Magnetostatic Structures Research Articles

Solid Isotropic Material with Penalization-Based Topology Optimization of Three-Dimensional Magnetic Circuits with Mechanical Constraints

Topology optimization is currently enjoying renewed interest thanks to the recent development of 3D printing techniques, which offer the possibility of producing these new complex designs. One of the difficulties encountered in manufacturing topologically optimized magnetostatic structures is that they are not necessarily mechanically stable. In order to take this mechanical constraint into account, we have developed a SIMP-based topology optimization algorithm which relies on numerical simulations of both the mechanical deformation and the magnetostatic behavior of the structure. Two variants are described in this paper, respectively taking into account the compliance or the von Mises constraint. By comparing the designs obtained with those from magnetostatic optimization alone, our approach proves effective in obtaining efficient and robust designs.

Self-Organizing Equilibrium Patterns of Multiple Permanent Magnets Floating Freely under the Action of a Central Attractive Magnetic Force

The present communication revisits the almost century-and-a-half-old problem of some identical small magnets floating freely on the water’s surface under the action of a superimposing magnetic field created by a stronger magnet placed above them. Originally introduced and performed by Alfred Marshall Mayer and reported in a series of articles starting from 1878 onward, the proposed experiments were intended to provide a model (theoretical and educational) for the building block of matter that, at a microscopic level, is the atom. The self-organizing patterns formed by the repelling small magnets under the influence of a single attractive central force are presented in a slightly different reenactment of the original experiments. Although the set-up is characterized by an axially symmetric magnetostatic structure, and the floated magnets are all identical, the resulting equilibrium patterns are not necessarily symmetrical, as one would expect. To the authors’ best knowledge, the present communication proposes for the first time a quantitative approach to that extremely complex conceptual problem by providing a methodology for computing the equilibrium point coordinates in the case of n = 1…20 floating magnets, as proposed by the original A.M. Mayer experiments. A good agreement between the experiments and computed data was demonstrated for n = 2…15 (1st variant), but it was less accurate while still preserving the experimental set-up configurations for n = 15 (2nd variant)…20. Finally, this study draws the conclusions from the performed experiments and their corresponding computer simulations, identifies some open issues, and outlines possible solutions to address them, as well as future developments concerning the subject in general.

Versatile, high brightness, cryogenic photoinjector electron source

Since the introduction of the radio-frequency (rf) photoinjector electron source over thirty years ago, peak performance demands have dictated the use of high accelerating electric fields. With recent strong advances in obtainable field values, attendant increases in beam brightness are expected to be dramatic. In this article, we examine the implementation of very high gradient acceleration in a high frequency, cryogenic rf photoinjector. We discuss in detail the effects of introducing, through an optimized rf cavity shape, rich spatial harmonic content in the accelerating modes in this device. Higher spatial harmonics give useful, enhanced linear focusing effects, as well as potentially deleterious nonlinear transverse forces. They also serve to strongly increase the ratio of average accelerating field to peak surface field, thus aiding in managing power and dark current-related challenges. We investigate two scenarios which are aimed at unique exploitation of the capabilities of this source. First, we investigate the obtaining of extremely high six-dimensional brightness for advanced free-electron laser applications. We also examine the use of a magnetized photocathode in the device for producing unprecedented low asymmetric emittance, high-current electron beams that reach linear collider-compatible performance. As both of the scenarios demand an advanced, compact solenoid design, we describe a novel cryogenic solenoid system. With the high field rf and magnetostatic structures introduced, we analyze the collective beam dynamics in these systems through theory and multi-particle simulations, including a particular emphasis on granularity effects associated with microscopic Coulomb interactions.

Large-Scale Magnetostatic Structures in the Solar Corona and a Model of the Polar Coronal Hole

A method for the theoretical calculation of large-scale magnetoplasma solar coronal structures with a rotational symmetry in the spherical coordinate system is presented. The method makes it possible to obtain analytical solutions for equilibrium spatial distributions of pressures, densities, and temperatures in any preset axisymmetrical magnetic configuration. The obtained solution is used to plot model polar coronal holes via the introduction of a small power correction in the force free distribution of the magnetic field for subpolar region. The thermodynamic parameters of the coronal hole represented in this model are close to the observed values.

Analytical theory of neutral current sheets with a sheared magnetic field in collisionless relativistic plasma

We derive and describe analytically a new wide class of self-consistent magnetostatic structures with sheared field lines and arbitrary energy distributions of particles. To do so we analyze superpositions of two planar current sheets with orthogonal magnetic fields and cylindrically symmetric momentum distribution functions, such that the magnetic field of one of them is directed along the symmetry axis of the distribution function of the other. These superpositions satisfy the pressure balance equation and allow one to construct configurations with an almost arbitrarily sheared magnetic field. We show that most of previously known current sheet families with sheared magnetic field lines are included in this novel class.

Magnetostatic structures in collisionless plasma and their synchrotron radiation

The properties of the magnetostatic structures in a collisionless relativistic plasma found by exactly solving the nonlinear self-consistent kinetic and Maxwell equations using the method of invariants of particle motion are analyzed. These structures include individual neutral current sheets and cylindrically symmetric filaments as well as their ensembles, admitting a wide variety of types of particle energy distribution functions. Relationships are established between the possible parameters of the current sheets and filaments—their sizes, currents and magnetic fields, and the degree of anisotropy of the particle momentum distribution. The extent to which these parameters are conditioned by the properties of the Weibel instability that can produce these structure is also discussed. The spectral peculiarities of the synchrotron radiation from the particles that form the current sheets and filaments are investigated in the special case of power-law energy distribution functions.

Force Computation by Hybrid Cell Method

Force computation in magnetostatic structures is approached by surface integration of Maxwell stress tensor. Two formulations based on the cell method are presented: the first one with volume discretization and the second one with a hybrid integral scheme. A case with permanent magnets where experimental values of force are available is used as benchmark for comparison of both accuracy and computational cost of the two approaches.

Magnetostatic structures of the solar corona. 2: The magnetic topology of quiescent prominences

view Abstract Citations (248) References (52) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Magnetostatic Structures of the Solar Corona. II. The Magnetic Topology of Quiescent Prominences Low, B. C. ; Hundhausen, J. R. Abstract This paper treats the magnetic properties of the quiescent prominence as a part of the larger coronal structure made up of the prominence, cavity, and helmet dome. A rigorous analysis of the mechanical support of a vertical prominence sheet suspended in equilibrium by magnetic fields in uniform gravity shows that the finite vertical extension of the prominence sheet has an important dynamic constraint. For the inverse topology with the prominence magnetic field pointing opposite to the field implied by the bipolar photospheric region below, this constraint requries the prominence sheet to be embedded in a horizontal, nearly force-free, magnetic flux rope which crucially supports a part of the prominence weight by current attraction from above. A similar analysis of the support problem is carried out for the prominence in the normal topology in which both prominence and photospheric magnetic fields point in the same sense. Starting with the observation that most prominences are of the inverse topology, a recent model is extended to show that this topology implies that the prominence sits in a two-flux magnetic system, one flux connecting the bipolar magnetic sources in the photosphere below and the other forming a rope which embeds the prominence and runs above and parallel to the photospheric polarity-inversion line. This model physically relates several pieces of well-known but hitherto disjoint observations. The prominence flux rope manifests itself as the cavity in the corona and as the filament channel in the chromosphere. The chromospheric fibril patterns associated with prominences and filament channels can, for the first time, be modeled faithfully. Several physical implications on the origin of the prominence and questions deriving from the results are discussed. Publication: The Astrophysical Journal Pub Date: April 1995 DOI: 10.1086/175572 Bibcode: 1995ApJ...443..818L Keywords: Magnetic Field Configurations; Magnetostatic Fields; Photosphere; Solar Corona; Solar Magnetic Field; Solar Prominences; Stellar Models; Topology; Cavities; Chromosphere; Current Sheets; Magnetic Dipoles; Magnetic Flux; Magnetohydrodynamics; Solar Gravitation; Solar Physics; MAGNETOHYDRODYNAMICS: MHD; SUN: CORONA; SUN: PROMINENCES full text sources ADS | Related Materials (2) Part 1: 1994ApJ...429..876H Part 3: 2004ApJ...609.1098L

Magnetostatic structures of the solar corona. 1: A model based on the Cauchy boundary value problem

Magnetostatic structures of the solar corona. 1: A model based on the Cauchy boundary value problem

Numerical modeling of solar magnetostatic structures bounded by current sheets

A numerical method for efficiently determining the magnetostatic equilibrium configuration of erupted solar flux concentrations, such as sunspots and flux tubes, is presented. The magnetic structures are taken to be approximately vertically oriented and axisymmetric in the surface layers and are assumed to be isolated from the surrounding photosphere by a vanishingly thin current sheet. Since the location of the current sheet is initially unknown, the final structure is generated iteratively as a free-surface problem, with the magnetic configuration for each iterate being obtained from the horizontal force balance equation, subject to the appropriate boundary conditions. Multigrid methods are used at each stage to solve the equilibrium equation, which is mapped algebraically into a body-fitted coordinate system via transfinite interpolation techniques. Several model flux tubes and sunspots are computed to illustrate the procedure, and the accuracy of the numerical method is assessed against exact analytic solutions. 32 refs.

Application of the sine-Poisson equation in solar magnetostatics

Solutions of the sine-Poisson equation are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model j is directed along the x-axis, where x is the horizontal ignorable coordinate. The current j varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. We investigate in detail solutions for the magnetostatic potential A corresponding to the one-soliton, two soliton, and breather solutions of the sine-Gordon equation. Depending on the values of the free parameters in the soliton solutions, horizontally, periodic magnetostatic structures are obtained possessing either (a) a single X-type neutral point, (b) multiple neutral X-points, or (c) solutions without X-points. The solution cases (b) and (c) contain two families of intersecting current sheets, in which the line of intersection forms flux concentration points (or singularities) for the magnetic field. The solutions illustrate the contribution of the anisotropic J × B force (B, magnetic field induction), the gravitational force, and the gas pressure gradient to the force balance.

Variable-period magnetostatic undulator designs based on iron-free current configurations

The design of a magnetostatic undulator based on iron-free current configuration is described. Equations describing its performance are derived. Based on this exercise, it is shown that other types of variable-period magnetostatic structures with significantly stronger fields could be implemented. A specific design for a variable-period dipole configuration with the potential for generating moderate fields on medium-energy (2-4 GeV) storage rings is proposed. >

Some general properties of helmeted coronal structures

A simplified analysis of helmeted coronal structures is carried out and some of the gross properties of such structures discussed. It is found that the magnetically closed region can have but a limited extension into the corona. For temperatures in excess of 1.5 × 106 °K, the maximum height above the limb is about 1.6 R ⊙. The maximum possible extension of the helmet from the solar center is exactly one-half the distance to the critical point (where the flow velocity passes through the speed of sound). For this reason, a helmet streamer, at least out to a few solar radii, is essentially a magnetostatic structure - the flow adjacent to the helmet having little effect upon its properties. For given base dimensions, there is a maximum temperature for which a helmet streamer can exist - giving an indication of why such streamers do not appear over young active regions. If the temperature in the helmet and in the streaming region are approximately the same, the helmet height, helmet shape, external flow velocity, and rate of outward decline in the magnetic field are shown to be much more dependent upon the photospheric field distribution than upon the field strength. The density enhancement, however, is a strong function of the field strength. This enhancement is preserved out to the top of the helmet with both the density inside and outside decreasing approximately as predicted by hydrostatic equilibrium. The possible existence of both domed helmets and cusped helmets is demonstrated with the former existing at lower temperatures and the latter at higher temperatures. Cusped helmets occur, however, over a relatively narrow temperature range and are, hence, expected to be less common. The expansion velocity outside the helmet is higher than that predicted by radial flow but increases outward much more slowly. The magnetic field decreases outward proportionally to the square root of the density and inversely proportionally to the velocity - bearing, in general, no relation to a potential field since the rate of decline in field strength is determined by the temperature.