Abstract The geodesic acoustic mode (GAM) is a high-frequency branch of zonal flows, considered as a mechanism of the turbulence self-regulation, which affect the radial transport of energy and particles. The GAM studies were performed in the T-10 tokamak, using the heavy ion beam probing (HIBP). The power spectral density of plasma potential has the main GAM peak with frequency f ~ 20 kHz, and two satellite peaks, high-frequency (HF) and low-frequency (LF) ones. In ohmic plasmas and in discharges with moderate electron cyclotron resonance heating (ECRH), both satellites are separated from the main peak by the Δ f ~± 3−4 kHz. Each of three peaks has the character of a global eigenmode of plasma oscillations with the frequency and amplitude of fluctuations almost constant in a wide radial region from the core to the edge. At the edge, the amplitude of the GAM peaks decreases to zero. Thus, the radial dependence of the GAM frequency does not obey the local Winsor formula f GAM ~ C s ( r )/ R , where C s ~ T e 1/2 is the ion-sound velocity. Nevertheless, in ohmic discharges and at the moderate ECRH power P EC <0.5 MW, the frequencies of all peaks depend on C s , taken in their birth points located at the edge. With a further increase in temperature or at the powerful ECRH (0.5 MW < P EC < 2.2 MW) the frequencies of all peaks deviate from the C s dependence and saturate. When temperature increases, the frequency difference between the main GAM peak and the HF-satellite decreases, and these two peaks merge into the single one, reaching the upper limit for f GAM . The bicoherence analysis finds the three-wave coupling of GAM with quasicoherent and stochastic low-frequency turbulent modes. Each peak has its own frequency range of coupling.

The results of heat and particle transport simulations for ohmic plasma in the T-10 tokamak with a circular limiter and for D-shaped plasma in the COMPASS tokamak with a divertor are presented. In addition, the H-mode with ohmic heating and with additional heating by the neutral beam injection (NBI) in the COMPASS was simulated. The simulations were carried out with the Canonical profile transport model (CPTM) using the ASTRA code. The obtained electron temperature and density profiles agree with the measured ones with standard deviations within the experimental accuracy of 10–15

Plasma was heated at the second harmonic of electron cyclotron resonance (ECR) in the L-2M stellarator and the T-10 tokamak. The concept of equivalent tokamak and stellarator discharges was extended to the case of both full and partial absorption of EC power. Comparison of experimental electron temperature profiles with profiles calculated using the canonical profiles transport model allows us to estimate the efficiency of ECR heating in the L-2M discharges without suprathermal electrons, which distort the distribution function, preventing reliable measurements of temperature. The dependence of the ECR heating efficiency on the plasma density was obtained, describing experiments on the L-2M and TJ-II stellarators, and on the T-10 tokamak. The energy characteristics (the stored energy and the confinement time) for L-2M discharges were calculated. Predictions for ECR heating in the T-15MD tokamak are considered. The features of solving the ill-posed transport problem for the L-2M are discussed.

The T-15MD tokamak with the warm toroidal field coils, elongated plasma cross section, and a low aspect ratio was commissioned at the National Research Center Kurchatov Institute in 2021. An economically viable fusion reactor requires long discharges or even a steady-state mode. The short pulse of the toroidal field is among the main obstacles on the way to the steady state. Therefore, as a next step after T-15MD, it is proposed at the NRC Kurchatov Institute to consider the design of a superconducting tokamak (SCT), which holds the basic geometric parameters of the T-15MD: R/a = 1.5 m/0.67 m with a field on the axis of B-0 < 5 T and a long pulse of current of I-p < 5 MA. The focus of the paper is the system of the toroidal magnetic field. A three-layer design of the toroidal field coil is proposed: an inner layer of a high-temperature superconductor (HTSC), a Nb3Sn middle layer, and a NbTi outer layer. On the basis of structural strength calculations, candidate materials for coil cases were selected. For cooling the coils, a semi-longitudinal pumping of low-pressure liquid helium is proposed. The design of the HTSC cable in conduit consisting of two halves is considered in detail. A mesh cryostat design that provides a convenient access for diagnostics and plasma heating is proposed. SCT systems similar to those used in the T-15MD are analyzed.

The optical thickness of the plasma is often insufficient to fully absorb the microwaves during heating at the second harmonic of the electron cyclotron frequency. An analysis of the experiments to the T-10 tokamak allows us to find the criteria for the full absorption, and to construct a canonical profile transport model for the full and partial absorptions of microwaves. The conditions to the equivalence of discharges in different tokamaks, and in a pair of tokamaks with the optimized W7-X stellarator are formulated. For equivalent discharges, calculations to the T-15MD tokamak under construction with the obtained model coincide with measurements of electron and ion temperatures in the W7-X over a wide range of plasma densities. The validated model is used to analyze future shots of T-15MD.

Heavy ion beam probe (HIBP) is a unique plasma diagnostics that makes it possible to measure the electric potential φ of high-temperature plasma and its fluctuations φ̃ , as well as the density ñ_e and poloidal magnetic field B̃_pol fluctuations. Position of the point of performing measurements in the plasma vertical cross-section depends on the beam energy and angle of its entrance into the plasma. The variation of these two parameters makes it possible to construct a two-dimensional (2D) detector grid, which covers the domain of possible measurements. The measurement results obtained in the detector grid points provide for constructing 2D distributions of plasma parameters. For the OH and ECRH stages of the T-10 tokamak shots, 2D distributions of the plasma electric potential are presented for the regime with the on-axis magnetic field of Bt = 2.2 T, plasma current of Ipl = 230 kA, line-average density of n̅_e ≈ 1.1 × 1019 m–3 and off-axis ECRH power of PECRH = 1.7 MW.

Radial distributions of the electric potential and plasma density oscillations have been measured in the T-10 tokamak ohmic plasma. Radial distributions of the amplitude and frequency of the geodesic acoustic mode are plotted according to the data on the fluctuations of the electric potential of the plasma, and radial distributions of the amplitude and frequency of the quasi-coherent mode are plotted according to the data on the fluctuations of the plasma density. The quasi-coherent mode corresponds to the major part of the turbulent particle flow, the geodesic acoustic mode as a high-frequency branch of zonal flows is involved in the turbulence regulation, which makes these objects very important for plasma physics. The paper presents the results obtained in different operating modes of the T-10 tokamak.

The concept of equivalent tokamak and stellarator discharges with the same electron and ion temperatures and with full absorption of the injected ECRH power was introduced in Dnestrovskij et al (2021 Plasma Phys. Control. Fusion 63 055012). In the present paper, the concept of the discharges equivalence is extended to the case of partial ECRH power absorption. The conditions of discharges equivalence for this case are formulated. It is shown that in equivalent discharges not only the electron temperatures, but also the absorbed powers are the same. Examples of equivalent experimental discharges of the TJ-II stellarator and simulated discharges of the T-10 tokamak with partial ECRH power absorption are studied. The absorbed ECRH power and energy confinement time are found for TJ-II low-density shots heated with ECRH only.

Processes associated with plasma self-organization in tokamaks are presented in the possible logical sequence. The resulting picture of physical processes in self-organized plasmas is predicted based on the nonrequiibrium thermodynamic approach, which uses the Smoluchowski-type equation for the energy balance. The self-organization of magnetized plasma leads to the formation of the universal MHD structure, where the normalized pressure profiles are similar. Finally, experimental confirmation of the proposed physical picture in magnetic fusion facilities is given.

We study the microwave absorption during electron cyclotron resonance heating (ECRH) by the extraordinary wave at second harmonic (X2 mode) in the T-10 tokamak and TJ-II stellarator in a wide range of plasma densities, and compare experiments with the classical formulas for the absorption of the injected ECR power. Empirical relations for the absorption efficiency and for the critical plasma density n_cr , which separates the regions with full and partial absorption of the injected ECR power, are obtained using the numerical simulation of the heat transport with the transport model of canonical profiles. It is shown that in both devices, the range of densities exists, where the absorption predicted by the classical formulas is almost full, while according with the empirical formula, only a small fraction of the power is absorbed. The obtained relations allow ones to optimize the conditions of ECRH in toroidal systems for magnetic plasma confinement.

Heavy ion beam probe (HIBP) is a unique tool for studying the electric potential and various turbulence characteristics both in the core and at the edge of toroidal plasmas. The position of the HIBP measurement point in the plasma is determined by the probe beam energy and its entrance angle into the plasma. The probe beam energy is constant during the plasma discharge and determines the maximum penetration depth of the beam into the plasma. The beam entrance angle into the plasma can vary during the discharge, and the set of positions of HIBP measurement points for different beam entrance angles creates a so-called detector line. The set of detector lines for different probe beam energies represents a 2D region (detector array) in the vertical cross section of the plasma. The article presents a method for constructing 2D distributions of plasma parameters over the detector array on the T-10 tokamak by the example of the plasma electric potential.

2D plasma potential ϕ distribution was measured in the electron cyclotron resonance heating (ECRH) and neutral beam injection (NBI) plasmas of the TJ-II stellarator with the heavy ion beam probe for the whole radial range and wide area of the poloidal angle, and supported by Langmuir probe data at the edge. The whole operation domain for the on-axis ECRH was explored ( nˉe = 0.45–0.8 ×1019 m−3, P EC = 220–470 kW), in addition, NBI plasmas with nˉe = 0.9–1.3 × 1019 m−3 and P NBI = 510 kW were studied. In ECRH plasmas the density ramp-up is accompanied by the evolution of the potential from the bell-like to the Mexican hat profile, while the density profiles were flat or slightly hollow. The potential has the positive peak at the centre, and LFS-HFS (low field—high field sides) and up-down symmetry. Equipotential lines are consistent with vacuum magnetic flux surfaces. In the high-density NBI scenario, the ϕ profile was fully negative with a minimum up to −300 V at the centre, while at low-density ECRH plasma, ϕ has a maximum up to +0.9 kV at the centre. Fluctuations of potential and density are stronger in low-density scenarios and not poloidally symmetric. At the mid-radius (area of the maximum density), root mean square (RMS) of fluctuations were up to ϕ ∼ 15 V at LFS vs ∼20 V at HFS; RMS n e ∼ 2% at LFS vs ∼3% at HFS. In the NBI plasmas with the density rise, the asymmetry decreases and finally vanishing at nˉe = 1.2 × 1019 m−3. 2D distribution of the NBI-induced Alfvén eigenmodes (AEs) shows asymmetric ballooning structure: contrary to broadband turbulence, AE-associated potential perturbation dominates in the LFS with a factor up to 1.7 respect to the HFS. The electrostatic mode, excited in ECRH plasmas by suprathermal electrons also shows asymmetric structures: density perturbation dominates in the top-bottom direction compared to LFS-HFS direction.

Ion heat conductivity in deuterium plasma of the circular limiter tokamak T-10 is analyzed in more than 100 Ohmic shots. Four data scans: plasma density, effective charge, plasma current, and toroidal magnetic field are presented. Each scan is formed with the preservation of other parameters. It is shown that at the plasma periphery, r/a=0.6−0.8, the ion heat conductivity exceeds neoclassical values up to three to eight times. The anomalous part χian increases with plasma density and effective charge, while it decreases with plasma current and does not depend on the toroidal magnetic field. The highest value of χian is observed in high-density low-current regimes. More negative values of plasma electric potential correlate with higher values of χian. The empirical scaling of χian is derived. The transport model based on this scaling allows us to describe experimental profiles of ion temperature Ti(r) within experimental error ±15%.

The study of Alfvén eigenmodes (AEs) driven by fast particles in toroidal plasmas is of a great importance for future fusion reactor with plasma, dominating by fusion alphas. The review is the first attempt to describe systematically AEs in the TJ-II stellarator with low magnetic shear, and to summarize more than 10 years of the direct application of the Heavy Ion Beam Probing (HIBP)—a diagnostic with unique capabilities to study AEs in toroidal plasmas by local measurement of the AE-excited electric potential and density perturbation in the plasma core along with magnetic potential perturbations. Experimental findings, including absolute values of plasma potential and density perturbation, and the mode radial location, are compared with numerical simulations that allows us to identify the observed modes as helicity induced Alfvén eigenmodes (HAE) and global Alfvén eigenmodes (GAE). On top of that, the mode poloidal rotation, mode numbers, and turbulent particle flux estimations are described. 2D poloidal map of the AEs demonstrates the ballooning character of plasma potential perturbation. AEs in both continuous frequency and chirping form shows strong evolution caused by rotational transform (iota) change, the suggested analytical model for the mode frequency describes the observation. AE frequency dynamics down to geodesic acoustic mode frequency with iota variation along with AE transformation from continuous to chirping form and back is observed.

Geodesic acoustic modes, Alfvén eigenmodes, stationary and oscillating components of the electric field, and their relations to plasma confinement have been studied. Theoretical concepts of the interaction of geodesic acoustic modes with other types of plasma turbulence have been tested. Concomitant problems such as the effect of heating methods on the plasma confinement and turbulence, as well as the properties of impurities and scrape-off layer have also been discussed. Key diagnostics such as heavy ion beam probe, correlation reflectometry, and multipurpose optical diagnostic complex have been described. The main experiments have been performed at the T-10 tokamak, which has a high-power electron cyclotron resonance heating system. The supporting experiments have been performed at the TJ-II stellarator in Spain, the COMPASS tokamak in Czech Republic, and the STOR-M tokamak in Canada. The results of the experiments have been compared with the analytical and numerical calculations.

TJ-II stellarator results on modelling and validation of plasma flow asymmetries due to on-surface potential variations, plasma fuelling physics, Alfvén eigenmodes (AEs) control and stability, the interplay between turbulence and neoclassical (NC) mechanisms and liquid metals are reported. Regarding the validation of the neoclassically predicted potential asymmetries, its impact on the radial electric field along the flux surface has been successfully validated against Doppler reflectometry measurements. Research on the physics and modelling of plasma core fuelling with pellets and tracer encapsulated solid pellet injection has shown that, although post-injection particle radial redistributions can be understood qualitatively from NC mechanisms, turbulence and fluctuations are strongly affected during the ablation process. Advanced analysis tools based on transfer entropy have shown that radial electric fields do not only affect the radial turbulence correlation length but are also capable of reducing the propagation of turbulence from the edge into the scrape-off layer. Direct experimental observation of long range correlated structures show that zonal flow structures are ubiquitous in the whole plasma cross-section in the TJ-II stellarator. Alfvénic activity control strategies using ECRH and ECCD as well as the relation between zonal structures and AEs are reported. Finally, the behaviour of liquid metals exposed to hot and cold plasmas in a capillary porous system container was investigated.

We analyze the highest energy confinement in tokamak plasmas based on thermodynamic approach (plasma self-organization). The energy transport coefficients in the saturated confinement regimes are calculated from experiments in the T-10 tokamak. Using these coefficients, we estimate the maximal energy confinement for JET, ASDEX Upgrade, JT-60U, DIII-D and KSTAR tokamaks. Calculated energy confinement is in a good agreement with measured ones. Obtained results allow us to predict the maximal energy confinement in newly constructed machines up to a fusion reactor. The energy confinement for two basic scenarios for ITER is accessed.

We study Alfvén eigenmodes (AEs) in the TJ-II heliac in hydrogen plasmas heated by hydrogen co-field neutral beam injector. Taking advantage of the unique TJ-II flexibility in a varying plasma current, we have observed strong variation of the AE frequency from fAE ∼ 30 to ∼220 kHz for selected modes. An advanced heavy-ion beam probe diagnostic determines the spatial location and internal amplitudes of the modes. The modes satisfy a local AE dispersion relation including the geodesic acoustic frequency that represents the lowest frequency of the mode. Linear MHD modeling with STELLGAP and FAR3D codes shows that the calculated temporal evolution of the mode frequency reproduces the observed maxima and minima at the same time intervals with a similar frequency range, and the radial profile peaks near the outer edge of the observed one.

Local fluctuations of electrostatic potential, poloidal electric field, magnetic potential and electron density are simultaneously measured in the T-10 tokamak by a heavy ion beam probe (HIBP) having a five-slit energy analyser, which allows an estimate of the turbulent particle flux and $\boldsymbol {E}\times \boldsymbol {B}$ rotation velocity in the off-minor-axis gradient zone of the toroidal plasma column. The high spatial and temporal resolution of the modern multichannel HIBP makes it an effective tool to study plasma oscillations. Motivated by previous work that has documented time-resolved interactions between measured plasma parameters using correlation analysis (coherence of $E_{\textrm {pol}}$ and density $n_e$ , and cross-phase), a new result from bicorrelation analysis (bicoherence of magnetic potential $A_\zeta$ and density $n_e$ , and biphase) is reported for documenting the evidence of wave–wave coupling and energy transfer associated with the interaction between geodesic acoustic modes (GAM) and broadband, quasi-coherent modes.