Overview of GLOBUS-M2 spherical tokamak results at the enhanced values of magnetic field and plasma current

The purpose of research carried out on spherical tokamaks is to create a scientific and technological basis for a compact purely thermonuclear reactor and/or for a fusion neutron source (FNS) for further use as a controlled core of a fusion–fission hybrid reactor. To solve both tasks, it is necessary to achieve long plasma confinement times, as well as to provide a spherical tokamak with effective methods and sources of non-inductive plasma heating and current drive to ensure a continuous operation. Along with this, it is required to solve a number of other problems, such as: (a) confinement of fast ions in a compact tokamak; (b) advanced tokamak high performance regimes with sub-fusion plasma parameters in compact ST; (c) interaction of plasma with the first wall under conditions of high energy flux densities, etc. These problems are the subject of research carried out on the Globus-M2 spherical tokamak [1]. Globus-M2 is a modernized version of the Globus-M tokamak in which the vacuum chamber and the entire diagnostic complex are preserved, and a new electromagnetic system is significantly strengthened in order to withstand higher currents and, accordingly, increased mechanical and thermal loads.

During the reported period, a number of improvements were made to the diagnostic complex of the Globus-M2 tokamak. First of all, the new Thomson scattering diagnostics were developed. This system includes a 1064 nm Nd:YAG pulsed laser with a 330 Hz repetition rate. The diagnostics provide measurements of radial profiles of electron temperature and density at ten spatial points. The spatial resolution is up to 20 mm in the plasma core and 10 mm in the vicinity of the last closed field surface from the low field side. The new TS system provides reliable measurements of T_e < 10 (eV) with moderate electron density. The neutral particle analyzer (NPA) complex was upgraded. A scanning system for two NPAs was installed on the tokamak. It allows us to perform shot-to-shot spatial scanning vertically for both analyzers, and also horizontally for one of them. Preparations for detailed neutron flux measurements are underway on Globus-M2. Two types of detectors are used in neutron measurements: B-10 counters and compact spectrometers, based on a liquid scintillator BC-501A. These spectrometers are planned to be enabled to study fast particle distributions in experiments with different NBI regimes. The Doppler backscattering (DBS) diagnostic has undergone modernization. The old reflectometer had four frequency channels: 20, 29, 39, 48 GHz. It was supplemented by a six-channel operating frequencies 50, 55, 60, 65, 70, 75 GHz. So now it can provide plasma probing up to the central region practically in all tokamak regimes. Also, such diagnostics have been developed as: laser interferometer, charge-exchange recombination spectroscopy and Z_eff diagnostics.

The tokamak was designed to reach the toroidal magnetic field as high as B_T = 1 T and the plasma current I_p = 0.5 MA. The magnetic system provides operation in the diverter single or double null configurations with the aspect ratio A = R/a = 1.5, plasma minor radius a = 0.24 m, triangularity up to δ ∼ 0.5 and elongation up to κ ∼ 2.2. Currently 80% of the highest magnetic field and plasma current value are reached, so during the reported period the experiments were performed with the toroidal magnetic field up to 0.8 T and plasma current up to 0.4 MA. With an increase in the magnetic field in experiments on additional heating of the plasma, an obvious improvement in plasma parameters was observed, including an increase in the energy content of the plasma.

An initial comparison of the stored plasma energy measured with the W^DIA diamagnetic loop in regimes with approximately constant q values and plasma density, but with different toroidal magnetic fields and plasma currents, showed a significant increase in W^DIA with increasing B_T and I_p (see figure 1(a)). The reasons for this may be associated with an improvement in confinement and/or a decrease in thermal energy losses from an external source of energetic particles.

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This article presents the results of a study of the reasons for the improvement of plasma parameters with an increase in the toroidal magnetic field and an overview of the results obtained on Globus-M2 in 2019–2020.

Section 2 describes the results of plasma heating and confinement study under conditions of increased field and current. Section 3 deals with the confinement and loss of fast particles formed as a result of NBI. Section 4 is devoted to the study of Alfvén instabilities. Section 5 presents the results of experiments on current generation by waves of the lower hybrid frequency range. Section 6 is devoted to the SOL research.

Previous research on spherical tokamaks MAST, NSTX and Globus-M has shown that a distinctive feature of STs is a strong dependence of the energy confinement time τ_E on the magnetic field and weak dependence on the plasma current ${\tau }_{\mathrm{E}}\sim {I}_{\mathrm{p}}^{0.48-0.59}{B}_{\mathrm{T}}^{1.04-1.4}$ [2–4], unlike the IPB98(y, 2) scaling for conventional tokamaks, where ${\tau }_{\mathrm{E}}\sim {I}_{\mathrm{p}}^{0.93}{B}_{\mathrm{T}}^{0.15}$ [5]. But all of these experiments were carried out on machines with B_T = 0.3–0.55 T. The other important point is that the 'engineering' scaling for τ_E in experiments on NSTX was different for various types of wall conditioning technique [6]. An ST-like dependence was observed (τ_E ∼ I_p ^0.57 B_T ^1.08) when boronization and between-shot glow discharge were used for wall conditioning. However, the different dependence was obtained on NSTX in discharges with lithium evaporation (τ_E ∼ I_p ^0.79 B_T ^−0.15). In spite of such differences, the common feature for the thermal energy confinement in all STs experiments is a strong electron heat diffusivity dependence on collisionality (ν^* ) for the H-mode regime. The question was: 'is the scaling for STs valid for higher B_T?'. Experiments on Globus-M2 have to answer this question.

Experiments on the Globus-M2 were carried out with an almost twofold increase of the toroidal magnetic field (compared with Globus-M). The magnetic configuration was exactly the same as in the Globus-M experiments. The ion drift was directed towards the lower null x-point, where the plasma major radius R = 0.35 m, minor radius a = 0.22 m and elongation κ = 1.9 was sustained in NB heated discharge in deuterium plasma. The aspect ratio A = 1.6 is higher in comparison with MAST and NSTX, where A ≈ 1.3. The experiments with neutral beam heating on Globus-M2 at higher magnetic field have demonstrated an increased efficiency, compared with the Globus-M ones, at the same NBI parameters (deuterium beam with particle energy 28 keV and the heating power 0.8 MW).

The details on the L–H transition in Globus-M2 were recently reported [7]. In order to reach H-mode in a tokamak high heating power is usually required exceeding empirical threshold: P_thr = 0.042n₂₀ ^0.73 B_T ^0.74 S^0.98 [8]. Here, S is the total surface of the plasma column. Experiments on spherical tokamaks have shown that the threshold power increases with A decreasing. The ratio of loss power (power flowing through the plasma surface) to the threshold power P_loss /P_thr is exceeding conventional scaling predictions, confirming a trend suggested by MAST and NSTX: P_thr = 0.072n₂₀ ^0.7 B_T ^0.7 S^0.9(Z_eff/2)^0.7 F(A)^0.5, where F(A) = 0.1A/f(A), f(A) = 1 − [2/(1 + A)]^0.5 [9]. In accordance with the ST corrected scaling the loss power for Globus-M2 conditions is in the range 0.08–0.1 MW, which is 4–8 times lower than the value of the loss power, observed in experiments. Such a strong discrepancy emphasizes that loss power is not the best parameter for predicting L–H transition. Recent experiments have demonstrated that ion heat flux value at the plasma column edge is more relevant for predicting L–H transition [10]. Modern empirical scalings based on ASDEX-U and Alcator C-mode data Q_i,L−H = 0.0029n₁₉ ^1.05 B_T ^0.68S^0.93 [11] predict 10–15 kW for the Globus-M2 case for plasma density n_e = (2–3) × 10¹⁹ m⁻³ at which we usually observe L–H transition. According to ASTRA simulations the edge ion heat flux before the transition Q_{i, edge} is 15–30 kW, which is rather close to the value obtained from the scaling.

The main parameters of shot #38800 with B_T = 0.8 T and I_p = 0.4 MA, including kinetic data on temperature measurements, are shown in figure 1(b). The electron temperature reached 1 keV and ion temperature 800 eV at the central density as high as 1 × 10²⁰ m⁻³. The comparison of plasma thermal energy in shots with different magnetic fields and plasma currents measured diamagnetically is shown in figure 2(a). It is seen from the figure that the thermal energy in the shots with B_T = 0.8 T and I_p = 0.4 MA increased up to 10 kJ, which is nearly three times as high as in Globus-M (B_T = 0.4 T and I_p = 0.2 MA). The absorbed heating power also increases in regimes with higher B_T. For the moderate density range n_e ≈ 6 × 10¹⁹ m⁻³ and B_T = 0.4 T scenario P_abs ≈ 0.6 MW, where the ohmic heating power corresponds to half of the P_abs. The regimes with B_T = 0.8 T are characterized with higher OH heating power P_OH ≈ 0.4 MW, as well as higher beam absorbed power P_abs ^NBI ≈ 0.45 MW.

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The energy confinement time obtained from the analysis for different combinations of plasma currents and magnetic fields is shown in figure 2(b). A slight saturation of the energy confinement is clearly pronounced for high density range in low B_T case. This saturation might be concerned with increasing heat losses through the ion heat flux that increases with density. From the figure one can see a threefold increase of τ_E at twofold increase of B_T. The predicted energy confinement time enhancement at the field of 0.8 T, using IPB98(y, 2) scaling and the Globus-M scaling for the B_T range 0.25–0.5 T is shown by open circles in the same figure [4]. From the figure, one can see that observed τ_E rise cannot be explained using strong τ_E dependence on plasma current only. Accurate analysis of the τ_E dependence on I_p and B_T was recently reported [5, 12]. It has been shown that both I_p and B_T increase, enhancing energy confinement, while the role of B_T is more important. The other analysis was carried out for a set of Glous-M2 shots with a small elongation and a fixed B_T = 0.7 T and n_e = 4–4.5 × 10¹⁹ m⁻³, while I_p was varied within the range 0.2–0.3 MA, see [13]. The main conclusion was that τ_E dependence on I_p was rather weak and can be approximated as τ_E ∼ I_p ^0.56.

The predictions of the ST scaling that suggest strong τ_E dependence on magnetic field and moderate dependence on plasma current accurately fit the new data. The new experimental results for B_T = 0.8 T are in a good agreement with the regression fit of the Globus-M/Globus-M2 confinement database carried out for NBI H-mode discharges [6]:

$$\begin{equation}{\tau }_{\mathrm{E}}^{\text{GLB}}=0.01{I}_{\mathrm{p}}^{0.43\pm 0.22}{B}_{\mathrm{T}}^{1.19\pm 0.1}{P}_{\text{abs}}^{-0.59\pm 0.23}{n}_{\mathrm{e}}^{0.58\pm 0.1},\end{equation} \tag{ 1 }$$

where P_abs is the absorbed heating power and n_e is the line average density. The scaling confirms relatively weak τ_E dependence on I_p that emphasizes the major role of B_T on perpendicular heat transport in spherical tokamaks. Comparison of the experiment confinement time values versus predicted using equation (1) is shown in figure 2(c).

Heat conductivity analysis was made on the basis of experimental data by means of the codes ASTRA 7.0 + SPIDER for solving power balance equations. For transport simulations, we used ASTRA 7.0 code coupled with the equilibrium code SPIDER [14]. NCLASS was used to calculate neoclassical ion heat diffusivity, plasma conductivity and bootstrap current fraction, while NUBEAM and 3D fast ion tracking algorithm were used to estimate the beam absorbed power. The profiles of the power absorbed by electrons and ions were estimated using the NUBEAM code. Verification of the obtained results was proposed, since NUBEAM simulations assume the guiding center model. Therefore, the first orbit losses were corrected according to the simulation results made by the full orbit fast particle code '3D fast ion tracking algorithm' [15]. The electron temperature and density profiles were measured with Thomson scattering. The simulated ion temperature profiles fit the values measured by means of a NPA well. The sum of the simulated ion stored energy W_i and calculated W_e using TS data corresponded well to W^DIA, measured by the diamagnetic loop. The difference seen in figure 2(a) corresponds to the perpendicular pressure of the fast ions, W^fast , which is in line with NUBEAM simulations and full orbit modeling using the 3D-fast ion tracking algorithm. Solving the equations for electron heat flux, we varied electron heat diffusivity in order to fit calculated T_e to T_e measured by TS. In order to simulate ion temperature profiles, we used neoclassical ion heat diffusivity provided by NCLASS. However, assuming neoclassical heat diffusivity (χ_i = χ_i ^neo) in ASTRA simulations for B_T = 0.8 T gives an almost twofold overestimation of the ion stored energy W_i = W^DIA − W_e − W^fast and ion temperature. Matching ASTRA simulations with experimental data becomes possible only in the case χ_i = 3χ_i ^neo. Electron density profiles were prescribed by TS, while ion density profiles were calculated assuming Z_eff uniform distribution and carbon as a main impurity. The absolute value of Z_eff was in the range 2–2.5 according to the measured bremsstrahlung radiation intensity [16] and verified by ASTAR simulations comparing the calculated and measured loop voltage. Estimated effective ion heat diffusivity χ_i values were as high as 1.5–3 m² s⁻¹ that is similar to the electron heat diffusivity (χ_i = χ_e) and it is 2–3 times higher than the neoclassical ion heat diffusivity values [12].

Enhanced plasma parameters allowed us to obtain regimes with much lower collisionality. That makes possible investigation of the dependence of the normalized energy confinement time (B_T τ_E) on collisionality in the wide range of plasma collisionalities 0.02 < ν* < 1. Collisionality was defined as ν* ∼ Z_eff n_e/T², i.e. without the safety factor. This choice of collisionality definition is idenical to that used in the ν∗ scans in MAST [16] and NSTX [6] and thus simplifies the comparison between different machines. This dependence, shown in figure 3(a), turned out to be rather strong ${B}_{\mathrm{T}}{\tau }_{\mathrm{E}}\sim {{\nu }^{\ast }}^{-0.74}$ for fixed values of the safety factor q ∼ B_T/I_p, normalized ion gyroradius ρ* ∼ T^0.5/B_T and parameter ${\beta }_{\mathrm{T}}\sim W/{B}_{\mathrm{T}}^{2}$ . However, the analysis of the multi-machine database has shown that the collisionality exponent index (α_ν ) depends on collisionality itself. For high collisionality regimes at JET, DIII-D and Alcator-CMOD α_ν values are similar to those obtained at STs for the same ν* range: α_ν = −0.5 ÷ −0.75 [18] (see figure 3(b)). For the lower collisionality regimes, the dependence of B_T τ_E on ν* becomes weaker yielding the well known relation: ${B}_{\mathrm{T}}{\tau }_{\mathrm{E}}\sim {{\nu }^{\ast }}^{-0.01}$. However, experiments carried out on Globus-M/M2 have shown an opposite trend for collisionality scaling. As the collisionality decreases, we observe a strong increase of the |α_ν | values, thus indicating the impact of the aspect ratio on energy confinement.

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Increase of I_p and B_T led to better confinement of fast ions arising at ionization of the injected neutral beam atoms. NUBEAM [19] and full orbit modeling [15] showed that at B_T = 0.4 T and I_p = 0.2 MA up to 90% of the injected power of the 30 keV ions is lost, while at B_T = 1 T and I_p = 0.5 MA the losses become much smaller: first orbit losses do not exceed 10%, while slowing down losses are around 20%. The experiment on Globus-M2 has confirmed the modeling results. While in Globus-M the fast ion losses level was similar to the level in START [20], which is also a small machine, in Globus-M2 this level became closer to the medium-size MAST [21] and NSTX [22]. An increase in the plasma current plays a major role in reducing energetic ion losses, which is similar to other tokamaks [20]. However there is also a weak dependence of the losses on the magnetic field [15]. It is not useful to increase I_p without B_T since the safety factor drop leads to a rise of the instabilities causing additional fast ion losses. In this regard I_p and B_T are increased simultaneously. Fast ion confinement improvement may be illustrated by figure 4(a), where charge exchange (CX) atomic spectra measured with a tangentially directed NPA in shots with different values of I_p and B_T are shown. The injected deuterium beam had the energy of 28 keV and power of 0.8 MW. For clarity, the spectra are normalized in the region of the injection energy. The rise of the spectra in the ∼14 keV region is associated with the half energy part of the injected beam. One can see a strong drop of the NPA fluxes in the region of 15–28 keV at low values of currents and fields, which arise due to losses of fast ions during their slowing down. The drop weakens at current and field rise, so at B_T = 0.8 T and I_p = 0.4 MA it practically disappears, which indicates significant improvement of the fast ion confinement.

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The NPA complex was upgraded. A scanning system for two NPAs was installed on the tokamak (figure 5). It allows us to perform shot-to-shot spatial scanning vertically for both analyzers, and also horizontally for one of them. High NBI current density and low horizontal size (full width at half maximum of the horizontal power distribution is ∼2 cm) allowed spatial localization of the NPA measurements using the active NPA signal. It is obtained as follows: the passive fraction, acquired when the NBI was off, is subtracted from the total signal. The experimental conditions are chosen in such a way that the active signal was at least equal to the passive one and an order of magnitude higher for the high energy channels. It was successfully applied for the core ion temperature reconstruction [23] and fast ion study: vertical NPA scan was performed in similar discharges, so atomic fluxes from different spatial points were measured. Thus, an active signal is obtained from the points corresponding to ρ from 0.23 to 0.65 ($\rho =\sqrt{\frac{\psi -{\psi }_{\text{axis}}}{{\psi }_{\text{LCFS}}-{\psi }_{\text{axis}}}}$ is the normalized poloidal radius, ψ is the poloidal magnetic flux, ψ_axis is ψ on the magnetic axis and ψ_LCFS is ψ at the last closed flux surface (LCFS)). The pitch angles of the former ions are changed slightly: from 48° to 40° correspondingly. An example of such a measurement in the series of the discharges with B_T = 0.5 T and I_p = 0.23 MA is presented in figure 4(b). This figure reflects spatial and energy fast ion distribution at dedicated pitch angles. Plasma opacity and energy dependence of the CX rate are not taken into account. NPA signal and hence ion concentration decrease with the minor radius increase. In the bottom left corner (high energy ions in the outer plasma region), a sharp drop of the spectra is observed. The reason for this drop is orbital losses, which is confirmed by the full orbit modeling. The gray surface corresponds to the one σ level of the statistical noise under the assumption that the number of the incident atoms is described by the Poisson distribution. The data are obtained with the temporal resolution of 0.3 ms (resolution, suggested to use in the studies on the fast ion redistribution due to instabilities), which led to the high standard error level (∼10%).

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As the fast ions in Globus-M2 are superalfvenic, they excite Alfvén instabilities, which, in turn, can influence the fast particles. As was shown in experiments on the tokamaks TFTR [24] and D-IIID [25], the toroidal Alfvén eigenmodes (TAE) are the most dangerous from the point of view of fast particle redistribution and losses. On NSTX, short TAE bursts of 1 ms duration resulted in the drop of the neutron rate by 40% associated with losses and redistribution of the fast particles [26] In our experiments, the study of Alfvén eigenmodes (AE) was started on Globus-M [27, 28] and continued on Globus-M2 during the reported period.

First of all, we were interested in the loss of fast particles caused by AE. As was shown earlier, the chirping TAEs of high amplitude induce the largest losses [28]. For observation of the losses, we used the NPA ACORD-24M with a line of sight directed tangentially to a circle with a radius equal to the impact parameter of the injected beam. The flux of charge-exchange atoms with energies of 28.5 keV (close to the energy of injected particles) was measured. A drop in the flux at the time of the TAE burst is proportional to fast ion losses. In our previous experiments, we found that the loss of fast particles decreases with increasing magnetic field and plasma current [28]. The data obtained on Globus-M2 made it possible to study this dependence in a wider range of parameters B_T = 0.4–0.8 T and I_p = 0.18–0.4 MA. We made the regression fit of the Globus-M/Globus-M2 data for relative fast particle losses (NPA flux drop ΔN/N) on I_p, B_T and the relative TAE amplitude (δB/B_T). It shows the scaling $\mathrm{d}N /N=A\cdot {\left(\frac{\delta B}{{B}_{\mathrm{T}}}\right)}^{0.42}\cdot {{B}_{\mathrm{T}}}^{-0.5}\cdot {I}_{\mathrm{p}}^{-1.21}$, which demonstrates a stronger dependence of losses on the magnitude of the current than on the field. However, in this case, the Pearson coefficients for the I_p and B_T (of the order of 0.6) show their strong correlation. Therefore, it seems to us that it is more correct to use the product B_T I_p in scaling. In this case, the regression fit gives:

$$\begin{equation}\mathrm{d}N /N=A\cdot {\left(\frac{\delta B}{{B}_{\mathrm{T}}}\right)}^{0.51\pm 0.15}\cdot {\left({B}_{\mathrm{T}}{I}_{\mathrm{p}}\right)}^{-0.94\pm 0.27},\end{equation} \tag{ 2 }$$

where A is a constant, δB is measured with an in vessel Mirnov probe at the low field side. The scaling includes the dependence of losses on the product of current and field, since in a tokamak, the field and current are usually changed proportionally to maintain a safety factor value. The experimentally measured relative drops in the fluxes of CX atoms with the energy of 28.5 keV in comparison with the obtained scaling are shown in figure 6. The simultaneous increase in the current and magnetic field is most efficient, because it reduces both the Larmor radius and the width of the fast ion orbit, while the safety factor remains the same. The ions moving in more compact orbits are less subject to losses, because their transition into unconfined trajectories requires a stronger TAE impact. The dependence obtained is promising for the operation of future compact FNSs based on a spherical tokamak, but, of course, it should be checked at plasma parameters closer to the FNS ones.

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An increase in plasma parameters and better fast particle confinement led to a change in the nature of AE and the expansion of their frequency spectrum (50–600 kHz). Together with single TAE, observed earlier on Globus-M, multiple TAEs and so-called Alfvén cascades (AC or reversed shear AE, RSAE) were identified. With a rapid increase in current due to the skin effect in the discharge, an inverted q profile (q—the safety factor) can be formed in the central region of the plasma with a q_min value not on the axis. When a neutral beam is injected at the stage of current growth, such a profile can be 'frozen' for some time due to the off-center contribution of the heating power. This, in turn, creates favorable conditions for the development of the cascade, since it can exist for any length of time without undergoing damping in the Alfvén continuum, only near a certain region, within which the magnetic shear r/q dq/dr vanishes (r—the minor radius) [29]. The AC spectra observed on Globus-M2 are very similar to the spectra studied on NSTX [30, 31]. We applied the approach proposed in the paper [30] to determine the evolution of q_min in a discharge. A detailed analysis of the spectra is given in [32]. In this paper, we present only a general approach and a result. Typical spectra of the Mirnov probe signal for a discharge with AC are shown in figure 7(a).

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The AC frequency in linear approach is determined by [31]:

$$\begin{equation}{\omega }_{\mathrm{A}\mathrm{C}}={\left[{\left(\frac{m}{{q}_{\mathrm{min}}}-n\right)}^{2}\frac{{V}_{\mathrm{A}}^{2}}{{R}_{0}^{2}}+\frac{2{T}_{\mathrm{e}}}{{M}_{\mathrm{i}}{R}_{0}^{2}}\left(1+\frac{7}{4}\frac{{T}_{\mathrm{i}}}{{T}_{\mathrm{e}}}\right)\right]}^{1/2},\end{equation} \tag{ 3 }$$

where m and n are the mode wave numbers, V_A is the Alfvén velocity, R₀—major radius, q_min—minimal value of the safety factor and the second term in square brackets is the square of the GAM frequency. Formula (3) is used for calculation of q_min from measured values of the AC frequency. Data on T_e and T_i profiles were obtained from Thomson scattering and NPA measurements. The mode wave numbers were determined with magnetic probes, and localization of the modеs was established by means of the DBS diagnostic [33]. The profile of the phase fluctuations amplitude of the reflected signal in relative units in shot # 39060 is shown in figure 7(c). It is seen from the figure that the mode maximum approximately corresponds to the minimum of the q profile calculated using the ASTRA code. A comparison of data obtained by means of the MHD-spectroscopy method with results of the ASTRA modeling (shown in figure 7(b)) demonstrates reasonable agreement.

Current drive using waves in the lower hybrid (LH) frequency range has been extensively and successfully studied on many tokamaks of the traditional type, for example [34–36]. On small tokamaks with a small aspect ratio, LH waves were used mainly in experiments on a non-inductive current start-up [37]. Experiments on maintaining the current in spherical tokamaks with the low value of the toroidal field, when ${\omega }_{\mathrm{p}\mathrm{e}}\gg {\omega }_{{B}_{\mathrm{e}}}$ (electron plasma and cyclotron frequencies) were considered to be unproductive, because to introduce RF power into the plasma, it was necessary to excite LH waves with a very high value of the toroidal refractive index N_|| about 8–10. Such waves should be rapidly absorbed at the discharge periphery. However, it was theoretically shown that a large poloidal inhomogeneity of the magnetic field, arising from the small aspect ratio and strong vertical elongation, inherent in spherical tokamaks, leads to: (1) a strong variation of the refractive index N along the wave trajectory, (2) a certain frequency range shows a new plasma resonance (poloidal resonance), in the vicinity of which the LH wave is strongly slowed down and absorbed [38, 39]. It was also shown that, under typical conditions at the periphery of spherical tokamaks, it is necessary to take into account the gradient terms of the dispersion equation, which leads to a change in the accessibility criterion: the plasma transparency turned out to depend not only on the value, but also on the sign of N_pol (refractive index in the poloidal direction) [40]. This theory was tested at the Globus-M tokamak with B_T = 0.4 T. The antenna-grill was oriented so that the electric field of the wave in the waveguide was perpendicular to the equatorial plane of the tokamak and excited waves with toroidal slowing down N_|| = 1 and poloidal slowing down N_pol = −3.7. Even without optimization of the discharge parameters, a good current generation efficiency η = 0.1 × 10¹⁹ A m⁻² W⁻¹ was obtained [41].

An increase of the toroidal field improves the accessibility of the center of the plasma even in the case of toroidal slowing down of the excited LH waves. Ray trajectories were calculated using the code described in [42]. Figure 8(a) shows the ray trajectories for a wave with N_|| = −3.0 for two values of the toroidal field, 0.6 T (solid red) and 1.0 T (dashed black) at N_||cr = 3.6 and 2.4, respectively, for ⟨n_e⟩ = 1.0 × 10¹⁹ m⁻³. Therefore, in the Globus-M2 tokamak, the same antenna-grill was oriented so that the electric field of the wave in the waveguide was parallel to the equatorial plane of the tokamak and excited waves with poloidal deceleration N_pol = 0, while the main peak in the spatial N_|| spectrum had a value of N_|| ≈ −3.0. A typical decrease in the loop voltage when a RF pulse is applied is shown in figure 8(b) for discharges #38686 (with RF pulse) and #38694 (without RF pulse). Discharge parameters: B_T = 0.8 T; I_p = 200 kA, ⟨n_e⟩ = 1.0–1.5 × 10¹⁹ m⁻³, T_e(0) = 500 eV, Z_eff = 2.5, f₀ = 2.45 GHz, P_inc = 150 kW, N_|| = −3.0.

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Depending on the value of the average density, the gap between the antenna and the separatrix, the input power, the effective plasma charge, the value of the relative voltage drop at the moment of application of the RF power varied within the range of ΔU/U ≈ (30–80)%, which corresponds to the value of the generated current I_LH ≈ (60–160) kA. Figure 9(a) shows the ΔU/U values versus the average density over a set of plasma discharges for two values of the magnetic field.

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The provided figures do not have points with a small voltage drop, because they were measured with large errors due to interference. The scatter of the experimental points is associated with both the insufficiently good reproducibility of the discharge and with the presence of poorly controlled parameters (the gap between the separatrix and the antenna, input power, etc).

The data refer to a series of experiments with different discharge parameters, such as plasma current, plasma column position, ion and electron temperatures. The selection of points in the figures is made only by two parameters: electron density and the toroidal field.

The value of CD efficiency is estimated as η = n_e (10¹⁹ m⁻³)R₀ (m)I_rf (MA)/P_inc (MW). Here, n_e is the average density, R₀ is the large radius of the tokamak, I_rf is the generated current, and P_inc is the RF input power. The improvement in the accessibility and efficiency of current generation with an increase in the toroidal field is confirmed by figure 9(b), which shows the efficiency of CD for all discharges versus the value of the average density for two values of the magnetic field. At a higher magnetic field, current generation takes place at a higher density and with a satisfactorily high efficiency. The achieved values of efficiency are on average η = (0.2–0.3) × 10¹⁹ A m⁻² W⁻¹, and are comparable with the results obtained on conventional tokamaks [43].

Globus-M2 has an open divertor where tiles are made of graphite RGTi [44]. Several diagnostics are used to measure SOL plasma parameters in Globus-M2 as shown in figure 10: Langmuir probes imbedded into divertor plates [45], and the movable nine-pin Langmuir probe, installed at the outer midplane [46].

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In the last experimental campaign, the infrared camera (IR-camera) [47] was installed at the upper dome of the vacuum vessel at a distance of 1.3 m from the lower divertor target. The detector of the IR camera is operated in the 3.5–4.7 μm wave range with 320 × 256 pixels for the full frame, which gives a 1.6 mm spatial resolution on the diverter target. The frame rate can be changed with different window size; measurements were carried out with 500 Hz frame rate for 191 × 171 pixels. The frame for lower single null discharge #39816 with B_T = 0.7 T, line averaged density ⟨n_e⟩ ≈ 1.8 × 10¹⁹ m⁻³, I_p = 200 kA is shown in figure 11(a) and the lower target temperature profile in figure 11(b).

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Infrared imaging diagnostics are useful tools for investigation of the temperature distribution and power deposition onto the divertor surface [48, 49]. Heat flux was computed solving the 2D inverse heat conduction problem using the approach proposed in [50]. The calculated heat flux profile for the outer divertor target is presented in figure 12. SOL width at the midplane (${\lambda }_{q}^{\text{mid}}$) [51] is a significant parameter of the edge plasma that determines the peak heat loads onto the divertor plates. This quantity could be evaluated from the SOL width $\left(\right. {\lambda }_{q}^{\text{div}}$) on the divertor target as ${\lambda }_{q}^{\text{mid}}={\lambda }_{q}^{\text{div}}/{f}_{ x}$, where f_x is flux expansion from upstream to the divertor. Eich fitting function [51] was applied on the measured heat flux profile to estimate ${\lambda }_{q}^{\text{div}}$. Flux expansion was determined from magnetic equilibrium reconstruction [47] as ${f}_{ x}\equiv {R}_{\mathrm{m}\mathrm{p}}{B}_{\text{pol}}^{\mathrm{m}\mathrm{p}}/{R}_{\text{div}}{B}_{\text{pol}}^{\text{div}}$, where R_mp(R_div) and ${B}_{\text{pol}}^{\mathrm{m}\mathrm{p}}({B}_{\text{div}}^{\mathrm{m}\mathrm{p}})$ are the major radius and poloidal magnetic field at the midplane (divertor target), respectively. For typical lower single null discharges with I_p = 200 kA, ${B}_{\text{pol}}^{\mathrm{m}\mathrm{p}}=0.18$ T and B_T = 0.7 T ${\lambda }_{q}^{\text{target}}$ is about 14–15 mm and f_x is 3.5–5, so ${\lambda }_{q}^{\text{mid}}$ is 3–4 mm. These preliminary results do not contradict the known Eich scaling [52]] (see figure 12):

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$\mathrm{E}\mathrm{i}\mathrm{c}\mathrm{h}-2013:{\lambda }_{q}^{\text{mid}}=1.3{P}_{\text{SOL}}^{-0.02}{B}_{\text{pol}}^{\mathrm{m}\mathrm{p}-0.9}{a}^{0.4}{R}_{0}^{-0.36}$, where P_SOL—power crossing the separatrix.

In the modernized Globus-M2 tokamak, discharges were carried out with a magnetic field of up to 0.8 T and plasma current of up to 400 kA, which is 80% of the design values. Regimes with higher plasma performance, longer pulse duration, temperatures in the keV range and with lower collisionality were obtained. The improvement in parameters is a consequence of an increase in the energy confinement time with a decrease in the loss of high-energy particles from the plasma under conditions of a doubling of the magnetic field and plasma current. The scaling of the energy confinement time for spherical tokamaks is favorable due to a strong dependence on the toroidal magnetic field in a wider range of parameters. An increase in the energy confinement time with a decrease in the normalized collision frequency is demonstrated. In experiments on current generation by waves of the lower hybrid frequency range, a high efficiency was obtained, comparable to the results for traditional tokamaks. The scaling of fast ion losses caused by TAE is obtained, which demonstrates their decrease with increasing magnetic field and current. The dependence obtained is promising for the operation of future compact FNSs based on a spherical tokamak, but, of course, it should be checked at plasma parameters closer to the FNS ones. A number of diagnostics have been commissioned and modernized, providing the most complete set of plasma data.

In the near future, it is planned to bring the tokamak to its design parameters, conduct experiments on plasma heating and current generation using a new injector (50 keV energy, 1 MW power), carry out experiments on ion cyclotron heating and also continue research in all areas covered in this paper.

The work is performed on the Unique Scientific Facility 'Spherical tokamak Globus-M', which is incorporated in the Federal Joint Research Center 'Material science and characterization' in advanced technology. Energy confinement and plasma heating efficiency investigation presented in section 2 were financially supported by RSF research project No. 17-72-20076. Fast ion distribution reconstruction (section 3) was supported by RSF research project No. 21-72-20007. The Alfvén mode investigation (section 4) was supported by RSF research project No. 17-12-01177. Experiments on lower hybrid current drive (section 5) were made within the framework of the Program of Scientific Research of State Academies of Sciences (0034-2021-0001) and SOL study (section 6) in accordance with Program 0040-2019-0023.