Arbitrary Magnetic Field Research Articles

Pitch-angle Diffusion and Bohm-type Approximations in Diffusive Shock Acceleration

Abstract The problem of accelerating cosmic rays is one of fundamental importance, particularly given the uncertainty in the conditions inside the acceleration sites. Here we examine diffusive shock acceleration in arbitrary turbulent magnetic fields, constructing a new model that is capable of bridging the gap between the very weak (δB/B 0 ≪ 1) and the strong turbulence regimes. To describe the diffusion we provide a quantitative analytical description of the “Bohm exponent” in each regime. We show that our results converge to the well known quasi-linear theory in the weak turbulence regime. In the strong regime, we quantify the limitations of the Bohm-type models. Furthermore, our results account for the anomalous diffusive behavior which has been noted previously. Finally, we discuss the implications of our model in the study of possible acceleration sites in different astronomical objects.

A WENO finite-difference scheme for a new class of Hamilton–Jacobi equations in nonlinear solid mechanics

This paper puts forth a high-order weighted essentially non-oscillatory (WENO) finite-difference scheme to numerically generate the viscosity solution of a new class of Hamilton–Jacobi (HJ) equations that has recently emerged in nonlinear solid mechanics. The solution W of the prototypical version of the HJ equations considered here corresponds physically to the homogenized free energy that describes the macroscopic magneto-electro-elastic response of a general class of two-phase particulate composite materials under arbitrary quasi-static finite deformations, electric fields, and magnetic fields in N=2,3 dimensions. An important mathematical implication of its physical meaning is that W – although it may exhibit steep gradients – is expected to be at least twice continuously differentiable. This is in contrast to the viscosity solutions of the majority of HJ equations that have appeared in other scientific disciplines, which are merely Lipschitz continuous. Three other defining mathematical features that differentiate this new class of HJ equations from most of the existing HJ equations in the literature are that: (i) their “space” variables are defined over non-periodic unbounded or semi-unbounded domains, (ii) their Hamiltonians depend explicitly on all variables, namely, on the “space” and “time” variables, the “space” derivatives of W, and on the function W itself, and (iii) in general, their integration in “time” needs to be carried out over very long “times”. The proposed WENO scheme addresses all these features by incorporating a high-order accurate treatment of the boundaries of the domains of computation and by employing a high-order accurate explicit Runge–Kutta “time” integration that remains stable over very large “time” integration ranges. The accuracy and convergence properties of the proposed scheme are demonstrated by direct comparison with a simple explicit solution W available for the case when the general HJ equation is specialized to model the elastic response of isotropic porous Gaussian elastomers. Finally, for showcasing purposes, the scheme is deployed to probe the magneto-elastic response of a novel class of magnetorheological elastomers filled with ferrofluid inclusions.

Integrable spin- Richardson–Gaudin XYZ models in an arbitrary magnetic field

We establish the most general class of spin- integrable Richardson–Gaudin models including an arbitrary magnetic field, returning a fully anisotropic (XYZ) model. The restriction to spin- relaxes the usual integrability constraints, allowing for a general solution where the couplings between spins lack the usual antisymmetric properties of Richardson–Gaudin models. The full set of conserved charges are constructed explicitly and shown to satisfy a set of quadratic equations, allowing for the numerical treatment of a fully anisotropic central spin in an external magnetic field. While this approach does not provide expressions for the exact eigenstates, it allows their eigenvalues to be obtained, and expectation values of local observables can then be calculated from the Hellmann–Feynman theorem.

Relations between Hall Plates with Complementary Contact Geometries

Singly connected Hall plates with N peripheral contacts can be mapped onto the upper half of the z-plane by a conformal transformation. Recently, Homentcovschi and Bercia derived the General Formula for the electric field in this region. We present an alternative intuitive derivation based on conformal mapping arguments. Then we apply the General Formula to complementary Hall plates, where contacts and insulating boundaries are swapped. The resistance matrix of the complementary device at reverse magnetic field is expressed in terms of the conductance matrix of the original device at non-reverse magnetic field. These findings are used to prove several symmetry properties of Hall plates and their complementary counterparts at arbitrary magnetic field.

Dynamics of an orbital polarization of twisted electron beams in electric and magnetic fields

Relativistic classical and quantum dynamics of twisted (vortex) Dirac particles in arbitrary electric and magnetic fields is constructed. The relativistic Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived. Methods for the extraction of an electron vortex beam with a given orbital polarization and for the manipulation of such a beam are developed. The new effect of a radiative orbital polarization of a twisted electron beam in a magnetic field resulting in a nonzero average projection of the intrinsic orbital angular momentum on the field direction is predicted.

Flexible Control of Magnetic Fields by Shaped-Optimized Three-Dimensional Coil Arrays

The synthesis of desired low-frequency magnetic fields is of high importance in electromagnetic design. The use of coil arrays (CAs) is among the most effective methods for realizing a desired field. However, in designing CAs, researchers are faced with a lack of design parameters. At low frequencies, the design parameters are usually limited to the size and phase of the source and the size and position of the coils. In this letter, with the help of three-dimensional (3-D) coils, the spatial current distribution, i.e., the shape of coils, is added to the design parameters of the CA problem. This novel 3-D coil array creates a high degree of freedom for the synthesis of the desired magnetic field which cannot be achieved by ordinary coil arrays or a single 3-D coil. The technological advances in the field of 3-D printing helps in the fabrication of these 3-D structures with high precision, low cost, and fast prototyping. In the design process, dyadic Green's functions are used to analytically calculate the magnetic field. Then, in order to define the shape of the 3-D coils, these shapes are extended based on the proper basis functions. By determining the coefficients of these basis functions by means of optimization methods, the shape of each 3-D coil in the array is obtained. This method is used to realize an arbitrary magnetic field along a line by means of a single-source array that includes three 3-D coils. The designed array is implemented with the use of fused-deposition-modeling 3-D printing. The design results, numerical simulations, and experimental tests demonstrate a high degree of accuracy in the fabrication process and the ability of 3-D arrays to synthesize magnetic fields.

Bosonic oscillator under a uniform magnetic field with Snyder-de Sitter algebra

We study the deformed two-dimensional relativistic Bosonic oscillator equation for charged spin 0 and spin 1 particles moving in a uniform magnetic field with the Snyder-de Sitter model. For the scalar case, we compute the energy eigenvalues and eigenfunctions for both Klein Gordon and Duffin–Kemmer–Petiau (DKP) cases for an arbitrary magnetic field intensity. We also deduce the behavior of the DKP equation and compute the non-relativistic energies for the case of spin 1 particle. Finally, we study the thermodynamic properties of the system.

Exact boundary free energy of the open XXZ chain with arbitrary boundary conditions

We derive an exact formula for the boundary free energy of the open Heisenberg XXZ spin chain. We allow for arbitrary boundary magnetic fields, but assume zero bulk magnetization. The result is completely analogous to earlier formulas for the so-called g-function: it is expressed as a combination of single integrals and two simple Fredholm determinants. Our expressions can be evaluated easily using numerical algorithms with arbitrary precision. We demonstrate that the boundary free energy can show a wide variety of behaviour as a function of the temperature, depending on the anisotropy and the boundary fields. We also compute the low temperature limit of the boundary free energy, and reproduce the known results for the ground state boundary energy, including the case of non-diagonal fields.

Electromagnetic spectral function and dilepton rate in a hot magnetized QCD medium

The dilepton production rate in hot QCD medium is studied within a effective description of the medium in the presence of magnetic field. This could be done by obtaining the one-loop self energy of photon due to the effective (quasi-) quark loop at finite temperature under an arbitrary external magnetic field while employing the real time formalism of Thermal Field Theory. The effective quarks and gluons encode hot QCD medium effective in terms of their respective effective fugacities. The magnetic field enters in the form of landau level quantization, in the matter sector (quarks, antiquarks). The full Schwinger proper time propagator including all the Landau levels is considered for the quasi quarks while calculating the photon self energy. The electromagnetic Debye screening (in terms of the self-energy) has seen to be influenced both by the hot QCD medium effects and magnetic field. Analogous results are also obtained from the semi classical transport theory. The imaginary part of the photon self energy function is obtained from the discontinuities of the self energy across the Unitary cuts which are also present at zero magnetic field and the Landau cuts which are purely due to the magnetic field. The dilepton production rate is then obtained in terms of the product of electromagnetic spectral functions due to quark loop and lepton loop. The modifications of both the quarks/antiquarks as well as leptons in presence of an arbitrary external magnetic field have been considered in the formalism. Significant enhancement of the low invariant mass dileptons due the appearance of the Landau cuts in the electromagnetic spectral function at finite external magnetic field has been observed. A substantial enhancement of dilepton rate is also found when the EOS effects are considered through the effective quarks/antiquraks.

Tensorial neutron tomography of three-dimensional magnetic vector fields in bulk materials

Knowing the distribution of a magnetic field in bulk materials is important for understanding basic phenomena and developing functional magnetic materials. Microscopic imaging techniques employing X-rays, light, electrons, or scanning probe methods have been used to quantify magnetic fields within planar thin magnetic films in 2D or magnetic vector fields within comparable thin volumes in 3D. Some years ago, neutron imaging has been demonstrated to be a unique tool to detect magnetic fields and magnetic domain structures within bulk materials. Here, we show how arbitrary magnetic vector fields within bulk materials can be visualized and quantified in 3D using a set of nine spin-polarized neutron imaging measurements and a novel tensorial multiplicative algebraic reconstruction technique (TMART). We first verify the method by measuring the known magnetic field of an electric coil and then investigate the unknown trapped magnetic flux within the type-I superconductor lead.

Symplectic realization of electric charge in fields of monopole distributions

We construct a symplectic realisation of the twisted Poisson structure on the phase space of an electric charge in the background of an arbitrary smooth magnetic monopole density in three dimensions. We use the extended phase space variables to study the classical and quantum dynamics of charged particles in arbitrary magnetic fields by constructing a suitable Hamiltonian that reproduces the Lorentz force law for the physical degrees of freedom. In the source-free case the auxiliary variables can be eliminated via Hamiltonian reduction, while for non-zero monopole densities they are necessary for a consistent formulation and are related to the extra degrees of freedom usually required in the Hamiltonian description of dissipative systems. We obtain new perspectives on the dynamics of dyons and motion in the field of a Dirac monopole, which can be formulated without Dirac strings. We compare our associative phase space formalism with the approach based on nonassociative quantum mechanics, reproducing extended versions of the characteristic translation group three-cocycles and minimal momentum space volumes, and prove that the two approaches are formally equivalent. We also comment on the implications of our symplectic realisation in the dual framework of non-geometric string theory and double field theory.

Magnetohydrodynamic stability of large scale liquid metal batteries

The aim of this paper is to develop a stability theory and a numerical model for three density-stratified electrically conductive liquid layers. Using regular perturbation methods to reduce the full three-dimensional problem to the shallow layer model, the coupled wave and electric current equations are derived. The problem set-up allows for weakly nonlinear velocity field action and an arbitrary vertical magnetic field. Further linearisation of the coupled equations is used for the linear stability analysis in the case of a uniform vertical magnetic field. New analytical stability criteria accounting for the viscous damping are derived for particular cases of practical interest and compared to the numerical solutions for a variety of materials used in batteries. These new criteria are equally applicable to the aluminium electrolysis cell magnetohydrodynamic (MHD) stability estimates.

At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model

This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. --- We extend a recently-eveloped Fermi-liquid (FL) theory for the asymmetric single-impurity Anderson model [C. Mora $et al.$, Phys. Rev. B, 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's low-lying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective low-energy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spin-dependent ground-state occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe Ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, $c_A$, describing its leading $\sim\varepsilon^2$ term, and the transport coefficients $c_V$ and $c_T$, describing the leading $\sim V^2$ and $\sim T^2$ terms in the nonlinear differential conductance. A sign change in $c_A$ or $c_V$ is indicative of a change from a local maximum to a local minimum in the spectral function or nonlinear conductance, respectively, as is expected to occur when an increasing magnetic field causes the Kondo resonance to split into two subpeaks. We find that the fields $B_A$, $B_T$ and $B_V$ at which $c_A$, $c_T$ and $c_V$ change sign, respectively, are all of order $T_K$, as expected, with $B_A = B_T = B_V = 0.75073\,T_K$ in the Kondo limit.

Relativistic Quantum Dynamics of Twisted Electron Beams in Arbitrary Electric and Magnetic Fields.

Relativistic quantum dynamics of twisted (vortex) Dirac particles in arbitrary electric and magnetic fields are constructed for the first time. This allows us to change the controversial contemporary situation when the nonrelativistic approximation is used for relativistic twisted electrons. The relativistic Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived. A critical experiment for a verification of the results obtained is proposed. The new important effect of a radiative orbital polarization of a twisted electron beam in a magnetic field resulting in a nonzero average projection of the intrinsic orbital angular momentum on the field direction is predicted.

Application of the Ito theory for Monte Carlo simulation of plasma diffusion

In this paper the full set of stochastic differential equations (SDEs) are presented describing the guiding centre motion of test charged particles in a plasma with an arbitrary inhomogeneous magnetic field, when the drift approximation is applicable. The derivation is based on the Ito formula which is used to determine stochastic differentials of functions of the non-gyro-averaged velocity diffusion in strict correspondence with the general kinetic equations involving Coulomb collision operators. The drift SDEs are obtained by calculating the Ito stochastic integrals within time intervals admitting the gyro-averaging procedure. The proposed SDEs reproduce the well-known Monte Carlo operators for orbital invariants, however additionally accounting for the spatial drift caused by the cross-field diffusion process with a classical diffusion coefficient. All SDE coefficients are explicitly expressed in terms of the Rosenbluth potentials in a gyro-tropic or isotropic background plasma. The SDEs are presented in particular for the case of an axisymmetric toroidal magnetic configuration to describe the spatial two-dimensional poloidal diffusion process providing a detailed description of neoclassical orbital effects.

Topology Exploration and Torque Component Analysis of Double Stator Biased Flux Machines Based on Magnetic Field Modulation Mechanism

Biased flux machines (BFMs) have biased magnetic flux in the core and allows flexibility to adjust the field with a dc current. The conventional topology exploration methods for BFMs are based on the flux observation. It is time consuming and ineffective since the initial structure searching process is guideless. Meanwhile, BFMs usually work with arbitrary magnetic field harmonics instead of the fundamental one. The torque components of these machines and their essential operation principle have not been fully revealed. To solve these issues, in this paper, a topology exploration method for BFM based on magnetic field modulation mechanism is proposed, and the torque generating principle is analyzed. With this method, some new BFM structures have been developed and their torque components have been developed. It is shown that various space harmonics have contributed to constant torque rather than the fundamental one. To verify the feasibility of this design method, one double stator BFM is selected as a case study. Simulation and experimental results have verified that this design method is feasible and effective since the prototype has good sinusoidal back electromotive force waveforms and well performance. Besides, it is practical to realize flux weakening and strengthening the control with biased current.

Electron dynamics in the laser and quasi-static electric and magnetic fields

3/2 dimensional Hamiltonian equations, accounting for arbitrary polarized plane wave laser radiation and arbitrary electric and magnetic fields in the directions both along and across to the direction of the laser beam propagation, are derived for superluminal phase velocity of the laser radiation. An impact of superluminal laser radiation phase velocity on the transition to stochastic electron motion is studied.

Invisible magnetic sensors

Sensing magnetic fields is essential in many applications in biomedicine, transportation, or smart cities. The distortion magnetic sensors create in response to the field they are detecting may hinder their use, for example, in applications requiring dense packaging of sensors or accurately shaped field distributions. For sensing electromagnetic waves, cloaking shells that reduce the scattering of sensors have been introduced. However, the problem of making a magnetic sensor undetectable remains unsolved. Here, we present a general strategy on how to make a sensor magnetically invisible while keeping its ability to sense. The sensor is rendered undetectable by surrounding it with a spherical shell having a tailored magnetic permeability. Our method can be applied to arbitrary shaped magnetic sensors in arbitrary magnetic fields. The invisibility can be made exact when the sensor is spherical and the probed field is uniform. A metasurface composed of superconducting pieces is presented as a practical realization of the ideal invisibility shell.

Coronal magnetic field measurements using forbidden emission lines

AbstractThe polarization measurement of coronal forbidden emission lines is the most promising method of determining the direction of magnetic fields in the corona. A classical theory for the forbidden lines was presented in Megha et al. (2017) for the case of arbitrary strength magnetic fields. Here we apply that theoretical formalism to study the effect of density distributions, magnetic field configurations, and velocity fields on the Stokes profiles formed in corona. For illustrations we use the atomic parameters of the [Fe xiii] 10747 Å coronal forbidden line.

A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields

Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.