Analytical configurations of a force-free magnetic cylinder in the solar wind

The problem of a smooth field configuration, which should be an initial configuration in modeling (using the method of coarse particles) the problem of a stationary solar wind flow around a magnetic cloud in the case of a spatially two-dimensional statement (when a magnetic cloud is considered as a force-free magnetic cylinder with a finite radius) is considered. It has been indicated that such a statement is possible only when the magnetic field in the solar wind is parallel to the cylinder axis. The method for finding the magnetic field of a force-free cylinder with a finite radius, when some field component is specified and another component is determined based on this one (which makes it possible to construct fields with preassigned properties), has been proposed. The variant for constructing the initial field configuration in the transition region around a cylinder has been proposed. This variant makes it possible to gradually pass from homogeneous crossed fields in the solar wind to a force-free magnetic and zero electric fields within a cylinder, an electric field being potential and orthogonal to a magnetic field (in the reference system related to a magnetic cloud).     

Dynamics of the spatial distribution of electrons and their gyrosynchrotron emission characteristics in a collapsing magnetic trap

The dynamics of the distribution of nonthermal electrons, injected into a collapsing magnetic trap, has been considered. The electron energy and pitch angle nonstationary spatial distributions in an extensive magnetic trap have been obtained for the first time for different laws of inhomogeneous magnetic field evolution in this trap by numerically solving the Fokker-Planck kinetic equation. The gyrosynchrotron emission intensity has been calculated for the obtained electron spatial distributions. It has been indicated that energetic electrons are effectively accumulated and accelerated at the top of a collapsing trap due to the first-order Fermi and betatron acceleration mechanisms at certain rates of variations in the magnetic field and background plasma density.     

On the propagation of disturbances in a composite viscoelastic layer in a magnetic field

Summary The propagation of disturbances in a composite viscoelastic layer when subjected to an impulsive force in the presence of a primary magnetic field, has been investigated in this note. The mechanical displacement has been derived from the electro-magnetic equations of Maxwell, the equation of motion and the stress-strain relations of the materials considered and has been computed for small values of time.     

Hydroacoustic wave in the external alternating magnetic field

The electromagnetic fields induced by hydroacoustic waves, propagating in a liquid conducting medium in an alternating magnetic field, have been considered. The equation, relating the induced magnetic field to the undisturbed antenna field and acoustic wave parameters, has been obtained. The spatial—temporal pattern of the induced field has been constructed in the case when acoustic wave propagates along a direct line with an alternating current.     

Infrasonic wave magnetic field in the oceanic waveguide

The magnetic field generated by an acoustic wave, propagating in the oceanic wave guide, has been considered. It has been indicated that the induced field is most substantial at frequencies when only the first normal mode exists. The dependences of the induced field component on the depth, frequency, and direction of the geomagnetic field have been obtained in this frequency band. The possibility of determining coordinates of a strong underwater earthquake using the acoustic field magnetic field has been considered.     

Modeling the partial ring current effect in a disturbed magnetosphere

The mathematical model of the magnetic field of the partial ring current has been proposed. This current is considered as a pair of spatial current circuits in the Northern and Southern hemispheres, either of which includes two ring zones, in the geomagnetic equator plane and ionosphere, and two zones of the field-aligned current, flowing along the geomagnetic dipole field lines and joining ring fragments of the circuit. The model parameters are: colatitude of the eastward electrojet, longitudinal shift relative to the Sun-Earth axis, circuit half-angle, and the total current flowing in the circuit. The Biot-Savart-Laplace law has been used to calculate the magnetic field of the current circuit. The magnetic field of the partial ring current has been calculated under the conditions typical of a strong magnetic storm. The technique for calculating the partial ring current intensity, using the Asym-H geomagnetic index, has been proposed.     

Interaction between the electromagnetic and acoustic fields in the marine environment

The possibility of generation of additional acoustic harmonics in the geomagnetic field after the propagation of an acoustic wave in the conducting medium through the region with a variable magnetic field has been considered. Two possible procedures of such a generation have been analyzed: the parametric procedure and the dynamic procedure related to ponderomotive forces. The expressions have been obtained for three acoustic harmonics generated by an oscillating magnetic field.     

Specific features of development of two-dimensional convection in a rotating compressible conducting fluid

An axisymmetric model of convection in a rotating cylinder in an external uniform magnetic field has been considered. In the considered model, the meridional circulation is created by a nonuniform rotation of the lower boundary relative to the other boundaries. In the considered model, the time of formation of the stationary regime in the magnetic field considerably increases if the vertical density (compressibility) inhomogeneity is taken into account for Ekman numbers of E = E _M = 3 × 10⁻³. This example shows that the compressibility of a medium should be taken into account in the convection and dynamics of the magnetic field when the magnetohydrodynamics of the Earth is analyzed.     

Ring current asymmetry during a magnetic storm

The ring current dynamics during the magnetic storm has been studied in the work. The response of the magnetospheric current systems to the external influence of the solar wind, specifically, resulting in the development of the asymmetric ring current component, has been calculated using the magnetic field paraboloid model. The asymmetric ring current has been considered as a family of spatial current circuits in the Northern and Southern hemispheres, composed of the zones of the partial ring current in the geomagnetic equator plane, which close through the system of field-aligned currents into the ionosphere. The value of the total partial ring current has been estimated by comparing the calculated asymmetry of the magnetospheric magnetic field at the geomagnetic equator with the value of the Asym-H geomagnetic index. The variations in the symmetric and asymmetric components of the ring current magnetic field have been calculated for the magnetic storm of November 6–14, 2004. The contributions of the magnetospheric current systems to the Dst and AU geomagnetic indices have been calculated.     

Magnetic field disturbance in magnetoactive plasma with a localized electrostatic field

Charged particle motion in magnetoactive plasma with an axially symmetric electrostatic field has been studied. It has been indicated that a difference between drift velocities of electrons and ions leads to a magnetic field disturbance. The equations for stationary magnetic field disturbances stretched along the magnetic field, which can be magnetic ducts for propagation of whistlers, have been obtained. The possibility of formation of such ducts by electrostatic fields from thunderstorm sources, penetrating into the ionosphere, has been estimated.     

Bifurcations in Spherical MHD Models

A series of numerical studies on the behaviour of magnetic fields and motions in a spherical body of an electrically conducting incompressible fluid have been carried out. The magnetic field was assumed to be maintained by a given electromotive force inside the body and to continue as a potential field in outer space. In view of the motion an external forcing was taken into account, and boundary conditions were considered which correspond to a stress-free surface. The stability of several steady states has been studied as well as the evolutions starting from unstable states. In this paper a configuration with a poloidal magnetic field and a differential rotation, both symmetric about the same axis, is considered. This configuration is stable only for sufficiently small Hartmann numbers but evolves, if disturbed, in the case of larger Hartmann numbers toward a non-axisymmetric state. In this case the well-known symmetrization effect of differential rotation in magnetic fields is destroyed.     

Spatial structure of the magnetic field induced by an infrasonic wave in the oceanic waveguide

The magnetic field generated by an acoustic wave propagating in the oceanic waveguide has been considered. The effect of the self-induction factor on the spatial structure of this field has been studied. It has been indicated that there exists a frequency range where it is necessary to take into consideration self-induction. It has been indicated that the induced field is most substantial at frequencies when only the first normal mode exists. The dependences of the induced field on the depth, frequency, and geomagnetic field direction have been obtained and analyzed for this frequency range.     

On the deformations in a general linear substance of a layered media subjected to a body force and a deforming magnetic field

Summary The propagation of disturbances has been studied in a layered media, comprising a liquid and a general linear substance, subject to a body force and permeated by an initial magnetic field acting normal to the plane of the contact. The effect of the body force due to some internal source has been considered in the problem and a set of results has been obtained under two possible extreme variants of the boundary conditions in the form of integral forms, which can be computed to visualize the displacement—time and displacement—depth variations, both in the presence and absence of the body force. The effect of body force on the substance has been, as a sample case, illustrated in the graphs. The stress-strain relation of the general linear substance and the electromagnetic equations of Maxwell have been used in working out the problem.     

Long-period variations in the magnetic field of small-scale solar structures

Thirty small-scale structures in the solar atmosphere, i.e., facula nodes at ±(20°–46°) latitudes, have been studied in order to analyze quasi-periodic variations in the magnetic field. SDO/HMI magnetograms have been used for this purpose. Long-period variations in the magnetic field strength of the considered objects in the 60–280 min range have been revealed as a result of data processing. It has been shown that there are no dependences between the magnetic field and period, nor between the magnetic field and object area. It has been assumed that the discovered variations are not natural oscillations of the magnetic field strength.     

Flow past spheres and spheroids in the presence of a toroidal magnetic field

Summary Stewartson [1]²) has considered the inviscid flow past a sphere in the presence of a uniform magnetic field andMurray andLudford [2] have investigated a similar problem in which the magnetic field originates from an axially symmetric dipole field situated at the centre of the sphere. In connection with the study of earth's magnetic field, the toroidal part of this field plays a dominant part. This gives rise to the importance of studying the effect of a toroidal magnetic field on flows past different bodies of revolution; specially past spheres and spheroids. In the present note inviscid flows past a sphere, and a spheroid, are considered, for the case of a toroidal magnetic field originating in the fluid. In the case of the sphere the field inside the sphere consists of an electric dipole directed along the axis of symmetry together with a uniform electric field which produces a uniform current along the axis. In the case of the spheroid, the field inside it is due to an electric dipole and quadrupole directed along the axis of symmetry, together with a uniform electric field which produces a uniform current along this axis.     

Unsteady hydromagnetic flow in a porous annulus with time-dependent pressure gradient

Summary Problem of unsteady motion of a conducting viscous incompressible fluid through an annulus with porous walls under an external radial magnetic field has been discussed. Taking the Reynolds number and the magnetic Reynolds number to be equal, exact solution of the problem is obtained in terms of Bessel functions when the motion is due to the time-dependent pressure gradient or the time-dependent velocity of either of the boundaries. Two types of dependence on time are considered; one, exponentially increasing, and the other, exponentially decreasing. Solutions in certain extreme cases are also discussed.     

Slow motion of a viscous conducting fluid past ellipsoids in the presence of a toroidal magnetic field

Summary An attempt has been made here, to obtain solutions for the velocity and magnetic field, for a flow past an ellipsoid, in the presence of a toroidal magnetic field, when magnetic Reynold number and Hartman number are small.     

Magnetic field behavior in the magnetosheath when the IMF slightly differs from the solar wind velocity vector

The magnetic field behavior in the magnetosheath, when the IMF and the solar wind velocity are almost collinear, has been analyzed based on the perturbation method. Magnetic disturbances are considered against a background of the stationary MHD solar wind flow around the magnetosphere when the magnetic field and the solar wind velocity are strictly collinear. It has been indicated that the angle between the magnetic field and velocity vectors increases considerably in a relatively thin layer near the magnetopause. The angle rise factor profiles have been determined for different distances from the subsolar point. The thickness of the layer, where the angle reaches values of about unity and more, has been estimated. It is important to take this layer into account when the magnetopause stability with respect to Kelvin-Helmholtz waves is analyzed.     

Plane discontinuities in collisionless plasmas: An analysis as applied to the magnetopause

Types of plane discontinuities possible in collisionless kinetics—thin current sheets with a nonzero normal component of the magnetic field—are considered. In a general case the electromagnetic field energy is transformed at such a discontinuity to the energy of ion flows. In addition to the known MHD discontinuities, the discontinuities that exist in the presence of pairs of interpenetrating flows on both sides of a discontinuity are studied. The application of the theory to an analysis of observations on the magnetopause has been considered.     

On disturbances in a semi-infinite medium traversed by a transverse magnetic field

Summary The method of operational calculus has been used to deal with the disturbances in an elastic medium traversed by a magnetic field.