Component Of Vector Potential Research Articles

Weakly guiding approximation of a three-dimensional waveguide model for extreme ultraviolet lithography simulation

A three-dimensional (3D) waveguide model is applied in extreme ultraviolet (EUV) lithography simulations. The 3D waveguide model is equivalent to rigorous coupled-wave analysis, but fewer field components are used to solve Maxwell’s equations. The 3D waveguide model uses two components of vector potential, A x and A y , corresponding to the two polarizations. The electric field of the A x polarization is approximately parallel to the x axis, and the electric field of the A y polarization is approximately parallel to the y axis. The 3D waveguide model solves a coupled vector wave equation for two polarizations. The refractive index of conventional EUV absorbers is close to that of vacuum. The weakly guiding approximation in optical fiber theory is applied to the 3D waveguide model. The coupled vector wave equations for the two polarizations are decoupled into two independent scalar wave equations. Maxwell’s equations are simplified to a set of scalar wave equations. The weakly guiding approximation reduces the computation time to solve the equations. The computation time required to solve the weakly guiding approximation is about 1/5 of the time to solve the original 3D waveguide model.

Photon quantization in cosmological spaces

Canonical quantization of the photon—a free massless vector field—is considered in cosmological spacetimes in a two-parameter family of linear gauges that treat all the vector potential components on equal footing. The goal is setting up a framework for computing photon two-point functions appropriate for loop computations in realistic inflationary spacetimes. The quantization is implemented without relying on spacetime symmetries, but rather it is based on the classical canonical structure. Special attention is paid to the quantization of the canonical first-class constraint structure that is implemented as the condition on the physical states. This condition gives rise to subsidiary conditions that the photon two-point functions must satisfy. Some of the de Sitter space photon propagators from the literature are found not to satisfy these subsidiary conditions, bringing into question their consistency. Published by the American Physical Society 2024

Prediction of novel effects in rotational nuclei at high speed

The study of high-speed rotating matter is a crucial research topic in physics due to the emergence of novel phenomena. In this letter, we combined cranking covariant density functional theory (CDFT) with a similarity renormalization group approach to decompose the Hamiltonian from the cranking CDFT into different Hermite components, including the non-relativistic term, the dynamical term, the spin-orbit coupling, and the Darwin term. Especially, we obtained the rotational term, the term relating to Zeeman-like effect, and the spin-rotation coupling due to consideration of rotation and spatial component of vector potential. By exploring these operators, we aim to identify novel phenomena that may occur in rotating nuclei. Signature splitting, Zeeman-like effect, and spin-rotation coupling are among the potential novelties that may arise in rotating nuclei. Additionally, we investigated the observability of these phenomena and their dependence on various factors such as nuclear deformation, rotational angular velocity, and magnetic field-like strength.

Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov–Maxwell equilibria

The construction of kinetic equilibrium states is important for studying stability and wave propagation in collisionless plasmas. Thus, many studies over the past decades have been focused on calculating Vlasov–Maxwell equilibria using analytical and numerical methods. However, the problem of kinetic equilibrium of hybrid models is less studied, and self-consistent treatments often adopt restrictive assumptions ruling out cases with irregular and chaotic behaviour, although such behaviour is observed in spacecraft observations of space plasmas. In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid Vlasov–Maxwell equilibrium model with kinetic ions and massless fluid electrons and derive associated solutions. The model allows for an electrostatic potential that is expressed in terms of the vector potential components through the quasineutrality condition. The equilibrium states are calculated upon solving an inhomogeneous Beltrami equation that determines the magnetic field, where the inhomogeneous term is the current density of the kinetic ions and the homogeneous term represents the electron current density. We show that the corresponding 1-D system is Hamiltonian, with position playing the role of time, and its trajectories have a regular, periodic behaviour for ion distribution functions that are symmetric in the two conserved particle canonical momenta. For asymmetric distribution functions, the system is nonintegrable, resulting in irregular and chaotic behaviour of the fields. The electron current density can modify the magnetic field phase space structure, inducing orbit trapping and the organization of orbits into large islands of stability. Thus, the electron contribution can be responsible for the emergence of localized electric field structures that induce ion trapping. We also provide a paradigm for the analytical construction of hybrid equilibria using a rotating two-dimensional harmonic oscillator Hamiltonian, enabling the calculation of analytic magnetic fields and the construction of the corresponding distribution functions in terms of Hermite polynomials.

Theoretical Predictions of Perturbed Magnetic Flux Density Components Due to Narrow Flaws in ECT

This work proposes a semianalytical technique based on the boundary element method (BEM) to predict the signals due to flaws (cracks) that are typically encountered in eddy current (ECT) nondestructive testing (NDT). Two case studies, for two different narrow opening notches in a finite thickness aluminium plate, were performed by experimental measurements to corroborate the theoretical model. The signal which has been modelled is the perturbation in the magnetic flux density (MFD) components <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B_x</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B_y</i> , and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B_z</i> due to narrow opening flaws. The proposed analytical model uses the magnetic vector potential (MVP), arising from electric dipole sources, to determine the voltage induced in a hypothetical small circular loop located around the evaluation point. Based on the linear relationship between the voltage induced and the magnetic flux in the surface enclosed by the hypothetical loop, a linearity constant that transforms the induced voltage to the MFD component has been computed. Appropriate vector potential Green’s functions have been used to transform the electric dipole sources to the magnetic vector potential components to determine the voltage induced in the hypothetical loop.

The evaluation of the interaction potential of two non-polar molecules in Green function approach

In this research, by assuming that the vacuum electric field fluctuations can convert a molecule (or an atom) into an oscillating electric dipole, the interaction potential of the two atoms or two non-polar molecules is calculated in terms of the molecular polarizabilities and the distance between them. Considering the net electric field at the position of a molecule as a sum of the vacuum electric field and the electric field due to the induced electric dipole of the other molecule, and substituting in the quadratic stark shift formula, the interaction potential of the two molecules is related to the vacuum electric field correlation function. By writing the interaction potential in terms of the imaginary parts of vector potential Green function tensor components (via the fluctuation- dissipation theorem and Kubo’s formula in statistical mechanics) and computing the required Green function components, the interaction potential between the two molecules is evaluated. The small and large distances limits of the general formula investigated and the consistencies with the previous works are shown.‎

Active Electric Dipole Energy Sources: Transduction via Electric Scalar and Vector Potentials.

The creation of electromagnetic energy may be realised by engineering a device with a method of transduction, which allows an external energy source, such as mechanical, chemical, nuclear, etc., to be impressed into the electromagnetic system through a mechanism that enables the separation of opposite polarity charges. For example, a voltage generator, such as a triboelectric nanogenerator, enables the separation of charges through the transduction of mechanical energy, creating an active physical dipole in the static case, or an active Hertzian dipole in the time-dependent case. The net result is the creation of a static or time-dependent permanent polarisation, respectively, without an applied electric field and with a non-zero vector curl. This system is the dual of a magnetic solenoid or permanent magnet excited by a circulating electrical current or fictitious bound current, respectively, which supplies a magnetomotive force described by a magnetic vector potential and a magnetic geometric phase proportional to the enclosed magnetic flux. Thus, the active electric dipole voltage generator has been described macroscopically by a circulating fictitious magnetic current boundary source and exhibits an electric vector potential with an electric geometric phase proportional to the enclosed electric flux density. This macroscopic description of an active dipole is a semi-classical average description of some underlying microscopic physics, which exhibits emergent nonconservative behaviour not found in classical closed-system laws of electrodynamics. We show that the electromotive force produced by an active dipole in general has both electric scalar and vector potential components to account for the magnitude of the electromotive force it produces. Independent of the electromagnetic gauge, we show that Faraday’s and Ampere’s law may be derived from the time rate of change of the magnetic and dual electric geometric phases. Finally, we analyse an active cylindrical dipole in terms of scalar and vector potential and confirm that the electromotive force produced, and hence potential difference across the terminals is a combination of vector and scalar potential difference depending on the aspect ratio (AR) of the dipole. For long thin active dipoles (AR approaches 0), the electric field is suppressed inside, and the voltage is determined mainly by the electric vector potential. For large flat active dipoles (AR approaches infinity), the electric flux density is suppressed inside, and the voltage is mainly determined by the scalar potential.

An Integrated Methodology to Assess AC Losses in the kHz Range Using the FEM and Partial Element Equivalent Circuit

This article proposes a new approach using the T-A formulation coupled to lumped parameters in the electrical circuit, considering the skin-depth approach. The finite-element method models the superconducting layer, the electrical circuit models the stabilizer and substrate layers as lumped parameters, and a coupling engine links both of them. The ac losses have been calculated by both T-A 1-D and T-A 2-D formulations: the first one uses the approach proposed in this article, and the second, two current vector potential components. For the three formulations, we have studied the average power dissipation as a function of frequency and current, and the peak current as a function of the frequency. We have compared the T-A 1-D and T-A 2-D formulations to H formulation results previously studied. Comparing the results of the average power dissipation, we have found the maximum error to be around 10.5% in T-A 1-D and 35% found in T-A 2-D. The efficiency of the proposed technique was evaluated as 16 times less costly when compared to the T-A 2-D formulation.

Спектры излучения в потоках ионизующихся газов для установки КСПУ-Т с продольным полем

The results of calculations of the spectral and integral characteristics of radiation in flows of ionizing gases in the channel of the quasi-stationary plasma accelerator in the presence of an additional longitudinal magnetic field are presented. The numerical model of the radiative magnetogasdynamics is based on the modified transport equations for the multicomponent medium consisting of atoms, ions, and electrons. The MHD equations for two-dimensional axisymmetric flows are presented in terms of the azimuthal components of magnetic field and vector potential of magnetic field, taking into account the electrical conductivity, thermal conductivity, and radiation transport. The spectral and integral characteristics of radiation were determined within the framework of the 3D model using the method of long characteristics in the multigroup approximation.

Light scattering of Laguerre-Gaussian vortex beams by arbitrarily shaped chiral particles.

Laguerre-Gaussian (LG) beams with vortex phase possess a handedness, which would produce chiroptical interactions with chiral matter and may be used to probe structural chirality of matter. In this paper, we numerically investigate the light scattering of LG vortex beams by chiral particles. Using the vector potential method, the electric and magnetic field components of the incident LG vortex beams are derived. The method of moments (MoM) based on surface integral equations (SIEs) is applied to solve the scattering problems involving arbitrarily shaped chiral particles. The numerical results for the differential scattering cross sections (DSCSs) of several selected chiral particles illuminated by LG vortex beams are presented and analyzed. In particular, we show how the DSCSs depend on the chiral parameter of the particles and on the parameters describing the incident LG vortex beams, including the topological charge, the state of circular polarization, and the beam waist. This research may provide useful insights into the interaction of vortex beams with chiral particles and its further applications.

Multipolar, polarization-shaped high-order harmonic generation by intense vector beams

High harmonic generation (HHG) is a manifestation of the strongly nonlinear response of matter to intense laser fields and has, as the basis for coherent XUV sources a variety of applications. Recently, HHG from atoms in a phase and polarization structured laser was demonstrated and interpreted based on the transverse electric field component of the driving pulse. Here we point out that as dictated by Maxwell equations, such fields have a longitudinal component which in general has a fundamental influence on the charge dynamics. For instance, its interplay with the transversal field component enables endowing the emitted radiation locally with circular polarization and a defined polarity. It is shown that the time-dependent Stokes parameters defining the polarization state of HHG can be tuned by varying the waist of the driving field which in turn, changes the ratio between the longitudinal and transverse electric-field components of the driving laser. In addition, employing a multipole expansion of the produced harmonics exposes the specific multipolar character and the relation to the spatial structure of the driving field polarization states. The scheme proposed here allows a full polarization control of the emitted harmonics by only one driving laser. A tighter focusing of the driving pulse renders possible the emission of harmonics with both even and odd spatial symmetry. The underlying mechanism is due to the fundamental interplay between the transverse and longitudinal components of the laser's electromagnetic vector potential. The ratio between those components is controllable by just focusing the laser spot, pointing to an accessible tool for polarization and polarity control of the high harmonics.

The Interaction Potential between an Atom and a Conductive Wall

In this work, the interaction potential between an atom (with definite Static Polarizability) and a perfect neutral conductive wall is evaluated in two approaches. First, using, the explicit form of the singlet and doublet parts of the vacuum vector potential operator in atomic quadratic stark shift formula and taking the expectation value in vacuum state. Second, writing, the quadratic stark shift formula in terms of electric field correlation function, relating the correlation function to the imaginary parts of the vector potential Green function tensor components (via fluctuation dissipation theorem in statistical mechanics) and the evaluation of the required vector potential Green function tensor components. The consistency of the two methods is shown.

Celestial current algebra from Low’s subleading soft theorem

The leading soft photon theorem implies that four-dimensional scattering amplitudes are controlled by a two-dimensional (2D) $U(1)$ Kac-Moody symmetry that acts on the celestial sphere at null infinity ($\mathcal{I}$). This celestial $U(1)$ current is realized by components of the electromagnetic vector potential on the boundaries of $\mathcal{I}$. Here, we develop a parallel story for Low's subleading soft photon theorem. It gives rise to a second celestial current, which is realized by vector potential components that are subleading in the large radius expansion about the boundaries of $\mathcal{I}$. The subleading soft photon theorem is reexpressed as a celestial Ward identity for this second current, which involves novel shifts by one unit in the conformal dimension of charged operators.

Building Up Solar-wind-like 3D Uniform-intensity Magnetic Fields

Abstract A numerical model representing a 3D turbulent constant-magnitude magnetic field B is described. Assuming a form for two components of the vector potential, the third component is calculated such as to obtain a uniform intensity for B . Singular surfaces are always present in the solution, in the form of rotational discontinuities. Using a spectrum for derivatives of the given vector potential components that satisfies the critical-balance condition, an anisotropic spectrum for B is obtained, with a prevalence of perpendicular wavevectors k ⊥ and a Kolmogorov power-law range with respect to k ⊥. These features make the model suitable to represent magnetic turbulence in solar wind fast-speed streams.

Analytical Solutions of Eddy-Current Problems in a Finite Length Cylinder

Magnetic field and eddy currents in a cylinder of finite length are calculated by separation of variables. The magnetic field outside the cylinder or inside the bore of the hollow cylinder and shell is expressed in terms of Bessel functions. Both axial and transverse applied fields are considered for the solid and hollow cylinders. The equations for the vector potential components are transformed in one-dimensional equations along the radial coordinate with the consequent integration by the method of variation of parameters. The equation for the scalar electric potential when required is also integrated analytically. Expressions for the magnetic moment and loss are derived. An alternative analytical solution in terms of scalar magnetic potential is derived for the finite length thin shells. All formulas are validated by the comparison with the solutions by finite–element and finite-difference methods.

TMz/TEz Vector Potentials Due to an Arbitrarily Oriented Dipole in 3‐D Space in the Presence of an Infinite Dielectric Cylinder

AbstractThis manuscript provides a new formulation for the classic electromagnetic scattering problem of a point dipole source in the presence of an infinite lossy dielectric cylinder embedded within a lossy space. The formulation is in terms of the TMz and TEz vector potential components (scalar potentials) Az and Fz for an arbitrary dipole orientation. A new Bessel function identity, apparently derived here for the first time, shows that the new solution is equivalent to the previous dyadic vector wave function solutions that solve for the electric and magnetic fields directly. Expressions for the scattered potential coefficients, for a dipole inside or outside the cylinder, can be reduced to a linear set of two equations that has a simple closed‐form solution. The new potential formulation should find application in the numerical solution of various problems in electromagnetics and geophysics involving tunnels or other structures that can be modeled as cylinders.

Axial magnetic field and toroidally streaming fast ions in the dense plasma focus are natural consequences of conservation laws in the curved axisymmetric geometry of the current sheath. II. Towards a first principles theory

This paper continues earlier discussion [S. K. H. Auluck, Phys. Plasmas 21, 102515 (2014)] concerning the formulation of conservation laws of mass, momentum, and energy in a local curvilinear coordinate system in the dense plasma focus. This formulation makes use of the revised Gratton-Vargas snowplow model [S. K. H. Auluck, Phys. Plasmas 20, 112501 (2013)], which provides an analytically defined imaginary surface in three dimensions which resembles the experimentally determined shape of the plasma. Unit vectors along the local tangent to this surface, along the azimuth, and along the local normal define a right-handed orthogonal local curvilinear coordinate system. The simplifying assumption that physical quantities have significant variation only along the normal enables writing laws of conservation of mass, momentum, and energy in the form of effectively one-dimensional hyperbolic conservation law equations using expressions for various differential operators derived for this coordinate system. This formulation demonstrates the highly non-trivial result that the axial magnetic field and toroidally streaming fast ions, experimentally observed by multiple prestigious laboratories, are natural consequences of conservation of mass, momentum, and energy in the curved geometry of the dense plasma focus current sheath. The present paper continues the discussion in the context of a 3-region shock structure similar to the one experimentally observed: an unperturbed region followed by a hydrodynamic shock containing some current followed by a magnetic piston. Rankine-Hugoniot conditions are derived, and expressions are obtained for the specific volumes and pressures using the mass-flux between the hydrodynamic shock and the magnetic piston and current fraction in the hydrodynamic shock as unknown parameters. For the special case of a magnetic piston that remains continuously in contact with the fluid being pushed, the theory gives closed form algebraic results for the fraction of current flowing in the hydrodynamic shock, specific volume, pressure, and fluid velocity of the hydrodynamic shock region, the tangential, normal, and azimuthal components of velocity in the magnetized plasma, the density of the magnetized plasma, the normal and tangential components of the magnetic field, and the tangential, normal, and azimuthal components of the electric field. This explains the occurrence of azimuthally streaming high energy deuterons experimentally observed by Frascati and Stuttgart. The expression derived for the azimuthal component of vector potential can serve as the basis for a proposed experimental test of the theory.

Quantum phase transition and unusual critical behavior in multi-Weyl semimetals

The low-energy behaviors of gapless double- and triple-Weyl fermions caused by the interplay of long-range Coulomb interaction and quenched disorder are studied by performing a renormalization group analysis. It is found that an arbitrarily weak disorder drives the double-Weyl semimetal to undergo a quantum phase transition into a compressible diffusive metal, independent of the disorder type and the Coulomb interaction strength. In contrast, the nature of the ground state of triple-Weyl fermion system relies sensitively on the specific disorder type in the noninteracting limit: The system is turned into a compressible diffusive metal state by an arbitrarily weak random scalar potential or $z$ component of random vector potential but exhibits stable critical behavior when there is only $x$ or $y$ component of random vector potential. In case the triple-Weyl fermions couple to random scalar potential, the system becomes a diffusive metal in the weak interaction regime but remains a semimetal if Coulomb interaction is sufficiently strong. Interplay of Coulomb interaction and $x$, or $y$, component of random vector potential leads to a stable infrared fixed point that is likely to be characterized by critical behavior. When Coulomb interaction coexists with the $z$ component of random vector potential, the system flows to the interaction-dominated strong coupling regime, which might drive a Mott insulating transition. It is thus clear that double- and triple-Weyl fermions exhibit distinct low-energy behavior in response to interaction and disorder. The physical explanation of such distinction is discussed in detail. The role played by long-range Coulomb impurity in triple-Weyl semimetal is also considered.

Bianchi type I universe filled with scalar field coupled with electromagnetic fields in f(R, T) theory of gravity

In f(R, T) theory of gravity, we have studied the interacting scalar and electromagnetic fields in Bianchi type I space–time, by considering the general cases f(R, T) = f 1(R) + λf 2(T), \(f\left( {R,T} \right) = f_{1} \left( R \right)f_{2} \left( T \right)\) and f(R) theory and its particular cases f(R, T) = R + λT, \(f\left( {R,T} \right) = RT\), f(R) = R. It is observed that, even though the cases of f(R, T) are distinct, the convergent and isotropic solution of metric functions can be evolved in each case along with the components of vector potential, corresponding to suitable integrable function in particular cases.

Scattering of electromagnetic plane wave from a perfect electric conducting strip placed at interface of topological insulator–chiral medium

In this manuscript, scattering from a perfect electric conducting strip located at planar interface of topological insulator (TI)–chiral medium is investigated using the Kobayashi Potential method. Longitudinal components of electric and magnetic vector potential in terms of unknown weighting function are considered. Use of related set of boundary conditions yields two algebraic equations and four dual integral equations (DIEs). Integrand of two DIEs are expanded in terms of the characteristic functions with expansion coefficients which must satisfy, simultaneously, the discontinuous property of the Weber–Schafheitlin integrals, required edge and boundary conditions. The resulting expressions are then combined with algebraic equations to express the weighting function in terms of expansion coefficients, these expansion coefficients are then substituted in remaining DIEs. The projection is applied using the Jacobi polynomials. This treatment yields matrix equation for expansion coefficients which is solved numerically. These unknown expansion coefficients are used to find the scattered field. The far zone scattering width is investigated with respect to different parameters of the geometry, i.e, chirality of chiral medium, angle of incidence, size of the strip. Significant effects of different parameters including TI parameter on the scattering width are noted.