Penetration of intense pulsed magnetic fields into a conductor

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 7–12, September–October, 1989.     

Diamagnetism of conductors moving in a magnetic field

Several theoretical [1–3] and experimental [4] studies have been made of the diamagnetic perturbations during expansion of a conducting material in a magnetic field. These studies have related either to superconducting media [1], or to a strong magnetic field which has a considerable effect on the motion of the medium [2], or to a weakly ionized media, in which the effects of field variation in the medium can be neglected [3]. In the following we examine the expansion of a substance with finite conductivity in a weak (having no effect on the motion of the medium) magnetic field with account for the effects of field attenuation within the expanding matter. This occurs in the diagnostics of the state of the matter of a spark at a laser focus on the basis of diamagnetic induction signals [4]. The relations obtained in the following appear to be applicable for estimating the diamagnetic properties of meteor trails.The method of solution of this problem may be of some interest; therefore, in the following the solution is obtained by several techniques for different basic geometries.     

Magnetic field in a cylindrical conductor moving with a velocity proportional to r−1

Nonstationary magnetic field problems in a moving conductor are of interest in connection with obtaining pulsed magnetic fields by magnetic cumulation [1], The field penetrates into the conductor as a result of the growth of the skin layer and is carried along with the conductor. The first mechanism of the interaction of a field with a conductor is called the diffusion of the field, and the second convection. Five self-similar solutions of magnetic field problems in a conductor which has a velocity v =q/2 r and a conductivity =const are discussed and a numerical solution of the problem of the compression of a field in a cylindrical cavity when the conductor moves toward the axis is presented. One of the self-similar solutions is compared with the numerical solution.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 18–25, September–October, 1973.     

Instability of the magnetic fluid shape in the field of a line conductor with current

The static shape of the surface of a finite magnetic fluid volume between horizontal plates is investigated theoretically. The nonuniform magnetic field is generated by a horizontal line conductor with current, which is placed above the upper plate. The variational problem of minimum energy relative to plane surface perturbations is considered for a simply connected magnetic fluid volume. The problem is solved for arbitrary magnetic fields in the noninductive approximation with account for the gravity force and surface tension. Unstable solutions are found. The possibility of stepwise behavior in response to quasi-static changes of the current in the conductor is investigated for the surface shape of a finite magnetic fluid volume.     

EM induction in a semi-infinite solid, impulsively moving in a uniform magnetic field

In this note the electromagnetic (EM) induction phenomena are considered, which appear, if a semi-infinite solid, bounded by a plane and immersed in a constant uniform magnetic field, perpendicular to its surface, is suddenly beginning to move in a direction parallel with the surface.It is shown that TEM waves are emitted from the surface as soon as the motion starts, while another type of wave penetrates into the solid. Several special cases are discussed.     

Equilibrium configurations of the surface of a perfectly conducting fluid in the magnetic field of a current-carrying linear conductor

This paper considers the problem of the possible equilibrium configurations of the free surface of a perfectly conducting fluid deformed by a nonuniform magnetic field. A family of exact solutions of the problem is obtained using conformal mappings; equilibrium is achieved due to the balance of capillary and magnetic pressures. According to these solution, the surface strain amplitude increases with increasing current and the hole is transformed into a two-dimensional bubble covering the linear conductor.     

An exact solution of boundary layer flow over a moving surface embedded into a nanofluid in the presence of magnetic field and suction/injection

The effects of magnetic field, suction/injection, nanoparticles type, and nanoparticle volume fraction on heat transfer characteristics and mechanical properties of a moving surface embedded into cooling medium consists of water with Cu, Ag or Al₂O₃ particles are studied. The governing boundary layer equations are transformed to ordinary differential equations containing, suction/injection parameter, magnetic parameter, nanoparticle and volume fraction. These equations are solved analytically. The velocity and temperature profiles within the boundary layer are plotted and discussed in details for various values of the different parameters.     

Some exact solutions of stationary gas flows in a perpendicular magnetic field

The plane flow of a perfectly conducting gas subject to a perpendicular magnetic field is considered. Ladikov [1] has solved this problem as a special case of the more general solution for a specific condition. It is shown that, following the method of [2], this problem may be reduced to the determination of the unknown function which satisfies a partial differential equation. Since the equation for is very complex, we have considered only two interesting cases, namely: 1) when the motion is irrotational, and 2) when the pressure is constant along the streamlines.     

Spectroscopic diagnostics of a plasma expanding into a background gas and a magnetic field

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 3, pp. 13–19, May–June, 1992.