A remark on a boundary value problem for force-free fields

Summary For the equation rotv–v=0 with not necessarily constant a boundary value problem of Neumann's type is solved by reducing it to an equivalent integral equation.

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Zusammenfassung Für die Gleichung rotv–v=0 mit nicht notwendig konstantem wird ein Neumannsches Randwertproblem durch Zuruckführung auf eine äquivalente Integralgleichung gelöst.

     

Approximation of linear force-free fields in bounded 3-D domains

We introduce and study some methods and algorithms for approximating linear forcefree fields solution of the equation curl B = αB in a bounded domain of R³. Several numerical tests are done in order to study approximation error, compare algorithms, and display some additional properties of force-free fields.     

On the dissipative effect of a magnetic field in a Mindlin-Timoshenko plate model

In this paper we are concerned with a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. The magnetic field that permeates the plate consists of a non-stationary part and a uniform (constant) part. When the uniform magnetic field is aligned with the mid-plane of the plate, a strongly interactive system emerges with direct coupling between the elastic field and the magnetic field occurring in all the equations of the system. The unique solvability of the model is established within the framework of semigroup theory. Spectral analysis methods are used to show strong asymptotic stability and determine the polynomial decay rate of weak solutions.     

Dirichlet problem for axisymmetric potential fields in a disk of the meridian plane. II

We develop new methods for the solution of boundary-value problems in the meridian plane of an axisymmetric potential solenoidal field with regard for the nature and specific features of axisymmetric problems. We determine the solutions of the Dirichlet problems for an axisymmetric potential and the Stokes flow function in a disk in an explicit form. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 748–757, June, 2000.     

Numerical analysis of dissipative instabilities in toroidal plasma configurations with a noncircular cross-section

Translated from Pryamye i Obratnye Zadachi Matematicheskoi Fiziki, pp. 198–203, 1991.     

Dirichlet problem for axisymmetric potential fields in a disk of the meridian plane. I

We develop new methods for the solution of boundary-value problems in the meridian plane of an antisymmetric potential solenoidal field with regard for the nature and specific features of axisymmetric problems. We determine the solutions of the Dirichlet problems for an axisymmetric potential and the Stokes flow function in a disk in an explicit form.     

Computation of axisymmetric MHD flows in a channel with an external longitudinal magnetic field

A numerical study of two-dimensional plasma flows in coaxial channels of plasma accelerators is presented. Two new results are obtained. First, for the computation of MHD problems belonging to the class under consideration, Zalesak’s method is used. It is based on an explicit finite difference scheme with flux correction. This method is free of space splitting, and, therefore, is well suited for parallel computations on multiprocessors. Second, the statement of the problem is extended so that the acceleration of the plasma by the azimuth magnetic self-field goes on in the presence of an external longitudinal field. The results of test computations demonstrate the efficiency of the method and made it possible to investigate the influence of the longitudinal field on the properties of the plasma flows.     

Simulating the effect of external helical magnetic fields on MHD stability of tokamak plasma

The effect of external helical magnetic fields on the stability of a rotating plasma in an axially symmetric tokamak machine is simulated numerically. Threshold amplitude effects are investigated using the NFTC code for the complete nonlinear dynamical 3-D system of MHD equations. The research was partially funded by Russian Foundation of Basic Research (grant 96-07-89110) and Ministry of Science grants 201.03.002 and 0201.03.003. Translated from Chislennye Metody i Vychislitel'nyi Eksperiment, Moscow State University, pp. 4–14, 1998.     

Structure of axisymmetric soliton solutions of Einstein's equations

Theoretical and Mathematical Physics -     

Compton scattering in intense magnetic fields

Compton scattering in intense magnetic fields in the general frame of reference is studied with the help of the QED perturbation theory in the incoming interaction picture. A general expression for the cross section is derived which reduces naturally to the one in the electron-rest frame of reference. This expression can be approximately simplified for the scattering of a high-energy electron with a low-frequency photon. Based on this simplified expreaaion, spectrum functions, as well as power spectra of scattered photons with high energies resulting from the inverse Compton scattering are calculated which manifest clearly a feature of resonances. Project supported by the National Natural Science Foundation of China (Grant No. 19573008) and the Science Research Division of Shanghai Jiaotong University.     

Rayleigh-Taylor instability of a compressible plasma in a horizontal magnetic field

A study of the Rayleigh instability of a compressible plasma, density stratified in horizontal planes and subjected to a horizontal magnetic field, is made. It is found that in the presence of the compressibility effects the magnetic field continues to affect the development of the Rayleigh instability even for disturbances that propagate across the magnetic field (taken perpendicular to gravity), contrary to the result for the case of an incompressible plasma. The special case of a plane interface separating two superposed uniform plasmas of different densities is treated as an example to illustrate the compressibility effects on the hydromagnetic Rayleigh instability. It is found that the compressibility effects have a stabilising nature.

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Zusammenfassung Es wird die Rayleigh-Instabilität eines kompressiblen Plasmas untersucht, mit Dichte-Schichtung in horizontalen Ebenen, in Gegenwart eines horizontalen Magnetfeldes. Es wird gezeigt, daß bei Kompressibilität das Magnetfeld auch die Instabilitätsentwicklung derjenigen Störungen beeinflußt, die sich quer zum Magnetfeld (welches senkrecht zur Gravitationsrichtung angenommen wurde) fortpflanzen; dies ist im kompressiblen Plasma nicht der Fall. Der Spezialfall einer ebenen Trennfläche zwischen zwei Plasmas mit verschiedenen gleichförmigen Dichten wird behandelt, um den Kompressibilitätseffekt auf die hydromagnetische Rayleigh-Instabilität zu zeigen; dieser erweist sich als stabilisierend.