General Magnetic Field Research Articles

Rotation of the Solar Equator

Regular measurements of the general magnetic field of the Sun, performed over about half a century at the Crimean Astrophysical Observatory, the J. Wilcox Solar Observatory, and five other observatories, are considered in detail for the time 1968 – 2016. They include more than twenty-six thousand daily values of the mean line-of-sight field strength of the visible solar hemisphere. On the basis of these values, the equatorial rotation period of the Sun is found to be 26.926(9) d (synodic). It is shown that its half-value coincides within error limits with both the main period of the magnetic four-sector structure, 13.4577(25) d, and the best-commensurate period of the slow motions of the major solar system bodies, 13.479(22) d (sidereal). The probability that the two periods coincide by chance is estimated to be about $10^{-7}$ . The true origin of this odd resonance is unknown.

Magnetic Chern bands and triplon Hall effect in an extended Shastry-Sutherland model

We study topological properties of one-triplon bands in an extended Shastry-Sutherland model relevant for the frustrated quantum magnet SrCu_2(BO_3)_2. To this end perturbative continuous unitary transformations are applied about the isolated dimer limit allowing to calculate the one-triplon dispersion up to high order in various couplings including intra and inter Dzyaloshinskii-Moriya interactions and a general uniform magnetic field. We determine the Berry curvature and the Chern number of the different one-triplon bands. We demonstrate the occurance of Chern numbers $\pm 1$ and $\pm 2$ for the case that two components of the magnetic field are finite. Finally, we also calculate the triplon Hall effect arising at finite temperatures.

Space dependent, full orbit effects on runaway electron dynamics in tokamak plasmas

The dynamics of RE (runaway electrons) in fusion plasmas span a wide range of temporal scales, from the fast gyro-motion, ∼10−11 s, to the observational time scales, ∼10−2→1 s. To cope with this scale separation, RE are usually studied within the bounce-average or the guiding center approximations. Although these approximations have yielded valuable insights, a study with predictive capabilities of RE in fusion plasmas calls for the incorporation of full orbit effects in configuration space in the presence of three-dimensional magnetic fields. We present numerical results on this problem using the Kinetic Orbit Runaway electrons Code that follows relativistic electrons in general electric and magnetic fields under the full Lorentz force, collisions, and radiation losses. At relativistic energies, the main energy loss is due to radiation damping, which we incorporate using the Landau-Lifshitz formulation of the Abraham-Lorentz-Dirac force. The main focus is on full orbit effects on synchrotron radiation. It is shown that even in the absence of magnetic field stochasticty, neglecting orbit dynamics can introduce significant errors in the computation of the total radiated power and the synchrotron spectra. The statistics of collisionless (i.e., full orbit induced) pitch angle dispersion, and its key role played on synchrotron radiation, are studied in detail. Numerical results are also presented on the pitch angle dependence of the spatial confinement of RE and on full orbit effects on the competition of electric field acceleration and radiation damping. Finally, full orbit calculations are used to explore the limitations of gyro-averaging in the relativistic regime. To explore the practical impact of the results, DIII-D and ITER-like parameters are used in the simulations.

Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method

We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for ∇∥ by following field lines between poloidal planes and interpolating within planes. Doing so removes the need for field-aligned coordinate systems that suffer from singularities in the metric tensor at null points in the magnetic field (or equivalently, when q→∞). One cost of this method is that as the field lines are not on the mesh, they may leave the domain at any point between neighbouring planes, complicating the application of boundary conditions.The Leg Value Fill (LVF) boundary condition scheme presented here involves an extrapolation/interpolation of the boundary value onto the field line end point. The usual finite difference scheme can then be used unmodified. We implement the LVF scheme in BOUT++ and use the Method of Manufactured Solutions to verify the implementation in a rectangular domain, and show that it does not modify the error scaling of the finite difference scheme. The use of LVF for arbitrary wall geometry is outlined.We also demonstrate the feasibility of using the FCI approach in non-axisymmetric configurations for a simple diffusion model in a “straight stellarator” magnetic field. A Gaussian blob diffuses along the field lines, tracing out flux surfaces. Dirichlet boundary conditions impose a last closed flux surface (LCFS) that confines the density. Including a poloidal limiter moves the LCFS to a smaller radius.The expected scaling of the numerical perpendicular diffusion, which is a consequence of the FCI method, in stellarator-like geometry is recovered. A novel technique for increasing the parallel resolution during post-processing, in order to reduce artefacts in visualisations, is described.

Solar 22 years cycle

Seven observatories performed in 1968–2015 numerous daily measurements of general magnetic field of the Sun seen as a star (of a mean line-of-sight field component of the visible solar hemisphere). The new data 2013–2015 confirmed the recent prediction about saw-edged profile of the mean curve of the Hale’s 22 years magnetic cycle and, thus, a hypothesis about its cosmological (partial) origin. This is supported by a special analysis of epochs of extrema of Wolf’s sunspot number, demonstrating a remarkable stability, since Galileo’s time, of the initial phase of the cycle, which can hardly be explained by dynamo theory exclusively.

Patterns of cosmogenic radionuclide production rates in the heliosphere and problems of solar modulation on a long time scale

The results of long-term studies of cosmogenic radionuclide production rates along the orbits of 39 chondrites that fell to the Earth between 1959 and 2013 are presented. They constitute a long series of homogeneous data, a statistical smoothing of which demonstrate some general patterns of the distribution and variations of Galactic cosmic rays (GCRs) with energy >100 MeV in the inner (<5 AU) heliosphere. A correlation analysis of the production rates of radionuclides with different half-lives suggests that the solar GCR modulation mechanism is constant over at least ~1 million years. The role of stochastic factors in the polarity reversal of the general solar magnetic field for the phases of maximum solar activity has been revealed. The subtle sensitivity of the 54Mn production rate in the Chelyabinsk chondrite to the short-term closure of the heliosphere for positively charged particles over 14 months between June 2012 and July 2013 is used as an example to show the high resolution of the method of using cosmogenic radionuclides in meteorites as natural GCR detectors.

Factorization in spin systems under general fields and separable ground-state engineering

We discuss ground state factorization schemes in spin $S$ arrays with general $XYZ$ couplings under general magnetic fields, not necessarily uniform or transverse. It is first shown that given arbitrary spin alignment directions at each site, nonzero couplings between any pair and fields at each site always exist such that the ensuing Hamiltonian has an exactly separable eigenstate with the spins pointing along the specified directions. Furthermore, by suitable tuning of the fields this eigenstate can always be cooled down to a nondegenerate ground state. It is also shown that in open one-dimensional systems with arbitrary $XYZ$ first neighbor couplings, at least one separable eigenstate compatible with an arbitrarily chosen spin direction at one site is always feasible if the fields at each site can be tuned. We demonstrate as well that in the vicinity of factorization, i.e., for small perturbations in the fields or couplings, pairwise entanglement reaches full range. Some noticeable examples of factorized eigenstates for uniform couplings are unveiled. The present results open the way for separable ground state engineering. A notation to quantify the complexity of a given type of solution according to the required control on the system couplings and fields is introduced.

Relativistic theory of spin relaxation mechanisms in the Landau-Lifshitz-Gilbert equation of spin dynamics

Starting from the Dirac-Kohn-Sham equation we derive the relativistic equation of motion of spin angular momentum in a magnetic solid under an external electromagnetic field. This equation of motion can be written in the form of the well-known Landau-Lifshitz-Gilbert equation for a harmonic external magnetic field, and leads to a more general magnetization dynamics equation for a general time-dependent magnetic field. In both cases with an electronic spin-relaxation term which stems from the spin-orbit interaction. We thus rigorously derive, from fundamental principles, a general expression for the anisotropic damping tensor which is shown to contain an isotropic Gilbert contribution as well as an anisotropic Ising-like and a chiral, Dzyaloshinskii-Moriya-like contribution. The expression for the spin relaxation tensor comprises furthermore both electronic interband and intraband transitions. We also show that when the externally applied electromagnetic field possesses spin angular momentum, this will lead to an optical spin torque exerted on the spin moment.

SPATIAL DISTRIBUTION OF PAIR PRODUCTION OVER THE PULSAR POLAR CAP

ABSTRACT Using an analytic, axisymmetric approach that includes general relativity, coupled to a condition for pair production deduced from simulations, we derive general results about the spatial distribution of pair-producing field lines over the pulsar polar cap. In particular, we show that pair production on magnetic field lines operates over only a fraction of the polar cap for an aligned rotator for general magnetic field configurations, assuming the magnetic field varies spatially on a scale that is larger than the size of the polar cap. We compare our result to force-free simulations of a pulsar with a dipole surface field and find excellent agreement. Our work has implications for first-principles simulations of pulsar magnetospheres and for explaining observations of pulsed radio and high-energy emission.

Evaluation of standoff distance method to determine the coronal magnetic field using CME-driven shocks

We have analyzed the propagation characteristics of four limb coronal mass ejections (CMEs) with their shocks. These CMEs were observed in 18 frames up to 18 solar radii using LASCO white light images. Gopalswamy and Yashiro (Astrophys. J. 736:L17, 2011) introduced the standoff distance method (SOD) to find the magnetic field in the corona using CME-driven shock. In this paper, we have used this technique to determine the magnetic field strength and to study the propagation/shock formation condition of these CMEs at 18 different locations. Since the thickness of shock sheath (standoff distance or SOD) is not constant around CME, we estimate the shock parameters and their variation in large and small SOD regions of the shock. The Mach number ranges from 1.7 to 2.8 and Alfven speed varies from \(197 \mbox{ to } 857~\mbox{km}\,\mbox{s}^{-1}\). Finally, we estimate the magnetic field variation in the corona. The magnetic field strength ranges from 4.9 to 26.2 mG from 8.3 to 17.5 solar radii. The estimated magnetic field strength in this study is consistent with the literature value (7.6 to 45.8 mG from Gopalswamy and Yashiro (Astrophys. J. 736:L17, 2011), and 6 to 105 mG from Kim et al. (Astrophys. J. 746:118, 2012)) and it smoothly follows the general coronal magnetic field profile.

Analysis and Simulation on the Effect of Rotor Interturn Short Circuit on Magnetic Flux Density of Turbo–Generator

Abstract The intent of this paper is to investigate the effect of the interturn short circuit fault (ISCF) in rotor on the magnetic flux density (MFD) of turbo-generator. Different from other studies, this work not only pays attention to the influence of the faulty degrees on the general magnetic field, but also investigates the effect of the short circuit positions on the harmonic components of MFD. The theoretical analysis and the digital simulation through the FEM software Ansoft are performed for a QSFN-600-2YHG turbo-generator. Several significant formulas and conclusions drawn from the analysis and the simulation results are obtained to indicate the relation between the harmonic amplitude of the MFD and the faulty degree (via nm , the number of the short circuit turns), and the relation between the MFD harmonic amplitude and the faulty position (via αr , the angle of the two slots in which the interturn short circuit occurs). Also, the developing tendency of the general magnetic field intensity, the distribution of the magnetic flux lines, and the peak-to-peak value of MFD are presented.

Wegner estimates, Lifshitz tails, and Anderson localization for Gaussian random magnetic fields

The Wegner estimate for the Hamiltonian of the Anderson model for the special Gaussian random magnetic field is extended to more general magnetic fields. The Lifshitz tail upper bounds of the integrated density of states as analyzed by Nakamura are reviewed and extended so that Gaussian random magnetic fields can be treated. By these and multiscale analysis, the Anderson localization at low energies is proven.

NUMERICAL STUDY OF A CHARGED PARTICLE IN A GENERAL MAGNETIC FIELD

In this work we propose a new numerical scheme to simulate the motion of a nonrelativistic charge in a general magnetic field. The scheme is very accurate in the sense that it shows a discrete analogous of the underlying continuous energy conservation law, as well as an analogous of the angular momentum variation law.

Dosimetric Uncertainties: Magnetic Field Coupling to Peripheral Nerve.

The International Commission on Non-ionizing Radiation Protection (ICNIRP) and the Institute for Electrical and Electronic Engineers (IEEE) have established magnetic field exposure limits for the general public between 400 Hz (ICNIRP)/759 Hz (IEEE) and 100 kHz to protect against adverse effects associated with peripheral nerve stimulation (PNS). Despite apparent common purpose and similarly stated principles, the two sets of limits diverge between 3.35-100 kHz by a factor of about 7.7 with respect to PNS. To address the basis for this difference and the more general issue of dosimetric uncertainty, this paper combines experimental data of PNS thresholds derived from human subjects exposed to magnetic fields together with published estimates of induced in situ electric field PNS thresholds to evaluate dosimetric relationships of external magnetic fields to induced fields at the threshold of PNS and the uncertainties inherent to such relationships. The analyses indicate that the logarithmic range of magnetic field thresholds constrains the bounds of uncertainty of in situ electric field PNS thresholds and coupling coefficients related to the peripheral nerve (the coupling coefficients define the dosimetric relationship of external field to induced electric field). The general public magnetic field exposure limit adopted by ICNIRP uses a coupling coefficient that falls above the bounds of dosimetric uncertainty, while IEEE's is within the bounds of uncertainty toward the lower end of the distribution. The analyses illustrate that dosimetric estimates can be derived without reliance on computational dosimetry and the associated values of tissue conductivity. With the limits now in place, investigative efforts would be required if a field measurement were to exceed ICNIRP's magnetic field limit (the reference level), even when there is a virtual certainty that the dose limit (the basic restriction) has not been exceeded. The constraints on the range of coupling coefficients described in this paper could facilitate a re-evaluation of ICNIRP and IEEE dose and exposure limits and possibly lead toward harmonization.

Three discontinuous Galerkin schemes for the anisotropic heat conduction equation on non-aligned grids

We present and discuss three discontinuous Galerkin (dG) discretizations for the anisotropic heat conduction equation on non-aligned cylindrical grids. Our non-aligned scheme relies on a self-adjoint local dG (LDG) discretization of the elliptic operator. It conserves the energy exactly and converges with arbitrary order. The pollution by numerical perpendicular heat fluxes decreases with superconvergence rates. We compare this scheme with aligned schemes that are based on the flux-coordinate independent approach for the discretization of parallel derivatives. Here, the dG method provides the necessary interpolation. The first aligned discretization can be used in an explicit time-integrator. However, the scheme violates conservation of energy and shows up stagnating convergence rates for very high resolutions. We overcome this partly by using the adjoint of the parallel derivative operator to construct a second self-adjoint aligned scheme. This scheme preserves energy, but reveals unphysical oscillations in the numerical tests, which result in a decreased order of convergence. Both aligned schemes exhibit low numerical heat fluxes into the perpendicular direction and are superior for flute-modes with finite parallel gradients. We build our argumentation on various numerical experiments on all three schemes for a general axisymmetric magnetic field, which is closed by a comparison to the aligned finite difference (FD) schemes of Stegmeir et al. (2014) and Stegmeir et al. (submitted for publication).

Graphical Representations for Ising and Potts Models in General External Fields

This work is concerned with the theory of Graphical Representation for the Ising and Potts Models over general lattices with non-translation invariant external field. We explicitly describe in terms of the Random Cluster Representation the distribution function and, consequently, the expected value of a single spin for the Ising and $q$-states Potts Models with general external fields. We also consider the Gibbs States for the Edwards-Sokal Representation of the Potts Model with non-translation invariant magnetic field and prove a version of the FKG Inequality for the so called General Random Cluster Model (GRC Model) with free and wired boundary conditions in the non-translation invariant case. Adding the amenability hypothesis on the lattice, we obtain the uniqueness of the infinite connected component and the quasilocality of the Gibbs Measures for the GRC Model with such general magnetic fields. As a final application of the theory developed, we show the uniqueness of the Gibbs Measures for the Ferromagnetic Ising Model with a positive power law decay magnetic field, as conjectured in [8].

From charge motion in general magnetic fields to the non perturbative gyrokinetic equation

The exact analytical description of non relativistic charge motion in general magnetic fields is, apparently, a simple problem, even if it has not been solved until now, apart for rare cases. The key feature of the present derivation is to adopt a non perturbative magnetic field description to find new solutions of motion. Among all solutions, two are particularly important: guiding particle and gyro-particle solutions. The guiding particle has been characterized to be minimally coupled to the magnetic field; the gyro-particle has been defined to be maximally coupled to the magnetic field and, also, to move on a closed orbit. The generic charged particle motion is shown to be expressed as the sum of such particular solutions. This non perturbative approach corresponds to the description of the particle motion in the gyro-center and/or guiding center reference frame obtained at all the orders of the modern gyro-center transformation. The Boltzmann equation is analyzed with the described exact guiding center coordinates. The obtained gyrokinetic equation is solved for the Boltzmann equation at marginal stability conditions.

On the origin of the 22 years solar cycle

Measurements of the general magnetic field of the Sun seen as a star were performed over last 45years by the CrAO and five other observatories (1968–2012, nearly 23 thousand daily strengths B). Analysis of the B time series showed that the most substantial long-term period of the field variation is the Hale’s cycle 22years, which cannot be explained by dynamo theory. It reveals a saw-edged profile, indicating perhaps a cosmic origin of the cycle.

The pathogenetic prerequisites for the application of the general magnetic therapy in the children presenting with cerebral ischemia

This article presents the analysis of the current literature and the original data of the authors providing the rationale for the use of magnetic therapy for the treatment of the children presenting with cerebral ischemia taking into consideration pathogenesis of this disease. It is demonstrated that the application of the general magnetic field decreases the tone of the cerebral vessels and improves blood flow to the brain which increases resistance to cerebral hypoxia. The results of investigations into the microcirculatory changes and liquor dynamics in conjunction with the ventriculometric measurements give evidence of the effectiveness of the combined treatment of cerebral ischemia making use of general magnetic therapy.

The ionization rate under a general magnetic field for microwave breakdown

The ionization rate under an extra magnetic field is studied by theory and particle-in-cell/Monte Carlo Collision simulations. The result shows that a magnetic field always decreases the ionization rate if 3ω &amp;lt; υm, while it may increase the ionization rate if 3ω &amp;gt; υm. The effect of the magnetic field on the ionization rate fades away when the angle between the magnetic field and the electric filed approaches to zero. Furthermore, the peak ionization rate among different magnetic fields is almost independent of ω. This peak ionization rate is in direct proportion to the gas pressure in the low pressure region, while it is about in inverse proportion to the gas pressure in the high pressure region.