2.1. Plasma gun layout

The plasma source is an axisymmetric system with planar circular hot cathode based on LaB $_6$ , a hollow copper anode, two main magnetic coils and a vacuum chamber 14 cm in diameter and 48 cm in length (Ivanov et al. Reference Ivanov, Ustyuzhanin, Sudnikov and Inzhevatkina2021). Figure 2 shows a layout of the plasma source with sketchy feeding diagram. LaB $_6$ , as a cathode material, offers several advantages: it remains reusable even after exposure to air or water leaks. It does not have to be recoated when the machine is exposed to air. The material can withstand the higher ion fluxes associated with higher current discharges. The cathode is a circular disc of sintered LaB $_6$ powder with diameter D = 5 cm and thickness h = 3 mm. It is indirectly heated by the radiation of a tungsten spiral, which is located behind the cathode (such as the tungsten spiral described by Goebel, Hirooka & Sketchley Reference Goebel, Hirooka and Sketchley1985). The spiral heats the cathode up to $T = {1900}\,\textrm {K}$ . The heater current is supplied via an insulated feeder at the cathode flange centre and completes the circuit on the vacuum side. A power of $N = {800}\,\textrm {W}$ is required to heat the cathode up to the operating temperature.

Figure 2. Plasma source geometry with main power supply diagramm. 1, LaB $_6$ cathode; 2, copper anode; 3, magnetic field coils; 4, floating diaphragms; 5, gas feeding system; 6, magnetic field lines; 7, limiter in entrance of the transport section; 8, limiter after the transport section; 9, radial segmented plasma endplate; K $_1$ , K $_2$ and K $_3$ , the IGBT transistors; the red rings, Hall probes.

The copper anode was grounded in the start operation mode (the short anode mode, SA mode, Sudnikov et al. Reference Sudnikov, Beklemishev, Inzhevatkina, Ivanov, Postupaev, Burdakov, Glinskiy, Kuklin, Rovenskikh and Ustyuzhanin2020; Ivanov et al. Reference Ivanov, Ustyuzhanin, Sudnikov and Inzhevatkina2021; Sudnikov et al. Reference Sudnikov, Ivanov, Inzhevatkina, Larichkin, Lomov, Postupaev, Tolkachev and Ustyuzhanin2022a , Reference Sudnikov, Ivanov, Inzhevatkina, Larichkin, Postupaev, Sklyarov, Tolkachev and Ustyuzhaninb ) because there was weak electrical conductivity between the anode and plasma. An anode potential control relative to the grounded SMOLA device appeared after it’s geometry change. The anode was extended along the device axis to increase the electric contact surface between the anode and plasma flow (the anode was lengthened from 2 to 7 cm to improve this contact, see dark red long triangle in figure 2); additionally, the elongation of the anode was greater than its aperture diameter, which led to effective plasma parameter regulation by varying of the anode–cathode magnetic insulation. So, currentlty, there are two experimental modes of the plasma gun: the grounded anode and the biased anode with regulated electric switches. Anode–cathode isolation (or the anode magnetic insulation) is created by a longitudinal magnetic field so the magnetic field line starting on the edge of the cathode (pink line in figure 2) usually touches the anode’s exit in standard magnetic configuration. In the operating mode, the anode is projected to the central limiter’s diaphragm at the confinement region through magnetic lines (green line in figure 2, the limiters are grounded) while the cathode is projected to the second plate of the plasma dump at the exit expander.

The gun’s magnetic field is created by two coils placed coplanarly to the cathode and the anode correspondingly. They are fed independently, so it allows for the required magnetic insulation and gun magnetic mirror ratio to be created with respect to the entrance expander of the device. In the discussed experiments, the mirrors of this trap were asymmetric with mirror ratios $R\approx 8$ on the plasma source side and $R \approx 3$ on the helical mirror side. In the paper, we define the anode magnetic insulation as cathode–anode magnetic field relation $B_c/B_a$ . The magnetic field in the cathode and the anode position is calculated from current measurements from the coils by Hall probes. We used values of the magnetic field at the z-location of the anode and cathode. In typical experiments with the SA mode, $B_c/B_a=2.67$ , and $B_c/B_a=1.34$ in the LA mode.

The volume between the cathode and the anode is limited by floating molybdenum diaphragms (FDs) in the source (Ivanov et al. Reference Ivanov, Ustyuzhanin, Sudnikov and Inzhevatkina2021). The diaphragms are placed in a ceramic box to isolate them from the source’s walls. This system was located in the interelectrode area of the gun to reduce the amount of puffing gas in the source and increase the gas efficiency of the gun.

The electric feeding of the plasma gun is carried out by a capacitor through the IGBT transistor (K $_1$ ) and resistive ballast. The inductive impedance of feeders is negligible in relation to the ballast. The feeding capacitor consists of a series of supercapacitors with a total capacity of 10 F. It is charged up from ${-150}\,\textrm {V}\;\textrm {to}\;{-300}\,\textrm {V}$ . The cathode is connected to the second plate of the exit plasma endplate through a resistance of 0.2 $\Omega$ . All plates of the pumper are powered by DC sources in 50 V steps,

(2.1) \begin{equation} \ U_k = -k \boldsymbol{\cdot} {U}, \end{equation}

where k = 1, 2,.. 5 is the plate number and $U=50\,\mathrm{V}$ (figure 2, see number 9 in the exit expander).

The anode potential (relative the grounded device) is regulated independently of the anode–cathode voltage in the plasma source. It is charged up from ${-200}\,\textrm {V} \;\textrm {to}\; {200}\,\textrm {V}$ . Two IGBT transistors in the anode circuit (K $_2$ and K $_3$ ) allow for the anode potential to be changed (from grounded to positive or negative, and back) during the experimental pulse.

The gas feeding of the plasma gun is carried out by two independent gas valves. The first serves for the fast filling of the gun volume and is open only for the first 310 ms with the discharge initiation and begins gas puffing simultaneously with the switching on of the cathode voltage. The amount of puffed hydrogen atoms is close to $10^{21}$ . The second works during the whole plasma discharge and carries out the stationary gas feeding through the thin long capillary for dumping the pulsations and smoothing out of the gas flow. The H $_{2}$ gas puff rate is within approximately $10^{19}$ – $10^{20}$ atoms $\mathrm{s}^{-1}$ (typical $J_{H_2}\approx$ $10^{21}$ atoms $\mathrm{s}^{-1}$ $\approx$ 60 eq.A) and is regulated by the working gas pressure on the high-pressure side of the valve. It lies within the limits of $10^{-1}$ – $2$ bar.

The typical experimental diagrams are shown in figure 3. First, the cathode heating switches off because the Ampere force of the current in the tungsten spiral in the external magnetic field of the gun can break the heater. Then, the confining magnetic field is switched on. It is created by different axial coils powered by the supercapacitors with corresponding voltages. When the current in the coils reaches the stationary phase, the fast gas valve opens and the cathode potential is switched on. This time corresponds to $t$ = 0 ms on the diagram. The stationary plasma discharge builds up during the first 4060 ms. Average values on the flattop of the discharge ( $t$ $\leq$ 120–180 ms) are used to plot radial profiles of the plasma parameters.

The experimental results of the research correspond to different regimes of the plasma source: the short anode mode (SA) with (and without) floating diaphragms and the long anode mode (LA) with floating diaphragms. All the following experiments were performed in the straight field regime of the SMOLA device without a helical field.

Figure 3. Typical plasma pulse in the SMOLA device. 1, cathode heating; 2, current in the magnetic coils; 3, cathode potential; 4, full discharge current; 5, fast gas valve; 6, slow gas valve. Green area corresponds to the stationary phase of the discharge for probe measurements.

2.2. Diagnostics

The following diagnostics were actively used in the described experiments. Radially movable sets of electrostatic probes were installed in the confinement region (z = 0.4 m), in the transport section at z = 2.04 m (second corrugation period). Each set includes a double probe and two radially shifted emissive probes. Double probes at z = 0.4, 2.04 m measure IV characteristic. The emissive probes with thoriated tungsten wires were heated by the plasma during 50 milliseconds at the initial part of the discharge, and then provided simultaneous measurements of plasma potential and radial electric field. The reach of the probe working temperature was verified by thermal radiation of the wire. The emissive probe reaches working temperature during $t$ $\leq 40$ ms at radial coordinates $r$ $\leq 60$ mm. At the outer region ( $r$ = 6080 mm), the heating duration is $t$ = 90 ms. The temperature rise time is consistent with the estimations of Hershkowitz et al. (Reference Hershkowitz, Nelson, Pew and Gates1983). At $t$ = 185 ms, the plasma source is turned off to avoid damaging the probes.

An imaging Doppler spectrometer in the confinement zone (z = 1.15 m) was used to monitor plasma rotation (Inzhevatkina et al. Reference Inzhevatkina, Burdakov, Ivanov, Lomov, Postupaev, Sudnikov and Ustyuzhanin2021) that can compare with the emissive probe’s electric field measurements. The spectrometers also provide the ion temperature measurement due to the Doppler broadening of the emission spectral line of the charge-exchanged hydrogen.

Hall probes measured the currents from electrodes (cathode, anode, central diaphragms in each limiter, and plates of plasma endplate) to plasma and back in the SMOLA device. Hall probes were located on each electrode (figure 2, red rings).

Gas measurements were realised by ionisation vacuum gauges in the confinement zone (z = 0.4 m), in the transport section at z = 2.76 m (sixth corrugation period) and the exit expander (z = 4.34 m). The gas pressures temporal dynamics can be used for gas density measurements to estimate plasma gas balance and collisional scale (note that all ionisation vacuum gauges have doubtful accuracy owing to the plasma ultraviolet emission: we shielded them from direct radiation to minimise this effect, but an accurate gas pressure estimation can only be made just after plasma disappearance).

We assumed that the radial distributions of plasma parameters are axially symmetric and that the radial displacement of the plasma axis is negligible compared with the plasma radius for all operating regimes. The first assumption relies on the axially symmetric configuration of the plasma source, confinement region and transport section in the straight field regime. The second one is set by the correction magnetic coils in the entrance and exit of the transport section.

The experimental data were obtained in the following way. We made approximately 20 identical experimental discharges in each configuration. Probe sets were moved radially between discharges.

4.1. The short anode mode

In the basic configuration of the source with the SA, only two parameters could be regulated: the cathode – anode voltage and the anode magnetic insulation. The anode in the SA mode was always grounded (see figure 2). In this mode, variation of the cathode anode voltage in the plasma gun was from 200 V to 300 V, the anode magnetic insulation as $B_c/B_a$ ranged from 2 to 3.3.

Figure 9. Radial distribution of the electric potential and the radial field in the plasma. Data are measured by the double emissive probe in the confinement zone (z = 0.4 m).

Figure 10. Axial distribution of the electric potential in the SMOLA device. Probes are located on the axis.

Typical radial distributions of the electric potential and field in the SA mode measured by the double emissive probes are shown in figure 9. Plasma in the confinement region has a negative potential on the axis (figure 9 a), which leads to plasma pinching towards the axis (Sudnikov et al. Reference Sudnikov, Beklemishev, Inzhevatkina, Ivanov, Postupaev, Burdakov, Glinskiy, Kuklin, Rovenskikh and Ustyuzhanin2020; Sudnikov et al. Reference Sudnikov, Ivanov, Inzhevatkina, Larichkin, Lomov, Postupaev, Tolkachev and Ustyuzhanin2022a ). In the straight-field mode, the plasma potential reaches $\varphi \approx (1.5\div 3)\boldsymbol{\cdot }{T_e}$ (figure 9 a). Direct measurements of the potentials (in the same points on z and $r$ ) agree with the radial electric field profile. The radial electric field increases linearly from the plasma centre ( $r=0$ $\mathrm{mm}$ ) to the edge (plasma SOL) in the core ( $r=50{-}60$ $\mathrm{mm}$ , see figure 9 b). This plasma core is limited by the central diaphragm of the limiters. Thus, the plasma rotates with a constant radial angular velocity $\omega$ in the solid-state mode (with rigid core) along the device according with Doppler shift measurements (Inzhevatkina et al. Reference Inzhevatkina, Burdakov, Ivanov, Lomov, Postupaev, Sudnikov and Ustyuzhanin2021). In standard electric and gas feeding ( $P_{\textrm{dis}}=40$ kW and $J_{\textrm{gas}}=50$ eq.A) of the plasma source with the SA, the plasma rotation velocity in the confinement region ( $z$ = 1.15 m) was $\omega =(0.8\div 1.1){\,\times\,} 10^{6}$ $\mathrm{s}^{-1}$ (Inzhevatkina et al. Reference Inzhevatkina, Burdakov, Ivanov, Lomov, Postupaev, Sudnikov and Ustyuzhanin2021) at $B_c/B_a=2.6$ . The complex of the emissive probes allows one to measure the axial distribution of the radial profile of the plasma potential (figure 10), which was obtained relative to the material vacuum wall. The main potential variation at $\varDelta \varphi \sim 100$ $\mathrm{V}$ is located between the cathode and the confinement zone ( $z$ = 0.4 m) and can be comparable with calculations according to the equality of the fluxes of ions and electrons to the wall $\varDelta \varphi \sim (3{-}4) {\,\cdot\,} T_e/e$ . In the rest of the facility along the magnetic field, the plasma potential changes insignificantly. This fact indicates that there is no significant thermal barrier between the transport section and the confinement zone. Double probes electron temperature measurements at $z$ = 0.4 m and $z$ = 2.04 m also confirm this fact.

In the grounded SA mode, variation of the cathode anode voltage in the plasma gun from 200 V to 300 V results in increasing of the electric field on the plasma core SOL border (figure 11); thus, extends the solid-state mode region. The angular rotational velocity of the rigid core was found to remain constant at the level of $\omega =(0.8\div 1.1){\,\times\,} 10^{6}\, \mathrm{s}^{-1}$ when the rigid core expands. Thus, more plasma pieces can be rotated with the maximal velocity $\omega$ and trapped by magnetic mirrors that enhances the helical plasma confinement efficiency. The magnetic insulation of the anode does not influence the radial electric field distribution. The axial distribution of the potential saved after variation of the cathode–anode voltage in the plasma gun. Obtained results correspond to axial movement of the magnetic perturbations in the reference frame of rotating plasma $V_Z=h \boldsymbol{\cdot }\omega _{E\boldsymbol{\times} {B}}/(2\pi )= (2.9{-}3.4){\,\times\,} {10^4}$ $\mathrm{m\,s}^{-1}$ , which is comparable and can be greater than the ion thermal velocity $V_{T_i}\sim 2{\,\times\,} {10^4}$ $\mathrm{m\,s}^{-1}$ . Thus, the condition of the helical confinement $V_Z \geqslant V_{T_i}$ is satisfied and the efficiency of the longitudinal plasma flow suppression can be changed by the configuration of the plasma source (regulation of the rotation velocity).

Figure 11. Radial electric field distribution at varied cathode potential. Data are measured at z = 0.4 m.

4.2. The long anode mode

The anode’s elongation by 3.5x (see figure 2) enhances the anode–plasma–cathode contact (the LA mode). This modification in the source leads to changes in the magnetic field configuration of the gun because the inner anode magnetic line needs to project on the cathode. In the LA mode, the inner anode magnetic line crosses only the cathode’s edge that increases the anode’s magnetic insulation and the electric resistance anode–cathode via the plasma. Such a change in the anode geometry can influence the currents in the system, radial electric field distribution and conditions of the stable discharge. In the experiments, the anode–ground voltage was varied and the anode’s magnetic insulation was regulated. Variation of the anode–ground voltage (the anode biasing, $U_{\textrm{an}}$ ) in the plasma gun was from −200 V to 200 V, the anode magnetic insulation as $B_c/B_a$ ranged from 1.15 to 1.7 in the LA mode experiments. The cathode–anode voltage stayed at a maximum value $U_{\textrm{cathode-anode}}=300$ $\mathrm{V}$ .

Radial electric field in the plasma is evidence of the radial current existence in the plasma, which is a source of torque Ampere’s force $j_r B_z$ that rotates the plasma column in the SMOLA device. The current from the plasma to each electrode (or vice versa) can have a radial component. In our measurements, the endplate’s current does not have a radial current from the plasma. Thus, radial currents from the anode and limiters transfer torque Ampere’s force for plasma rotation. In all experiments with the grounded anode (SA mode and LA mode), there is a current disparity in the SMOLA device (figure 12). In the grounded anode mode, only half of full current moves in the plasma via the anode, and approximately 50 % of the residual current’s part is detected in the limiters. Thus, a significant part of the current can form behind the anode.

Variation of the anode biasing in the LA mode has led to current redistribution. In the negative biasing LA mode, the anode-plasma current is minimised, while only the limiters’ currents are detected; moreover, this current is less than 50 % the full current (figure 12). Such results give an idea that the remaining radial current can be formed between the plasma and the grounded wall of the entrance expander (confinement zone) and the transport section. Thus, this additional current is also one of the sources of the torque Ampere’s force for the plasma rotation because the limiters have a thin radial border with the plasma and cannot collect all the remaining current. In the positive biasing LA mode, the full discharge current becomes less stable and after $U_{\textrm{an}}\geqslant 100$ $\mathrm{V}$ , the discharge is extinguished. The full discharge current in the LA mode linearly reduces at anode biasing from negative to positive in any magnitude of the $B_c/B_a$ (figure 13). This current behaviour might be caused by potential shielding effects of the anode on the outer plasma column. Thus, the main experiments with radial electric field regulation have been performed with the negative biasing LA mode and the grounded LA mode.

Figure 12. Dynamics of the currents in each electrode without the plasma dump in the modes with grounded LA and biasing LA. The limiters are grounded.

Figure 13. Discharge current at different anode biasing with regulated cathode–anode magnetic field ratio.

In the negative biasing LA mode, the plasma core–edge boundary was shifted outward by 15–20 mm (from $r=80$ mm to $r=95{-}100$ mm, figure 14) compare with the grounded LA mode in the confinement zone. The radial electric field at the plasma SOL increased by a factor of 2–3 (from 0.5 to 1.5 kV m $^{-1}$ ). So, the negative biasing LA mode allows for better rotation of the plasma edge without changing the electric field in the solid-state core and more pieces of the plasma will be rotated with the maximal angular rotation velocity $\omega$ . The anode’s magnetic insulation also affects the radial electric field in the negative biasing LA mode (figure 15). Reducing the anode magnetic insulation (increasing contact surface of the LA with the cathode), the radial electric field can also be increased by a factor of 3 in the plasma SOL at negative anode biasing. At the same time, Doppler spectroscopy measured similar values of the angular rotational velocity $\omega \leqslant 1.1{\,\times\,} {10^6}$ $\mathrm{s}^{-1}$ as the grounded SA mode. As a result, the condition of the helical confinement $V_Z \geqslant V_{T_i}$ is satisfied in the LA mode saving the scale of the $V_Z$ . The restriction of $\omega$ may be related to the the Kelvin–Helmholtz instability on the border between rigid core and SOL (Beklemishev Reference Beklemishev2024).

Figure 14. Radial distribution of the radial electric field in the LA mode with negative biasing and the grounded LA mode in the confinement zone (z = 0.4 m).

Figure 15. Radial distribution of the radial electric field in the LA mode with negative biasing (example radial profile at $U_{\textrm{an}}=-80 \,\mathrm{V}$ ) and different anode’s magnetic insulation in the confinement zone (z = 0.4 m).