The production of the artificial 51Cr neutrino source with activity > 3 MCi for the experiment BEST is presented. This procedure consisted of making a 50Cr target and irradiating it with thermal neutrons in a nuclear reactor SM-3. The production of a target in the form of disks with a thickness of 4 mm and a diameter of 84 and 88 mm included enrichment (to 96.5% in 50Cr) of natural chromium in the form of oxyfluoride by gas centrifugation, electrolytic reduction and refining of metallic chromium, as well as the formation of chromium disks by spark plasma sintering. Simulations of various source geometries, neutron flux and nuclear transmutation were carried out to validate the design of the source, the irradiation device and the transport container, the required chemical purity of the target and the irradiation schedule in the reactor. The calculated activity of the source after 75 effective days of irradiation was 3.55 MCi. The activity of the source was measured by the calorimetric method and amounted to 3.41 MCi at the time of its delivery to the Baksan Neutrino Observatory. This is the most intense chemically pure neutrino source ever produced.

This paper presents the results of numerical modeling of the spatial structure and saturation of Alfven eigenmodes in the GLOBUS-M spherical tokamak with the KINX and VENUS codes. Measurements with the multichannel Doppler backscattering reflectometry provided experimental evidence of the mode localization near the plasma boundary when excited by energetic particles during neutral beam injection heating. The numerical results suggest the Alfven-sound eigenmode, in particular the beta-induced Alfven acoustic eigenmode, as the candidate instability responsible for the observed localization pattern. The mode linear growth rates and nonlinear saturation levels are found to be highly sensitive to the parameters of the model.

The code developed by the authors for calculating the MHD stability of two-dimensional plasma configurations with an arbitrary magnetic field topology is presented. The choice of an appropriate version of the finite element method on hybrid unstructured computational grids and test calculations are discussed. Examples of using the code for modeling the plasma stability in Galatea traps and in divertor configurations of tokamak taking into account the plasma beyond the separatrix are given.

Object and purpose of research. The object of the work is the power supply systems of submersibles. The aim is to assess the characteristics of the submersible energy supply systems and find ways to improve them. Materials and methods. The study was conducted on the basis of analytical methods and computer simulation of electromagnetic processes of the systems of energy supply of submersibles. Main results. A comparative assessment of the characteristics of the main systems of energy supply of submersibles has been carried out. New ways and devices powering submersibles, developed methods for calculating these devices. Ways to improve the power supply systems of submersibles are shown. Conclusion. The results of the research allow us to identify ways to further improve the characteristics of the power supply systems of submersibles and to speed up the process of their implementation in practice.

This paper considers the prospects of outer X-point tokamak configurations that exhibit MHD stability properties similar to those of negative triangularity tokamaks.The most recent numerical studies of ideal MHD stability for outer X-point configurations provide evidence of beta limits, β N ≥ 3, and the passive stabilization of axisymmetric modes in plasmas with an elongation close to unity.Formation of an outer X-point with the help of a simple magnetic system is examined.A more general outlook on the external X-point tokamaks is offered including power exhaust, edge stability and divertor geometry.

This paper presents the results of analytical and numerical calculations of the sideways force acting on the resistive wall due to eddy currents induced by n=1 kink instability. The inertia-less ideal MHD model for resistive wall mode is explicitly shown to be compatible with the condition of vanishing sideways force in the ideal wall limit. In the frame of standard high aspect ratio approximation, assuming that tokamak plasma is separated from the coaxial resistive wall by a vacuum layer, we calculate analytically the sideways force as a function of the growth rate γ taking into account the known relation between γ and the value of the safety factor q. It is noted that this dependence is determined by the single mode m/n=1/1 instability in the range of q-values q<1 giving the maximal force at γτw≥2, where τw is the resistive wall time. The numerically estimated magnitude of the sideways force for ITER relevant cases with q>1 is smaller because the sideways force is generated by toroidally coupled satellite harmonic m/n=1/1. The forces due to resistive wall mode with conformal and one-sided wall proximity to the plasma boundary are compared.

This paper finalizes the self-consistent study of the sideways force acting on the resistive wall due to eddy currents induced by n = 1 kink instability under variations of the external poloidal field and its impact on the force peaking factor as outlined in A. A. Martynov and S. Yu. Medvedev, Phys. Plasmas 27, 012508 (2020). A proper analytical treatment of the sideways forces for a large aspect ratio circular tokamak is limited to the case q < 1 with a dominating m/n = 1/1 mode and only weak coupling to sideband poloidal harmonics, which asymptotically does not contribute to the force. The present paper shows that in the 1D case, the net sideways force does not depend on variations of the external equilibrium poloidal field with a difference in the force peaking factor only: the corresponding analytic expressions have been derived. For realistic 2D cases, the behavior of both the net force and the peaking factor changes due to mode coupling and does depend on the variations of the equilibrium magnetic field at the wall. In particular, for q > 1 at the plasma boundary, the sideways force is generated by a sideband m/n = 1/1 harmonic, which gives lower net force as compared to the q < 1 case, but with a higher peaking. The numerically estimated magnitude of the sideways force density was found to be insignificant for ITER that calls for taking into account the plasma−wall contact in disruption modeling.

Ideal magnetohydrodynamic (MHD) properties depending on the plasma pressure are considered for axisymmetric equilibrium magnetoplasma configurations in the Galatea trap with three ring current-carrying conductors embedded in plasma. The study of ideal MHD modes with different toroidal wave numbers takes into account the plasma compressibility with an adiabatic index of 5/3 in the perturbed potential energy functional in the framework of the energy principle. The stability calculations are performed in the presence of a vacuum layer between the plasma and the vacuum chamber. The limiting pressure values corresponding to stable multiply connected plasma configurations without an assumption of nested magnetic surfaces are estimated.

Abandoning the assumption of nested magnetic surfaces in tokamak plasma expands the field of research and opens up new approaches for both theoretical and experimental plasma physics. The computer code KINX for calculations of the ideal MHD stability was developed for studies of doublet plasmas with two magnetic axes and using block-structured grids in each subdomain with nested magnetic surfaces. Then, the MHD_NX code on unstructured grids was developed to calculate the stability of two-dimensional equilibria with an arbitrary topology of magnetic surfaces. The study of equilibrium and stability of equilibrium configurations with toroidal current density reversal and axisymmetric n = 0 islands, which are associated with internal transport barrier and low current density at the magnetic axis, as well as with the operation of tokamaks in the alternating current regime, leads to more general issues of MHD stability of two-dimensional solutions of the Grad−Shafranov equations with islands under other types of symmetry—chain of islands in helical symmetry and cylindrically symmetric m = 0 islands in configurations with the longitudinal field reversal. New ideal MHD unstable modes have been discovered for various types of two-dimensional island configurations. The energy principle with MHD-compatible boundary conditions at open magnetic field lines is necessary for the self-consistent stability analysis of divertor configurations in tokamaks with a finite current density at the separatrix, taking into account the plasma outside the separatrix. Several codes have been developed for calculations of plasma equilibrium and stability, taking into account the influence of currents outside the separatrix, which are ready for integration with other codes for edge plasma modeling.

Recent research at three small tokamaks with different parameters located at the Ioffe Institute—the spherical tokamak Globus-M, the large aspect ratio tokamak FT-2 and the compact tokamak TUMAN-3M—are reviewed. This overview covers energy confinement (Globus-M and FT-2), L–H transition (TUMAN-3M and FT-2), Alfvén waves (Globus-M and TUMAN-3M), ion cyclotron emission (TUMAN-3M), major plasma discharge disruption (Globus-M) and scrape-off layer (Globus-M) studies. A full-f global gyrokinetic modeling benchmark using synthetic diagnostics in FT-2 is described. Anomalous absorption and emission in electron cyclotron resonance heating experiments due to the parametric excitation of localized upper hybrid waves are analyzed theoretically. Progress in the development of the neutral particle analysis, gamma-ray spectrometry and divertor Thomson scattering combined with laser-induced fluorescence diagnostics for ITER is discussed. The status of the new Globus-M2 spherical tokamak is reported.

О р д е н а Л е н и н а ИНСТИТУТ ПРИКЛАДНОЙ МАТЕМАТИКИ имени М.В.Келдыша Р о с с и й с к о й а к а д е м и и н а у к С.Ю.Медведев, А.А.Мартынов, В.В.Савельев, А.Н.Козлов Расчеты идеальной МГД устойчивости плазмы в ловушке-галатее «Тримикс» Москва -2018 Медведев С.Ю., Мартынов А.А., Савельев В.В., Козлов А.Н

Within the framework of the BEST experiment project, a calorimetric system was developed to measure the activity of high-intensity (several MCi) neutrino sources based on 51 Cr. In the range of thermal capacities of 250–520 W, the uncertainty of the heat release measurement is less than 0.25%. Taking into account the uncertainty of the energy release value for the 51 Cr decay (0.23%), the activity of the neutrino source can be determined with an accuracy of ∼0.5%.

AbstractConditions of the excitation of toroidal Alfvén eigenmodes (TAEs) and their inf luence on the confinement of fast particles into the Globus-M spherical tokamak have been studied by KINX code calculations of the magnetohydrodynamic spectra of reconstructed divertor equilibrium configurations with stability margin q _0 > 1 on the magnetic axis. The sensitivity of the frequencies of TAE modes with toroidal wavenumber n = 1 to the type of boundary conditions and choice of boundary surface has been studied. It has been established that the frequencies of modes with dominating poloidal harmonics m = 1 and 2 in the gap of continuum are significantly higher than those observed in the spectra of signals measured in the Mirnov coil probes, especially under the assumption of free plasma boundary with allowance for its compressibility. The TAE modes with lower frequencies and higher poloidal wavenumbers localized near the plasma boundary may be responsible for the oscillations observed in the experiment. However, these modes are characterized by the interaction with continuum and, probably, exhibit related damping.

Yu.V. Petrov 1 , N.N. Bakharev 1 , V.V. Bulanin 2 , V.K. Gusev 1 , G.S. Kurskiev 1 ,A.A. Martynov, 3 S.Yu Medvedev 3 , V.B. Minaev 1 , M.I. Patrov 1 , A.V. Petrov 2 , N.V. Sakharov 1 , P.B. Shchegolev 1 , A.Yu. Telnova, S.Yu. Tolstyakov 1 , A.Yu. Yashin 2 . 1 Ioffe Institute, St. Petersburg, Russia 2 Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia 3 Keldysh Institute of Applied Mathematics, Moscow, Russia.

Going beyond nested flux surfaces in tokamak plasmas brings new insights both for theoretical and experimental plasma physics. Starting from the research of doublet plasmas with two magnetic axes the ideal MHD stability code KINX [1] was employed to investigate the subject dealing with structured grid in each sub-domain with nested flux surfaces. The MHD_NX stability code on unstructured grids was developed to treat 2D equilibria with arbitrary topology of magnetic surfaces [2]. The study of equilibrium and stability of the reversed current configurations with axisymmetric n = 0 islands related to the current hole and AC operation in tokamak [3] brings more general questions of MHD stability of 2D equilibrium solutions with islands and other types of symmetry – chains of tearing-like islands in straight helix and cylindrically symmetric m = 0 islands related to the RFP configurations. For all these 2D island configurations new ideally unstable modes were discovered [4]. The energy principle formulation with MHD compatible boundary conditions at the open field lines is needed for treatment of tokamak plasmas with SOL region in order to self-consistently investigate stability of diverted tokamak configurations with finite current density at the separatrix. What are MHD pedestal height limits with very thin SOL and high pressure gradients outside the separatrix taken into account? How could recently discovered separatrix localized n = 0 peeling mode be related to the M-mode in JET? The suite of equilibrium and stability codes for diverted plasmas with SOL has been developed to answer these questions and ready for integration with other plasma edge modeling codes [5].

The calorimetric system based on mass-flow calorimeter for high-precision determination of neutrino flux from Cr-51 source with activity 3MCi and higher is created for experiment BEST. The achieved heat release uncertainties are less than 0.25% in the whole range of the heat power and less than 0.1% in the range of 250-500 W. Total value the uncertainty considering the uncertainty of the energy release in the Cr-51 decay (0.23%) shows that the activity of 3MCi Cr-51 neutrino source can be determined with accuracy better than 0.5%.