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At least 253 records · Page 14

Design considerations for an air core magnetic actuator

Equations for the force produced by an air core electromagnet on a permanent magnet core as a function of the coil height, coil inner and outer radii, and core displacement are developed. The magnetization vector of the permanent magnet core is assumed to be aligned with the central axis of the electromagnet and the forces which are produced lie along the same axis. Variations in force due to changes in electromagnet parameters and core displacement are investigated and parameter plots which should be useful for coil design are presented.

Groom, Nelson J.↗

Novel Integration Radial and Axial Magnetic Bearing

Typically, fully active magnetically suspended systems require one axial and two radial magnetic bearings. Combining radial and axial functions into a single device allows for more compact and elegant packaging. Furthermore, in the case of high-speed devices such as energy storage flywheels, it is beneficial to minimize shaft length to keep rotor mode frequencies as high as possible. Attempts have been made to combine radial and axial functionality, but with certain drawbacks. One approach requires magnetic control flux to flow through a bias magnet reducing control effectiveness, thus resulting in increased resistive losses. This approach also requires axial force producing magnetic flux to flow in a direction into the rotor laminate that is undesirable for minimizing eddy-current losses resulting in rotational losses. Another approach applies a conical rotor shape to what otherwise would be a radial heteropolar magnetic bearing configuration. However, positional non-linear effects are introduced with this scheme and the same windings are used for bias, radial, and axial control adding complexity to the controller and electronics. For this approach, the amount of axial capability must be limited. It would be desirable for an integrated radial and axial magnetic bearing to have the following characteristics; separate inputs for radial and axial control for electronics and control simplicity, all magnetic control fluxes should only flow through their respective air gaps and should not flow through any bias magnets for minimal resistive losses, be of a homopolar design to minimize rotational losses, position related non-linear effects should be minimized, and dependent upon the design parameters, be able to achieve any radial/axial force or power ratio as desired. The integrated radial and axial magnetic bearing described in this paper exhibits all these characteristics. Magnetic circuit design, design equations, and magnetic field modeling results will be presented.

Blumenstock, Kenneth↗

Expanded Equations for Torque and Force on a Cylindrical Permanent Magnet Core in a Large-Gap Magnetic Suspension System

The expanded equations for torque and force on a cylindrical permanent magnet core in a large-gap magnetic suspension system are presented. The core is assumed to be uniformly magnetized, and equations are developed for two orientations of the magnetization vector. One orientation is parallel to the axis of symmetry, and the other is perpendicular to this axis. Fields and gradients produced by suspension system electromagnets are assumed to be calculated at a point in inertial space which coincides with the origin of the core axis system in its initial alignment. Fields at a given point in the core are defined by expanding the fields produced at the origin as a Taylor series. The assumption is made that the fields can be adequately defined by expansion up to second-order terms. Examination of the expanded equations for the case where the magnetization vector is perpendicular to the axis of symmetry reveals that some of the second-order gradient terms provide a method of generating torque about the axis of magnetization and therefore provide the ability to produce six-degree-of-freedom control.

Groom, Nelson J.↗

Structure preserving transport stabilized compatible finite element methods for magnetohydrodynamics

Here, we present compatible finite element space discretizations for the ideal compressible magnetohydrodynamic equations. The magnetic field is considered both in div- and curl-conforming spaces, leading to a strongly or weakly preserved zero-divergence condition, respectively. The equations are discretized in space such that transfers between the kinetic, internal, and magnetic energies are consistent, leading to a preserved total energy. We also discuss further adjustments to the discretization required to additionally achieve magnetic helicity preservation. Finally, we describe new transport stabilization methods for the magnetic field equation which maintain the zero-divergence and energy conservation properties, including one method which also preserves magnetic helicity. The methods' preservation and improved stability properties are confirmed numerically using a steady state and a magnetic dynamo test case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamic analysis of a magnetic bearing system with flux control

Using measured values of two-dimensional forces in a magnetic actuator, equations of motion for an active magnetic bearing are presented. The presence of geometric coupling between coordinate directions causes the equations of motion to be nonlinear. Two methods are used to examine the unbalance response of the system: simulation by direct integration in time; and determination of approximate steady state solutions by harmonic balance. For relatively large values of the derivative control coefficient, the system behaves in an essentially linear manner, but for lower values of this parameter, or for higher values of the coupling coefficient, the response shows a split of amplitudes in the two principal directions. This bifurcation is sensitive to initial conditions. The harmonic balance solution shows that the separation of amplitudes actually corresponds to a change in stability of multiple coexisting solutions.

Knight, Josiah↗

Transient scattering from dielectric cylinders - E-field, H-field, and combined field solutions

In this work, the problem of transient scattering by arbitrarily shaped two-dimensional dielectric cylinders is solved using the marching-on-in-time technique. The dielectric problem is approached via the equivalence principle. Three different formulations, namely, the electric field integral equation formulation, the magnetic field integral equation formulation, and the combined field integral equation formulation are considered. Numerical results are presented for two cross sections, namely, a circle and a square, and compared with inverse discrete Fourier transform (IDFT) techniques. In each case, good agreement is obtained with the IDFT solution.

Vechinski, Douglas A.↗

Transport equations for dilute plasma in a magnetic field.

Using the Chapman-Enskog procedure, equations are derived for near-equilibrium transport of plasma in a strong magnetic field. It is shown that these equations reduce properly to collision dominated equations and to collisionless Chew-Goldberger-Low (1956) equations in the respective limits. The results presented are more complete than those of Stringer and Connor (1971) and correct their erroneous partition of conducted thermal energy.

Price, J. C.↗

An Integrated Magnetic Circuit Model and Finite Element Model Approach to Magnetic Bearing Design

A code for designing magnetic bearings is described. The code generates curves from magnetic circuit equations relating important bearing performance parameters. Bearing parameters selected from the curves by a designer to meet the requirements of a particular application are input directly by the code into a three-dimensional finite element analysis preprocessor. This means that a three-dimensional computer model of the bearing being developed is immediately available for viewing. The finite element model solution can be used to show areas of magnetic saturation and make more accurate predictions of the bearing load capacity, current stiffness, position stiffness, and inductance than the magnetic circuit equations did at the start of the design process. In summary, the code combines one-dimensional and three-dimensional modeling methods for designing magnetic bearings.

Provenza, Andrew J.↗

A magnetic analog of pressure–strain interaction

We study the evolution equation for magnetic energy density for a non-relativistic magnetized plasma in the (Lagrangian) reference frame comoving with the electron bulk velocity. Analyzing the terms that arise due to the ideal electric field, namely, perpendicular electron compression and magnetic field line bending, we recast them to reveal a quantity with a functional form analogous to the often-studied pressure–strain interaction term that describes one piece of internal energy density evolution of the species in a plasma, except with the species pressure tensor replaced by the magnetic stress tensor. We dub it the “magnetic stress–strain interaction.” We discuss decompositions of the magnetic stress–strain interaction analogous to those used for pressure–strain interaction. These analogies facilitate the interpretation of the evolution of the various forms of energy in magnetized plasmas and should be useful for a wide array of applications, including magnetic reconnection, turbulence, collisionless shocks, and wave–particle interactions. We display and analyze all the terms that can change magnetic energy density in the Lagrangian reference frame of the electrons using a particle-in-cell simulation of magnetic reconnection.

Barbhuiya, M. Hasan (ORCID:0000000163301650)↗

Stellarator equilibrium axis-expansion to all orders in distance from the axis for arbitrary plasma beta

A systematic theory of the asymptotic expansion of the magnetohydrostatics (MHS) equilibrium in the distance from the magnetic axis is developed to include arbitrary smooth currents near the magnetic axis. Compared with the vacuum and the force-free system, an additional magnetic differential equation must be solved to obtain the pressure-driven currents. It is shown that there exist variables in which the rest of the MHS system closely mimics the vacuum system. Thus, a unified treatment of MHS fields is possible. The mathematical structure of the near-axis expansions to arbitrary order is examined carefully to show that the double-periodicity of physical quantities in a toroidal domain can be satisfied order by order. The essential role played by the leading-order Birkhoff–Gustavson normal form in solving the magnetic differential equations is highlighted. Several explicit examples of vacuum, force-free and MHS equilibrium in different geometries are presented.

Physics↗

Effects of Coulomb collisions on cyclotron maser and plasma wave growth in magnetic loops

The evolution of nonthermal electrons accelerated in magnetic loops is determined by solving the kinetic equation, including magnetic field convergence and Coulomb collisions in order to determine the effects of these interactions on the induced cyclotron maser and plasma wave growth. It is found that the growth rates are larger and the possibility of cyclotron maser action is stronger for smaller loop column density, for larger magnetic field convergence, for a more isotropic injected electron pitch angle distribution, and for more impulsive acceleration. For modest values of the column density in the coronal portion of a flaring loop, the growth rates of instabilities are significantly reduced, and the reduction is much larger for the cyclotron modes than for the plasma wave modes. The rapid decrease in the growth rates with increasing loop column density suggests that, in flare loops when such phenomena occur, the densities are lower than commonly accepted.

Hamilton, Russell J.↗

High-voltage electron collection by a spherical satellite

The numerical solution to the cold electron flow equations is presented for the region surrounding an ionospheric satellite at high positive potential. The momentum, continuity, and Poisson equations are solved simultaneously for satellite potentials of 1000, 10,000, 30,000, and 100,000 kT(kT = 0.17 eV). The electron velocity vectors in the sheath region are presented. The electron current density to the satellite surface is also reported. Electrons impact the satellite surface with average velocity vectors having angles of incidence (relative to the surface normal) that increase from the satellite's magnetic pole to equator. A toroidal flow develops in the vicinity of the magnetic equator and expands away from the satellite surface as the surface potential is increased. The current density to the satellite surface increases with increasing satellite potential and decreases with increasing polar angle.

Sheldon, J. W.↗

Surface structure of neutron stars with high magnetic fields

The equation of state of cold dense matter in strong magnetic fields is calculated in the Thomas-Fermi and Thomas-Fermi-Dirac approximations. For use in the latter calculation, a new expression is derived for the exchange energy of the uniform electron gas in a strong magnetic field. Detailed calculations of the density profile in the surface region of a neutron star are described for a variety of equations of state, and these show that the surface density profile is strongly affected by the magnetic field, irrespective of whether or not matter in a magnetic field has a condensed state bound with respect to isolated atoms. It is also shown that, as a consequence of the field dependence of the screening potential, magnetic fields can significantly increase nuclear reaction rates.

Fushiki, I.↗

Role of magnetic fields in physics and astrophysics; Proceedings of the Conference, Copenhagen, Denmark, June 5-7, 1974

The papers deal with the role of magnetism in astrophysics and the properties of matter in the presence of unusually large magnetic fields. Topics include a quantum-mechanical treatment of high-energy charged particles radiating in a homogeneous magnetic field, the solution and properties of the Dirac equation for magnetic fields of any strength up to 10 to the 13th power gauss, experimental difficulties encountered and overcome in generating megagauss fields, the effect of strong radiation damping for an ultrarelativistic charge in an external electromagnetic field, magnetic susceptibilities of nuclei and elementary particles, and Compton scattering in strong external electromagnetic fields. Other papers examine static uniform electric and magnetic polarizabilities of the vacuum in arbitrarily strong magnetic fields, quantum-mechanical processes in neutron stars, basic ideas of mean-field magnetohydrodynamics, helical MHD turbulence, relations between cosmic and laboratory plasma physics, and insights into the nature of magnetism provided by relativity and cosmology. Individual items are announced in this issue.

Canuto, V.↗