Formation studies of field-reversed configurations on the HFRC-F device Yue Peng¹, Bo Rao¹*, Yong Yang¹, Ming Zhang¹, Zhijiang Wang¹ and Yuan Pan¹ ¹ International Joint Research Laboratory of Magnetic Confinement Fusion and Plasma Physics, State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China *E-mail: [email protected] Collisional-merging is a way to form high-performance field-reversed configuration (FRC) plasma. To improve the properties of merged plasma, one feasible way is to optimize the formation process. An experimental device named HFRC-F has been constructed in Huazhong University of Science and Technology, which is used to investigate the field reversed theta-pinch (FRTP) formation process of FRCs. Initial HFRC-F experiments obtain typical parameters with plasma density of 4 × 10²⁰ m⁻³ and lifetime of 75 μs with Bbias = -0.015 T, BPI = 0.015 T and Bmain = 0.035 T. The results also show that, 1) the larger the main magnetic field, the higher the density. 2) the VPI should be appropriate to obtain a larger frozen magnetic flux. A field-reversed configuration (FRC) is a compact toroid (CT) that has a predominant poloidal magnetic field but no or little toroidal field [1]. It has a simple axisymmetric structure. The averaged beta is near unity [2]. FRCs can also be translated [3], merged [4] and compressed [5] to optimize its properties. To improve the properties of the final plasma, one feasible way is to optimize the formation process. In order to investigate the field reversed theta-pinch (FRTP) formation process of FRCs, an experimental device named HFRC-F has been constructed in Huazhong University of Science and Technology. Field reversed theta-pinch (FRTP), which is investigated in this work, is a common way to form high-performance FRCs [6]. The typical magnetic field waveform is shown in figure 1. This process can be approximately divided into 3 stages: (a) bias and pre-ionization [7], (b) field-reversal, and (c) compression and equilibrium [8]. Several parameters in this process can be tuned to optimize the properties of the formed FRC. This paper focuses on the formation process, aiming at studying the influence on the plasma properties. This paper is organized as follows. The experimental device is introduced in section 2. The experimental results are presented in section 3. Lastly, a summary is provided in section 4. Figure 2 shows the diagram of the HFRC-F device, which can be roughly divided into five regions: the east-west end chamber, the east-west transition section and the quartz tube area. A total of 3 windows are opened on both sides and above the midplane of the quartz tube for the diagnostic system. The coil system consists of 12 theta-pinch coils and 4 quasi-steady state coils. The design parameters can achieve a bias magnetic field of -0.16 T, the PI magnetic field oscillation frequency of 150 kHz, and the main field to rise to 0.5 T within 5 μs. The quasi-steady state coils can be divided into 2 groups according to the radius (600 mm, 400 mm). A magnetic field of 1.0 T at the axis of the transition section can be obtained under rated conditions. The diagnostic system consists of a carbon dioxide interferometer [9], an array of internal magnetic probes, several point magnetic probes and single loops [10]. The internal magnetic probe is arranged in the window above the quartz tube. The carbon dioxide interferometer is arranged in the midplane horizontal window of the quartz tube. The point magnetic probe and single loop are installed on the outer side of the quartz tube between each two theta-pinch coils. At present, test of the HFRC-F device and the diagnostic system, as well as the quasi-steady state power supply and some theta-pinch power supplies have been completed. The maximum operating parameters are Vbias = 10 kV, VPI = 20 kV, and Vmain = 24 kV. 3.1 Typical Result Under the discharge conditions of Vbias = 5 kV, VPI = 12 kV, Vmain = 12 kV, the following typical results are obtained. When the outer gas is ionized, the formed plasma inhibits the penetration of the high-frequency magnetic field to a certain extent, and the remaining bias magnetic field is coupled with the subsequent ionized plasma to form an initial frozen magnetic flux. The results of the internal probe show that in the main and crowbar stage, the FRC plasma has a process of inward contraction, rebound, and finally inward contraction. It can also be seen from the results of the internal probe that the lifetime of the FRC is about 75 μs. The density results show that the main ionization occurs after the main field is triggered, at which time a rapid density climb can be observed. A subsequent compression process in the crowbar stage further increases the density. 3.2 The effect of VPI on pre-ionization The response of the plasma under different PI voltage conditions was studied, and the results of the internal probe were obtained as shown in the figures 4. The results show that the magnitude of the PI voltage affects the timing of ionization. When the bias magnetic field is introduced, different ionization moments will lead to different superimposed magnetic fields during ionization, which will make the initial frozen magnetic flux different. Appropriate voltage coordination can increase the initial frozen magnetic flux. 3.3 The effect of VPI and VMain on density The typical results above show that the density evolution during FRC formation can be divided into three stages. This subsection mainly studies the effects of different PI voltages and different main voltages on the plasma density. The results show that under the same main voltage condition, changing the magnitude of the PI voltage only affects the plasma density in the pre-ionization stage. The final plasma density is affected by the main voltage, the higher the main voltage, the higher the density. For example, the density is almost 4 times as the voltage rise from 9 kV to 15 kV. A device named HFRC-F has been designed to study the formation process of the FRC plasma and improve its parameters. The device contains 12 theta-pinch coils and 4 quasi-steady state coils. The design parameters can reach the maximum bias magnetic field of -0.16 T, the PI frequency of 150 kHz, the main rises to 0.5 T within 5 μs, and the quasi-steady state field of 1.0 T. The device is equipped with internal magnetic probes, point magnetic probes, single loops, and a carbon dioxide interferometer to measure the evolution and distribution of plasma parameters. The experimental study shows that the appropriate PI voltage can increase the initial frozen magnetic flux, thereby prolonging the plasma life. The higher the main voltage, the higher the density of formed plasma. The authors are very grateful for the help of J-TEXT team. This work is supported by the National Key R&D Program of China under Grant No. 2017YFE0301803 and by the National Natural Science Foundation of China (51821005). [1] Tuszewski M. 1988 Field reversed configurations Nucl. Fusion 28 2033 [2] Steinhauer L.C. 2011 Review of field-reversed configurations Phys. Plasmas 18 070501 [3] Sekiguchi J. 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