Design and construction of two biased electrodes and preliminary experiments on the Keda Torus eXperiment

1.   Introduction

Electromagnetic turbulence significantly impacts the confinement properties of magnetically confined plasmas [1, 2]. Unlike tokamaks, which feature a strong toroidal magnetic field (B_t), reversed field pinch (RFP) plasmas have a lower magnetic field, resulting in stronger electromagnetic turbulence. In RFP plasmas, this turbulence exhibits distinct three-dimensional characteristics [3, 4]. Magnetic turbulence governs both particle and energy transports within the plasma core, while electrostatic turbulence dominates particle transport at the edge [5]. Therefore, effective suppression of electromagnetic turbulence is essential for improving plasma confinement in the RFP configuration. It has been reported that electrostatic turbulence can be suppressed by enhancing flow shear, which can be attained by controlling the radial electric field [6]. Similarly, magnetic turbulence can be suppressed by controlling the current profile [7]. This underscores the critical importance of electric field and current profile control for suppressing turbulence, highlighting the significance of experimental studies in this area.

The biased electrode represents an ideal approach for controlling the edge radial electric field to suppress electrostatic turbulence [8, 9] and the edge parallel current profile to suppress magnetic turbulence [7, 10]. Thus, the biased electrode is a promising tool for experimental studies on electric field and current profile control within the Keda Torus eXperiment (KTX).

In this study, we have designed two electrode systems aimed at controlling the edge radial electric fields and parallel current profiles, tailored to the operational conditions of KTX. Subsequently, experiments focused on edge electric field control and edge parallel current profile control were conducted.

The rest of this paper is organized as follows. Section 2 outlines the design and construction of the biased electrode systems. Section 3 describes the experimental setups and results for both edge electric field control and edge parallel current profile control. Finally, the study is concluded in section 4.

2.   Design and construction of the biased electrodes

The edge radial electric field can be controlled based on the Ohm’s law, expressed as ${j}_{\mathrm{r}}={\sigma }_{\perp }({E}_{\mathrm{r}}-{E}_{\mathrm{r}0})$ [11], where j_r is the radial current induced by the electrode, ${\sigma }_{\perp }$ is the conductivity perpendicular to the magnetic field line, E_r0 is the initial radial electric field, and E_r is the radial electric field under bias. This indicates that control over the edge electric field can be achieved by adjusting the current driven by the electrodes, and when the driven current is sufficiently high, a strong electric field can be established at the edge. Edge electric field control via electrodes has been extensively studied on tokamaks [8, 12], where the required current is relatively low, typically not exceeding 100 A. To drive a significant radial current at high temperatures, a wide range of bias voltages, approaching ±1000 V, is required.

The edge parallel current profile can be controlled through the edge current drive, where the current originates from the electrodes and follows the magnetic field lines, ultimately returning to the vacuum chamber. Due to the three-dimensional nature of RFP plasmas, a complete modification of the edge current profile requires driving current in multiple toroidal regions, necessitating the installation of numerous electrodes around the torus [7, 13]. Furthermore, given the high current density in RFP, the current density driven by the electrodes must be sufficiently high. On Madison Symmetric Torus (MST), more than 16 electrodes are used for the edge parallel current profile control, with the total injected current reaching 10 kA [10]. Similarly, on RFX, each electrode drives approximately 10 kA [14].

KTX is an RFP device with a major radius of 1.4 m and a minor radius of 0.4 m, equipped with limiters at r = 38 cm. It can operate in three modes: low-current tokamak (q_a > 1), ultra-low-q (0 < q_a < 1), and RFP (F < 0) [15]. Based on the MST results, the current profile control in KTX requires the installation of as many electrodes as possible, with the total driven current approaching 10 kA. According to the Continuous Current Tokamak (CCT) and Tokamak Experiment for Technology Oriented Research (TEXTOR) results, the electric field control in KTX may require bias voltages up to ±1000 V at high plasma temperatures. Furthermore, since the radial position of the electrode head determines the affected edge area, the electrode head should cover a large radial extent.

The parameters from these biasing experiments, including those conducted on KTX, are summarized in table 1.

Table  1.  Parameters of biasing experiments on tokamaks and RFPs.

Parameters	CCT (tokamak)	TEXTOR (tokamak)	MST (RFP)	RFX (RFP)	KTX (RFP)
a/R (cm)	40/150	46/175	52/150	46/200	40/140
< Bt > (T)	0.3	2.35	0.1	< 0.4	$\leqslant$ 0.2
Ip (MA)	0.05	0.19	0.22	0.15–0.4	$\leqslant$ 0.5
Edge electron temperature Te (eV)	30	30	< 50	20	20
Edge electron density ne (1019 m−3)	0.1	0.1	< 0.2	1	$\geqslant$ 0.1
Number of electrodes	1	1	16	2	2
Electrode shape	Cylindrical	Canoe	Arc gun	Mushroom	Flat disc
Electrode material	W, LaB6, graphite	Carbon	Molybdenum	Carbon-carbon composite	Graphite
Electrode area (cm2)	50	39	-	25	14
Normalized rEB	0.63	0.85	0.9	0.79	0.7
Typical bias voltage (V) of each electrode	−1500	$\pm$900	−300	−300(U1), −100(U2)	$\pm$300(U1), $\pm$1000(U2)
Typical bias current (A) of each electrode	20	−30 to 130	500	10000	3000

 | Show Table

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2.1   Layout of electrodes

To effectively control the edge current profile, it is necessary to maximize the number of electrodes installed on the torus. Given the limited availability of spare windows on KTX, two windows, toroidally separated by 120° on the mid-plane, are selected for electrode installation (figure 1). Each electrode is equipped with its own power supply, and a schematic of the experimental setup with the two independent biased electrodes is shown in figure 2. Future experiments will involve installing additional electrodes to further refine and enhance control over the current profile.

Figure  1.  Layout of the two independent biased electrodes and diagnostic systems on KTX.

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Figure  2.  Schematic of the two independent biased electrodes on KTX.

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2.2   Mechanical design and construction

The mechanical structure of the electrode system serves multiple purposes, including enabling radial displacement of the electrode head, ensuring a high-vacuum connection with the vacuum chamber, providing electrical connection to the power supply, and maintaining electrical insulation from the vessel shell. Each aspect is described below.

Due to the short plasma discharge duration (${\tau }_{{\mathrm{discharge}}}$ $\leqslant$ 100 ms), the electrode head is moved to a standby location before plasma discharge begins. Magnetic transmission (figure 3(i)) is employed for this displacement, which primarily includes two magnetic components: a pulling magnet located outside the vacuum vessel and an internal loaded magnet. Manual movement of the pulling magnet induces a corresponding movement in the loaded magnet connected to the electrode head, driven by a strong magnetic force. To maximize radial coverage of electrodes, the electrode heads are designed to reach a minimum radial position of 28 cm.

Figure  3.  Mechanical structure diagram of Electrode 2: (a) electrode head replacement chamber, (b) glass observation window, (c) graphite electrode head, (d) boron nitride tube, (e) stainless steel pipe, (f) PTFE tube, (g) stainless steel rod, (h) stainless steel shell, (i) magnetic transmission, (j) PTFE gaskets, (k) nuts, (l) PTFE insulated helical wire, and (m) vacuum electrode flange.

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The mechanical structure is connected to the vacuum chamber via a high-vacuum gate valve. The electrical connection is established as follows. The electrode head (figure 3(c)) is attached to a stainless steel rod (figure 3(g)), which is connected to a helical wire (figure 3(l)). The helical wire, designed to accommodate movements, is connected to a rod of the vacuum electrode flange (figure 3(m)), eventually linking to a coaxial wire (figure 4).

Figure  4.  Electrical diagram of a biased electrode.

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To insulate the stainless steel rod (figure 3(g)) from the plasma environment, a high-purity boron nitride tube (figure 3(d)) is employed. Additionally, the electrode head is insulated from the vessel shells (figures 3(e) and (h)) by a polytetrafluoroethylene (PTFE) tube and gaskets (figures 3(f) and (k)). After installation of the mechanical structure, a successful DC withstand test under a voltage of 1000 V for 60 s is conducted between the electrode head and the vacuum chamber.

Electrode 1 and Electrode 2 are identical, with the exception that Electrode 1 lacks an electrode head replacement chamber.

2.3   Electrode head for driving large current

The control of E_r is governed by ${\Delta E}_{\mathrm{r}}=\left({E}_{\mathrm{r}}-{E}_{\mathrm{r}0}\right)=\dfrac{{j}_{\mathrm{r}}}{{\sigma }_{\perp }}$, where ${\sigma }_{\perp }\propto \dfrac{1}{{B}^{2}}$. Based on similar plasma parameters as CCT, the required electrode current for KTX is approximately 200 A. This value is feasible if the effective area of the electrode head exceeds 10 cm², which is estimated based on the electron saturation current observed in tokamak configurations [16]. Consequently, we have designed an electrode head in the form of a flat disc with a diameter of 35 mm and a height of 20 mm, constructed from high-purity graphite material (figure 3(c)).

To effectively control the edge parallel current profile, the electrodes must be able to drive substantial currents. Although arc guns are suitable for high-current injection [13, 17], their complex structure poses challenges. RFX has successfully used conventional electrodes for driving high-current [14], motivating us to adopt a similar electrode design for edge parallel current profile control.

Initially, the excessive electrode current phenomenon is observed in the current-voltage curve of the electrode (figure 5), suggesting the electrode’s potential to modify current profiles. Therefore, this electrode head is utilized in both electric field control and current profile control experiments.

Figure  5.  Current-voltage characteristics of Electrode 1 under tokamak and RFP configurations.

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2.4   Power supplies for biased electrodes

Based on the RFP biasing experiments presented in table 1, the current induced by the electrodes is in the kA level, with the maximum power reaching MW level. Since 220 V AC is insufficient for such high power outputs, electrolytic capacitor banks are used for energy storage. Additionally, high-speed switching is required to achieve rapid current turn-on and turn-off. The circuit, depicted in figure 4, incorporates insulated gate bipolar transistor (IGBT) H-bridges to achieve high-speed on and off switching of high currents and can also alter the polarity of the output voltage.

The power supply operates through three phases: charging, bleeding, and discharging. During the charging phase, 220 V AC is boosted to 1000 V via an isolation transformer and then rectified with a full-wave rectifier into the energy storage capacitor banks, controlled by an IGBT. In the bleeding phase, the stored energy is gradually released into a resistor through a relay. In the discharging phase, when the power supply receives a trigger signal, the energy stored in the capacitors is rapidly delivered to the electrode through the IGBT H-bridges.

In addition, the electrode voltage and the electrode current are measured using a high-voltage probe and Rogowski coil, respectively.

Initially, an initial version of the power supply was developed for driving the biased electrode system, with a maximum voltage and rated current of ±300 V and 200 A, respectively. During experiments, it was observed that under high negative bias, the electrode drove currents significantly exceeding 200 A, implying its potential to modify the edge parallel current profile. Subsequently, to enhance its capability for modifying the edge parallel current profile, this power supply was upgraded, increasing its maximum output current to 3000 A. Additionally, another power supply with a wider voltage range was fabricated for higher plasma temperatures. Then, the maximum parameters of the two power supplies were ±300 V, 3000 A and ±1000 V, 3000 A, respectively.

3.   Experimental setup and results

3.1   Excessive electrode current phenomenon

After constructing the electrodes, the current-voltage characteristic curves of the electrode system were obtained using the initial version of the power supply, under both tokamak and RFP discharges. In these curves, the voltage represents the power supply voltage, while the current represents the peak electrode current, with the power supply voltage varied for each discharge. In both configurations, the electrode was positioned at r = 30 cm and a Langmuir probe array was placed at r = 35 cm. Based on previous experimental results [16], the gradients of electron temperature and density at the edge are relatively small. Therefore, the probe results are used to provide an order-of-magnitude estimate of the ion saturation current collected by the electrode. On KTX, due to the higher electron density in the RFP configuration compared to the low-current tokamak configuration, the current collected by the electrode under the same bias voltage is greater in the RFP configuration. In the tokamak configuration, the ion saturation current collected by the electrode is approximately 20 A, whereas in the RFP configuration, it is around 50 A.

However, the curves indicate that when the voltage exceeds a certain threshold, approximately −50 V (figure 5), the current driven by the electrodes significantly exceeds the ion saturation current. This indicates that under high negative bias, the electrode emits a significant electron current. This substantial current is precisely what is needed to alter the current profile.

The unexpected excessive current phenomenon is indicated by the arc marks on the surface of the electrode head (figure 6). However, due to the lack of precise observation techniques for arcs, further research is necessary to thoroughly understand the initiation mechanism of electrode arcs.

Figure  6.  Appearance of the electrode head: (a) unused electrode head; (b) electrode head after dozens of shots.

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3.2   Edge radial electric field control experiments

The edge electric field control experiments were conducted to assess the effectiveness of the electrodes in controlling the electric field and their impact on the edge plasma, using the initial version of the power supply. Due to the pronounced three-dimensional characteristics of RFP plasmas, the modifications of the edge radial electric field by the biased electrode may be localized toroidally. Given the toroidal distance between the Langmuir probe and the electrode, the influence of the biased electrode on the electric field at the probe location may be minimal during RFP discharges. In contrast, tokamak plasmas exhibit toroidal symmetry, meaning that even if the probe is located far from the electrode, the biased electrode can still significantly affect the electric field at the probe location. Therefore, the edge radial electric field control experiments were carried out in the tokamak configuration.

The experiments were performed using hydrogen plasma in tokamak configuration, with a toroidal magnetic field B_t > 0.1 T, a plasma current I_p < 20 kA, and an edge safety factor q_a $\geqslant$ 3. Only one electrode was activated, with the electrode head located at r = 30 cm. The core plasma density was estimated from the line-averaged density measured by a terahertz interferometer located at the ‘B’ vertical window. The plasma confinement was monitored through the H_α signal detected at the ‘H’ top window. The electron density (n_e), electron temperature (T_e), floating potential (V_f), and radial electric field (E_r) at the edge were measured by a Langmuir probe array located at a radial position of r = 35 cm, installed in the ‘O’ horizontal window. E_r was calculated from V_f, and the influence of T_e gradient was neglected based on the previous experiments showing minimal T_e gradient [16].

The experimental results compare two discharges with and without bias voltage, as shown in figure 7. Electrode 2 is biased at −300 V (figure 7(h)), while Electrode 1 is biased at −200 V (figure 7(n)) under similar discharge conditions. During the biasing period, the floating potential V_f and electric field E_r are altered (figures 7(c) and (d)). It is evident that the plasma current duration and the line-averaged density are increased under bias (figures 7(a), (i), and (k)).

Figure  7.  Single-electrode biasing experiments under tokamak configuration: (a) plasma current, (b) loop voltage; (c), (d), (e), and (f) floating potential, radial electric field, electron temperature, and electron density measured by the edge Langmuir probe array, respectively, (g) current and (h) voltage of Electrode 2. (i)‒(n) Single-electrode experiments under similar configuration: (i) plasma current, (j) loop voltage, (k) line-averaged electron density from the interferometer central chord, (l) spectral line intensity of H_α central chord, (m) current and (n) voltage of Electrode 1.

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These results confirm that the electrodes can effectively control the radial electric field. Notably, the application of biased electrodes results in an increased plasma density and duration.

3.3   Edge parallel current profile control experiments

After the construction of two high-current power supplies, the edge parallel current profile control experiments were conducted to investigate the electrodes’ ability to manipulate the current profile and their influence on the edge plasma. Hydrogen plasma in RFP configuration was utilized, with a plasma current I_p = 100 kA and a reversal parameter F < 0. Both electrodes were activated, with the electrode heads located at r = 30 cm. The diagnostics were similar to those employed in the previous experiments, with the Langmuir probe array located at r = 35 cm and installed at the ‘M’ horizontal window. Additionally, changes in the boundary toroidal magnetic field were detected by magnetic probes mounted at different toroidal angles (ϕ) on the inner wall of the vacuum chamber.

The experimental results compare two discharges with and without bias voltage, as shown in figure 8. During the flat-top I_p phase, the plasma exhibits a weak reversed field, with relatively poor confinement throughout the discharge, as indicated by the saturation of the H_α signal (figure 8(c)). Under bias, a decrease in H_α and an increase in line-averaged density are observed. According to Langmuir probe results, the anticipated ion saturation current of the electrode heads (I_S,EB) is less than 50 A. The actual electrode current significantly exceeds this anticipated value (figure 8(e)), and it is primarily contributed by the emitted electron current. However, the Langmuir probe results show no significant changes in V_f and E_r during bias (figures 8(f)–(j)).

Figure  8.  The two independent electrodes biasing experiments under RFP configuration: (a) plasma current, (b) loop voltage, (c) spectral line intensity of H_α central chord, (d) and (e) voltage and current of the two biased electrodes, respectively, (f) line-averaged electron density of the interferometer central chord, (g)–(j) floating potential, radial electric field, electron temperature, and electron density measured by the Langmuir probe array, respectively, (k)–(q) B_t measured by magnetic probes installed on the vacuum chamber wall at varying toroidal positions.

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According to magnetic flux conservation principles, the modification in the edge parallel current profile can be qualitatively estimated through the variations in the boundary toroidal magnetic field. Based on the direction of the emitted electron current relative to the poloidal magnetic field (B_p) generated by the plasma current, changes in the core and boundary toroidal magnetic fields can be estimated. If the emitted electron current flows in the same direction as B_p, then the toroidal magnetic field in the core is enhanced, leading to a corresponding increase in the reversed toroidal magnetic field at the boundary. Conversely, if the emitted electron current flows in the opposite direction to B_p, then the reversed toroidal magnetic field at the boundary is weakened.

The reversed magnetic fields at ϕ = 300°, 312°, 30°, and 78° (figures 8(k)–(q)) are intensified under bias, while the toroidal magnetic flux remains unaffected. This indicates that the biased electrodes induce local plasmas into a deeper reversed field state. These results also suggest that the electrode current flows along the direction of B_p.

The toroidal direction of the electrode current can be determined based on the distribution of the affected boundary magnetic field areas. The intensified B_t at these locations and the unchanged B_t at ϕ = 252°, 348°, and 105° imply that the electrode current flows near these magnetic probes in the regions of ϕ = 300°–312° and ϕ = 30°–78° before returning to the vacuum chamber wall. Based on the regions where the boundary magnetic field is affected, the electrode current likely flows in the direction of the plasma current.

Based on the electrode current direction, the diagnostic results can be interpreted as follows. The H_α detector is located near Electrode 1, which influences the edge parallel current profile and improves plasma confinement to a certain extent, thus the H_α signal decreases. Similarly, the interferometer is located in the region where the current from Electrode 2 flows, thereby detecting an increase in density. The Langmuir probe array is located near the magnetic probe at ϕ = 252°, where the current from Electrode 2 mostly returns to the wall, thus no changes in the radial electric field are observed.

These results indicate that the two independent biased electrodes enable local plasma to reach a deeper reversed field state by altering the edge parallel current profile.

3.4   The impact of biased electrode on turbulence

In the electric field control experiments (figures 9(a) and (b)), both magnetic and electrostatic fluctuations showed a degree of enhancement under bias. Specifically, a significant peak in the magnetic signal was observed at a frequency of 23.4 kHz with a mode number of m/n = 2/1, which is suspected to correspond to a tearing mode. Additionally, a peak was detected in both the potential and magnetic signals at around 7.8 kHz, with a mode number of m/n = 4/1, which may also be linked to a tearing mode. This enhancement of fluctuations contrasts with the suppression of electrostatic fluctuations seen in previous biasing experiments [8, 9]. The mechanism behind this enhancement remains unclear and requires further investigation.

Figure  9.  The impact on biased electrode on electrostatic and magnetic fluctuations: (a) and (b) are magnetic fluctuations and electrostatic fluctuations under the edge radial electric field control experiment, respectively, (c), (d) and (e) are magnetic fluctuations and electrostatic fluctuations under the edge parallel current profile control experiment, respectively.

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In the current profile control experiments (figures 9(c)–(e)), a reduction in the amplitude of magnetic fluctuations was observed within the reversed field enhanced region, with peaks occurring at frequencies of 9.8 kHz and 21.5 kHz, possibly corresponding to mode numbers of m/n = 5/1 and m/n = 6/1, respectively. However, electrostatic fluctuations did not show a significant reduction, which may be due to the probe being positioned outside the region influenced by the electrode. These results suggest that the biased electrode exerts a certain level of suppression on magnetic perturbations.

4.   Conclusions

The electromagnetic turbulence in RFP plasmas exhibits distinct three-dimensional characteristics. Effective suppression of this turbulence is crucial for enhancing plasma confinement, necessitating control over the electric field or the current profile. To address this issue, two sets of electrodes were designed and installed on KTX. Since a substantial current was required to alter the edge current profile, each electrode was equipped with a high-power pulse modulation power supply capable of delivering large currents. The maximum output parameters of the two power supplies were ±300 V, 3000 A and ±1000 V, 3000 A, respectively. The electric energy of the power supplies was stored in capacitor banks, and their output pulse was controlled by IGBT H-bridges. The electrodes were radially displaced through magnetic transmission, and the electrode head was a graphite flat disc.

Typically, the electrode current derived from the plasma is insufficient to alter the plasma current profile. However, the excessive current phenomenon was observed in the current-voltage curve of the electrode, indicating that the electrode could be utilized for altering the current profile. Subsequently, experiments were conducted to explore control over the edge radial electric field and the edge parallel current profile.

The edge radial electric field control experiments were conducted under tokamak configuration with one electrode. The results demonstrated that under bias, the edge radial electric field was altered, accompanied with an increase in the electron density and plasma duration. However, under bias, both electrostatic and magnetic fluctuations were observed to be enhanced. Peaks in fluctuations were detected at frequencies of 23.4 kHz and 7.8 kHz, corresponding to mode numbers of m/n = 2/1 and m/n = 4/1, respectively, which are suspected to be associated with tearing modes. Currently, the mechanism behind the enhancement of these fluctuations remains unclear and necessitates further investigation in future studies.

The edge parallel current profile control experiments were conducted in RFP configuration using two electrodes. Under bias, plasmas with locally deeper reversed fields and higher densities were achieved by modifying the edge parallel current profile. A reduction in magnetic fluctuations was observed within the reversed field enhanced region, indicating that the biased electrodes exert a suppressive effect on magnetic perturbations.

These findings highlight the effectiveness of biased electrodes in controlling both the edge radial electric field and the edge parallel current profile, which is vital for enhancing plasma confinement in RFPs.

Acknowledgments

The authors greatly thank the KTX team for their support of these experiments. This work was supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2022YFE03100004, 2017YFE0301700 and 2017YFE0301701) and National Natural Science Foundation of China (Nos. 12375226, 11875255, 11635008, 11375188 and 11975231).