The measured radiation resistance of the antenna allows expecting that a power of up to 250 kW can be introduced into the plasma using the quadrupole antenna. At the same time, the excitation of coaxial modes by this antenna will be considerably weaker compared to the single-loop antenna used in this test experiment.