Study of the Design and Assembly of a High Harmonic Fast Wave Antenna for an LAPD

*e simulation survey of TAE Technologies has demonstrated that high harmonic fast wave (HHFW) heating is a promising method for core electron heating of FRC plasma.*is studymainly describes the HHFW antennamechanical design and assembly on the basis of the results of electromagnetic simulations performed by Oak Ridge National Laboratory (ORNL), the available port dimensions, and antenna installation position of the LAPD. Compared to the original scheme, this antenna is also optimized in the design. It is found that the E field distribution of optimized antenna becomes even, and the maximum electric field decreases by approximately 14%. *e current on the antenna box and FS is reduced after optimization, whereas the maximum J density decreases from 53.3 kA to 14.5 kA. *e reflection performance of the port at 30MHz is also improved after the structural optimization; *e k// spectrum distribution is sharper at the monopole phase (0, 0, 0, 0) and dipole phase (0, π, 0, π) and (0, 90, 270,180) than other phases. *e optimized antenna can obtain a maximum |k//| spectrum, which peaks about |k//|� 30m at the dipole phase (0, π, 0, π). *e analysis results and assembly strategy can provide useful reference and guidance for the study of HHFW antenna design and fabrication in LAPD or other magnetic confined fusion devices.


Introduction
Antennas can transform guided waves propagating along transmission lines into electromagnetic waves propagating in unbounded media, or vice versa. Radio communication, radio, television, radar, navigation, electronic countermeasure, remote sensing, radio astronomy, and other engineering systems all use electromagnetic waves to transmit information and all rely on the antenna to work [1][2][3][4]. In addition, antenna is an important method of heating plasma in magnetic confined fusion devices. For instance, ion cyclotron radiofrequency (ICRF) heating is an important method of heating in tokamaks, and the main equipment used is antenna.
Effectively heating the core electrons of field-reversed configuration (FRC) plasma is challenging due to its unique magnetic field profile. A recent survey by Tri Alpha Energy (TAE) Technologies indicates that high harmonic fast wave (HHFW) heating, which has been successfully adapted to high beta, over-dense spherical Tokamak plasmas, such as the National Spherical Torus Experiment (NSTX), for the experiments of core electron heating and off-axis current drive, can balance the conflict between good wave accessibility and efficient power damping of electrons [5,6]. is discovery motivates a project on the experimental study of HHFW antenna-plasma coupling and wave propagation on a reliable test bench, such as the large plasma device (LAPD) at the University of California-Los Angeles (UCLA), before the method of HHFW electron heating is employed on the C-2W, an advanced beam-drive field-reversed configuration (FRC) device recently built at TAE. erefore, in the framework of the collaboration agreement between TAE and Institute of Plasma Physics, Chinese Academy of Sciences (ASIPP), ASIPP is in charge of the design and fabrication of a high-power capable, phased array (four strap) HHFW antenna for the radio frequency (RF) project of TAE on the LAPD at UCLA. Ion cyclotron range of frequencies (ICRF) antennas have been used as an efficient heating method in many tokamak devices, such as the Tokamak Fusion Test Reactor (TFTR), Joint European Torus (JET), Experimental Advanced Superconducting Tokamak (EAST), and ITER. ese antennas can provide steady high-power input with high efficiency in tokamaks [7]. However, the radio frequency (RF) sheath effect has been found to be detrimental. e RF rectification sheath potential not only reduces the heating performance of the ICRF antenna through the acceleration of ions but also causes a local hot spot on the ICRF structure, which has been observed during the experiments hosted in tokamaks.
e JET experiment has shown that the maximum temperature on the ICRF structure can reach 800°C due to the hotspot [8]. e edge-RF phenomenon can not only affect the plasma density but also cause bright spots and erode the Faraday shield (FS). e fluxes of ions are accelerated in the RF-driven sheaths near the antenna, causing parasitic impurity sputtering, arcs, and hotspots on the antenna surface [9]. e RF sheath effect arises and narrows the gap between the FS elements, thereby increasing the electric fields and accelerating ions to an appreciable fraction of the gap voltage, which is approximately 1 kV per gap for the TFTR and JET antennas [10]. e RF sheath effect can also be amplified due to FS elements that are imperfectly aligned with the combined poloidal and toroidal magnetic fields according to the research from Princeton Plasma Physics Laboratory (PPPL) [11]. e HHFW power loss is normally researched through the scrape-off layer (SOL) and plasma wall interaction (PWI). Due to the high heating power of the ICRF system, edge loss can be due to erosion or impurity production [12]. Certain developments in the RF sheath, which causes the ICRF-edge interaction, have shown that theorization, modelling, and experiments can be performed together to progress in the understanding and control of the ICRF-edge interaction in several tokamaks [13]. For example, TOPICA code was developed to compute the antenna near field for the study of RF-PSI effects. Some 1D particle-in-cell simulation codes were developed to investigate plasma sheath structures around a high-voltage transmitting antenna in the inner magnetosphere, and the results were assessed by experiments [14]. A device was designed to determine the method for predicting the performance of the ICRF antenna under the loss of RF sheath [15]. An LAPD, which is a linear device, was designed to accommodate various experiments for basic plasma physics research. An LAPD was designed with the capability to diagnose and model the effect of RF rectification sheath potential and impurity production on an ICRF antenna. Some experiments on an LAPD were proposed to investigate the sheaths caused by an actively powered RF antenna [16].

Motivation and Design Requirements of the HHFW Antenna
Conventional electron heating scenarios, such as electron cyclotron resonant heating and fast wave mode conversion heating, which are widely utilized in tokamaks or stellations, cannot be adapted in field-reversed configuration (FRC) plasmas due to the conflict between the wave penetration into core plasmas and the efficiency of power damping on electrons. Given that an increase in electron temperature can help reduce charge exchange losses and increase fast particles that slow down time, thereby enhancing the efficiency of neutral beam heating and current drive and improving FRC plasma confinement and performance, numerous efforts have been recently made at TAE to explore various microwave and RF heating scenarios, including upper-hybrid resonant waves, electron Bernstein waves, Whistler (helicon) waves, and HHFW heating. Among these scenarios, studies with the GENRAY-C ray-tracing code have demonstrated that HHFW may be a promising path for the core electron heating of C-2U-like FRC plasmas. Under the motivation of these promising simulation results, HHFW is designed for the LAPD. Based on the current RF generator and LAPD ports for the HHFW antenna, the design requirements are as follows: (1) e impedance of the transmission lien is 50 Ω (2) e motion range is from 0 mm to 200 mm, adapting to the experimental requirements (3) Easy installation and maintenance are required

Integration of the HHFW Antenna.
e HHFW antenna is composed of four modules, and each module comprises an FS, a current strap, and a transmission line (TL). To form a seal with the LAPD device, one adaptor tube connected with one bellow is sealed with a port and a movable plate by an O ring. One limiter made of BN is fixed between two modules, and four modules are fixed into integration by bolts on the top and bottom of the FS inside of the vacuum vessel (VV) and the flanges of the movable base outside of the VV. e HHFW antenna can move along the radius in the range from 0 mm to 200 mm by means of one driving motor located at the rear of the antenna because this adapts to the plasma operation scenario and meets the requirements of easy installation and maintenance. e detailed structure is shown in Figure 1.

FS.
Four independent modules of FS are integrated into one large component for the HHFW antenna, as displayed in Figure 2, to protect the straps from particle bombardment. Each FS consists of eight bars and one box that are made of the stainless-steel SS 316L. On the basis of the easy assembly and disassembly of the straps, the FS bars are fixed on the box by the bolts. Each box has many slots; thus, magnetic flux can penetrate the boundary. Two BN limiters are placed at both sides of each FS module to cover the slot to prevent connection between the plasma and the strap.

Strap and Transmission Line (TL).
For the HHFW antenna, four straps are designed for the coupling power to plasma. Each strap is made of copper to reduce the RF loss, and one end is connected with the feed of an inner conductor, while the other is connected to the ground. e shape of the strap is designed as a curve to meet the plasma operation requirements.
e TL is composed of the inner conductor, outer conductor, and some supporting structures, which mainly transmit power from the generator to the plasma. For the HHFW antenna system, one end of the inner conductor serves as a feeder connected with a strap; the outer conductor is docked on the outer shell of the vacuum chamber, and the other is connected with the RF generator. Due to the VV port dimension limit, the front end of the TL is designed with a tapered shape, as shown in Figure 3.
In view of the requirement for a strap that is easy to assemble and limits deformation to within the requirements, the structure optimization of the strap and TL is conducted under gravity. Different thicknesses and materials are selected to perform the simulation. Based on the results, the strap thickness is 12 mm and the inner conductor thickness is 1.5 mm. As illustrated in Figure 4, the deformation of the strap is 0.02 mm, which is far below the design requirements.

Support System.
To make the HHFW antenna stable and for safe operation, two trusses are designed to support the antenna: one is installed inside of the VV to support the   Science and Technology of Nuclear Installations weight of the forepart of the HHFW antenna, and the other is fixed outside of the VV to support the rear part of the HHFW antenna. e detailed structure is shown in Figure 5.
To easily install four TLs, which are connected with the fore parts of the HHFW antenna through the VV ports, the rear truss is designed with an adjustment function so that it can be adjusted with three degrees of freedom in the X-, Y-, and Z-directions. Additionally, the fore truss has an adjustment structure to keep the top surface parallel with that of the rear truss within the design requirements, ensuring that the antenna can be moved smoothly along the radian direction in the range of 0 mm to 200 mm. Apart from these trusses, four upper pylons are designed to temporarily support the rear parts of the HHFW antenna during installation and are removed after assembly.

Optimization of the Antenna Structure.
In many tokamak experiments, hotspots are found when ICRF antennas work at a high-power feed; the impurities generated can then increase the RF loss and greatly affect the antenna performance, which is related to the high electric field on the antenna components [12]. With the help of the software HFSS, a simulation at 10-50 MHz of the water load is conducted, and high electric field distribution and current densities are observed in some components of the structure. To reduce the possibility of generating impurities from high field and current densities on the antenna FS, straps, and box, two optimizations for the HHFW antenna are performed: one is the antenna box flipped at 180°, and the other has shifted FS elements. e original and optimized structures are presented in Figure 6. Figure 7 shows the normalized electric field distribution of the two versions of the antenna at 30 MHz and (0, 0, 0, 0), where the power fed into each port is 1 MW. e E field is normalized here according to the breakdown electric field limit given in [17]. e electric field value is relatively high in the upper area of the front end of the current straps before optimization, and it is almost in the same poloidal position. Figure 7 also displays that the overall electric field is still very high, even though the input power is relatively high; the field distribution becomes even, and the maximum electric field decreases by approximately 14%. Figure 8 illustrates the normalized J density distribution of the two versions of the antenna. e high current density area is mainly concentrated on the edge and at the end of the strap. e current on the antenna box and FS is reduced after optimization, whereas the maximum J density decreases from 53.3 kA to 14.5 kA because the mutual coupling in the high field area is reduced to an extent due to the change in the location of adjacent straps with high fields. To minimize the fluctuation in the power spectrum change, we retain the strap structure but switch the feed and ground points. e shifted FS elements after optimization also intercept the flow of parallel currents, which contributes to the RF potential. e S11 parameters before and after antenna optimization are also compared here, as shown in Figure 9. e reflection performance of the port at a certain frequency (30 MHz in this study) is improved after the structural optimization. For the optimized three-dimensional electromagnetic simulation model, the electromagnetic field distribution at about 3 cm in front of the antenna is taken for     Science and Technology of Nuclear Installations k // spectrum calculation. e results in Figure 9 show that the k // spectrum distribution is sharper at the monopole phase (0, 0, 0, 0) and dipole phase (0, π, 0, π) and (0, 90, 270,180) than other phases, which is conducive to penetrating the cut-off layer of plasma boundary and has better coupling performance. e optimized antenna can obtain a maximum |k // | spectrum, which peaks about |k // | � 30 m −1 at the dipole phase (0, π, 0, π).

Assembly Strategy of the HHFW Antenna
Considering that the HHFW antenna is integrated in the LAPD VV to participate in the plasma campaign, the assembly for the antenna not only is within design tolerances but also ensures that the antenna can move smoothly, adapting to different plasma configurations. To meet the assembly tolerances and to achieve simple installation, the assembly strategy for the HHFW antenna is investigated. On the basis of the HHFW antenna and VV structure, the fore truss in the VV, four temporarily pylons, rear truss outside the VV, and outer conductors are installed using the measuring datum network and are placed according to the required position. Four FS modules, four inner conductors, and five ceramic baffles are sequentially installed in that order; the parallelism of the four outer conductors required is no more than 0.1 mm. Subsequently, FS bars are installed on the FS boxes, and four small bottom plates and one large bottom base are connected to the FS. e temporary upper pylons are also removed, ensuring that the wheels are fixed on the bottom base for connection with the surface of the fore truss at the end. e assembly process and final assembly status of the HHFW antenna are shown in Figures 10  and 11, respectively. After the assembly is finished, the movable test of the antenna is conducted by the drive system. e result demonstrates that the antenna can be moved smoothly, and the stroke reaches 200 mm, both of which satisfy the requirements.

Summary
In this study, we introduce the key components and dimensions of the HHFW antenna. en, we compared the antenna performance before and after optimization. e simulation results have demonstrated that the E field distribution of optimized antenna becomes even, and the maximum electric field decreases by approximately 14%. e   current on the antenna box and FS is reduced after optimization, whereas the maximum J density decreases from 53.3 kA to 14.5 kA. e reflection performance of the port at 30 MHz is also improved after the structural optimization. e k // spectrum distribution is sharper at the monopole phase (0, 0, 0, 0) and dipole phase (0, π, 0, π) and (0, 90, 270,180) than other phases. e optimized antenna can obtain a maximum |k // | spectrum, which peaks about |k // | � 30 m −1 at the dipole phase (0, π, 0, π). Furthermore, structure analysis of the antenna was carried out for optimization to meet the requirements of easy installation and steady and safe operation. In addition, the assembly strategy was carefully considered and formulated, which will help engineers to understand the assembly process and to install antennas in a highly efficient manner.
In summary, in collaboration with TAE, ORNL, and UCLA partners, the HHFW antenna mechanical design and fabrication have been completed. e design strategy and analysis results in this paper can provide useful reference and guidance for the study of HHFW antenna design and fabrication in LAPD or other magnetic confined fusion devices [17].

Data Availability
e figures used to support the findings of this study are available from TAE upon application at https://tae.com/.   Science and Technology of Nuclear Installations 7