Axially-symmetric Magnetic Field Research Articles

Inter-correlation between Sunspot Oscillations and Their Internal Structures

Three- and five-minute oscillations are commonly observed in any sunspot. Because they are modulated by the internal thermal and magnetic structures of a sunspot, they could be used as an effective tool for researching sunspot seismology. In this paper, we investigate the properties of oscillations in sunspot groups with varying sizes and magnetic fields, and aim to establish the relationships between sunspot oscillations and its internal structure comparatively. We selected three groups of the unipolar sunspot with approximately axial-symmetric magnetic field and calculated their Fourier spectra based on the ultraviolet/extreme ultraviolet emission intensity variations recorded by the Solar Dynamics Observatory/Atmospheric Imaging Assembly. We found that the distribution of three-minute oscillation is defined by the joint effect of diverging magnetic field and the stratification of the sunspot atmosphere. Its distribution could be modified by any invading magnetic structures in the umbra. In contrast, the five-minute oscillations are more prominent in small spots, implying that five-minute oscillation is very closely connected with umbral dynamics.

On finite energy monopole solutions in Weinberg–Salam model

We study the problem of existence of finite energy monopole solutions in the Weinberg–Salam model starting with the most general ansatz for static axially-symmetric electroweak magnetic fields. The ansatz includes an explicit construction of field configurations with various topologies described by the monopole and Hopf charges. We introduce a unique [Formula: see text] gauge invariant definition for the electromagnetic field. It has been proved that the magnetic charge of any finite energy monopole solution must be screened at far distance. This implies nonexistence of finite energy monopole solutions with a nonzero total magnetic charge. In the case of a special axially-symmetric Dashen–Hasslacher–Neveu ansatz, we revise the structure of the sphaleron solution and show that sphaleron represents a nontrivial system of monopole and antimonopole with their centers located in one point. This is different from the known interpretation of the sphaleron as a monopole–antimonopole pair like Nambu’s “dumb-bell.” In general, the axially-symmetric magnetic field may admit a helical structure. We conjecture that such a solution exists and estimate an upper bound for its energy, [Formula: see text].

К выводу соотношения Десслера-Паркера-Скопке

We propose a simple derivation of the known Dessler–Parker–Sckopke (DPS) relation which connects the magnetic field produced by the ring current with the kinetic energy of its particles. We start from the distribution function of particles which depends on the integrals of motion in an axially-symmetric magnetic field and calculate the corresponding moments (current and kinetic energy). Unlike the derivation of the DPS relation given in the pioneer works, the approach pro-posed here is more straightforward and is based on the first principles.

Dynamics of intense particle beam in axial-symmetric magnetic field

Axial-symmetric magnetic field is often used in focusing of particle beams. Most existing ion Low Energy Beam Transport lines are based on solenoid focusing. Modern accelerator projects utilize superconducting solenoids in combination with superconducting accelerating cavities for acceleration of high-intensity particle beams. Present article discusses conditions for matched beam in axial-symmetric magnetic field. Analysis allows us to minimize power consumption of solenoids and beam emittance growth due to nonlinear space charge, lens aberrations, and maximize acceptance of the channel. Expressions for maximum beam current in focusing structure, beam emittance growth due to spherical aberrations and non-linear space charge forces are derived.

Stability analysis for axially-symmetric magnetic field levitation of a superconducting sphere

For a magnetically levitated superconducting sphere, the stability analysis in both axial and radial directions is analyzed theoretically using a direct boundary-value problem approach. The external magnetic field is produced by a system of current-carrying coils with axial symmetry. We also assume complete exclusion of magnetic fields from the interior of the superconductor. Use of the P l 1 associated Legendre functions as a basis set allows for a simple series solution for the magnetic stiffness coefficients as tridiagonal quadratic forms in terms of the expansion coefficients. Analysis shows that stability for this problem is not guaranteed in general. Stability is guaranteed though, if coil windings are designed in such away that all but one of the expansion coefficients are zero. Further cases with two and three non-zero coefficients are also solved. In particular the important 1, 3 and 2, 4 cases are treated in detail, and stability maps have been produced. Finally, the case where levitation is attempted by one pair of discrete current coils has been solved and stability mapping has been thoroughly explored.

Direct-current vacuum contractor for railway transport

The results of studies of switching off a direct current using a vacuum interrupter with a transverse axial-symmetric magnetic field at a recovery voltage of up to 9 kV are presented. The prototype of the DC vacuum contactor based on this vacuum interrupter was developed and manufactured for applications in railways. The contactor is intended for switching off DC current at a rated voltage of 3 kV. The main technical parameters of the vacuum contactor are presented.

A Polarization Current Approach to the Calculation of Inductances and the Solution of Field Problems Involving Magnetic Materials

This paper introduces a polarization surface current approach to the computation of the equivalent circuit self and mutual inductances required to predict the surge response of transformer windings. The effect of the magnetic core is accounted for by means of polarization currents circulating on the core surface. The application of the proposed method can be easily extended to solve axially-symmetric magnetic field problems. The method's algorithm is suitable for digital computer programming. Accurate results are very efficiently obtained.

Torque and Force on a Modifed Superconducting Gyro Design in an Axially Symmetric Magnetic Field

The second-order expression for the torque (or acceleration torque) existing on two arrangements of a modified cryogenic gyro design is derived assuming that an axially-symmetric magnetic field is used for the suspension of the rotor. The modified design consists of interchanging the role of the current coils and the superconductor in the conventional design. In the modified design the coils are now situated on the rotor with the superconductor utilized as the stator (reverse of the conventional design). The two types of arrangements resulting are either the coils, or rotor, surrounding the stator, or the stator surrounding the rotor. For the first arrangement, that of the coils surrounding the rotor, the torque calculations are performed by two methods in order to check the manipulations. For the second arrangement, only one derivation is used. The first-order restoring-force expression for the first arrangement is also presented. The main result for the first arrangement is that when all the components of the first-order restoring force are equal, the second-order torque vanishes. It is also theoretically possible to achieve an ideal, or continuous, distribution of current for the support field such that the constraint of equality on the components of the first-order restoring force is satisfied.

On the Unsteady Motion of a Viscous Hydromagnetic Fluid, Contained Between Rotating Coaxial Cylinders of Finite Length

AbstractThe problem of unsteady rotational motion of electrically conducting viscous, incompressible fluid, contained within two axially concentric cylinders of finite length in the presence of an axial symmetric magnetic field of constant strength, has been solved exactly using finite Hankel transform in combination with a technique presented in this paper.This paper presents a complete solution of the problem under consideration, which has been of interest for many years; moreover the Pneuman‐Lykoudis solution in Magnetohydrodynamics and Ghildyal solution in hydrodynamics appears as a special case of this study. The analysis shows that the disturbance in the fluid disappears quickly by increasing the magnetic field.

Electron Trajectories in a Nonuniform Axially Symmetric Magnetic Field

Electrons injected along the flux lines of a spatially varying, axially symmetric magnetic field that is increasing in the direction of electron motion will follow approximately helical trajectories about the flux lines. If the field increases too rapidly, the electrons will not be able to penetrate the magnetic field beyond a certain point and will be turned back by the magnetic mirror formed by the increasing field. For more slowly varying fields, the electrons can penetrate the mirror with a large fraction of their energy in axial velocity. The equations of motion for electrons in a sinusoidally varying magnetic field have been solved on a computer, and the results are presented in graphical form. An application of this field configuration as a device for converging a hollow cylindrical electron beam has been tested, and measured area convergences of 15 to 1 have been obtained by photographing a movable carbon screen collector that is heated by the beam. The beam is started out with a conventional parallel flow gun immersed in the magnetic field. As the beam leaves the first accelerating electrode it enters the region of increasing magnetic field. It then shrinks in diameter and thickness, and hence in area, approximately in proportion to the increase in the magnetic field. The actual area convergence will be less than this increase by an amount depending on the length and rate of the magnetic field taper.

A low potential collector employing an asymmetrical electrode in an axially-symmetric magnetic field

A collector for a beam-type tube with an axial magnetic focusing field can be made to operate at a potential near cathode potential without returning secondary electrons, if the beam is deflected and caused to pass an asymmetrical electrode properly positioned in the axially symmetric magnetic focusing field. Collection takes place in a region of radial electric field. Experimental results on such a device indicate successful operation, provided the velocity spread in the beam is not too large.

An electromagnetic apparatus with a high resolving power for the separation of the isotopes of the heavy elements

The operating principles and the main features of an electromagnetic apparatus which has been designed and constructed for the separation of isotopes with a relative mass difference of about 1/240 are here described. An axially-symmetric magnetic field is used (focussing angle 225 °) in which the dispersion is proportional to the square of the focussing angle. The dispersion obtained with the separation apparatus is 20 mm for a 1% relative difference in mass. The magnetic field of the apparatus is stabilized to within 0.005% with the help of a circuit containing electron-beam regulators. Ion sources, with a discharge in the vapor of the working and auxiliary substances, were developed for the separation of large and small quantities of the raw material. General-purpose ion collectors were also developed. Some results of the separation of lead, uranium and plutonium isotopes are given. The enrichment factor in the separation of lead isotopes reaches 300, while for uranium and plutonium it is ∼ 1000.