Персона: Стёпин, Евгений Викторович
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Институт лазерных и плазменных технологий
Стратегическая цель Института ЛаПлаз – стать ведущей научной школой и ядром развития инноваций по лазерным, плазменным, радиационным и ускорительным технологиям, с уникальными образовательными программами, востребованными на российском и мировом рынке образовательных услуг.
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Руководитель научной группы "Плазменные двигатели в космических исследованиях"
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Стёпин
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Евгений Викторович
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- ПубликацияОткрытый доступPlasma equilibrium and stability in a current-carrying conductor vicinity(2020) Brushlinskii, K. V.; Stepin, E. V.; Брушлинский, Константин Владимирович; Стёпин, Евгений Викторович© Published under licence by IOP Publishing Ltd.Our paper is connected with a cycle of works on mathematical modeling of plasma confinement processes in the magnetic traps - Galateas. A magnetic field confining plasma is created in these traps by current-carrying conductors which are immersed in the plasma volume but not in contact with the hot dense plasma. The idealized models of strictly equilibrium configurations of infinitely conductive plasma in traps possessing symmetry are based on two-dimensional boundary value problems with the scalar Grad-Shafranov equation for the magnetic flux function. Magnetic traps have a perspective in the controlled thermonuclear fusion problem if plasma configurations in them are stable. In our former publications, a question about stability of the configurations around a straight conductor was raised and particularly solved. Here these studies are continued. An area of maximal pressure and a section of its decrease near the outer boundary are included into the considered vicinity. The main result is that the instabilities observed here can be weakened if the plasma pressure slowly decreases near the trap outer boundary.
- ПубликацияТолько метаданныеOn the Stability of Plasma Equilibrium in the Neighborhood of a Straight Current Conductor(2020) Brushlinskii, K. V.; Krivtsov, S. A.; Stepin, E. V.; Брушлинский, Константин Владимирович; Стёпин, Евгений Викторович© 2020, Pleiades Publishing, Ltd.Abstract: The article presents a mathematical model of an equilibrium magnetoplasma configuration in a plasma cylinder containing on its axis a conductor of finite diameter with a current creating a magnetic field confining the plasma. The annular configurations considered here are the simplest elements of a wide class of galatea traps with conductors immersed in the plasma volume. The problems concerning such configurations have a simple analytical solution in terms of ordinary differential equations. A simple result on the existence of smooth equilibrium configurations with restrictions on the maximum plasma pressure related to magnetic units is obtained. The problems of the stability of the configurations—full-scale MHD stability and intermediate stability to perturbations of the same dimension—are formulated and solved. It is shown that intermediate stability takes place within a specified restrictions on pressure and MHD stability tightens this restrictions due to corrugated perturbations depending on the axial coordinate.
- ПубликацияТолько метаданныеMathematical model and stability investigation of plasma equilibrium around a current-carrying conductor(2020) Brushlinskii, K. V.; Stepin, E. V.; Брушлинский, Константин Владимирович; Стёпин, Евгений Викторович© Published under licence by IOP Publishing Ltd.Magnetic Galatea-traps with current-carrying conductors immersed into the plasma are permanent topics of theoretical, experimental and numerical investigations in the controlled thermonuclear fusion field. Our paper presents a mathematical model of equilibrium magnetoplasma configurations around a straight conductor non-contacting with it. Some necessary regularities in the connection between quantitative characteristics of configurations are established. Problems on their MHD stability are set up and partially solved.
- ПубликацияТолько метаданныеMathematical Models of Equilibrium Configurations of Plasma Surrounding Current-Carrying Conductors(2020) Brushlinskii, K. V.; Stepin, E. V.; Брушлинский, Константин Владимирович; Стёпин, Евгений Викторович© 2020, Pleiades Publishing, Ltd.Abstract: This work belongs in the field of mathematical modeling and numerical studies ofequilibrium configurations of plasma, magnetic field, and electric current in Galathea traps withcurrent-carrying conductors immersed in a plasma volume. Models of permissible configurations inthe annular neighborhood of a straight conductor that are not in contact with its surface areconstructed and investigated. Such configurations can be considered a common basic element ofany Galathea. The dependence of the configurations on the position of the outer boundary of theneighborhood is considered, and the MHD-stability of equilibrium configurations with respect tothree-dimensional perturbations in the linear approximation is studied. Quantitative lawsgoverning the restrictions on the plasma pressure are found that ensure the existence and stabilityof the configurations under consideration.
- ПубликацияТолько метаданныеNumerical Model of Compression Plasma Flows in Channels under a Longitudinal Magnetic Field(2019) Brushlinskii, K. V.; Stepin, E. V.; Брушлинский, Константин Владимирович; Стёпин, Евгений Викторович© 2019, Pleiades Publishing, Ltd.We consider a mathematical model of plasma flows in nozzle channels formed by two coaxial electrodes. The acceleration of plasma in an azimuthal magnetic field is accompanied by its compression and heating in the compression zone at the channel axis past the tip of the shorter central electrode. The mathematical apparatus of the model is based on numerically solving two-dimensional MHD problems using the Zalesak flux-corrected transport (Z-FCT) scheme. In the computations, we study the dependence of the compression phenomenon and its quantitative characteristics on the channel geometry, the problem parameters, and the additional longitudinal magnetic field present in the channel.
- ПубликацияТолько метаданныеStability Issues in Two-Dimensional Mathematical Models of Plasma Equilibrium in Magnetic Galathea Traps(2021) Brushlinskii, K. V.; Stepin, E. V.; Брушлинский, Константин Владимирович; Стёпин, Евгений Викторович© 2021, Pleiades Publishing, Ltd.Abstract: Galathea traps for confining plasma in a magnetic field created by current-carryingconductors immersed in the plasma volume constitute a promising class of objects for developmentin the field of controlled thermonuclear fusion. After describing the main properties andquantitative characteristics of the traps, the central problem is to study the stability ofequilibrium magnetoplasma configurations. Mathematical modeling and calculations performed interms of the differential equations of magnetohydrodynamics play an essential role here. Theseequations are described using the example of a toroidal “Galathea belt” trap straightened into acylinder. The article presents its plasmastatic model and several approaches to studying thestability of configurations: the convergence of iterative methods for establishing equilibrium intwo-dimensional models, a brief survey of the research into the magnetohydrodynamic stability ofone-dimensional configurations surrounding a straight current-carrying conductor, and a rigorousstudy of the stability of configurations with respect to two-dimensional perturbations in the linearapproximation. Stability criteria and their relationship to each other are obtained numerically invarious approximations. Ways of generalizing the results to three-dimensional perturbations areindicated.
- ПубликацияТолько метаданныеNumerical Investigations of the Dynamics of Development of Two-Dimensional Perturbations in Magnetic Galathea Traps(2022) Brushlinskii, K. V.; Stepin, E. V.; Брушлинский, Константин Владимирович; Стёпин, Евгений ВикторовичAbstract: Studying the stability of traps for magnetic plasma confinement is one of the main tasks in solving the problem of controlled thermonuclear fusion. The main trends and qualitative and quantitative patterns in this matter can be obtained in terms of mathematical modeling and computational experiment. The object of simulation in this paper is magnetoplasma configurations in a Galathea-belt toroidal trap straightened into a cylinder; these configurations are brought out of equilibrium by small perturbations. The mathematical apparatus of the study consists of problems with two-dimensional time-varying differential equations of magnetohydrodynamics for perturbations of the main parameters of the plasma and magnetic field obtained in a linear approximation. In a series of calculations with various initial data, the picture of the development of disturbances over time is studied and its main laws are described. A limit is obtained for the maximum plasma pressure, expressed in dimensionless units, within which perturbations do not grow with time, i.e., the stability of the configurations discussed is preserved.
- ПубликацияТолько метаданныеMathematical Model and Numerical Simulation of Equilibrium Plasma Configurations in ‘‘Threeleaf’’ Magnetic Traps(2023) Brushlinskii, K. V.; Stepin, E. V.; Брушлинский, Константин Владимирович; Стёпин, Евгений ВикторовичAbstract: In this paper, the results of numerical studies of plasma configurations confined in equilibrium state by a magnetic field in the trap ‘‘Threeleaf’’ are presented. This trap belongs to the promising class of magnetic traps ‘‘Galatea’’ with electric current conductors immersed into the plasma and has a toroidal form with three conductors. The mathematical model is constructed in terms of numerical solution of boundary value problems with the well-known Grad–Shafranov differential equation. Geometry of the trap and its quantitative characteristics dependent on the problem physical parameters are researched. These results are compared with the calculations of traps close in geometry. The compliance of symmetry types of the trap considered and the corresponding mathematical problem solved is highlighted.
- ПубликацияТолько метаданныеOn equilibrium magnetoplasma configurations in "Galatea-Belt" magnetic traps(2021) Brushlinskii, K. V.; Stepin, E. V.; Брушлинский, Константин Владимирович; Стёпин, Евгений Викторович© 2021 Institute of Physics Publishing. All rights reserved.The computation results of equilibrium magnetoplasma configurations in magnetic Galatea-traps developed for solution of controlled thermonuclear fusion problem are presented in the paper. In traps of this type, electric current conductors creating a confining magnetic field are immersed into the plasma volume but do not come in contact with it. In numerical solution of two-dimensional boundary value problems with the elliptic Grad-Shafranov equation, distributions of the main parameters of the plasma and the magnetic field in the trap “Galatea-Belt” with two electric current conductors are obtained. In the series of numerical experiments, the research on how the problem parameters such as the maximum plasma pressure measured in magnetic units, the relative radius of the electric current conductors and the configuration transverse size influence on the properties and characteristics of the configurations is provided.