Arbitrary Magnetic Field Research Articles

Potential risk resulting from the influence of static magnetic field upon living organisms. Numerically simulated effects of the static magnetic field upon metalloporphyrines

Background: An attempt to recognize the effects of a static magnetic field (SMF) of varying flux density on flora and fauna.. For this purpose the influence of static magnetic field upon molecules of Mg(II), Fe(II), Fe(III), Co(II), Co(III) and Cu(II) metalloporphyrins is studied. Methods: Computations of the effect of real SMF 0.0, 0.1, 1, 10 and 100 AFU (Arbitrary Magnetic Field Unit; here 1AMFU > 1000 T) flux density were performed in silico (computer vacuum) involving advanced computational methods. Results: The static magnetic field (SMF) decreased the stability of the metalloporphyrine molecules. This effect depended on the situation of the molecule in respect to the direction of the SMF of the Cartesian system. An increase in the value of heat of formation was accompanied by an increase in the dipole moment. It was an effect of deformations of the molecule which involved pyrrole rings holding the hydrogen atoms at the ring nitrogen atoms and the length of the C-H and N-H bonds. As a consequence, that macrocyclic ring lost its planarity. Conclusions: SMF even of the lowest, 0.1 AMFU flux density influences the biological role of metalloporphyrines associated with their central metal atoms. This effect is generated by changes in the electron density at these atoms, its steric hindering and polarization of particular bonds from pure valence bonds possibly into ionic bonds.

Toward a magnetic warm inflation scenario

In this work we explore the effects that a possible primordial magnetic field can have on the inflaton effective potential, taking as the underlying model a warm inflation scenario, based on global supersymmetry with a new-inflation-type potential. The decay scheme for the inflaton field is a two-step process of radiation production, where the inflaton couples to heavy intermediate superfields, which in turn interact with light particles. In this context, we consider that both sectors, heavy and light, are charged and work in the strong magnetic field approximation for the light fields. We find an analytical expression for the one-loop effective potential, for an arbitrary magnetic field strength, and show that the trend of the magnetic contribution is to make the potential flatter in the origin's vicinity, preserving the conditions for a successful inflationary process. This result is backed up by the behavior of slow-roll parameter $\ensuremath{\epsilon}$. The viability of this magnetic warm inflation scenario is also supported by the estimation of the effect of the magnetic field on the heavy particles decay width.

Numerical solutions to linear transfer problems of polarized radiation

Context. The polarization signals produced by the scattering of anistropic radiation in strong resonance lines encode important information about the elusive magnetic fields in the outer layers of the solar atmosphere. An accurate modeling of these signals is a very challenging problem from the computational point of view, in particular when partial frequency redistribution (PRD) effects in scattering processes are accounted for with a general angle-dependent treatment. Aims. We aim at solving the radiative transfer problem for polarized radiation in nonlocal thermodynamic equilibrium conditions, taking angle-dependent PRD effects into account. The problem is formulated for a two-level atomic model in the presence of arbitrary magnetic and bulk velocity fields. The polarization produced by scattering processes and the Zeeman effect is considered. Methods. The proposed solution strategy is based on an algebraic formulation of the problem and relies on a convenient physical assumption, which allows its linearization. We applied a nested matrix-free GMRES iterative method. Effective preconditioning is obtained in a multifidelity framework by considering the light-weight description of scattering processes in the limit of complete frequency redistribution (CRD). Results. Numerical experiments for a one-dimensional (1D) atmospheric model show near optimal strong and weak scaling of the proposed CRD-preconditioned GMRES method, which converges in few iterations, independently of the discretization parameters. A suitable parallelization strategy and high-performance computing tools lead to competitive run times, providing accurate solutions in a few minutes. Conclusions. The proposed solution strategy allows the fast systematic modeling of the scattering polarization signals of strong resonance lines, taking angle-dependent PRD effects into account together with the impact of arbitrary magnetic and bulk velocity fields. Almost optimal strong and weak scaling results suggest that this strategy is applicable to realistic 3D models. Moreover, the proposed strategy is general, and applications to more complex atomic models are possible.

The transfer of polarized radiation in resonance lines with partial frequency redistribution, J-state interference, and arbitrary magnetic fields

Aims. We present the theoretical framework and numerical methods we have implemented to solve the problem of the generation and transfer of polarized radiation in spectral lines without assuming local thermodynamical equilibrium, while accounting for scattering polarization, partial frequency redistribution (due to both the Doppler effect and elastic collisions), J-state interference, and hyperfine structure. The resulting radiative transfer code allows one to model the impact of magnetic fields of an arbitrary strength and orientation through the Hanle, incomplete Paschen-Back, and magneto-optical effects. We also evaluate the suitability of a series of approximations for modeling the scattering polarization in the wings of strong resonance lines at a much lower computational cost, which is particularly valuable for the numerically intensive case of three-dimensional radiative transfer. Methods. We examine the suitability of the considered approximations by using our radiative transfer code to model the Stokes profiles of the Mg II h & k lines and of the H I Lyman-α line in magnetized one-dimensional models of the solar atmosphere. Results. Neglecting Doppler redistribution in the scattering processes that are unperturbed by elastic collisions (i.e., treating them as coherent in the observer’s frame) produces a negligible error in the scattering polarization wings of the Mg II resonance lines and a minor one in the Lyman-α wings, although it is unsuitable to model the cores of these lines. For both lines, the scattering processes that are perturbed by elastic collisions only give a significant contribution to the intensity component of the emissivity. Neglecting collisional as well as Doppler redistribution (so that all scattering processes are coherent) represents a rough but suitable approximation for the wings of the Mg II resonance lines, but a very poor one for the Lyman-α wings. The magnetic sensitivity in the scattering polarization wings of the considered lines can be modeled by accounting for the magnetic field in only the ηI and ρV coefficients of the Stokes-vector transfer equation (i.e., using the zero-field expression for the emissivity).

TIC: A Stokes Inversion Code for Scattering Polarization with Partial Frequency Redistribution and Arbitrary Magnetic Fields

We present the Tenerife Inversion Code (TIC), which has been developed to infer the magnetic and plasma properties of the solar chromosphere and transition region via full Stokes inversion of polarized spectral lines. The code is based on the HanleRT forward engine, which takes into account many of the physical mechanisms that are critical for a proper modeling of the Stokes profiles of spectral lines originating in the tenuous and highly dynamic plasmas of the chromosphere and transition region: the scattering polarization produced by quantum level imbalance and interference (atomic polarization), the effects of frequency coherence in polarized resonance scattering (partial redistribution), and the impact of arbitrary magnetic fields on the atomic polarization and the radiation field. We present first results of atmospheric and magnetic inversions, and discuss future developments for the project.

Entanglement entropy in quantum spin chains with broken parity number symmetry

Consider a generic quantum spin chain that can be mapped to free quadratic fermions via Jordan-Wigner (JW) transformation. In the presence of arbitrary boundary magnetic fields, this Hamiltonian is no longer a quadratic Hamiltonian after JW transformation. Using ancillary sites and enlarging the Hamiltonian we first introduce a bigger quadratic Hamiltonian. Then we diagonalize this enlarged Hamiltonian in its most generic form and show that all the states are degenerate because of the presence of a zero mode. The eigenstates of the original spin chain with boundary magnetic fields can be derived after appropriate projection. We study in depth the properties of the eigenstates of the enlarged Hamiltonian. In particular we find: 1) the eigenstates in configuration bases, 2) calculate all the correlation functions, 3) find the reduced density matrices, 4) calculate the entanglement entropy. We show that the generic eigenstate of the enlarged Hamiltonian (including the eigenstates of the original spin chain) breaks the parity number symmetry and consequently one needs to take care of some technicalities regarding the calculation of the reduced density matrix and entanglement entropy. Interestingly we show that the entanglement structure of these eigenstates is quite universal and independent of the Hamiltonian. We support our results by applying them to a couple of examples.

Onset of Electron Captures and Shallow Heating in Magnetars

The loss of magnetic pressure accompanying the decay of the magnetic field in a magnetar may trigger exothermic electron captures by nuclei in the shallow layers of the stellar crust. Very accurate analytical formulas are obtained for the threshold density and pressure, as well as for the maximum amount of heat that can be possibly released, taking into account the Landau–Rabi quantization of electron motion. These formulas are valid for arbitrary magnetic field strengths, from the weakly quantizing regime to the most extreme situation in which electrons are all confined to the lowest level. Numerical results are also presented based on experimental nuclear data supplemented with predictions from the Brussels-Montreal model HFB-24. This same nuclear model has been already employed to calculate the equation of state in all regions of magnetars.

Hydrogen atom in a magnetic field as an exactly solvable system without dynamical symmetries?

According to the generally accepted classification, there are supersymmetric superintegrable systems for which the Schrödinger equation is separable in more than one coordinate system and which admit an exact solution. A classic example of a superintegrable system is a hydrogen atom. It is believed that the converse is also true: an exactly solvable system has many integrals of motion corresponding to the separation constants of the Schrödinger equation in more than one coordinate system, which also means a high symmetry group of the system. It is shown that the existence of an exact solution for a hydrogen atom in an arbitrary strong uniform magnetic field apparently contradicts this classification.

A three-dimensional boundary element method algorithm for simulations of magnetic fluid droplet dynamics

This paper outlines a numerical algorithm capable of simulating the full three-dimensional dynamics of magnetic fluid droplets in external magnetic fields by solving boundary integral equations. The algorithm works with arbitrary droplet and carrier fluid viscosity ratios. It is validated with known theoretical relationships. It also enables evaluating various approximations often used to describe ellipsoidal droplets by comparing the droplet dynamics calculated from such approximations to the results obtained from first principles using our numerical algorithm. The algorithm may be used to investigate droplet configurations in arbitrary magnetic fields and to indirectly calculate the physical properties of magnetic fluid droplets and predicting the magnetic field thresholds above which the droplet shape can develop instabilities in the form of various spikes.

Anisotropic spin dynamics in semiconductor narrow wires from the interplay between spin-orbit interaction and planar magnetic field

The anisotropic spin dynamics in wires based on a [001]-oriented semiconductor quantum well were investigated to determine the effect of applying an in-plane magnetic field both parallel to and perpendicular to the spin-orbit magnetic field, and the interaction between them. In one-dimensional spin motion where the wire width is less than the spin-precession length, it is known that the global spin precession is essentially determined by the spin-orbit induced precession along the wire direction. In this study, our objective is to investigate the nature of anisotropic spin dynamics in such narrow semiconductor wires along various crystal orientations. We proposed an analytic expression for the anisotropic spin-relaxation rates and the Larmor-precession frequencies for the arbitrary magnetic field orientation based on a theoretical understanding of the spin dynamics in the narrow wire structure. This expression describes the interaction between the spin-orbit field and all orientations of the in-plane magnetic field. We experimentally investigated the spin dynamics for lithographically defined 800-nm-width wires oriented along the $[\overline{1}10]$, [100], and [110] crystal orientations using a [001] GaAs/AlGaAs quantum well. Time-resolved Kerr rotation microscopy measurements indicated that the spin-relaxation time was the longest for the in-plane magnetic field perpendicular to the spin-orbit field, whereas the parallel configuration was found to be the shortest among all the directions. The precession frequency was found to have the opposite symmetry. These relations are well explained by the theoretical considerations developed in this work. Because the Rashba and Dresselhaus spin-orbit fields are mutually orthogonal in the [100] crystal orientation, it is possible to evaluate both spin-orbit coefficients from the precession anisotropy. These findings suggest that it is possible to control the spin state in narrow wires approaching the one-dimensional state and evaluate the spin-orbit coefficient. This has the potential to provide a greater understanding of quantum and topological information in semiconductor one-dimensional wires.

Stream-aligned Magnetohydrodynamics for Solar Wind Simulations

Abstract We present a reduced magnetohydrodynamic (MHD) mathematical model describing the dynamical behavior of highly conducting plasmas with frozen-in magnetic fields, constrained by the assumption that there exists a frame of reference, where the magnetic field vector, B , is aligned with the plasma velocity vector, u , at each point. We call this solution “stream-aligned MHD” (SA-MHD). Within the framework of this model, the electric field, E = − u × B ≡ 0, in the induction equation vanishes identically and so does the electromagnetic energy flux (Poynting flux), E × B ≡ 0, in the energy equation. At the same time, the force effect from the magnetic field on the plasma motion (the Ampère force) is fully taken into account in the momentum equation. Any steady-state solution of the proposed model is a legitimate solution of the full MHD system of equations. However, the converse statement is not true: in an arbitrary steady-state magnetic field, the electric field does not have to vanish identically (its curl has to, though). Specifically, realistic three-dimensional solutions for the steady-state (“ambient”) solar atmosphere in the form of so-called Parker spirals can be efficiently generated within the stream-aligned MHD (SA-MHD) with no loss in generality.

Out-of-equilibrium dynamics of the XY spin chain from form factor expansion

We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. We argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following [1], provides a natural and unified framework for out-of-equilibrium physics in this model. We show that all correlation functions in the CE can be computed using form factor expansion and expressed in terms of Fredholm determinants. In particular, we present exact out-of-equilibrium expressions in the thermodynamic limit for the previously unknown order parameter 1-point function, dynamical 2-point function and equal-time 3-point function.

MHD_NX: код идеальной МГД-устойчивости на двумерных неструктурированных сетках

The code developed by the authors for calculating the MHD stability of two-dimensional plasma configurations with an arbitrary magnetic field topology is presented. The choice of an appropriate version of the finite element method on hybrid unstructured computational grids and test calculations are discussed. Examples of using the code for modeling the plasma stability in Galatea traps and in divertor configurations of tokamak taking into account the plasma beyond the separatrix are given.

Propagation of Chorus Waves Generated in Minimum‐B Pockets

AbstractWe present the first ray tracing results of chorus waves generated in minimum‐B pockets. A new ray tracer is developed to accommodate an arbitrary magnetic field model, which enables us to construct minimum‐B pocket geometries using the Tsyganenko (1989) model. Rays with different frequencies and initial wave normal angles are launched from minimum‐B pockets and traced under different geomagnetic activity and hot electron density conditions. Our results indicate that chorus waves generated from minimum‐B pockets are usually highly localized and thus are unlikely to be detected unless the spacecraft is very close to the source region. These waves are also very unlikely to propagate into the plasmasphere. The propagation distances generally decrease with increasing geomagnetic activity.

Modeling the scattering polarization of the solar Ca I 4227 Å line with angle-dependent partial frequency redistribution

Context. The correct modeling of the scattering polarization signals observed in several strong resonance lines requires taking partial frequency redistribution (PRD) phenomena into account. Modeling scattering polarization with PRD effects is very computationally demanding and the simplifying angle-averaged (AA) approximation is therefore commonly applied. Aims. This work aims to assess the impact and the range of validity of the AA approximation with respect to the general angle-dependent (AD) treatment of PRD effects in the modeling of scattering polarization in strong resonance lines, with a focus on the solar Ca I 4227 Å line. Methods. Spectral line polarization was modeled by solving the radiative transfer problem for polarized radiation, under nonlocal thermodynamic equilibrium conditions, taking PRD effects into account in static one-dimensional semi-empirical atmospheric models presenting arbitrary magnetic fields. The problem was solved through a two-step approach. In step 1, the problem was solved for the intensity only, considering a multilevel atom. In step 2, the problem was solved including polarization, considering a two-level atom with an unpolarized and infinitely sharp lower level, and fixing the lower level population calculated at step 1. Results. The results for the Ca I 4227 Å line show a good agreement between the AA and AD calculations for the Q/I and U/I wings’ signals. However, AA calculations reveal an artificial trough in the line-core peak of the linear polarization profiles, whereas AD calculations show a sharper peak in agreement with the observations. Conclusions. An AD treatment of PRD effects is essential to correctly model the line-core peak of the scattering polarization signal of the Ca I 4227 Å line. By contrast, in the considered static case, the AA approximation seems to be suitable to model the wing scattering polarization lobes and their magnetic sensitivity through magneto-optical effects.

Explicit phenomenological solutions for magnetization exposed to an arbitrary NMR diffusion steady state pulse sequence.

Explicit phenomenological solutions to recurrence relations for the bulk transverse and longitudinal magnetization found using the Torrey-Bloch equations with relaxation effects are used to investigate nuclear magnetic resonance (NMR) diffusion measurements. Of particular interest are steady state NMR (self-)diffusion measurements that reduce experimental time that can extend the techniques to quickly reacting systems. The solutions for bulk transverse and longitudinal magnetization presented here are used to investigate the average behavior of the transverse and longitudinal magnetization in forming a steady state and are used to derive new expressions for the steady state longitudinal magnetization. These solutions can be applied to a noninteracting spin 1/2 ensemble undergoing free diffusion exposed to an arbitrary NMR pulse sequence containing arbitrary magnetic field gradient waveforms. The closed algebraic form method presented here has an advantage over iterative procedures for calculating transverse and longitudinal magnetization for the analysis and development of steady state pulse sequences. Previous theoretical results for steady state diffusion measurements are also reproduced. The Mathematica code for these solutions is provided in the supplementary material.

Impact of partially thermal electrons on the propagation characteristics of extraordinary mode in relativistic regime

Abstract On employing linearized Vlasov–Maxwell equations the solution of relativistic electromagnetic extraordinary mode is investigated for the wave propagating perpendicular to a uniform ambient magnetic field (in the presence of arbitrary magnetic field limit i.e., ω > Ω > k.v) in partially degenerate (i.e., for T F ≥ T and T ≠ 0) electron plasma under long wavelength limit (ω ≫ k.v). Due to the inclusion of weak quantum degeneracy the relativistic Fermi–Dirac distribution function is expanded under the relativistic limit ( m 0 2 c 2 2 p 2 < 1 $\frac{{m}_{0}^{2}{c}^{2}}{2{p}^{2}}< 1$ ) to perform momentum integrations which generate the Polylog functions. The propagation characteristics and shifting of cutoff points of the extraordinary mode are examined in different relativistic density and magnetic field ranges. The novel graphical results of extraordinary mode in relativistic quantum partially degenerate (for μ T = 0 $\frac{\mu }{T}=0$ ), nondegenerate (for μ T ≈ − 1 $\frac{\mu }{T}\approx -1$ ) and fully/completely degenerate (for μ T ≈ $\frac{\mu }{T}\approx $ 1) environments are obtained and the previously reported results are retraced as well.

Understanding and prediction of magnetization state of elliptic cross-section matrices in high gradient magnetic separation

Theoretical prediction of magnetization state of matrices in high gradient magnetic separation is of importance to the separation performance analysis. However, the existing methods are limited to the cases where a magnetic field is parallel or perpendicular to one axis of magnetic elements in matrices. To solve this issue, in this work, we propose an easily understood method to construct the correlation between the magnetization of an elliptic cross-section element and the externally applied magnetic field. On this basis, we develop a simple relation to rapidly determine the demarcation for judging the magnetization sate of the element, which is suitable for the cases with an arbitrary magnetic field direction. Furthermore, we reveal the influence of the shape coefficient of the element on the prediction accuracy of its magnetization process. This work has important theoretical value for understanding the magnetization process of elliptic cross-section matrices under different magnetic fields.

A magnetoelastic theory for Kirchhoff rods having uniformly distributed paramagnetic inclusions and its buckling

We present a theory for finite and spatial elastic deformation of rods under the influence of arbitrary magnetic field and boundary condition. The rod is modeled as a Kirchhoff rod and is assumed to have uniformly distributed array of uniaxial spheroidal paramagnetic inclusions embedded in it all pointing in the same direction in the undeformed state. The governing equations of the magnetoelastic rod are derived which are further non-dimensionalized and linearized to investigate buckling in such rods. Analytical expressions for the onset of buckling from the rod’s trivial state are obtained in terms of loading parameters (applied magnetic field, axial load, torque) as well as geometric (inclusion orientation in the undeformed state) and material (ratio of bending and torsional stiffnesses) parameters for different combinations of boundary conditions. The buckled shape of the rod at the onset of buckling is also examined. The presented work can be useful in simulation and design of magnetic soft continuum robots.

A Map between Time-Dependent and Time-Independent Quantum Many-Body Hamiltonians

Given a time-independent Hamiltonian $\widetilde H$, one can construct a time-dependent Hamiltonian $H_t$ by means of the gauge transformation $H_t=U_t \widetilde H \, U^\dagger_t-i\, U_t\, \partial_t U_t^\dagger$. Here $U_t$ is the unitary transformation that relates the solutions of the corresponding Schrodinger equations. In the many-body case one is usually interested in Hamiltonians with few-body (often, at most two-body) interactions. We refer to such Hamiltonians as "physical". We formulate sufficient conditions on $U_t$ ensuring that $H_t$ is physical as long as $\widetilde H$ is physical (and vice versa). This way we obtain a general method for finding such pairs of physical Hamiltonians $H_t$, $\widetilde H$ that the driven many-body dynamics governed by $H_t$ can be reduced to the quench dynamics due to the time-independent $\widetilde H$. We apply this method to a number of many-body systems. First we review the mapping of a spin system with isotropic Heisenberg interaction and arbitrary time-dependent magnetic field to the time-independent system without a magnetic field [F. Yan, L. Yang, B. Li, Phys. Lett. A 251, 289 (1999); Phys. Lett. A 259, 207 (1999)]. Then we demonstrate that essentially the same gauge transformation eliminates an arbitrary time-dependent magnetic field from a system of interacting fermions. Further, we apply the method to the quantum Ising spin system and a spin coupled to a bosonic environment. We also discuss a more general situation where $\widetilde H = \widetilde H_t$ is time-dependent but dynamically integrable.