Axisymmetric Solutions in the Geomagnetic Direction Problem

The magnetic field outside the earth is in good approximation a harmonic vector field determined by its values at the earth’s surface. The direction problem seeks to determine harmonic vector fields vanishing at infinity and with the prescribed direction of the field vector at the surface. In general this type of data neither guarantees the existence nor the uniqueness of solutions of the corresponding nonlinear boundary value problem. To determine conditions for existence, to specify the non-uniqueness and to identify cases of uniqueness is of particular interest when modeling the earth’s (or any other celestial body’s) magnetic field from these data. Here we consider the case of axisymmetric harmonic fields $$\mathbf{B}$$ B outside the sphere $$S^2 \subset {{\mathbb {R}}}^3$$ S 2 ⊂ R 3 . We introduce a rotation number $${r\!o}\in {{\mathbb {Z}}}$$ r o ∈ Z along a meridian of $$S^2$$ S 2 for any axisymmetric Hölder continuous direction field $$\mathbf{D}\ne 0$$ D ≠ 0 on $$S^2$$ S 2 and, moreover, the (exact) decay order $$3 \le \delta \in {{\mathbb {Z}}}$$ 3 ≤ δ ∈ Z of any axisymmetric harmonic field $$\mathbf{B}$$ B at infinity. Fixing a meridional plane and in this plane $${r\!o}- \delta +1 \geqq 0$$ r o - δ + 1 ≧ 0 points $$z_n$$ z n (symmetric with respect to the symmetry axis and with $$|z_n| > 1$$ | z n | > 1 , $$n = 1,\ldots ,{r\!o}-\delta +1$$ n = 1 , … , r o - δ + 1 ), we prove the existence of an (up to a positive constant factor) unique harmonic field $$\mathbf{B}$$ B vanishing at $$z_n$$ z n and nowhere else, with decay order $$\delta $$ δ at infinity, and with direction $$\mathbf{D}$$ D at $$S^2$$ S 2 . The proof is based on the global solution of a nonlinear elliptic boundary value problem, which arises from a complex analytic ansatz for the axisymmetric harmonic field in the meridional plane. The coefficients of the elliptic equation are discontinuous and singular at the symmetry axis, and this requires solution techniques that are adapted to this special situation.

Quench position reconstruction through harmonic field analysis in superconducting magnets

The performances of superconducting magnets for particle accelerators are limited by instabilities or disturbances which lead to the transition of the superconducting material to the normal resistive state and the activation of the quench protection system to prevent damage to the magnet. To locate the position of the state transition, voltage taps or quench antenna are the most commonly used technologies for their reliability and accuracy. However, during the production phase of a magnet, the number of voltage taps is commonly reduced to simplify the construction process, and quench antennae are generally used only for dipoles or quadrupoles to limit the antenna design complexity. To increase the accuracy in the reconstruction of the quench event position, a novel method, suitable for magnets with independent superconducting coils and quench protected without the use of quench heaters is proposed in this paper. This method, based on standard magnetic measurement techniques for field harmonic analysis, can locate the position of the superconductor transition inside the magnet after the quench event when the magnet has been discharged. Analyzing the not allowed harmonics produced in the field quality at zero current, the position of the quenched coils can be retrieved for any magnet orders without increasing the complexity of the dedicated measurement technique.

On quantum analogue of instable oscillating states of an inverted oscillator in external poly-harmonic field

Nonstationary Schroedinger equation (NSE) is solved analytically and numerically to study a phenomenon of dynamical stabilization of the inverted oscillator driven by polyharmonic in time and spatially uniform force with specially chosen phase shifts. It is shown that for Gaussian wave packet asymptotically fitting the initial condition (IC) it occurs temporary delay of the packet center about top of the parabolic potential for about 2 fundamental time periods followed by the center bifurcation.

High-Efficient Brushless Wound Rotor Synchronous Machine Topology Based on Sub-Harmonic Field-Excitation Technique

This paper presents a new high-efficient three-phase brushless wound rotor synchronous machine (BL-WRSM) based on a sub-harmonic field excitation technique. In the proposed machine topology, the stator is equipped with two different three-phase windings: (1) main armature winding, and (2) additional armature winding. The main armature winding is based on a 4-pole winding configuration, whereas the additional armature winding is based on a 2-pole winding configuration. Both windings are supplied current from two different inverters, i.e., inverter-1, inverter-2, and simultaneously. Inverter-1 provides the regular input current to the main armature winding, whereas inverter-2 provides a three-phase current of low magnitude to the 2-pole additional armature winding. This generates an additional sub-harmonic component of MMF in the airgap beside the fundamental MMF. On the other side, the rotor is equipped with (1) harmonic, and (2) field windings. These windings are electrically coupled via a rectifier. The fundamental component of MMF produces the main rotating magnetic field, whereas the sub-harmonic MMF gets induced in the harmonic winding to produce harmonic current. This current is rectified to give DC to the rotor field winding to attain brushless operation. To authenticate the operation and analyze its performance, the proposed BL-WRSM topology is supported using 2-D finite element analysis (FEA) in JMAG-Designer. Later on, the performance of the proposed brushless topology is compared with the customary BL-WRSM topology to verify its high efficiency, high output torque, low torque ripple, and low unbalanced radial force on the rotor.

Prismatic mesh generation based on anisotropic volume harmonic field

In this paper, we present an effective prismatic mesh generation method for viscous flow simulations. To address the prismatic mesh collisions in recessed cavities or slit areas, we exploit 3D tensors controlled anisotropic volume harmonic field to generate prismatic meshes. Specially, a well-fitting tetrahedral mesh is first constructed to serve as the discrete computation domain of volume harmonic fields. Then, 3D tensors are exploited to control the volume harmonic field that better fits the shape geometry. From the topological perspective, the generation of the prismatic mesh can be treated as a topology-preserved morphing of the viscous wall. Therefore, iso-surfaces in the volume harmonic field should be homeomorphic to the viscous wall while fitting its shapes. Finally, a full prismatic mesh can be induced by estimating the forward directions and visible regions in the volume harmonic field. Moreover, to be compatible with different simulation situations, the thickness of prismatic meshes should be variable. Our approach provides local adjustable thickness of prismatic meshes, which can be achieved by controlling local 3D tensors. The proposed anisotropic volume harmonic field based prismatic meshes are efficient and robust, and a full prismatic mesh can be guaranteed without low quality collisions. Various experiments have shown that our proposed prismatic meshes have obvious advantages in terms of efficiency and effectiveness.

Klynotron with using the open resonator and symmetric conical corrugated mirrors – goratron

А further development of the radial klynoorotron idea – klynotron with symmetric conical radial corrugated resonator mirrors, is presented in the article. Strong coupling volume and surface resonance fields in the double conical mirrors in such a device is formed due to which the synchronous harmonic field is in the entire intermirror space. All saying above makes it possible to use a wide electronic flow. The conical mirror geometry provides a klynotron effect. As a result, not only the permissible device power is increased, but also its efficiency in comparison with a conventional radial klynoorotron. The article presents the calculating results of the Goratron at b0 = 0.51. The solution of the two-dimensional boundary value problem for the potentialV(r, z) = rBj(r, z), which determines Goratron resonator axisymmetric oscillation Em01, was carried out by standard packages for solving general partial differential equations using finite elements. The distribution analysis Er(r, z), Ez(r, z), Bj(r, z) shows that the field periodic component exists in the entire space between the comb mirrors. Given feature allows to use a wide (up to l/4) electron flow. Goratron electron flow modelcontains 16 layers along z, the equations of motion were relativistic. The electronic efficiency averaged over all layers is more than 30 %, which is 1.5 times higher than that obtained in the radial klynotron efficiency calculations.

Gradient-boosted equivalent sources for gridding large gravity and magnetic datasets

<p>The equivalent source technique is a well known method for interpolating gravity and magnetic data. It consists in defining a set of finite sources that generate the same observed field and using them to predict the values of the field at unobserved locations. The equivalent source technique has some advantages over general-purpose interpolators: the variation of the field due to the height of the observation points is taken into account and the predicted values belong to an harmonic field. These make equivalent sources a more suited interpolator for any data deriving from a harmonic field (like gravity disturbances and magnetic anomalies). Nevertheless, it has one drawback: the computational cost. The process of estimating the coefficients of the sources that best fit the observed values is very computationally demanding: a Jacobian matrix with number of observation points times number of sources elements must be built and then used to fit the source coefficients though a least-squares method. Increasing the number of data points can make the Jacobian matrix to grow so large that it cannot fit in computer memory.</p><p>We present a gradient-boosting equivalent source method for interpolating large datasets. In it, we define small subsets of equivalent sources that are fitted against neighbouring data points. The process is iteratively carried out, fitting one subset of sources on each iteration to the residual field from previous iterations. This new method is inspired by the gradient-boosting technique, mainly used in machine learning solutions.</p><p>We show that the gradient-boosted equivalent sources are capable of producing accurate predictions by testing against synthetic surveys. Moreover, we were able to grid a gravity dataset from Australia with more than 1.7 million points on a modest personal computer in less than half an hour.</p>

Prismatic mesh generation based on anisotropic volume harmonic field

In this paper, we present an effective prismatic mesh generation method for viscous flow simulations. To address the prismatic mesh collisions in recessed cavities or slit areas, we exploit 3D tensors controlled anisotropic volume harmonic field to generate prismatic meshes. Specially, a well-fitting tetrahedral mesh is first constructed to serve as the discrete computation domain of volume harmonic fields. Then, 3D tensors are exploited to control the volume harmonic field that better fits the shape geometry. From the topological perspective, the generation of the prismatic mesh can be treated as a topology-preserved morphing of the viscous wall. Therefore, iso-surfaces in the volume harmonic field should be homeomorphic to the viscous wall while fitting its shapes. Finally, a full prismatic mesh can be induced by estimating the forward directions and visible regions in the volume harmonic field. Moreover, to be compatible with different simulation situations, the thickness of prismatic meshes should be variable. Our approach provides local adjustable thickness of prismatic meshes, which can be achieved by controlling local 3D tensors. The proposed anisotropic volume harmonic field based prismatic meshes are efficient and robust, and a full prismatic mesh can be guaranteed without low quality collisions. Various experiments have shown that our proposed prismatic meshes have obvious advantages in terms of efficiency and effectiveness.