Arbitrary Magnetic Field Research Articles

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.

Evolution of localized magnetic field perturbations and the nature of turbulent dynamo

Kinematic dynamo in incompressible isotropic turbulent flows with high magnetic Prandtl number is considered. The approach interpreting an arbitrary magnetic field distribution as a superposition of localized perturbations (blobs) is developed. We derive a general relation between stochastic properties of an isolated blob and a stochastically homogenous distribution of magnetic field advected by the same stochastic flow. This relation allows us to investigate the evolution of a localized blob at a late stage when its size exceeds the viscous scale. It is shown that in three-dimensional flows, the average magnetic field of the blob increases exponentially in the inertial range of turbulence, as opposed to the late-batchelor stage when it decreases. Our approach reveals the mechanism of dynamo generation in the inertial range both for blobs and homogenous contributions. It explains the absence of dynamo in the two-dimensional case and its efficiency in three dimensions. We propose a way to observe the mechanism in numerical simulations.

Thermomagnetic modification of the anomalous magnetic moment of quarks using the NJL model

The effective photon-quark-antiquark ($\gamma q \overline{q}$) vertex function is evaluated at finite temperature in the presence of an arbitrary external magnetic field using the two-flavor gauged Nambu--Jona-Lasinio (NJL) model in the mean field approximation. The lowest order diagram contributing to the magnetic form factor and the anomalous magnetic moment (AMM) of the quarks is calculated at finite temperature and external magnetic field using the imaginary time formalism of finite temperature field theory and the Schwinger proper time formalism. The Schwinger propagator including all the Landau levels with non-zero AMM of the dressed quarks is considered while calculating the loop diagram. Using sharp as well as smooth three momentum cutoff, we regularize the UV divergences arising from the vertex function and the parameters of our model are chosen to reproduce the well known phenomenological quantities at zero temperature and zero magnetic field, such as pion-decay constant ($f_\pi$), vacuum quark condensate, vacuum pion mass ($m_\pi$) as well as the magnetic moments of proton and neutron. We then study the temperature and magnetic field dependence of the AMM and constituent mass of the quark. We found that, the AMM as well as the constituent quark mass are large at the chiral symmetry broken phase in the low temperature region. Around the pseudo-chiral phase transition they decrease rapidly and at high temperatures both of them approach vanishingly small values in the symmetry restored phase.

Nonclassical correlations in two-qubit Ising model with an arbitrary magnetic field: Local quantum Fisher information and local quantum uncertainty

Nonclassical correlations in two-qubit Ising model with an arbitrary magnetic field: Local quantum Fisher information and local quantum uncertainty

One-loop Kubo estimations of the shear and bulk viscous coefficients for hot and magnetized bosonic and fermionic systems

The expressions of the shear viscosity and the bulk viscosity components in the presence of an arbitrary external magnetic field for a system of hot charged scalar bosons (spin 0) as well as for a system of hot charged Dirac fermions (spin $\frac{1}{2}$) have been derived by employing the one-loop Kubo formalism. This is done by explicitly evaluating the thermomagnetic spectral functions of the energy-momentum tensors using the real time formalism of finite temperature field theory and the Schwinger proper time formalism. In the present work, a rich quantum field theoretical structure in the expressions of the viscous coefficients in nonzero magnetic field are found, which are different from their respective expressions obtained earlier via kinetic-theory-based calculations; though, in the absence of a magnetic field, the one-loop Kubo and the kinetic-theory-based expressions for the viscosities are known to be identical. We have identified that Kubo and kinetic-theory-based results of viscosity components follow a similar kind of temperature and magnetic field dependency. The relaxation time and the synchrotron frequency in the kinetic theory formalism are realized to be connected, respectively, with the thermal width of propagator and the transitions among the Landau levels of the charged particles in the Kubo formalism. We believe that the connection of the latter quantities is quite new and probably the present work is the first time addressing this interpretation along with the new expressions of viscosity components, not seen in existing works.

Magneto-optical effects in a high-Q whispering-gallery-mode resonator with a large Verdet constant.

We have studied magneto-optical effects in an optical whispering-gallery-mode resonator (WGMR) manufactured from a Faraday-rotator material with, to the best of our knowledge, the record quality factor ($Q = 1.45 \times {10^8}$) achieved for such materials. We have experimentally measured the eigenfrequencies' deviation amplitude under the application of an external magnetic field and demonstrated the polarization plane declination over the light path. An analytical model for arbitrary magnetic field geometries in magneto-optic birefringent WRMRs has been developed.

Effect of collisions on the plasma sheath in the presence of an inhomogeneous magnetic field

A low-pressure magnetized plasma is studied to find the dependency of sheath properties on ion-neutral collisions in presence of an inhomogeneous magnetic field. A self-consistent one-dimensional two-fluid hydrodynamic model is considered, and the system of equations is solved numerically. The study reveals that the width of the plasma sheath expands and space charge increases with collisions. The ion-neutral collisions and the inhomogeneous magnetic field restrict the ions to move towards the surface. The movement of the ions towards the wall can be controlled by choosing a suitable configuration of the magnetic field and ion-neutral collision frequency. A comparison between two different magnetic field configurations has been presented alongside to differentiate the commonly found scenarios in the field. The outcome of the study is supposed to help in understanding the complex dynamics of ions in plasma confinement and plasma processing of materials. Furthermore, the present work seeks to create a framework for two-fluid modeling of magnetized plasmas with any arbitrary magnetic field profiles. The analysis provided here is supposed to act as a basis for any future work in the respective field.

The on-axis magnetic well and Mercier's criterion for arbitrary stellarator geometries

A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct coordinate approach is used by expressing the toroidal magnetic flux in terms of powers of the radial distance to the magnetic axis. For the first time, the magnetic well and Mercier's criterion are then written as a one-dimensional integral with respect to the axis arclength. When compared with the original work of Mercier, the derivation here is presented using modern notation and in a more streamlined manner that highlights essential steps. Finally, these expressions are verified numerically using several quasisymmetric and non-quasisymmetric stellarator configurations including Wendelstein 7-X.

Magnetic-field-dependent intervalley relaxation time in Weyl semimetals

The zeroth Landau levels in Weyl semimetals (WSMs) are singular, which result in the anomalous nonsaturated positive longitudinal magnetoconductivity (LMC). The LMC exhibits periodic-in-$1/B$ quantum oscillations attributable to the the oscillating electron density of states in a magnetic field. The intervalley relaxation time ${\ensuremath{\tau}}^{a}$ is a key material parameter determining the magnitude of the LMC directly. In existing theories of the LMC, the magnetic field dependence of ${\ensuremath{\tau}}^{a}$ is usually neglected. Based upon the Boltzmann equation, we derive analytical expression for the intervalley relaxation time for short-range impurity scattering potential and arbitrary magnetic field strength. Taking the magnetic field dependence of ${\ensuremath{\tau}}^{a}$ into consideration, we find that the quantum oscillations of the LMC are enhanced. Numerical calculations are also carried out to verify the analytical derivations. Moreover, we provide an explanation for the anomalous behavior of the LMC observed in WSMs that the amplitude of LMC first increases and then decreases with increasing temperature.

Chiral magnetic domain walls under transverse fields: A semi-analytical model

An analytical model for the domain wall structure in ultrathin films with perpendicular easy axis and interfacial Dzyaloshinskii-Moriya interaction, submitted to an arbitrary in-plane magnetic field, is presented. Its solution is simplified to the numerical minimization of an analytic function of just one variable. The model predictions are compared to numerical micromagnetic simulations, using parameters of existing samples, revealing a very good agreement. Remaining differences are analyzed, and partly corrected. Differences with the predictions of the simplest model, usually found in the literature, in which only the domain wall moment’s in-plane orientation can vary, are exemplified. The model allows accurate computations, as a function of in-plane field module and orientation, of the domain wall tension and width, quantities controlling the creep motion of domain walls in such films.

Two-State Quantum Systems Revisited: A Clifford Algebra Approach

We revisit the topic of two-state quantum systems using Geometric Algebra (GA) in three dimensions $\mathcal G_3$. In this description, both the quantum states and Hermitian operators are written as elements of $\mathcal G_3$. By writing the quantum states as elements of the minimal left ideals of this algebra, we compute the energy eigenvalues and eigenvectors for the Hamiltonian of an arbitrary two-state system. The geometric interpretation of the Hermitian operators enables us to introduce an algebraic method to diagonalize these operators in GA. We then use this approach to revisit the problem of a spin-$1/2$ particle interacting with an external arbitrary constant magnetic field, obtaining the same results as in the conventional theory. However, GA reveals the underlying geometry of these systems, which reduces to the Larmor precession in an arbitrary plane of $\mathcal G_3$.

Noncommutativity of the static and homogeneous limit of the axial chemical potential in the chiral magnetic effect

We study the noncommutativity of different orders of zero energy-momentum limit pertaining to the axial chemical potential in the chiral magnetic effect. While this noncommutativity issue originates from the pinching singularity at one-loop order, it cannot be removed by introducing a damping term to the fermion propagators. The physical reason is that modifying the propagator alone would violate the axial-vector Ward identity and as a result a modification of the longitudinal component of the axial-vector vertex is required, which contributes to chiral magnetic effect (CME). The pinching singularity with free fermion propagators was then taken over by the singularity stemming from the dressed axial-vector vertex. We show this mechanism by a concrete example. Moreover, we proved, in general, the vanishing CME in the limit order that the static limit was taken prior to the homogeneous limit in the light of Coleman-Hill theorem for a static external magnetic field. For the opposite limit that the homogeneous limit is taken first, we show that the nonvanishing CME was a consequence of the nonrenormalization of chiral anomaly for an arbitrary external magnetic field.

Dynamical characteristic of entropic uncertainty relation in the long-range Ising model with an arbitrary magnetic field

In this work, we explore the quantum-memory-assisted entropic uncertainty relation (QMA-EUR) and the entanglement concurrence for the long-range Ising (LRI) model in the presence of an arbitrary magnetic field. The long-range interaction is considered as type of the Calogero–Moser interaction that is inversely proportional to the square of the distance between the spins. It is shown that the measurement’s uncertainty and the entanglement concurrence are extremely sensitive to the effects of the distance between spins, the magnitude, and the direction of the external magnetic field. The evaluation of the QMA-EUR is fully related to the entanglement concurrence in case of the LRI model. At larger distances between the spins, there is inflation in the measuring uncertainty due to the fragile entanglement between them. The evolutions of the entanglement and the uncertainty show only similar dynamical characteristics in antiferromagnetic and ferromagnetic frames when the magnetic field is perpendicular to the z-axis.

The Origin of Switchbacks in the Solar Corona: Linear Theory

Abstract The origin, structure, and propagation characteristics of a switchback are compelling questions posed by Parker Solar Probe (PSP) observations of velocity spikes and magnetic field reversals. By assuming interchange reconnection between coronal loop and open magnetic field, we show that this results in the generation of upward (into the heliosphere) and downward complex structures propagating at the fast magnetosonic speed (i.e., the Alfvén speed in the low plasma beta corona) that can have an arbitrary radial magnetic field deflection, including “S-shaped.” We derive the evolution equation for the switchback radial magnetic field as it propagates through the inhomogeneous supersonic solar corona. An analytic solution for arbitrary initial conditions is used to investigate the properties of a switchback propagating from launch ∼6 to ∼35 R ⊙ where PSP observed switchbacks during its first encounter. We provide a detailed comparison to an example event, showing that the magnetic field and plasma solutions are in accord with PSP observations. For a simple single switchback, the model predicts either a single or a double-humped structure; the former corresponding to PSP observing either the main body or the flanks of the switchback. The clustering of switchbacks and their sometimes complicated structure may be due to the formation of multiple closely spaced switchbacks created by interchange reconnection with numerous open and loop magnetic field lines over a short period. We show that their evolution yields a complex, aggregated group of switchbacks that includes “sheaths” with large-amplitude radial magnetic field and velocity fluctuations.

Origin and nature of the emissive sheath surrounding hot tungsten tokamak surfaces

The accurate description of the emitted current that escapes from hot tungsten surfaces is essential for reliable predictions of the macroscopic deformation due to melt motion induced by fast transient events. A comprehensive analytical electron emission model is developed and its implementation in the particle-in-cell 2D3V code SPICE2 is discussed. The properties of emissive sheaths of present tokamaks, where thermionic emission is strongly suppressed by space-charge effects and by prompt re-deposition, are reviewed for arbitrary magnetic field inclination angles. The unique characteristics of emissive sheaths that emerge during ITER ELMs, where weakly impeded thermionic emission is coupled with field emission and competes with electron-induced emission, are revealed. The first ITER simulations are reported for normal inclinations. • The properties of emissive sheaths relevant for present day tokamaks are reviewed. • A comprehensive electron emission model has been implemented in the SPICE2 PIC code. • Electron-induced electron emission is revealed to be important during ITER ELMs. • Thermionic emission is revealed to be coupled to field emission during ITER ELMs.

The zero-field resonance in optical pumping experiments

It is common for senior physics students at many universities to perform optical pumping experiments using a rubidium cell in an integrated apparatus. Such experiments provide an encounter with atomic structure in the context of a standard technique of modern atomic physics. Typically, students investigate radiofrequency resonances between Zeeman levels and measure hyperfine splitting. Despite its pivotal role in aligning the apparatus the so-called zero-field resonance is usually not investigated in such experiments. However it is instructive to look more closely at this phenomenon. We show that it is a consequence of a residual transverse magnetic field that is the result of the inability to align precisely the optical axis of the apparatus in the local N–S direction. The measured width and depth of the resonance-like minimum in transmission is found to be consistent with a very small relaxation rate for the rubidium atoms. In an appendix we show further that the measurements compare well with theory for the Hanle effect in the ground state for an arbitrary magnetic field direction relative to the optical axis of the experiment.

General solution for rapid scan EPR deconvolution problem

A general solution for the RS EPR deconvolution problem has been derived. This solution permits the use of arbitrary magnetic field scans. As a result, constraints on the current experimental designs can be lifted. For example, a trapezoidal waveform can be used to accelerate the scan rate without affecting the signal bandwidth. The assumptions made to develop the previous algorithms are mathematically validated.

Importance of Angle-dependent Partial Frequency Redistribution in Hyperfine Structure Transitions Under the Incomplete Paschen–Back Effect Regime

Abstract Angle-frequency coupling in scattering of polarized light on atoms is represented by the angle-dependent (AD) partial frequency redistribution (PRD) matrices. There are several lines in the linearly polarized solar spectrum, for which PRD combined with quantum interference between hyperfine structure states play a significant role. Here we present the solution of the polarized line transfer equation including the AD-PRD matrix for scattering on a two-level atom with hyperfine structure splitting and an unpolarized lower level. We account for the effects of arbitrary magnetic fields (including the incomplete Paschen–Back effect regime) and elastic collisions. For exploratory purposes we consider a self-emitting isothermal planar atmosphere and use atomic parameters that represent an isolated Na i D2 line. For this case we show that the AD-PRD effects are significant for field strengths below about 30 G, but that the computationally much less demanding approximation of angle-averaged PRD may be used for stronger fields.

Sensitivity Kernels for Inferring Lorentz Stresses from Normal-mode Frequency Splittings in the Sun

Abstract Departures from standard spherically symmetric solar models, in the form of perturbations such as global and local-scale flows and structural asphericities, result in the splitting of eigenfrequencies in the observed spectrum of solar oscillations. Drawing from prevalent ideas in normal-mode-coupling theory in geophysical literature, we devise a procedure that enables the computation of sensitivity kernels for general Lorentz-stress fields in the Sun. Mode coupling due to any perturbation requires careful consideration of self- and cross coupling of multiplets. Invoking the isolated-multiplet approximation allows for limiting the treatment to purely self coupling, requiring significantly less computational resources. We identify the presence of such isolated multiplets under the effect of Lorentz stresses in the Sun. Currently, solar missions allow for precise measurements of self coupling of multiplets via “a-coefficients” and the cross-spectral correlation signal that enables the estimation of the “structure coefficients”. We demonstrate the forward problem for both self coupling (a-coefficients) and cross coupling (structure coefficients). In doing so, we plot the self-coupling kernels and estimate a-coefficients arising from a combination of deep-toroidal and surface-dipolar axisymmetric fields. We also compute the structure coefficients for an arbitrary general magnetic field (real and solenoidal) and plot the corresponding “splitting function”, a convenient way to visualize the splitting of multiplets under 3D internal perturbations. The results discussed in this paper pave the way to formally pose an inverse problem and infer solar internal magnetic fields.