Levitation of a rapidly oscillating magnetic dipole above a metallic sheet

We show that such a magnetic dipole suspended at a height h above a conducting sheet experiences a lift force proportional to $1/h^2$. This represents an order of magnitude improvement over the $1/h^4$ lift obtained in the quasistatic limit.     

导磁导电球体在均匀谐变磁场中产生的磁场分布规律

从求解导磁导电各向同性球体的赫兹矢量π*出发,推导出了导磁导电球体置于均匀谐变低频弱磁场中球体产生的磁场分布规律和球频率函数.     

Vertical component of the extremely low-frequency electric field excited by the grounded horizontal dipole

A representation of the vertical component of the electric field emitted by the grounded linear dipole is obtained in the form of an integral of an oscillating function and a method of its numerical integration is described. For the particular case in which the medium under the antenna is homogeneous and the field is calculated on the interface, the function obtained is transformed with the help of the Fock integrals to the form convenient for deriving simple approximate formulas and for analyzing the field behavior. Calculations performed by the expressions obtained corroborate the theoretical results.     

Screening of a low-frequency magnetic field by an open thin-wall spherical shell

The solution to the problem of penetration of a low-frequency magnetic field through a semitransparent open spherical shell is reduced to solving the system of second-order Fredholm integral equations. The effect of the opening angle of the open shell and of some geometrical parameters of the screen as well as electrophysical properties of the spherical shell material on the attenuation of the field in the spherical shell is analyzed numerically.     

Compensation of gradient-induced magnetic field perturbations

Pulsed magnetic field gradients are essential for MR imaging and localized spectroscopy applications. However, besides the desired linear field gradients, pulsed currents in a strong external magnetic field also generate unwanted effects like eddy currents, gradient coil vibrations and acoustic noise. While the temporal magnetic field perturbations associated with eddy currents lead to spectral line shape distortions and signal loss, the vibration-related modulations lead to anti-symmetrical sidebands of any large signal (i.e. water), thereby obliterating the signals from low-concentration metabolites. Here the measurement, characterization and compensation of vibration-related magnetic field perturbations is presented. Following a quantitative evaluation of the various temporal components of the main magnetic field, a digital B0 magnetic field waveform is generated which reduces all temporal variations of the main magnetic field to within the spectral noise level.     

Levitation and lateral forces between a point magnetic dipole and a superconducting sphere

The dipole–dipole interaction model is employed to investigate the angular dependence of the levitation and lateral forces acting on a small magnet in an anti-symmetric magnet/superconducting sphere system. Breaking the symmetry of the system enables us to study the lateral force which is important in the stability of the magnet above a superconducting sphere in the Meissner state. Under the assumption that the lateral displacement of the magnet is small compared to the physical dimensions of our proposed system, analytical expressions are obtained for the levitation and lateral forces as a function of the geometrical parameters of the superconductor as well as the height, the lateral displacement, and the orientation of the magnetic moment of the magnet. The dependence of the levitation force on the height of the levitating magnet is similar to that in the symmetric magnet/superconducting sphere system within the range of proposed lateral displacements. It is found that the levitation force is linearly dependent on the lateral displacement whereas the lateral force is independent of this displacement. A sinusoidal variation of both forces as a function of the polar and azimuthal angles specifying the orientation of the magnetic moment is observed. The relationship between the stability and the orientation of the magnetic moment is discussed for different orientations.     

On a hollow superconducting sphere in a magnetic field

A system consisting of a single-domain ferromagnetic ball surrounded by a spherical superconducting shell and current-carrying wires wound on the shell is considered. The magnetic moment of the superconductor is calculated in terms of the London theory, in particular, for the case when the sum of the magnetic moments of the ball and system of currents is equal to a null vector.     

Force and torque on a sphere with electric dipole moment moving in a dielectric fluid in the presence of a uniform magnetic field

The torque exerted by a magnetic field on a sphere with permanent electric dipole moment moving steadily in a dielectric fluid is calculated to lowest order in the dipole moment. Hence the force exerted on a steadily rotating sphere with electric dipole moment is found by Onsager symmetry. The modification from the vacuum values of torque and force depends only on the slip parameter and the static dielectric constant of the fluid. It is suggested that for a macroscopic ferro electric sphere the calculated effects could be measured experimentally without great difficulty.     

On the relation between plasma rotation induced by low-frequency resonant magnetic perturbations and transport in ergodic magnetic fields

The penetration of low-frequency resonant magnetic perturbations into a tokamak plasma and their influence on the plasma rotation are analyzed in linear and quaslisinear kinetic approaches. There are two explanations of experimentally observed acceleration of plasma rotation in the direction of the plasma current. First, it is a result of the resonant absorption of the momentum of the perturbation field by the plasma. Second, it is a result of a change in the radial electric field due to the ergodization of the magnetic field and the corresponding increase in the radial electron transport. It is shown that there is no contradiction between these two explanations. These are just two different interpretations of the same phenomenon. Published in Russian in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 6, pp. 420–423. The article was translated by the authors.     

On the gravitational field of a mass possessing a magnetic dipole moment

A solution of the Einstein-Maxwell magnetostatic equations describing the gravitational field of a mass endowed with a magnetic dipole moment is presented. It reduces to the Schwarzschild solution if the magnetic field vanishes.     

垂直电偶极子在球外侧电磁场的闭合解及验证

给出了理想导体球外侧垂直电偶极子激励电场的闭合解，解决了直接场的级数表达式的不连续性问题.同球外电磁场直接级数求和表达式的计算结果进行了比较.在相同的电磁模型下，利用闭合解对一种近似方法进行了验证：当垂直电偶极子以及场点在球体表面附近并且频率较低时，这两种方法的计算结果非常一致；当垂直电偶极子以及场点不在球体表面附近并且频率较高时，闭合解的计算结果逐渐出现了近似方法未出现的干涉现象.     

Electrodynamics of rotating planetary plasmaspheres in a dipole magnetic field

As a model of the actual structure of the planetary plasmasphere, we consider the electrodynamical problem of electric field and current generation by a planet with a dipole magnetic field corotating with the plasma envelope. The plasma envelope is characterized by the conductivity and angular velocity of the magnetospheric plasma as functions of the distance τ from the planet center and the angle ? measured from the rotation axis. The exact solutions of the Maxwell equations are obtained in the axially symmetric case within the framework of unipole electrodynamics when the rotational and magnetic axes coincide. These solutions describe the possible distributions of electric fields, currents, and charges in the rotating plasma envelope surrounding the magnetized planet. As an exmple, we constructed, using the theory proposed, the exact solution corresponding to the following structure of the plasmasphere:

1. the plasmasphere region corotating with the planet and located between L-shells (L=τ/Rsin ² ?, where R is the radius of the planet) from L=1 to L=L_*;
2. the polar region with differential, spherically symmetric rotation;
3. the transient region of the plasmasphere rotating differentially with the angular velocity dependent on the L-number and located between L-shells from L=L_* to L=L_*+L₀;
4. the external (vacuum) region.

Analysis of the multipole expansion of the electrostatic potential showed that the electric field potential is equal to zero in the external region (L>L_*+L₀), independently of the number of the boundary L-shell. This solution can serve as a basis for simulation of the plasmasphere formation processes, taking into account the actual conditions in the near-planetary plasma envelopes.     

Dynamics of charged particles in the field of a spherical magnetic dipole

The results of numerical simulation of the dynamics of charged particles in the field of a spherical magnetic dipole are reported. Interesting features revealed in this dynamics can be used in analysis of near-Earth space with the help of charged particle beams.     

Electromagnetic field of a rotating magnetic dipole and electric-charge motion in this field

In this paper, we present the results of a study of the electromagnetic field in the near and intermediate zones of a magnetic dipole rotating in free space. Examples of solving the relativistic equations of the charged-particle motion in this field are given. The energy, which can be acquired by the particles during acceleration, is estimated.