2.1. Plasma gun

To create the target plasma, a washer-stack plasma gun with a ring-shaped discharge channel is used; this type of plasma gun has been extensively studied at the AMBAL facilities (Dimov et al. Reference Dimov, Ivanov and Roslyakov1982, Reference Dimov, Kabantsev, Kuz’min, Sokolov and Taskaev1993; Akhmetov et al. Reference Akhmetov1997) and at an axisymmetric mirror stand (Kabantsev & Taskaev Reference Kabantsev and Taskaev1990). The configuration of the generator is illustrated in figure 3. The cathode is an aluminium ring with an inner diameter of 110 mm and a width of 10 mm with an azimuthal groove increasing the cathode area. The discharge channel consists of 23 pairs of floating stainless steel rings. The gun operates with hydrogen as the working gas. Two valves provide independent gas injection into the near-cathode and near-anode regions. The opening and closing times are set for each individual valve. The hydrogen flow rate is varied by changing the pressures at the valve inlets, which are also set independently. The annular discharge volume is embedded in a uniform magnetic field of 0.1–0.5 T produced by a gun solenoid. In the earlier experiments, the molybdenum anode had an inner radius 1 mm greater than the outer radius of the cathode, and the discharge channel was a cylindrical ring. The discharge voltage observed in various operational modes of the plasma gun ranged from 100 to 400 V. At the maximum charging voltage of the forming line of 3.0 kV, the discharge current reached 20 kA.

Figure 3. Washer-stack axially symmetric plasma gun including molybdenum anode, two gas valves and pulsed solenoid. Stainless steel housing of the gun is not shown.

Radial separation of the gun electrodes produces the inward radial electric field leading to $E\times B$ plasma rotation, which is almost rigid in the plasma core, but is strongly sheared near the projection of the discharge channel. Previous experiments with a plasma gun of the same design showed that this sheared rotation drives the Kelvin–Helmholtz instability (Kabantsev & Taskaev Reference Kabantsev and Taskaev1990) and small-scale fluctuating electric fields, which increase primarily transverse ion energy. The ion energy in the plasma produced by this gun is close to or higher than the electron temperature. As the ions with the anisotropic velocity distribution move almost without collisions along the increasing magnetic field towards the mirror, they experience partial reflection. Hence, the ion density decreases towards the mirror, resulting in the formation of an electrostatic potential well, which effectively suppresses the energy exchange between cold 5–10 eV electrons near the plasma gun and warm 30–50 eV electrons in the confinement region. This so-called ‘thermal barrier’ allows the generation of the target plasma with an electron temperature of approximately 50 eV in the confinement mirror cell (Dimov et al. Reference Dimov, Kabantsev, Kuz’min, Sokolov and Taskaev1993; Akhmetov et al. Reference Akhmetov1997). The elevated electron temperature in the confinement region is crucial for increasing the lifetime of hot ions.

Despite the previous favourable outcomes of this configuration of the gun, its arc discharge with a cold duralumin cathode is characterised by electrode sputtering and gradual melting of the edges of the stainless steel washers of the discharge channel with subsequent metal deposition on insulating ceramics between these washers. One of the reasons for this behaviour was hypothesised to be the finite time required for the magnetic field of the gun solenoid to diffuse through a stainless steel housing into the discharge region. An electromagnetic simulation that accounted for the primary metal components of the gun showed that the magnetic field in the discharge channel reached steady state approximately 6 ms after the onset of the solenoid current pulse. Thus, the solenoid power supply was upgraded to extend the duration of the current pulse from the forming line and operate the discharge in a steady-state, uniform magnetic field.

The inner radius of the anode was increased to be 10 mm greater than the outer radius of the cathode. To reduce the thermal load on the outer floating washers in the annular discharge channel, their inner radii were increased to form an imaginary conical surface connecting the outer cathode edge with the anode. This technique allows increasing the lifetime of the ceramic insulators of the gun due to effective anode insulation. The experiments described in this paper used this design of the discharge channel.

2.2. Neutral beam injection

The neutral beam injection system for the CAT device was described in detail by Davydenko et al. (Reference Davydenko, Deichuli, Ivanov and Murakhtin2019). Each of two identical injectors consists of a plasma source, an ion extractor/accelerator and a neutraliser. The maximum hydrogen ion beam current, which is limited by breakdown of the accelerating gap, reaches 130 A at an energy of 15 keV (Deichuli et al. Reference Deichuli, Davydenko, Ivanov, Korepanov, Mishagin, Smirnov, Sorokin and Stupishin2015). The equilibrium yield of neutral hydrogen atoms from the neutraliser is approximately 85 %; thus, the injection power in neutrals is 1.7 MW rather than 2.0 MW. The pulse length of 5 ms does not require active cooling of the grids. The beam extractor/accelerator features multi-slit triode ion optics with spherically shaped grids that provide ballistic beam focusing. In the grids, the slits cover a circular area 34 cm in diameter. To achieve maximum power density and minimum beam size, individual beamlets are aimed at a common point 250 cm from the grids. Also inferred from the profile measurements are the beam divergence half-angles across and along the slits, 37 and 10 mrad, respectively. The current experiments with neutral beam injection have been started with one injector. The current density of a neutral beam in the focal plane has a Gaussian distribution, so the lines of constant current density are ellipses. The slits in the electrodes of the ion extractor/accelerator are oriented perpendicular to the device axis, so that the half-axis of an ellipse at a $1/\mathrm{e}$ level of the current density at the beam axis is 2.7 cm in the radial direction of the device and 8.7 cm along the device axis.

The current density distribution of the beam is measured in two directions using secondary emission detector (SED) arrays. The arrays are placed at a distance of 4.0 m from the NBI grids. Each detector is a 4 mm diameter stainless steel plate. The current density distribution in the radial direction of the device is measured by seven detectors separated from each other by a distance of 4.5 cm. The current distribution in the axial direction is measured by 13 detectors with 5 cm separation.

The beam current trapped in the plasma $I_{\textrm {t}} = I_{\textrm {b}} (1 - \exp (-\int \sigma _{\textrm {tot}}n\,\text{d}l)) \equiv \eta I_{\textrm {b}}$ , where $I_{\textrm {b}}$ is the current of neutral beam, $n$ is the density of the target plasma, $\sigma _{\textrm {tot}} = \sigma _{\textrm {cx}} + \langle \sigma _{\textrm {ie}} v_{\textrm {e}} \rangle /v_{\textrm {b}} + \sigma _{\textrm {ii}}$ is the effective sum of the charge exchange, electron impact and proton impact ionisation cross-sections, where the electron impact cross-section is averaged over the Maxwellian electron distribution function, $v_{\textrm {b}}$ is the speed of the beam atoms, $\eta$ is the trapping efficiency, and the integral is taken along the straight beam trajectory. For the energy of beam atoms $\varepsilon _{\textrm {b}} = 15$ keV and the electron temperature of the target plasma $T_{\textrm {e}} = 30$ eV, collisional cross-section data (Janev et al. Reference Janev, Langer, Post and Evans1987; Janev & Smith Reference Janev and Smith1993) give $\sigma _{\textrm {cx}}\approx 6{\times }10^{-16}$ cm $^2$ , $\langle \sigma _{\textrm {ie}} v_{\textrm {e}} \rangle /v_{\textrm {b}} \approx 1.2{\times }10^{-16}$ cm $^2$ and $\sigma _{\textrm {ii}} \approx 0.4{\times }10^{-16}$ cm $^2$ ; hence, $\sigma _{\textrm {tot}} \approx 7.6{\times }10^{-16}$ cm $^2$ . The line density along the beam axis is determined by the plasma density at radii exceeding the impact parameter $a$ of injection; hence, the details of the density distribution in the plasma core, $r \lt a$ , are unimportant. Taking a Gaussian profile $n(r) = n_0 \exp (-r^2/r_0^2)$ with $r_0 = a$ as an approximation of the measured density profile at $r \gt a$ , one obtains $\int n\,\text{d}l \approx 0.65 n_0 a$ . For 7.6 MW gun discharge power with standard gas flow rate, $n_0 \sim 2{\times }10^{13}$ cm $^{-3}$ , and the target plasma provides the trapping efficiency of $\eta \simeq \sigma _{\textrm {tot}} \langle nl \rangle \simeq 0.1$ for a beam injected at $a = 10$ cm from the device axis. Efficient beam trapping implies $\sigma _{\textrm {tot}} \langle nl \rangle \sim 0.5$ ; thus, the density of the target plasma should be increased.

An intense ion ring formed by NBI in the target plasma is charge neutralised, but must not be current neutralised. It consists of ions of charge $e$ , mass $m_{\textrm {i}}$ and kinetic energy $\varepsilon _{\textrm {b}}$ circulating about an axis in an external magnetic field $B_0$ . In the CGS system of units, the ion ring with a radius $R$ and current $I_{\textrm {f}}$ produces a magnetic field at the axis $\varDelta B = \gamma 2\pi I_{\textrm {f}}/cR$ , where $\gamma$ is a geometric factor of order unity, depending on the ring shape. If fast-ion losses during the injection time $\tau _{\textrm {inj}}$ can be neglected, the accumulated fast-ion electric charge is $\eta I_{\textrm {b}}\tau _{\textrm {inj}}$ and it makes the full turn around the axis in time $2\pi /\omega _{\textrm {ci}}$ , where $\omega _{\textrm {ci}} = e B_0/m_{\textrm {i}}c$ is the ion gyrofrequency. Thus, the ring current is $I_{\textrm {f}} = \eta I_{\textrm {b}}\tau _{\textrm {inj}}\omega _{\textrm {ci}}/2\pi$ and the field-reversal parameter

(2.1) \begin{equation} \zeta = \frac {\varDelta B}{B_0} = \frac {\gamma \eta e I_{\textrm {b}}\tau _{\textrm {inj}}}{m_{\textrm {i}} R c^2}, \end{equation}

so, to achieve field reversal, i. e. $\zeta = 1$ , the condition $\tau _{\textrm {inj}} \gtrsim m_{\textrm {i}} Rc^2/\gamma \eta e I_{\textrm {b}}$ must be satisfied. For a hydrogen beam with $I_{\textrm {b}} = 220$ A, $\eta = 0.5$ , $\gamma = 1$ , $B_0 = 0.2$ T and $R = a = 10$ cm, this estimate gives $\tau _{\textrm {inj}} \gtrsim 0.1$ ms. In practice, the fast-ion current is determined by the balance between the beam trapping and ion loss; thus, only a part of the ionised beam atoms efficiently contributes to the ring current, so the time required to achieve a high- $\beta$ state will be greater.

In the absence of instabilities, which can prevent fast-ion accumulation, the fast-ion loss rate is determined by the electron drag and by charge exchange collisions with the residual gas, $\tau _{\textrm {loss}}^{-1} = \tau _{\textrm {dr}}^{-1} + \tau _{\textrm {cx}}^{-1}$ . For $\varepsilon _{\textrm {b}} = 15$ keV and $T_{\textrm {e}} \approx 30$ eV, the ratio $m_{\textrm {e}} \varepsilon _{\textrm {b}}/m_{\textrm {i}} T_{\textrm {e}}\approx 0.27 \ll 1$ , where $m_{\textrm {e}}$ is the electron mass. Thus, in later estimates, the beam ions can be considered slow relative to the plasma electrons. In this limiting case, the fast ion slowing down time is determined by the electron temperature (Trubnikov Reference Trubnikov and Leontovich1965; Huba Reference Huba2016): $\tau _{\textrm {dr}} \approx 5{\times }10^7 \,T_{\textrm {e}}^{3/2}/n$ , where $\tau _{\textrm {dr}}$ is in seconds, the electron temperature $T_{\textrm {e}}$ is in eV and the plasma density $n$ is in cm $^{-3}$ . In the target plasma with $n \sim 2{\times }10^{13}$ cm $^{-3}$ , the fast ions are slowed down in $\tau _{\textrm {dr}} \simeq 0.4$ ms, which is followed by angle scattering and escape into the loss cone. An ion mean free path relative to charge exchange collisions is determined by the neutral density, which can be expressed in terms of neutral pressure $p_{\textrm {n}}\,[\textrm {Pa}]$ assuming that neutrals are at room temperature, $\lambda _{\textrm {cx}}\,[\textrm {cm}] = 1/n_{\textrm {n}}\sigma _{\textrm {cx}} \approx 6.2/p_{\textrm {n}}$ . Fast-ion build-up is effective, when slowing down is faster than charge exchange, $\tau _{\textrm {dr}} \lesssim \tau _{\textrm {cx}} = \lambda _{\textrm {cx}}/v_{\textrm {b}}$ , which gives the upper limit for the neutral pressure, $p_{\textrm {n}} \lesssim 6.2/v_{\textrm {b}}\tau _{\textrm {dr}} \simeq 10^{-4}$ Pa. This pressure is provided by the pumping system of the CAT device. However, it should be taken into account that with increasing density (in the first approximation), $\eta$ grows linearly, compensating for decreasing time $\tau _{\textrm {dr}}$ . It is not the value of stationary $\zeta$ that will depend on the density, but the time for which it will be reached. Thus, for a successful field reversal experiment, it is necessary to create a target plasma with relatively high electron temperature, and a low gas pressure must be maintained in the vacuum chamber.

2.3. Diagnostics

Parameters of the target plasma produced by the gun were simultaneously measured at three axial locations using radially movable triple probes (Chen & Sekiguchi Reference Chen and Sekiguchi1965). The first probe measured the ion saturation current, the electron temperature and the probe floating potential before the main mirror cell at $z = -0.71$ m, the second one was located at the midplane of the mirror cell ( $z = 0$ ), and the third one was located at $z = 0.76$ m in the expanding magnetic field between the exit mirror and the plasma absorber end plates. The probe positions are shown in figure 1. In previous experiments, an additional probe was placed in the transport section at $z = -1.30$ m. However, it operated very unstably due to the high plasma density and large amplitude of potential fluctuations. The triple probe consists of three molybdenum wires $D = 0.4\,$ mm in diameter each housed in a quartz tube with a $l = 2.0$ mm protrusion of an electrode tip. Quartz has to be used because of the large heat flux from the plasma to the probe. In earlier experiments, a cylindrical alumina insulator with three axial holes was used, but the ceramic repeatedly failed due to cracking under local overheating. No such issues were encountered with the quartz insulator. The probes could be moved radially from 20 cm to the device axis.

For the ion temperature $T_{\textrm {i}} \sim 20$ eV and $B = 0.2$ T, the ratio of the ion gyroradius to the probe diameter $r_i/D \simeq 6$ , so ion current collection by the probe is unaffected by magnetic field. Unlike ions, electrons are strongly magnetised, $r_e \ll D$ , and can be collected only from the magnetic flux tube which connects to the probe; therefore, the electron current decreases. However, plasma parameters can still be satisfactorily evaluated from probe measurements (Chen Reference Chen1965). Measurement of the electron temperature and density requires a voltage of $\gtrsim 3 T_{\mathrm{e}}/e$ between two electrodes, while maintaining one of the probe tips at the floating potential $U_{\mathrm{f}}$ . The voltage between the positively biased and the floating electrodes gives the electron temperature. The plasma density is determined from the ion saturation current $I_{\mathrm{sat}}$ between the negatively and positively biased electrodes, and the plasma potential $U_{\mathrm{p}}$ is calculated with an error of $\simeq \pm 0.5 T_{\mathrm{e}}/e$ caused by the effects of magnetic field and particular geometry

(2.2) \begin{equation} T_{\textrm {e}} = \frac {e(U_+ - U_{\textrm {f}})}{\ln 2}, \quad I_{\textrm {sat}} = \alpha n e A \sqrt {\frac {T_{\textrm {e}}}{m_{\textrm {i}}}}, \quad U_{\textrm {p}} \approx U_{\textrm {f}} + 3.3 \frac {T_{\textrm {e}}}{e}\, , \end{equation}

where $U_+$ is the potential of the positively biased probe, $A\approx \pi D l$ is the ion collecting area of a thin cylindrical probe, and the dimensionless factor $\alpha$ of order unity depends on geometry, finite ion temperature and magnetic field effects. To determine absolute plasma parameters from probe measurements, it is usually necessary to calibrate probes with other diagnostic techniques. The parameter $\alpha$ , allowing exctraction of the plasma density from the ion saturation current using (2.2), was determined from the comparison of the probe data with the line density obtained by a microwave interferometer (see § 3.1).

Gas pressure in the chamber during the shot is measured by two fast vacuum gauges with 0.3 ms time resolution. They are used to monitor the dynamics of the spreading of neutral gas in the chamber.

The diagnostic suite will be significantly extended in the upcoming experiments on the confinement of a high-beta plasma. Diamagnetic loops will provide an average value of the stored plasma energy in the confinement zone. Perturbations of the radial magnetic field will be analysed using two azimuthal arrays, each consisting of 12 Mirnov coils. Spatially resolved magnetic field measurement based on the motional Stark effect was used earlier in the gas-dynamic trap experiment (Lizunov et al. Reference Lizunov, Den Hartog, Donin, Ivanov and Prikhodko2011). The radial profile of the magnetic field in CAT will be measured using the motional Stark effect with laser induced fluorescence diagnostic (MSE-LIF) that has several advantages over MSE using collisionally induced fluorescence (Foley & Levinton Reference Foley and Levinton2013). This diagnostic will allow measurement of fields less than 0.05 T in the midplane of the confinement volume with a spatial resolution of a few centimetres.

A parallel plate electrostatic analyser of charge-exchange neutrals with 45 $^{\circ }$ angle of entrance to the electric field will measure the fast-ion energy spectrum in the midplane of the confinement cell. Another ion diagnostic is an end-loss analyser installed in the expander behind the end plates to measure the current and the axial energy distribution of ions escaping along magnetic field lines. It is an electrostatic retarding-potential gridded analyser similar to the one developed for experiments at 2XIIB and TMX (Molvik Reference Molvik1981). Its collector, located behind several mesh electrodes, measures the ion current as a function of the swept repelling potential.

Parameters of the NBI system are determined by several diagnostics, including an array of SEDs that measure the distribution of the beam current density (see § 2.2), and wire calorimeters that measure the beam power and profile. All these diagnostics will soon be put into operation, allowing the study of a high- $\beta$ plasma. Table 2 summarises these diagnostics and their availability status.

Table 2. CAT diagnostic suite.

2.4. Experiment scenario

Figure 4 illustrates current traces in a typical experiment with the target plasma production. The main magnetic field coils are turned on 15 ms before the ‘0’ setting, which allows the magnetic field inside the vacuum chamber to reach steady state by the time the discharge in the plasma gun is initiated. The current in the gun solenoid is turned on at $-5$ ms, and thus ensures a nearly constant magnetic field throughout the entire discharge.

Figure 4. Scenario of experiment at the CAT device. All currents are given in arbitrary units.

Two gas valves of the plasma gun are opened 3 ms before the ignition of the arc discharge to let hydrogen fill the discharge channel. At time 0 ms, the voltage is applied to the gun electrodes, the ancillary high-voltage ignition electrodes initiate gas breakdown and the main arc discharge proceeds for 5 ms, while the gas flow rate remains constant.

The time evolution of the discharge voltage measured using a frequency-compensated divider is shown in figure 5(a). The discharge voltage $U_{\textrm {d}}$ reaches its maximum at the beginning and slowly decreases towards the end of the discharge. The discharge current $I_{\textrm {d}}$ was measured by a flexible Rogowski coil with a 100 kHz integrator. Its characteristic time trace is shown in figure 5(b). The current grows for 0.5 ms, then remains almost constant for 3 ms and finally decreases.

Figure 5. Typical time traces of arc discharge in plasma gun: (a) voltage and (b) current.

The plasma parameters were optimised by varying the discharge power (by altering the charging voltage on the pulse forming network that creates the arc discharge), the hydrogen feed rate (by changing the pressure at the valve inlet) and the current in the external coil, which could possibly create a thermal barrier. During the plasma parameter optimisation process, the magnetic field in the central cell was set to 0.3 T as the optimal value and all presented results correspond to this configuration.

3.1. Plasma density and electron temperature

Plasma density measured by the probes was compared with the line density $\langle n l\rangle _{\textrm {MW}} = \int n\,\text{d}l$ along the plasma diameter obtained by a quadrature microwave interferometer operating at 76.2 GHz. Strong fluctuations of the plasma density typical for this gun limited the comparison to a relatively low-density range ( $n\lesssim 10^{13}\,\textrm {cm}^{-3}$ ), which is shown in figure 6. It should be noted that the interferometer readings were confused during the first millisecond because the plasma density was too high, but throughout the rest of the shot, the radiation passed through the plasma and allowed the line density to be determined. The triple probe measurements were carried out in parallel with the microwave interferometer measurements. Importantly, the interferometer readings did not depend on the probe position within the plasma, indicating that the presence and movement of the probe did not perturb the global line-averaged density measurement. The correction factor $\alpha$ in (2.2) for plasma density calculation from the ion saturation current was found by minimisation of $(\int n_{\textrm {probe}}\,\text{d}l - \langle n l\rangle _{\textrm {MW}})^2$ . The best agreement of the probe data with the interferometer data is achieved with $\alpha =0.6$ . This value is quite close to $\exp (-1/2)$ , corresponding to the model of an unmagnetised plasma with cold ions.

Figure 6. Line density measured by microwave interferometer and calculated from radial profile of plasma density measured by a triple probe with proper calibration.

Figure 7 shows the time evolution of the electron temperature (panel a) and plasma density (panel c) in the midplane for different modes of gun operation. These signals were smoothed using a passive low-pass filter with a time constant $RC = 0.1$ ms. Short spikes observed in the signals are attributed to electrical breakdowns occurring between the wires of the triple probe. In two of them, the total gas flow rate $q_{\textrm {tot}} = 40$ Pa m $^3$ s⁻¹ through the anode and cathode valves at an average discharge power of 4.8 and 7.6 MW, and a curve is given for the total flow rate $q_{\textrm {tot}} = 25$ Pa m $^3$ s⁻¹ and average discharge power $P_{\textrm {d}} = 4.8$ MW. The mode in which the probe was calibrated, with $q_{\textrm {tot}} = 15$ Pa m $^3$ s⁻¹ and $P_{\textrm {d}} = 2$ MW, is also plotted. The power is averaged over the time interval from 0 to 5 ms. Measurements were made near the projection of the arc channel. The flow rates of the cathode and anode valves were the same.

Figure 7. Time traces and radial profiles of (a, b) electron temperature and (c, d) plasma density in the midplane of the confinement mirror cell. Time traces are taken at $R=6.0$ cm. Radial profiles are obtained by averaging signals from 1.0 to 2.0 ms. Legend shows corresponding plasma gun discharge power. Gas flow rates: standard, 40 Pa m $^3$ s⁻¹; reduced, 25 Pa m $^3$ s⁻¹ ( $\ast$ ); low-density mode for probe calibration, 15 Pa m $^3$ s⁻¹ ( $\ast \ast$ ). Shaded area indicates projection of gun discharge channel to the midplane.

Figure 8. Neutral gas pressure near the wall at (a) $z = 0$ and (b) $z = -0.71$ m. Legend shows corresponding plasma gun discharge power. Gas flow rates: standard, 40 Pa m $^3$ s⁻¹; reduced, 25 Pa m $^3$ s⁻¹ ( $\ast$ ); low-density mode for probe calibration, 15 Pa m $^3$ s⁻¹ ( $\ast \ast$ ).

Target plasma production by the gun can be divided into several stages. During the first millisecond of the shot, the plasma density grows rapidly compared with the electron temperature. This stage is characterised by high plasma density associated with the desorption of gas from the walls and an earlier activation of the hydrogen influx. During the second stage, which lasts approximately from 1 to 2 ms, the temperature and density remain almost constant indicating a steady-state operation of the plasma gun, when hydrogen supplied through its valves is completely consumed. However, after 2 ms, the plasma density starts rising. This is probably due to an increase in the density of the neutral gas surrounding plasma.

The time traces in figure 7 indicate that the electron temperature reaches its maximum faster when the discharge power is increased and the gas flow rate is reduced. This effect is likely observed because, at higher discharge power or lower gas flow, the pre-injected gas in the vacuum chamber and the discharge volume is ionised more efficiently. However, the mechanism leading to this enhanced ionisation remains unclear.

Figure 8 shows the neutral gas pressure near the wall at $z = 0$ m and at $z = -0.71$ m. In the central mirror cell, the gas pressure throughout the entire discharge does not exceed $10^{-2}$ Pa. At a pressure of $10^{-2}$ Pa, the gas flow through a lateral plasma surface with a radius of 20 cm and a length of 400 cm is equal to the gas flow in the plasma gun through the valves, $q_{\textrm {tot}}$ = 40 Pa m $^3$ s⁻¹. In the thermal barrier region, however, the pressure begins to rise almost linearly immediately after the start of the pulse, with a marked increase in the rate of rise after the gun is turned off between 4 and 5 ms. In addition, it is noteworthy that the equilibrium gas pressure measured after turning on of the gun (at 20–25 ms) corresponds to an amount of gas an order of magnitude greater than that released during the gun operation. Thus, the observed increase in plasma density during the shot can be attributed to the accumulation of desorbed wall gas in the transport and thermal barrier sections, which causes the chamber itself to act as a gas box.

The radial profiles of the electron temperature and plasma density are shown in figures 7(b) and 7(d), respectively. Each data point was obtained as a mean value of three shots, where the signal in each shot was in turn averaged over the time window from 1 to 2 ms. Although $T_{\textrm {e}}(r)$ and $n(r)$ in the confinement region are still peaked around the projection of the annular discharge channel of the gun, they are much broader than this channel, implying substantial cross-field diffusion. The electron temperature has a maximum of 30 eV near the channel projection, which is evidence of the effective heating by the discharge. However, the electron temperature and plasma density near the axis are noticeably lower than the maximum value. The reason might be both the low heating power concentration near the arc channel projection and the small distance between the plasma gun and the central cell, which does not allow the plasma to mix sufficiently.

Although an optimal regime providing relatively high density of the target plasma has been found in these experiments, the captured power does not exceed 20 % due to shine-through losses, which is still low for effective hot-ion accumulation (see § 3.2). The plasma density can be increased by enhancing the hydrogen feed rate, but this would also increase the neutral density near the wall, leading to increased charge-exchange losses of fast ions. The density of the target plasma in the main confinement cell is relatively low because the plasma streaming from the gun has to pass the thermal barrier region with a strong magnetic field. To increase the plasma density, the transport region can be extended by reducing the thermal barrier field. Taking into account that in the current experiments, the formation of the thermal barrier (i.e. substantial increase of the electron temperature in the main cell) was not detected, such a step should increase the plasma density without changing the electron temperature. Another way to increase the target plasma density is plasma fuelling by gas injection downstream from the thermal barrier. Changing the gun design also has a huge impact on the parameters of the plasma. For example, reducing the size of the gun should lead to better filling of the near-axis region. Some of these changes will be implemented in the near future.

3.2. Neutral beam trapping

If the beam neutrals are trapped mainly at the warm target plasma, the fast-ion density $n_{\textrm {f}}$ in the volume $V$ is evaluated from the particle balance,

(3.1) \begin{equation} \frac {\text{d} n_{\textrm {f}} V}{\text{d}t} = \frac {I_{\textrm {t}}}{e} - \frac {n_{\textrm {f}} V}{\tau _{\textrm {loss}}} = \frac {I_{\textrm {b}}}{e}\left (1 - \exp \left (-\int \sigma _{\textrm {tot}}n\,\text{d}l\right )\right ) - \frac {n_{\textrm {f}} V}{\tau _{\textrm {loss}}} \,. \end{equation}

This equation implies that for relatively small neutral beam trapping, $\sigma _{\textrm {tot}}nl \ll 1$ , in the steady state $n_{\textrm {f}}/n \propto I_{\textrm {b}}\tau _{\textrm {loss}}$ . Therefore, increasing the fast-ion lifetime by increasing the electron temperature and by reducing the neutral pressure in the main vacuum vessel plays a fundamental role in the successful fast ion build-up and plasma $\beta$ growth in CAT. This dependence of the fast-ion density on the beam current would indicate that the central-cell plasma pressure is not limited by an instability, but is otherwise determined by the particle balance. The experimental results on fast-ion accumulation will be compared with this simple balance model and with PIC simulations (Tsidulko & Chernoshtanov Reference Tsidulko and Chernoshtanov2016).

Figure 9. Current density profiles of neutral beam at a distance of 4.0 m from the injector grids (1.5 m past the device axis) measured by the SED arrays. SED signals are averaged from 0.5 to 0.6 ms. Gaussian fits for cases with and without plasma are shown by solid and dashed lines, respectively. $x = 0$ corresponds to NBI aimed at the radius $r = 10$ cm. The $z = 0$ plane is shifted axially by 6 cm from the main mirror midplane.

The target plasma must have sufficient density to provide effective beam capture and relatively high electron temperature to reduce fast ion slowing down. This optimisation was carried out by varying the discharge power and gas injection rate. High gas injection rate decreases the electron temperature, whereas low gas injection rate is not practical due to the low density of the resulting plasma. Several cases are shown in figure 7. It is evident that the plasma temperature increases with power and with reduced gas injection. At the same time, the density of the target plasma is relatively unaffected by the discharge power alone.

In addition, the initial hypothesis that a thermal barrier should develop between the central cell and the plasma gun was also tested by varying the magnetic field of the intermediate coil. However, the electron temperature, as well as the plasma density, practically does not depend on the local field in the thermal barrier. This field cannot be too small, otherwise, the plasma touches the vacuum chamber wall, breakdowns occur and the temperature drops. At high discharge currents, the threshold value of the magnetic field providing the correct operation of the system increases. The mode with a stronger field in the thermal barrier is preferred because it allows operation at a higher current. Thus, an optimum regime of target plasma production was found. This regime is characterised by the discharge power of the plasma gun $P_{\textrm {d}} = 7.6$ MW and inlet gas flow rate $q_{\textrm {tot}} = 40$ Pa m $^3$ s⁻¹. In this mode, the beam power capture coefficient was measured.

Figure 9 shows the beam current density profiles along and across the device axis, measured by the SEDs. These profiles are described well by Gaussian functions. Therefore, with the power density distribution represented as the product of two Gaussian functions, the total power absorbed by the plasma is determined by integrating this power density over the entire beam cross-sectional area. The captured power is determined from the normalised difference in the signals with and without the target plasma $\eta = (J_{\text{w/o plasma}} - J_{\text{w/ plasma}}) / J_{\text{w/o plasma}}$ . The capture coefficient changes from 10 % to 20 % during the shot (figure 10). The rest of the beam power shines through. The growth of the captured power over time, as previously discussed in this section, indicates that the absorbed gas is being released from the walls. This additional influx of particles increases the density of the target plasma. Large amplitude oscillations of the SED signals are related to the strong density fluctuations in the rotating plasma. Alternatively, the captured power can be estimated from the density profiles measured by the triple probes. The probe measurements were performed in a separate series of experiments without NBI. For relatively low plasma densities, the NBI capture coefficient simplifies to $\eta \approx \sigma _{\textrm {tot}}\int n(\sqrt {l^2 + a^2})\,\text{d}l$ , where the line integral is taken along the chord with an impact parameter of $a = 10$ cm, where the beam axis is aimed. The agreement between the triple probe estimate and the NB trapping measurements also indicates that the calibration factor $\alpha$ for the probes has been determined correctly.

Figure 10. Time-dependent beam power capture: measured by secondary electron emission detectors in the beam dump (blue dashed line) and calculated from density profile measured by triple probe (orange solid line).