Development of an arch antenna for LHCD in a spherical tokamak

A lower-hybrid frequency surface wave antenna called arch is designed and fabricated in this paper for the spherical tokamak named EXL-50. It is used to drive plasma current and heat plasma at 2.45 GHz. The arch antenna consists of 27 antenna elements. The left and right rectangular waveguides integrated with the antenna are used for microwave input and output, respectively. The refraction parallel index of this proposed antenna is 4.3 , which is favorable for the lower hybrid current drive. The measurement results in the absence of plasma show that the reflection and transmission coefficients ( S11 and S21 ) are −12.5dB and −12.6dB , respectively. The antenna was installed and tested on EXL-50. Up to a 35 kA plasma current was achieved using the arch antenna with a microwave of 70 kW .


Introduction
Spherical tokamaks (STs), such as Globus-M and M2, NSTX-U, TST-2, etc, have grown rapidly worldwide since the 1990s to advance the goal of obtaining economic power from nuclear fusion [1][2][3][4][5]. These STs usually work at a low aspect ratio and look like a cored apple instead of a ring doughnut [6]. Recently, EXL-50, an ST, was developed in the Hebei Key Laboratory of Compact Fusion, China. It will help researchers understand a wide range of phenomena, including the confinement, plasma current drive, etc [7]. * Author to whom any correspondence should be addressed.
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Lower hybrid current drive (LHCD) has been proven to be an efficient tool to heat plasma in many experiments with traditional large tokamaks such as EAST [8]. The antenna is one of the most important parts of the lower hybrid wave (LHW) system. The plasma current drive efficiency will decrease if the parallel refractive index (n ∥ ) does not satisfy the accessibility criterion or the power coupling efficiency becomes lower [9].
In recent decades, multiple LHCD antennas have been developed for conventional large tokamaks. The first LHW excitation launcher, the conventional 'grill', has been installed and tested on PLT, Alcator C-Mod, etc [10][11][12]. The launcher structure is generally complex, and its phase can be changed in real time. To simplify the grill architecture, multi-junction grills (MJs) have been designed and used on JET, EAST, Tore Supra, etc [13][14][15][16]. The phase shifters are used to obtain the proper n ∥ spectrum to be coupled [13]. Nevertheless, one of the primary challenges with utilizing the grill and MJ is the limited coupling power when the density close to the launcher mouth becomes lower than the cut-off density [9]. Two methods are currently proposed for obtaining good coupling. One method relies on the passive active multi-junction (PAM) [17]. The advantages include simple, robust, efficient heat removal channel and low reflectivity even in close proximity to the cut-off density. The reported effective plasma-antenna distance is about 0.1−0.15 m [9]. It has been installed on FTU [18], Tore Supra [19,20]. Another depends on local gas injection to increase the electron density around the antenna, which is coupled over a gap of ∼ 0.11 m and often used in JET [9,21].
However, in EXL-50, the distance between the antenna and the plasma is around 0.4−0.6 m. Therefore, it would encounter power coupling difficulties if these conventional LHCD antennas were used, including grill, MJ, and PAM. Furthermore, using the corresponding parameters of EXL-50, the n ∥ spectrum should be designed higher than 4.1. Most large tokamak antennas are usually working with n ∥ spectrums ranging from 1.0 to 3.0 [22][23][24]. Hence, the conventional antennas are not proper for EXL-50 considering the accessibility criterion, cutoff plasma density, the antenna dimension, and many others [25] at the same time.
Antennas used in the LHW frequency for STs comprise finline in Japan [26] and grill in Russia [1]. The finline antenna manipulated at 2.45 GHz with n ∥ fixed at 2.59 has been tested on TST-2. Previous research pointed out that the expected plasma current using the present finline was less than 1 kA and the antenna parameters may be improved [26]. So, it cannot be considered for EXL-50. In Russia, Dyachenko et al applied a 'grill' antenna that aims to damp RF waves in the poloidal direction rather than the traditional toroidal direction [1,3,25]. But, at present, the method is a misfit for EXL-50 because of different ST parameters and coupling problems. Therefore, antennas driven at lower hybrid frequency (2.45 GHz) used in EXL-50 are urgently needed.
For this purpose, this paper will focus on discussing an outboard antenna called arch applied to EXL-50. This paper will concentrate on the exhibition of the arch antenna and is organized as described below. First, an overview of the proposed arch antenna is presented. Then, the general characteristics of n ∥ and energy transmission of the antenna are revealed. Finally, the antenna was tested on EXL-50, and its current drive efficiency is given.

Antenna description
The overall structure of the proposed arch antenna working at 2.45 GHz is shown in figure 1. Figure 1(a) presents the vertical view of EXL-50 with the arch antenna. The antenna is used as the outer mid-plane launcher for EXL-50. The semidiameter of the limiter is approximately 0.6 m and denoted as the blue dashed line. The distance between the plasma and the outboard is in the range of 0.4−0.6 m, which is measured by the magnetic probe.
The antenna is designed to meet the demands of feeding simply, as shown in figure 1(b). The two waveguides on either side serve as input and output ports. The light orange canopy on either side is used as a mode converter, which can also protect the arch during experiments. The plate at the bottom is used as the basic transmission configuration. A row of small waveguides called elements is arranged on the plate. The elements are used for wave excitation and generating a wave with a velocity slower than the light speed. The antenna is based on the principle of surface waves. The antenna is designed with an angle of θ to be as close as possible to the plasma and couple more energy into the plasma during experiments. This design is used because the electric field intensity will be attenuated in the radial direction. Figure 1(c) illustrates the top view of the arch.

Parallel refractive index
Theoretically, the LHW can heat plasma only if the wave satisfies the accessibility criterion [9] where ω, ω pe , ω pi , and ω ce are the applied source frequency, electron plasma frequency, icon plasma frequency and electron cyclotron frequency, respectively. In EXL-50, the electron density (n e ) was measured via the interferometer, and the line-averaged electron density is 4 × 10 18 m −3 . The relationship between the n e and n ∥ in the calculation is shown in figure 2.
Obviously, the n ∥ accessibility criterion is approximately 4.1 after analysis with the parameters of EXL-50 (B = 0.156 T, n e ≈ 4 × 10 18 m −3 ). Thus, the n ∥ requirement of EXL-50 should be greater than 4.1 according to its parameters. The n ∥ was chosen to be 4.3 with considering the manufacturing technology and required wavelength for LHW excitation simultaneously.
The surface wave antenna can support the TEM mode, and its field intensity is transmitted with e −jky in the toroidal direction, as shown in figure 3. The parameters comprise of gap between elements (g), groove depth (d), fin thickness (t) and steps (s).
There are many elements and grooves in a wavelength. The function of guide wave can be enhanced by grooves and elements. In theory, the corrugation period (a = g + t) should be adequately enough shorter than the wavelength [26,27]: where λ 0 is the wavelength in free space. The grooves between the elements can support the TEM mode wave, which forms a standing wave up and down in the grooves. The grooves can be seen as net reactance for incident waves in vacuum [28]: where d is the depth of grooves, Z 0 is the intrinsic impedance of the air: the input impedance is: The grooves may store energy if the antenna is excited with microwave [22]: Therefore, the propagation constant diverges when d = λ 0 /4. If the groove is deeper than λ 0 /4, it is expected that the higher order mode is formed inside the groove [26][27][28].
The constrained condition is calculated using equation (7) to obtain inductive reactance [27,28]: Thus, the impedance of the corrugated surface is [28]: where k 0 the propagation constant in vacuum. It is assumed that the equation (9) is applicable to the groove surface, the impedance of the element surface is zero, the inclination angle θ is zero, and considering the element thickness (t), the surface wave propagation constant is approximately expressed as [28]: Accordingly, to design the n ∥ of the proposed arch antenna, the calculation results between parameters (t, g, d) and n ∥ are exhibited in figure 4.
The effects of the gap (g), groove depth (d), and element thickness (t) on n ∥ are shown in figure 4. Based on these results, n ∥ increases with d and decreases with t and g. In addition, the parameters should also be considered to determine their effects on microwave transmission theory, S11, S21, and electric field intensity simultaneously. These effects will be analyzed in the next section.

The S parameters
Two points should be introduced first to distinguish the LHW and the radiation microwave power (P). LHWs are also known as slow waves and generally launched by LHW antennas [9]. In the GHz range of frequencies, exciting slow waves into a tokamak plasma aims to damp RF waves at high parallel phase velocities relative to the electron thermal speed in the purpose to drive plasma current. The radiation microwave power (P) is one of the antenna basic characteristics [27] and usually calculated through microwave engineering theory [27,29]. For the surface wave antenna, only part of P can be excited into LHW [26].
Based on the microwave transmission line theory [29], the normalized radiation microwave power in figure 5 is expressed as: where S11 and S21 is the reflection and transmission coefficient, respectively. To better understand the simulation results, a roughly simplified model of the presented arch antenna is introduced below. The microwave was transmitted from the power source to the antenna using a waveguide. The maximum electric field strength is emitted from the top of the arch when the antenna is resonated [29]: where f, L and C are resonant frequency, inductance and capacitance of the launcher, respectively, and they are determined by the impedance parameters in figure 5. Moreover, considering the periodic structure on a mental plate surface, the energy in the input and output ports are affected by the t, g, and d simultaneously [26,30,31]. However, it is difficult to analyze this antenna with rigorous mathematical formula, and the FDTD methods or simulations are often used in literatures [28]. Hence, in vacuum, the dependence of the S parameters on (t, g, and d) geometry is presented below.
In particular, the results presented in figure 6 were simulated in vacuum. The parameters should be regulated to minimize S11 and S21 while keeping n ∥ close to 4.3.
Therefore, the mentioned corrugation period, element height and space affect antenna performance simultaneously. First, if the thickness t increases, the values of the inductor L n may increase, the phenomenon of frequency drift is obvious, which would decrease the working frequency of the arch antenna. Second, g also has a much greater effect on the center frequency than S11. If g increases from 4.3to 4.7 mm, the value of the capacitor C n,n−1 may decrease, the center frequency shifts from 2.438 GHz to 2.456 GHz. Third, the depth d may be correlated with C n,n−1 , L n , and R n synchronously, which is distinguished from the other parameters, and it exhibits great effect both on the value of S parameters and the frequency. These results provide regulation guidance for experiments.

Antenna dimension and performance
Based on the theory and simulation described above, the parameters of the arch antenna are shown in table 1. The final parameter dimension for processing were simulated in vacuum using the finite element codes (high frequency structure simulator). The arch antenna characteristics launched in vacuum are shown below, including electric field intensity, S11, and S12.

The electric field intensity
The arch antenna designed in curve is to be much closer to the plasma during launch experiments. The distribution of the electric field intensity at 2.45 GHz in vacuum is presented in figure 7. It can be observed that the electric field on the middle position of the antenna is the strongest.

S11 and S21
The wave is launched into a vacuum and corresponding S parameters are shown in figure 8. The graph presents the simulated reflection coefficient (S11) and transmission coefficient (S21). S11 is less than −10 dB with the bandwidth of 10 MHz, and the S21 is less than −10 dB from 2.434 to 2.48 GHz. Therefore, according to equation (12), the radiation microwave power (P) at 2.45 GHz is more than 80% because S11 and S12 are both less than −12 dB under this situation. Specifically, 80% is the total radiation microwave power, but not the LHW power. Because only part of P is excited into LHW for the arch antenna in EXL-50. Thus, the effective LHW for current drive is far less than 80%.
Here, this paper will present the antenna for manufacturing and analysis in experiments to validate the design theory. The comparison between the simulation results and the measured results is provided in section 4.

Measurement results
In this chapter, the measurements of the arch launcher were carried out in air environment, including S11, S21, RF magnetic field intensity, phase profiles, and n ∥ spectrum.

Prototype production
The entire configuration dimension of the arch antenna is already shown in section 3. The bottom plate and elements are fabricated from oxygen-free copper, and the oxygen content is less than 0.3%. The canopies are made of stainless steel, as shown in figure 9.
The arch antenna electrical characteristics were initially measured in air for convenience. Similar methods were used in [26]. A series of numerical and measurement results obtained with the prototype are presented to confirm the design.

Measurements
To measure the reflection and transmission coefficient, the two ports of the arch antenna were connected to the two ports of the vector network analyzer at the same time, respectively. The curves between the simulation and experiments are similar to each other, and the small discrepancy may be due to the very little difference between air and vacuum, the fabrication and assembly tolerances, as illustrated in figure 10.
Hereby, at 2.45 GHz, the antenna can radiate no less than 80% of microwave power in air with considering S11 = −12.5 dB and S21 = −12.6 dB according to P = 1 − S11 2 − S21 2 . Noting that P is the total radiation microwave power, but not the LHW power. Only part of the P is excited into LHW for the arch antenna in EXL-50. Thus, the effective LHW for current drive is far less than 80%.  Another characteristic of the arch antenna is n ∥ , which was confirmed by performing microwave magnetic probe measurements. The spatial distributions of the magnetic field were detected using magnetic probes located at various places at a frequency of 2.45 GHz. Probes directly in front of the antenna detect the strongest signal in both cases.
The microwave magnetic field is measured with the magnetic probe 2 mm placed in front of the top of the corrugation. The intensity and phase angle measured in front of the antenna are shown in figure 11. The simulated and measured results are consistent in terms of the trend for the traces, which can satisfy engineering requirements. They are used to calculate the parallel refractive index.
The antenna n ∥ spectrum at 2.45 GHz is 4.3, as shown in figure 12. The simulation and experimental results agree well with each other. They both show that the Fourier spectrum of the electric field has a peak at 4.3, which satisfies the engineering requirements, as shown in figure 12. Therefore, at 2.45 GHz, the antenna with a density power spectrum peaked around n ∥ = 4.3. In addition, for the simulated and experimental results of the parallel refractive index (4.3) are both smaller than the calculated ones (6.1), which may be due to the arch antenna inclination angle θ in this paper.
Therefore, the proposed antenna has the advantages of simple feeding, high directivity and compact size, and is a traveling wave antenna used in LHW for EXL-50.

Arch antenna launch experiments
In this section, the antenna is tested on EXL-50. The arch antenna was installed inside the EXL-50 vacuum vessel, as shown in figure 13. The experimental results contain LHCD power trial and plasma current ramp up testing.

LHCD power testing
In EXL-50, a lower hybrid power around 97 kW was injected into the antenna with approximately 8 kW reflected, as shown in figure 14.

Plasma current ramp-up experiments
LHCD start-up experiments have been performed on the EXL-50 ST. In this part, the arch antenna was tested with plasma to assess its validity. It is confirmed to be preferable for the ST plasma because of its low energy loss, sharp wavenumber spectrum and high directivity of the excited wave. The arch antenna was used successfully to perform plasma current ramp-up experiments on EXL-50.
The waveform of a typical plasma current start-up discharge with the arch antenna is shown in figure 15. The only difference between 18 647 and 18 646 is microwave power. Obviously, the non-inductive plasma current can be observed (in yellow). The increase in electron density may be due to the LH power being stopped at t = 4 s.
The incident lower hybrid power was approximately 70 kW. Up to 35 kA of plasma current was achieved using the antenna. The current drive efficiency formula is expressed as follows [1]: where I CD is the LH driven current (MA), P LH is the microwave power (MW), n e is the line-averaged electron density (m −3 ), R is the large plasma radius (m). The experimental η CD of arch in EXL-50 is approximately 1.2 × 10 18 A · m −2 W −1 . The initial experiments on surface wave antenna carried out on EXL-50 demonstrated the possibility of the arch antenna current drive in ST.

Discussion and future plans
In this paper, the total microwave power radiated to the air or vacuum at 2.45 GHz is estimated via P = 1 − S11 2 − S21 2 . However, P is not the LHW power. Only part of P is excited into LHW for the surface wave antenna because LHWs are excited when the longitudinal electric field contacts the plasma [26]. Thus, the effective LHW for current drive is far less than 80%. For this EXL-50 system, how much radiation microwave power is excited into LHW for current drive will be studied in the future.
It should be noted that there is no feedback system on EXL-50 at present. Dyachenko et al explained that since the plasma current in experiments on tokamaks is controlled by a feedback system, the excitation of RF current can be evidenced by the loop voltage drop [1]. Fisch indicated that a change ∆V in the loop voltage may be found with assuming that the plasma current is approximately constant [32]. Lu et al showed that the loop voltage dropped when the plasma parameters (plasma current and density) kept constant [33]. However, the plasma current using the arch launcher in EXL-50 cannot be maintained constant by the feedback system [34][35][36][37], so the loop voltage is not involved in this cases.
In addition, the loop voltage could provide valuable information for LHCD experimental study, including plasma current, position, and shape control in tokamaks [35]. The feedback system will be added in next sphere tokamak generation. We hope that the relevant experimental conditions will be optimized to improve the efficiency of LHCD on EXL-50 in future.

Conclusions
In this paper, a surface wave antenna working at 2.45 GHz used in LHW for EXL-50 has been presented. The experimental performance characteristics of the arch antenna were consistent with the simulated results within a reasonable range. Notably, the antenna in this article was designed by considering several aspects, including the working frequency, refraction parallel index, reflection and transmission coefficients. The optimized LHW arch antenna possesses the advantages of simple feeding, a low energy loss and high directivity.
Importantly, the proposed antenna is mounted on the tokamak of EXL-50, and successful ST plasma start-up and plasma current ramp-up have been confirmed using this setup. The current drive efficiency was 1.2 × 10 18 A · m −2 W −1 using the arch antenna in experiments. This paper reports the first attempt at plasma current start-up in ST using the LHW antenna launched from the outboard of the plasma, which will provide some references for small tokamaks.