1 INTRODUCTION

In recent years, considerable progress have been made in the physics and technology of alternative systems for high-temperature plasma confinement with fully or partially linear topology, including open traps of various types and field-reversed configurations (see, for example, [1–3]). This progress motivated the development of the GDMT project, which is a modular open trap for creating plasma with the sub-fusion parameters [4, 5]. One of the important elements of the GDMT concept is the use of special sections with the multi-mirror magnetic field (the magnetic field periodically changing along the axis). The multi-mirror sections are designed to suppress the longitudinal losses of particles and energy from the confinement region and, thereby, to increase the plasma energy lifetime. Experimental confirmation of operating capacity of all new physical elements included in the GDMT project will clear the way for developing the promising (from the point of view of technology) sources of fusion neutrons and fusion reactors operating without tritium fuel.

Currently, the physics of multi-mirror confinement, the idea of which was proposed in [6, 7], is well developed in theory (see reviews [8, 9]). The most striking experimental demonstration of the resources of this technology is a multiple increase in the energy lifetime of the plasma with sub-fusion parameters reached at the GOL-3 facility when its magnetic system configuration was changed to the multi-mirror one [10]. The distinctive feature of the GOL-3 facility was applying the technology of plasma heating with the help of high-current relativistic electron beam. As a result, different collective processes significantly affect the plasma confinement [11]. In the next stage of research, the GOL-NB facility will be put into operation, which will use neutral beam injection for plasma heating [12]. According to calculations, this will make it possible to reach the quasi-stationary state during a few milliseconds [13].

The GOL-NB facility is an open system for the plasma confinement, which includes the central mirror machine: the 2.5-meter-long gas-dynamic trap with an axial field of up to 0.3 T, two high magnetic field sections joined to it, and two end magnetic flow expanders [14]. The high magnetic field sections may be either long solenoids with a field of up to 4.5 T, or multi-mirror systems consisting of thirteen 22-cm-long separate cells with a magnetic field ripple of 1.4. Neutral beams (25 keV, power up to 1.5 MW) will be injected into the central trap.

At the GOL-NB, one of the initial stages of a typical experimental scenario is the preliminary filling of the central trap with the low-temperature starting plasma. It is just this plasma that will be the target for capturing fast atoms of the neutral beams heating the plasma. In this case, the starting plasma in the central mirror machine should have sufficiently high density, not less than nL ~ 1019 m–2 (hereinafter, we will use the notation nL for the linear density, which is understood as an integral of the density over the diameter). In the GOL-NB facility, the widespread technique for the target plasma formation is used: the plasma jet produced by the plasma generator (arc plasma gun) is injected into the trap along the magnetic field.

The design of the GOL-NB facility has the modular structure. This made it possible to start experiments (in accordance with the scientific program) in the starting facility configuration, even before the design magnetovacuum system is perfectly ready. The first important physical problem to be solved was the transport of the low-temperature starting plasma flow from the plasma gun through the long (as compared to the plasma diameter) high magnetic field section in two configurations: the long solenoid and multi-mirror trap. In the preliminary experiments [15, 16], the authors for the first time confirmed the prediction, which was considered obvious in theory [17], that the moderate ripple of the magnetic field will have no considerable effect on the flow of low-temperature plasma, in which the ion free path is much shorter than the period of the field ripple. At the same time, the mentioned studies revealed an exponential decrease in the plasma flow density as the plasma moved along the high magnetic field section, which indicated the presence of the additional channel for the transverse plasma losses. This circumstance motivated the search for the ways to reduce plasma losses during its transport, improve the starting plasma generation system and optimize its operating regimes. Discussion of the results of these studies is the goal of this article.

2 SYSTEM FOR STARTING PLASMA PRODUCTION

In the stage of plasma confinement, the sections with the multi-mirror magnetic field will efficiently operate, if the ion mean free path fits the period of the magnetic field ripples. At the design magnetic field configuration and power of the neutral beam injection, this can be reached at an average plasma density in the central trap of n = (3–5) × 1019 m–3. In the stage of the facility design, different ways were considered for solving the problem of producing such a plasma, in particular, the sources with the hot cathode [18, 19], sources with the high-current longitudinal discharge [20] and ring plasma guns [21, 22] were considered. As a result, the solution was chosen based on the design of the plasma source used at the GDT facility [23].

For this experiment, the facility configuration is shown in Fig. 1. The entire system consisted of two identical magnetic field expanders with 1-m-diameter vacuum volumes, between which the high magnetic field section was installed: the solenoid consisting of the modules intended to be used as a multi-mirror system in the full-scale GOL-NB experiment. The solenoid length was 3.74 m. The plasma gun was installed at a distance of 1.1 m from the first coil of the solenoid. In further consideration, the longitudinal coordinate will be counted from the anode of the plasma gun, which is taken as z = 0. The expansion coefficient and the profile of the magnetic field lines in the expanders corresponded to those calculated for the full-scale GOL-NB experiment. A distinctive feature of these experiments, as well as other experiments in the starting configuration of the facility, was the reduced m-agnetic induction in the high field sections (Bmax = 1.8 T).

Fig. 1.
figure 1

General schematic of the GOL-NB facility. (1) Inlet expander; (2) coils of the expander magnetic system; (3, 7) sectioned plasma dumpers; (4) schematic drawing of the magnetic field lines: the lower line starts from the anode edge, the middle line starts from the edge of the central plasma dumper and touches limiter (9), and the upper line starts from the edge of the second plasma dumper; (5) coils of the high magnetic field of the base solenoid; (6) outlet expander; (8) double Langmuir probe; and (10) plasma gun with the magnetic field coils. The coordinate z0 = 0 corresponds to the plasma gun anode, and the outlet plasma dumper is installed at z2 = 5.7 m.

Full size image

The plasma gun is made in the form of the axially symmetric structure that shapes the flow of plasma produced by the high-current electric discharge in the working gas. The main elements of the gun are the hollow cathode with an inner volume of L × π × R2 ≈ 3.5 × π × 2.52 ≈ 69 cm3 and the anode spaced from the cathode by a distance of ~150 mm in the direction along the magnetic field and having the inner aperture with a diameter of ~50 mm. The floating limiters are installed along the discharge gap to stabilize the arc. The general schematic of the plasma gun design is shown in Fig. 2. The plasma gun operates more stably in the presence of the external magnetic field with an induction of the order of ~0.1 T, which ensures the magnetic insulation of the discharge channel. This field is created either by the magnetic system of the facility, or by a pair of self-contained coils installed in accordance with the Helmholtz geometry. The gas is supplied to the gun through the tubular firing electrode installed inside the cathode and is controlled by the pulsed valve. All inner metal elements of the gun in contact with the plasma are made of molybdenum. The high-density Al2O3 ceramics was used for insulation of all structural elements. As a result, the working gas flowed out along the discharge channel, being efficiently ionized.

Fig. 2.
figure 2

Plasma gun geometry. The gun is an axially symmetric system. (1) Vacuum gun body (vacuum is to the right of it); (2) magnetic field coils; (3) sectioned plasma dumpers; (4) vacuum volume, which is part of the facility volume; (5) anode; (6) envelope of the floating limiters; (7) cathode; (8) discharge-initiating electrode; (9) tube for working gas puffing; (10) ceramic insulators; and (11) volume at the atmospheric pressure.

Full size image

The plasma gun is powered by a forming line with an operating voltage of up to 4 kV and pulse duration of ~2 ms. Typical waveform of the discharge current is shown in Fig. 3 (top). The amplitude of the arc current is determined by the impedance of the supplying feeder and the plasma gun. It varies in the range 5‒15 kA, depending on the charging voltage and gas supply conditions.

Fig. 3.
figure 3

From top to bottom: cathode current of the gun, pressure, and saturation current of the double Langmuir probe at a distance of z = 2.02 m. Graphs 1, 3, 5, 7 and 2, 4, 6, 8 correspond to the experiments performed with the industrial MH-1 valve (experiment NB3322) and the fast valve designed at BINP (experiment NB3364), respectively. Time dependences of pressure 3, 4 and 5, 6 were measured in the inlet expander containing the plasma gun and at a distance of z = 2.02 m, respectively.

Full size image

3 OPTIMIZATION OF WORKING GAS PUFFING

The main factors affecting the stable discharge ignition in the gun are the presence of the sufficient amount of gas in the cathode–anode gap and triggering time of the pulsed valve. At the same time, it is required that the second condition should be satisfied: the inflow of unionized gas into the facility working volume should be minimized. Further, this gas will considerably impair the transport of the plasma flow along the system and also affect its parameters. During the experiments, the plasma parameters were studied and the operating regimes of two different fast valves were optimized.

The first one is the MH-1 industrial valve (FESTO, Germany) with the additionally modified valve seat, and the second one was designed in Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences (BINP). The main difference between these valves is their opening speed. It turned out that this parameter considerably affects the initial gas pressure in the inlet expander, in which the gun is installed (see Fig. 3, curves 3 and 4). After optimizing the gas puffing system, in experiments using the faster valve designed in BINP, the amount of gas accumulated in the inlet expander volume by the beginning of discharge initiation t = 0 was reduced twice, as compared with the experiments using the MH-1 valve. This di-fference is ΔP ≈ 43 mPa, which corresponds to a decrease in the amount of unionized gas of ΔN ≈ 1019 hydrogen molecules. When performing this comparison, the initial gas pressures and triggering times of the valves were chosen so as to obtain the same discharge current in the gun. With allowance for the algorithm for choosing the triggering times of the valves, we obtain that almost the same gas concentration is formed inside the gun providing the possibility of the discharge initiation.

Further analysis of the gas pressure dynamics in the system showed that in the case of using the faster valve, all other things being equal, the amount of gas admitted into the facility during the discharge is less by ΔN ≈ 5 × 1019 molecules which is rather large amount of gas, as compared to the total number of ions generated by the gun. This is important not only from the point of view of the efficiency of the working gas utilization, but also from the point of view of the effect of this gas on the charge exchange and ionization losses of the plasma, as well as on the subsequent plasma transport along the magnetic field. An example of how the additional gas present in the plasma flow affects the experimental conditions is shown in Fig. 3 (curves 7 and 8), which presents the saturation currents of the double Langmuir probe measured at a distance of z = 2.02 m. In the plasma images taken in the visible wavelength range, the excess amount of gas puffed through the slower valve is also clearly visible, see Fig. 4. In this case, the plasma glow diameter in the regions near the plasma gun and the sectioned dumpers becomes larger, as the gas puffing into the system increases, which indicates a large number of excited atoms in these regions.

Fig. 4.
figure 4

Image (negative) of plasma glow in the region of its formation: (a) the MH-1 valve, and (b) the valve designed in BINP. (1) Gun anode region; (2) sectioned plasma dumpers; (3) geometry of vacuum chamber of the inlet expander, and (4) region of the magnetic flux compression at the entrance to the high field section.

Full size image

Optimization of the triggering time of the gas valve operation was performed using the following procedure. The vacuum chamber filling with gas was investigated using the vacuum gauges with the PMM-46 manometric tube and the recording system that provided the time resolution τ = 0.8 ± 0.1 ms. The system for vacuum measurements was calibrated using the Pfeiffer PKR-251 instrument. The manometric tubes were equipped with the additional shields protecting them from the plasma ultraviolet radiation, which makes it possible to study the pressure dynamics in experiments with the plasma. The triggering time was chosen so that the pressure in the high magnetic field section did not increase by the beginning of the discharge (see Fig. 5, graphs 3 and 5, in comparison with graph 1).

Fig. 5.
figure 5

Pressure in the system measured at different coordinates along the facility length after optimization of the gas fast-valve gas puffing (bottom). Curves (1, 2), (3, 5) and (4, 6) were measured in the inlet tank, and at distances z = 2.02 and 4.4 m, respectively. Graphs 1, 3, and 4 correspond to the NB4592 experiment with the discharge in the plasma gun, while graphs 2, 5 and 6 correspond to the NB4583 experiment, in which only the gas puffing system was triggered in the gun.

Full size image

When considering the gas motion in the experiment without plasma, we can assume that the system filling with the gas occurs as a result of diffusion:

$$\frac{{\partial n}}{{\partial t}} = D\frac{{{{\partial }^{2}}n}}{{\partial {{z}^{2}}}},$$
(1)

where D is the diffusion coefficient. The solution to Eq. (1) is as follows:

$$P(z,t) = \frac{1}{{\sqrt {4\pi Dt} }}\exp ( - {{z}^{2}}{\text{/}}(4Dt)).$$
(2)

Since the mean free path of molecules is much longer than the diameter of the vacuum chamber in the high magnetic field section, the diffusion coefficient was calculated based on the effective free path equal to the chamber diameter λ ~ 0.13 m: D ≈ 78 m2/s. The diffusion coefficient calculated from the data presented in Fig. 5 is equal to Dexp = 70 ± 3 m2/s, which is in good agreement with the theoretical estimate.

When the discharge in the plasma gun is switched on, the gas propagation through the chamber considerably changes. Gas appears in the chamber with the lesser delay. Under these conditions, we can estimate the hydrogen propagation velocity along the chamber as \({{{v}}_{{\text{g}}}}\) = 1.5 ± 0.2 km/s. This velocity is comparable with the speed of sound in hydrogen under normal conditions and several times less than the velocity of plasma propagation along the axis \({{{v}}_{{\text{p}}}}\) ≈ 8.1 km/s measured by the set of the Langmuir probes [16]. Thus, in the section with the high magnetic field, which is far from the plasma gun, the non-diffusion transport is observed of the gas accompanying the plasma jet. The gas pressure dynamics at different coordinates cannot be explained by the recombination of the low-temperature plasma flow.

4 GEOMETRIC PARAMETERS AND PROPERTIES OF THE PLASMA FLOW

The process of generation and formation of the starting plasma flow essentially depends not only on the operating regimes of the plasma gun, but also on the configuration of the electric field created by the additional electrodes. In addition to the set of the sectioned electrodes of the plasma dumper and plasma gun shown in Figs. 1 and 2, the additional group of electrodes was mounted inside the facility (element 9 in Fig. 1) consisting of the base limiter with a circular aperture and several protective disk electrodes located on both sides of it. Molybdenum is used as a material for all electrodes. This engineering solution increases the threshold for the occurrence of unipolar arcs. The electrodes of this limiter and the sectioned plasma dumpers can be connected to the source of the constant bias potential or left under the floating potential.

The experiments have shown that the envelope of the low-temperature starting plasma flow corresponds to the change in the diameter of the magnetic field tube calculated at different longitudinal coordinates, except for one important detail. The diameter of the plasma flow corresponds to the projection of the aperture in the central electrode of the inlet plasma dumper, but not to the aperture in the anode of the plasma gun, which is much lesser. Most likely, this is due to the fact that in the region between the anode and the electrodes of the plasma dumper, the considerable amount of the accompanying gas accumulates and its additional ionization occurs. In this case, in the anode region, the plasma leans upon the radially sectioned molybdenum insulated disks (element 3 in Fig. 2) up to the radius of the inner aperture in the central plasma dumper. The characteristic scales of the main elements affecting the discharge geometry are given in Table 1.

Table 1. Characteristic scales of the main constructional elements of the plasma system affecting the discharge geometry, as compared to the size of the glowing plasma region
Full size table

The installation of the inlet limiter had a positive effect on the plasma transport along the magnetic field. This can be clearly demonstrated by the radial distribution of the Hα line intensity (see Fig. 6b). Measurements of the radial profile of the Hα line intensity also show that the limiter affects the motion of the accompanying gas (it affects the Hα line intensity) and stabilizes the discharge geometry in the transverse direction (profile shape becomes more uniform). The discharge nonuniformity (filamentation) becomes considerably decreased, especially in the final stage of the discharge. This effect is well-known; it is associated with the minimization of the azimuthal component of the electric field at the plasma periphery near the conducting limiter.

Fig. 6.
figure 6

Intensity of the Hα line of plasma emission as a function of chord radius R. Intensity was measured at the distance z = 2.02 m at times (a) 0.5 and (b) 2 ms. Dashed, dotted, and solid curves correspond to the measurements performed before the installation of the inlet diaphragm (with the MH-1 valve), after the installation of the limiter (with the MH-1 valve), and after the installation of the limiter (with the fast valve designed at BINP).

Full size image

After optimizing the triggering times of all subsystems of the plasma gun and the final installation of the intrachamber electrodes, a series of experiments was performed to study the parameters of the transported plasma as functions of the discharge current and pressure in the gas main supplying the gun valve with the gas. It turned out that the saturation current of the double Langmuir probe (which is an indicator of the plasma ion flow) increases almost linearly with an increase in these parameters (see Figs. 7 and 8) within the entire range of parameters available in the experiment. The linear increase in the saturation current of the Langmuir probes with increasing gas pressure in the valve indicates that in the upgraded system, the gas efficiency of the discharge is considerably high.

Fig. 7.
figure 7

Saturation current of the double Langmuir probe averaged over time interval t = 1–1.5 ms as a function of the cathode current of the gun at a pressure in front of the gun valve of 7 × 105 Pa. Circles and crosses correspond to z = 2.68 and 3.8 m, respectively.

Full size image
Fig. 8.
figure 8

Pressure increment P1 in the inlet expander at time t = 2.5 ms (after switching off the gun current) and saturation current I of the double Langmuir probe averaged over time interval t = 1–1.5 ms (probe is installed at z = 2.6 m) as functions of pressure P0 in front of the gun valve. The cathode current of the gun is ~9.5 kA.

Full size image

Optimization of all subsystems of the starting plasma source resulted in the improved efficiency of the plasma jet transport along the entire length of the facility. In [16], we previously noted that there was observed an exponential decrease in the plasma density along the length of the high magnetic field section, which was associated with the presence of the accompanying gas in the plasma flow. The detailed data on the spatial and temporal dynamics of the starting plasma were also presented there. In this work, the dependence of the number of ions per unit length, i.e., the density integrated over the cross section of the chamber, is shown in Fig. 9. This is the fundamental result of the optimization of the system forming the starting plasma. It can be seen from the graph that at a distance of z ≈ 4 m, the starting plasma flow increased by more than four times. In the design configuration of the GOL-NB facility, this corresponds to a proportional increase in the starting plasma flow from the transport section to the central trap.

Fig. 9.
figure 9

Distributions of the linear plasma density in different operating regimes of the working gas supply system. Crosses and diamonds correspond to the results of this study (with the optimized gas supply system) and the results of the first plasma campaign at the GOL-NB facility [16], respectively.

Full size image

When the starting plasma flow is injected into the central trap, first, the magnetic field tube expands as it moves from the magnetic mirror to the central plane of the trap, and then it shrinks during the subsequent flow motion towards the second magnetic mirror (the outlet section with the high magnetic field). In model calculations [13] of the plasma heating and confinement performed using the kinetic code DOL, it was assumed that in the baseline scenario, the linear plasma density will be nL = 1.2 × 1019 m–2 (at n = 3 × 1019 m–3 and a = 0.20 m). In this case, the expected efficiency of capturing the heating neutral beams is estimated to be 50%. In the most pessimistic scenario, the data shown in Fig. 9 allows expecting that when the magnetic induction in the high field sections will be increased up to the design induction B = 4.5 T, the linear plasma density will be nL ~ 9.5 × 1017 m–2. The given density nL corresponds to the case of the absence of angular scattering of plasma particles during their flight through the central trap, and all particles of the starting plasma pass through the central trap and leave it.

More realistic is the situation when a part of the starting plasma flow is captured due to the reflection of particles from the magnetic mirror as a result of their angular scattering during their stay inside the central trap. In this case, the density and radius of the plasma in the trap will be also determined by other processes, including the transverse diffusion. As a conservative estimate, we can take the coefficient of the density increase in the trap as compared to the “purely transit” case, K = R1/2/2 ≈ 2, where R = 15 is the mirror ratio of the central trap. Thus, formal taking into account only the angular scattering of particles results in the estimate nL ~ 1.8 × 1018 m–2. However, in the experiments at the GDT facility [23], the additional accumulation of plasma in the trap was observed when using the plasma gun of similar design. In this case, the radius of the starting plasma was considerably larger than the formally calculated plasma gun projection onto the central plane of the GDT. In the case under consideration, if the magnetic induction in the high field sections is increased from B = 1.8 T (present value) to B = 4.5 T (design value), then the more optimal shape of the magnetic field lines near the plasma gun will provide one more additional coefficient of the order of 1.5.

We note that the main goal of the presented study was to optimize the operating regimes of the plasma gun in order to reduce plasma losses during its transport. The obtained parameters of the plasma flow make it possible to start experiments on plasma heating after completion of the facility assembling in the design configuration with the central trap of the gas-dynamic type and two heating injectors. The work intended to maximize the plasma flow was not performed in the presented study. However, the dependences shown in Figs. 7 and 8 intend that the plasma flow can be increased, if the gas puffing into the plasma gun and the discharge current will be simultaneously increased. In any case, in experiments on the neutral beam injection into the central GOL-NB trap, it is assumed that the additional gas injection system will be used to maintain the balance of matter. Discussion of such a system is beyond the scope of this work.

5 CONCLUSIONS

In the first stage of experiments at the GOL-NB facility, the plasma formation system was successfully launched, which was designed to fill the central mirror machine with the target plasma. The plasma flow is formed in the arc plasma gun installed in a relatively weak magnetic field. Further, it is compressed in the increasing magnetic field and then transported to a distance of approximately 4 m. The design of the plasma gun is described. Optimization of the operating regimes and scenarios of the system for creating the starting plasma made it possible to reduce the gas load onto the vacuum system of the facility. This resulted in the reduction of losses associated with the presence of gas dragged along together with the plasma. The plasma flow at the outlet from the high magnetic field section was increased approximately four times, as compared to the results of the first plasma campaign [16]. It was discussed how the limiters and other intrachamber electrodes affect the plasma flow formation. The achieved plasma flow parameters will be sufficient to start experiments on plasma heating with the help of neutral beams at the GOL-NB multi-mirror trap in its full-design configuration.