Fusion plasma is an active research field that aims to address the global energy problem. Various magnetic confinement fusion devices such as tokamaks and stellarators that use magnetic fields to confin_e plasma have been proposed for fusion reactions. Among these, a spherical torus (ST) is characterized by an aspect ratio that is lower than that of conventional tokamaks and is distinguished for its compact design. However, owing to an intrinsic drawback of STs, specifically, the reduced central region caused by the low aspect ratio, a non-inductive startup method is required to compensate for the limited inductive current drive capability. To this end, several non-inductive startup methods such as coaxial helicity injection, merging-compression plasma formation, and various radio frequency (RF) heating methods have been developed and studied, both theoretically and experimentally, for STs [1]. Among these, the merging-compression plasma formation method is widely utilized across devices. For instance, devices such as mega ampere spherical tokamak (MAST) and small tight aspect ratio tokamak routinely start by producing two plasma discharges, which are then merged quickly, leading to plasma formation on a closed flux surface (CFS) with the highest plasma current, I_p [2,3]. Although many devices apply the merging-compression plasma formation method, its future applicability may be limited as it depends on internal coils located inside the vacuum chamber. These internal coils are used to induce a strong loop voltage around the coil, enabling two initial plasma discharges. However, internal coils cannot be used in future ST reactors as they are exposed to a high neutron flux. To address this issue, double null merging (DNM) was introduced, enabling the formation of plasma at a null point detached from the external coils, thereby creating a space to shield and protect the coils. It has been reported that MAST can successfully form plasma at a null point between the internal coils and that the merging-compression method can be applied to study the feasibility of DNM operations, which are not actively used yet [4]. Therefore, to facilitate the concept of merging plasma startup in the future, other feasible methods for initial plasma discharges are required.

On_e feasible method for producing two initial plasma discharges is using external coils with multiple turns. Furthermore, to apply a high loop voltage under high toroidal field strength conditions, a coil operating near the toroidal field coil would be advantageous. Note that an ST can induce a high toroidal magnetic field, B_t, in the vicinity of a central coil. To develop a novel startup method for STs and to test the operational concept of using external coils in a high B_t, the versatile experiment ST (VEST) at the Seoul National University has a specially designed center coil structure. For context, the details are reviewed briefly here. Unlike many other STs, the VEST features two partial solenoid coils located at the top and bottom of its center stack. These coils are designed to drive a toroidal electric field, E_t, in their vicinity. This initiates plasma discharge and drives I_p in both upper and lower chambers. This configuration enables VEST to potentially form two plasma discharges within two separate CFSs. It was anticipated that by subsequently combining these two plasma discharges, VEST could achieve merging compression startup, thereby expanding its operational capability. However, attempts to discharge plasma in both chambers using the partial solenoid coils failed owing to an uncontrollable vacuum magnetic field structure and a high resistivity environment. This uncontrollability originated from the uncontrollable coil currents, resulting in high stray fields, B_stray, caused by the asymmetric vessel wall surrounding the partial solenoid coils, as well as a vertically unstable magnetic field. Thus, VEST has failed to produce two plasma discharges for merging-compression with a novel startup method to date.

This paper reports the first experimental results demonstrating the successful plasma discharge and formation of a CFS with I_p in the upper chamber of VEST in a controlled magnetic field structure with an effective pre-ionization via Bernstein wave (EBW). A vacuum field structure that compensates for B_stray was created using preprogrammed current waveforms on the outer poloidal field (PF) coils. When an electron cyclotron wave (ECW) was launched into the target vacuum field at a specific pressure level, the plasma resistivity, η_plasma, was reduced effectively by EBW heating. The partial solenoid coils also generated inherently curved magnetic flux, ψ, contours, forming a trapped particle configuration (TPC), which enhanced the preionization using a mirror-like structure [5]. Finally, by applying a loop voltage from the partial solenoid coils, I_p was measured. This verified the formation of a CFS during the investigated operational window based on three parameters: E_t, B_stray, and wave power. After CFS was formed with a self-field higher than B_stray, the direct loss was reduced significantly by an infinite connection length. This occurred because the charged particles followed the closed ψ lines, thereby enabling I_p to be ramped up.

The remainder of this paper is organized as follows. Section 2 presents a two-dimensional (2D) vacuum field analysis to demonstrate the problem of partial solenoid startup, identifies the problems of partial solenoid startup, and recommends the feasible solutions for CFS formation. Additionally, a favorable field is recommended. Section 3 presents η_plasma reduction to form CFS directly and EBW preionization testing. Section 4 presents how B_stray, E_t, and the electron cyclotron heating (ECH) power were scanned and the CFS formation window was identified experimentally. Finally, Section 5 summarizes the experimental results.

Plasma discharge and CFS formation under embedded magnetic field conditions (such as those found in tokamaks and STs) are significantly influenced by the magnetic field structure and its strength. Therefore, accurately identifying the structure and controlling its time evolution are important. This section describes the testing and analysis of various 2D vacuum field structures under certain PF coil currents to determin_e a favorable magnetic field structure for plasma discharge and CFS formation in the upper chamber of VEST.

The current waveforms of the coils and their locations are depicted in Fig. 1. The signs of the currents are based on the cylindrical coordinates. The current of PF2 (partial solenoid coil) crosses zero at 301.7 ms. Here, PF34S and PF57S indicates that the coils PF3 and PF4 and coils PF5 and PF7 are connected serially, respectively. Thus, the current on each coil is identical. The current waveform of the PF2 and PF57S coils are controlled by pre-programmed power supplies, whereas the current waveform of the PF34S coil is determined based on the RLC value of the power system. The current slope, di/dt, of the partial solenoid for a high E_t has the maximum value based on the limitations of the pre-programmed power supply capabilities.

Figure 1. (a) Upper-half poloidal cross-section of VEST vacuum vessel and PF coil location. (b) Coil current waveform for partial solenoid (PF2, orange). PF coils 3 and 4 are in series (green) and 5 and 7 are in series (blue).

To analyze the vacuum field in the upper region of the VEST in detail, the upper chamber region was divided into two parts based on the center of the partial solenoid coil (PF2, Z = 0.98 m). In this paper, the region above Z = 0.98 m is referred to as the ‘upper part,’ whereas the region between Z = 0.98 and 0.80 m is referred to as the ‘lower part.’ Note that the red-dashed lin_e in Fig. 2 indicates the center lin_e. During the basic analysis, the vacuum fields, radial B_r, vertical B_v, and B_stray driven by partial solenoid coils were calculated using the green function. These are presented in Fig. 2(a) [Fig. 1(b), orange lin_e, PF2]. The B_r = 0 lin_e should preferably be located on the center lin_e. However, it is located in the lower part. In addition, as anticipated from the electromagnetism, the B_r at the upper part decreases whereas that of the lower part increases with time. This verifies the imbalance in B_r strength between the upper and lower parts. The unbalanced |B_r| originated from the thick wall of the top vacuum vessel. Consequently, B_r was high at the upper corner, identical to B_v. It could be compensated if the top vacuum vessel wall is thin. Nevertheless, this imbalance is unpreventable unless a symmetric vacuum vessel around the partial solenoid is feasible.

Figure 2. 2D contour plot of time evolution of stray magnetic field, B_stray (bottom three plots), and its radial (B_r, top three plots) and vertical (B_v, middle three plots) magnetic components induced by the coil current of (a) only PF2 and (b) PF2, PF34S, and PF57S. The coil current waveform is illustrated in Fig. 1(b).

In addition to the inequality, a high B_r is a major problem of partial solenoid startup. Conventionally, B_r is not the main issue for inductive startup owing to its low strength compared to that of B_v. However, B_r is comparable to B_v at partial solenoid startup as shown in Fig. 2(a). B_r is the dominant component of B_stray at 301.6 ms, and B_v is dominant at 302.0 ms. Subsequently, the magnitude of |B_stray| increases with comparable B_v and B_r on the center lin_e at 302.4 ms.

As described in the previous section and paragraphs, the usage of partial solenoid coils displays potential. However, it has an intrinsic limitation owing to the chamber and coil geometry. To overcome this limitation, various combinations of coils were tested. As a result, the most favorable combination was achieved, as shown in Fig. 2(b). The combination of coil currents is shown in Fig. 1(b). The negative current of PF57S induces negative B_v and negative B_r in the upper part and a positive B_r in the lower part. However, the magnitude of B is inversely proportional to the radial distance. Furthermore, a high B_v gradient near the partial solenoid cannot be compensated using PF57S alon_e. To further reduce B_v and B_r imbalance, PF34S was used. The negative current on PF34S effectively induced a positive B_r and negative B_v on the inboard side and a positive B_v on the outboard side. At 301.6 ms, unlike the case with only on_e partial solenoid coil [Fig. 2(a)], the B_r = 0 lin_e occurred on the center lin_e. The lowest B_stray of 0.11 G occurred at R = 0.41 m and Z = 0.90 m, with B_stray of 0.26 G and 1.07 G occurring at R = 0.29 m and Z = 1.02 m at 302.0 ms and R = 0.29 m and Z = 1.02 m at 302.4 ms, respectively. However, notwithstanding these efforts, the B_r in the lower part could not be reduced sufficiently owing to the coil geometry. The uncontrollable radial magnetic field B_r in the lower part of the chamber remains an inherent issue in partial solenoid startup methods. To address this, future chamber designs should consider employing a longer partial solenoid to achieve a symmetric B_r and adopting a symmetric vacuum vessel based on a center lin_e to reduce B_r in the lower part by enabling a symmetrical placement of the PF coils. Finally, as shown in the three bottom plots of Fig. 2(b), the B_r component can cause ψ curvature, and the mirrorlike structure, TPC, can be formed near the partial solenoid, enhancing pre-ionization. Section 4 presents the CFS formation tests based on TPC, and low B_stray.

Along with the carefully constructed magnetic field structure described in Section 2, another important requirement is to achieve minimum η_plasma for a given field. ECH pre-ionization is widely used during the startup operation of various tokamaks to reduce η_plasma. Specifically, in VEST [6,7] and other STs [8], owing to the low B_t and high electron density, n_e, EBW pre-ionization (which has no density cutoff) is used. Here, the feasibility of utilizing the EBW pre-ionization in the upper chamber of VEST is tested without B_stray.

A 2.45 GHz, 10 kW, NL-10245 magnetron is used in the RF generator, the parameters are listed in Table I, and it is located at Z = 0.98 m and launches the X-mode wave. The ECH power is measured at the power coupler before the wave enters the chamber and is controlled by modifying the filament current. For a given B_t = 0.065 T at R = 0.4 m and prefill pressure = 3.33 × 10⁻³ Pa, n_e, the electron temperature, T_e, is measured using a triple Langmuir probe (TLP). The dimensions of the probe tip and plasma parameters are as follows. The radius of the tungsten cylindrical tip is 0.15 mm, the tip length is 2 mm with each tip separated by 1.5 mm, and the axis of the cylinder is perpendicular to B_t. The Larmor radius of electron is 0.14 mm at T_e = 12.6 eV. Considering the deficiency of low ion temperature measurements, the ion temperature is assumed as T_e, the Larmor radius of hydrogen is 6 mm, and the Debye length is 0.06 mm. This setup satisfies the conventional Langmuir probe requirements under a magnetic field [9].

Table I. Specification of NL-10245 RF generator..

Operation length (ms)	Filament current (A)	Electromagnet current (A)	Bias voltage (kV)
10	50.5 − 53.5	3.18	11.1

The result of EBW pre-ionization in the upper chamber is shown in Fig. 3. Figure 3(a) shows the radial n_e and T_e profile at Z = 0.98 m with the fundamental and second electron cyclotron resonance (ECR) layer (R = 0.274, 0.548 m, respectively, red lines), upper hybrid resonance (UHR) layer (R = 0.420 m, green lin_e), R-cutoff layer (R = 0.576 m, purple lin_e), and L-cutoff layer (R = 0.341 m, blue lin_e). A small n_e peak is observed near the second ECR layer. The increased n_e is caused by the second harmonic ECH considering a low n_e at R = 0.43 − 0.53 m. As shown in Fig. 3(b), the thickness of the R-cutoff is small compared with the wavelength of ECW (~12 cm). Thus, ECW can tunnel through the R-cutoff. In addition, another R-cutoff layer exists at R = 0.439 m. This cutoff pair can trap ECW. The triplet of R-cutoff, R = 0.439 m, UHR, and L-cutoff also traps ECW, and the EBW mode conversion rate can be calculated based on a Budden triplet analysis [10]. The mode conversion coefficient can be determined as follows:

Figure 3. (a) Radial profile of n_e, T_e, at B_t = 0.065 T and R = 0.4 m without vacuum PF. The ECH power is 5 kW with a pressure of 3.33 × 10⁻³ Pa. The outer gray box (R = 0.6 m) indicates a vacuum vessel. Meanwhile, the inner gray box (R = 0.13 m) indicates a center stack. (b) Radial profile of cutoff and resonance of X-wave by cold plasma dispersion relation.

where the Budden parameter $\eta =\frac{{\omega }_{ce}{L}_n}{c}\frac{\alpha }{\sqrt{{\alpha }^2+2\left(L_n/L_B\right)}}\left[\frac{\sqrt{1+{\alpha }^2}-1}{{\alpha }^2+\left(\frac{L_n}{L_B}\right)\sqrt{1+{\alpha }^2}}\right]$; L_n and L_B are the density and magnetic field scale length, respectively; $\alpha ={\left|\frac{{\omega }_{pe}}{{\omega }_{ce}}\right|}_{UHR}$; and ω_ce and ω_pe are the electron cyclotron frequency and electron plasma frequency, respectively.

Here, n_e has two peaks at R = 0.33 and 0.39 m. According to previous wave conversion research and analysis results [11], the highest peak at R = 0.33 m is the result of EBW heating, and the other peak is the result of collisional damping of EBW. Note that a low n_e between the two peaks is another indication for the interpretation that two different mechanisms are reasonable. In addition, the shift of the highest peak to the lower field side is the result of a Doppler shift. Moreover, the reduced T_e at the n_e peaks compared with R = 0.3 m is the result of ionization collision. The error bar in Fig. 3(a) represents the maximum and minimum n_e, T_e within a time interval of 0.04 ms. It shows highly fluctuating n_e, T_e at both the peaks. The Budden parameter is 0.05. The maximum mode conversion efficiency is calculated to be 55 % by the Budden triplet analysis. As this value is high, over-dense plasma can be formed. EBW pre-ionization shows a lower T_e and high n_e at R = 0.33 m. The Spitzer resistivity with an electron–electron collision correction term is 4.3 × 10⁻⁵ Ω⋅m, and the electron-neutral collision resistivity is 1.62 × 10⁻⁵ Ω⋅m. As a result, overdense plasma by EBW heating effectively reduces the local η_plasma.

Using the field structures and EBW pre-ionization results presented in Sections 2 and 3 respectively, CFS formation experiments using partial solenoid coils were conducted and are described in this section. To identify rigorous conditions to the extent feasible, the CFS formation was analyzed based on an experimentally recommended criterion. For a successful CFS formation, various conditions such as a high E_t and low B_stray are required. In particular, the self-field strength driven by I_p should overcome the vacuum field strength. Based on these conditions, the CFS formation experimental criterion can be described using Eq. (2) [12].

CFS is formed when the poloidal magnetic field, Bp, generated by I_p exceeds B_stray. Assuming that plasma has a circular cross-section with radius a and resistivity η_plasma under an applied E_t, then B_stray and Bp can be calculated using Ampere‘s law. Based on this, the criterion for CFS formation can be determined. To test the criterion used in this study, the radius of the circular cross-section of plasma was assumed to be 5 cm, B_stray was averaged within the circle, and E_t was selected at the center of the circle. To identify the experimental window of CFS formation, the ECH power, E_t, and B_stray were scanned separately for clarifying the CFS formation criterion.

First, ECH power was scanned to understand the pre-ionization effect on CFS formation through experiments. The experimental results are shown in Fig. 4 with a prefill pressure of 3.6 × 10⁻³ Pa and B_t of 0.065 T [similar to those observed in Figs. 1(b) and 2(b)]. The ECH power of #44261, #44276, #44298, and #44300 was set to 4.0, 3.3, 2.8, and 2.4 kW, respectively, with a PF coil current equal to that in Fig. 2(b). The ECH power is controlled by modifying the filament current of the magnetron. This is shown in Fig. 4(c). Time-varying ECH power originates from different impedances of plasma with time and is measured at the power coupler before the antenna.The I_p of each shot is shown in Fig. 4(a). The B_stray and E_t at R = 0.27 m and Z = 0.98 m is shown in Fig. 4(b). A low ECH power results in delayed I_p onset. The H_α lin_e signal, measured horizontally at Z = 0.98 m, is shown in Fig. 4(d). The delayed onset of H_α indicates a delay in the EC breakdown timing. A high H_α signal indicates a high electron multiplication by the avalanche at the breakdown phase. Note that a high n_e can reduce the electron-neutral resistivity. Therefore, the magnitude of exponential growth of an H_α signal is indirectly related to η_plasma. The relationship between delayed I_p onset and H_α signal implies the dependence of CFS formation on resistivity. For a higher resistivity, a higher E_t/B_stray is required. Moreover, E_t/B_stray increases with time, as shown in Fig. 4(c).

Figure 4. Discharge results of field configuration of coil current Fig. 1(b) and vacuum field Fig. 2(b). (a) Toroidal plasma current, I_p. (b) Toroidal electric field and stray magnetic field at R = 0.27 m and Z = 0.98 m. (c) ECH power. (d) H_α signal horizontally measured at Z = 0.94 m.

Second, B_stray and E_t were scanned for CFS formation experiments. The prefill pressure was approximately 3.3 × 10⁻³ Pa, and the ECH injected power was 4 kW, which is similar to the condition for #44261. The field was controlled by shifting the PF57S in Fig. 1(b) by moving 0.1, 0.2, 0.4, and 0.6 ms from #44301 to #44304, respectively.

The scan results are shown at Fig. 5(a). The abrupt I_p increase is observed only for #44261. To determin_e the effect of each E_t, B_stray component and experimentally indicated component $\frac{E_{\text{t}}}{B_{\text{stray}}}$ , each E_t, B_stray, and $\frac{E_{\text{t}}}{B_{\text{stray}}}$ at R = 0.27 m and Z = 0.98 m was calculated. These are depicted in Figs. 5(b)–(d). As indicated by the experimental criterion [Eq. (1)], the abrupt increase in I_p [the deep blue lin_e in Fig. 5(a)] coincided with the highest value of $\frac{E_{\text{t}}}{B_{\text{stray}}}$ [the deep blue lin_e in Fig. 5(b)]. Note that the $\frac{E_{\text{t}}}{B_{\text{stray}}}$ value at I_p onset did not differ significantly. As a result, a detailed analysis did not match well with a 0D analysis using E_t and B_stray [Figs. 5(c) and 5(d)]. However, experimentally, CFS formation and current initiation were dependent on the highest $\frac{E_{\text{t}}}{B_{\text{stray}}}$ level. This is shown in Fig. 5(b). For an ECH power of 4 kW, the lower limit of $\frac{E_{\text{t}}}{B_{\text{stray}}}$ was #44301, 0.55 $\left[\frac{V}{m}\cdot G^{-1}\right]$. As a result, high $\frac{E_{\text{t}}}{B_{\text{stray}}}$ and ECH power were required for CFS formation. This can be anticipated with Eq. (1).

Figure 5. (a) Toroidal plasma current, I_p. (b) $\frac{E_{\text{t}}}{B_{\text{stray}}}$. (c) Stray field strength, B_stray. (d) Toroidal electric field, E_t. Note that the I_p onset is dependent on E_t, and the I_p increment is dependent on $\frac{E_{\text{t}}}{B_{\text{stray}}}$.

Figure 6 shows the experimental time-evolution results of a successful CFS formation (#44261) in VEST. For this discharge, the prefill pressure was 3.0 × 10⁻³ Pa, and the ECH power was 4 kW. Figure 6(a) illustrates E_t, which increases abruptly at 301.5 ms. Figure 6(b) illustrates B_stray. It attains its minimum at 301.9 ms. Figure 6(c) illustrates the η_plasma calculated by a TLP measurement of n_e and T_e based on the Spitzer resistivity. Figure 6(d) illustrates I_p. Figure 6(e) illustrates the CFS formation criterion, and it satisfies the criterion when the value is greater than 1. The experimental criterion of CFS formation is satisfied at 301.5 ms. Additionally, it is noteworthy that it matches well with the I_p onset timing. The yellow-vertical lin_e at 301.5 ms in Fig. 6 represents the timing when both CFS criteria are satisfied and I_p starts to increase. The CFS is formed at 301.78 ms. A time delay exists between the criterion and CFS formation; this may have originated from the reduced I_p caused by an open field current with the opposite direction at -0.8 m < Z < 0.8 m. However, this requires further investigation for verification. The fast camera images are shown in Fig. 7.

Figure 6. CFS criterion analysis for #44261. (a) Toroidal electric field, E_t. (b) Strength of stray field, B_stray. (c) Plasma resistivity, η_plasma. (d) Toroidal plasma current, I_p. (e) CFS criterion. The center of the plasma column is assumed as R = 0.27 m based on a fast camera and probe measurement. I_p increases when the CFS criterion is matched at 301.5 ms (highlighted).

Figure 7. Fast camera images of #44261 with fish-eyed lens at 2,500 fps and 5 k shutter speed.

Figure 8 illustrates both vacuum ψ contour and ψ contour with plasma. Based on the current initiation dependence on $\frac{E_{\text{t}}}{B_{\text{stray}}}$ and ECH power, the CFS at 301.78, 302.00, and 302.20 ms is shown in Fig. 8. The contour plot was calculated based on the 2D field by a coil and I_p. Here, I_p is located at R = 0.33, 0.37, and 0.45 m, Z = 0.98, 0.98, and 0.85 m, each with a minor radius of 5, 8, and 10 cm, respectively. The center of the CFS displays an outward movement. Note that the CFS contour exists only after the criterion has been satisfied. To understand the underlying mechanisms of time delay associated with satisfying the CFS formation criterion and the subsequent appearance of the CFS contour, further investigation is required; this was not considered in the study. Except for the time delay, the CFS criterion matched well with the CFS formation. However, even when the CFS was formed, the plasma was exposed to a high B_stray as it expanded, and it decreased after 302.2 ms. To maintain plasma stability, the meticulous control of the PF current or a high-$\frac{d{I}_p}{dt}$ experiment to overcome B_stray will be investigated in the future.

Figure 8. Magnetic flux ψ contour of #44261 (a) without ψ component of I_p at 301.6, 302.0, and 302.4 ms and (b) with ψ component of I_p at 301.78, 302.00, and 302.20 ms.

Various non-inductive current drive methods have been investigated to enhance VEST’s discharge capability [13,14]. Although, most of these methods were successful in enhancing the capability of VEST, the merging-compression plasma formation method using partial solenoid coils (a novel concept for the future operation of ST) failed owing to an asymmetric field structure [15]. In this study, through a systematic consideration of magnetic field structures and the use of a pre-programmed power supply, a low B_stray configuration was achieved. However, with time, the B_r in the lower part of VEST could not be compensated fully owing to the limitations imposed by the coil geometry. Experimental investigations on EBW preionization demonstrated the generation of over-dense plasma, which effectively reduced the plasma resistivity. This reduction in resistivity is attributed to a decrease in the electron-neutral collision-induced resistivity. CFS formation with an abrupt increase in current was observed, and it can be anticipated using the CFS formation criterion. A high E_t and rapid reduction in B_stray resulted in a high I_p. However, as the plasma expanded, it was limited by obstructions located at R = 0.46 m, and a rapid reduction in I_p was observed. In the future, after removing the obstructions, force balance control for plasma equilibrium in the burn-through phase will be conducted experimentally for a high I_p. Moreover, the feasibility of a successful partial solenoid startup will be reported.

This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIT) (NRF-2021M3F7A1084418).