Abstract Efficient laser-target energy coupling is of critical importance in inertial confinement fusion, where collisional absorption and laser-plasma instabilities (LPIs) compete to determine overall energy deposition. However, few studies have simultaneously captured both collisional absorption and LPIs, particularly in the kinetic regime. In this work, we develop a code capable of performing unified kinetic simulations of these two kinds of competing processes on sub-nanosecond timescales. The code builds upon a previous one-dimensional particle-mesh code PM1D, which was originally designed to simulate only LPIs, by self-consistently incorporating various collisional effects. It integrates collisional absorption and collisional damping terms into the electromagnetic wave equation and the motion equations for electrons and ions, coupled with the temperature evolution equations that describe energy deposition and thermal equilibration. Numerical tests verify that the upgraded PM1D code accurately simulates collisional effects across a broad range of laser-plasma parameters while maintaining robust numerical stability and high computational efficiency. Our simulations further reveal that collisional damping can effectively suppress stimulated Brillouin scattering, while its direct impact on stimulated Raman scattering (SRS) is negligible. Notably, collisional effects not only contribute directly to collisional absorption but can also enhance the anomalous absorption driven by various LPI processes. Moreover, the increase in plasma temperature resulting from collisional absorption elevates the electron plasma wave frequency, which may manifest as an experimentally observable redshift of the SRS scattered light. This work therefore establishes a robust numerical framework for investigating the complex interplay between collisional processes and LPIs in laser-target coupling.

A bstract We study novel conformal twist defects in 4d Maxwell theory, around which electric and magnetic fields are exchanged. These are codimension-2 defects living at the end of topological defects for certain non-invertible global symmetries. We determine the operator spectrum of the twist defect by solving classical electromagnetic wave equations subject to a twisted boundary condition. Using techniques from defect CFT, we show that correlation functions of these defect operators factorize into two sectors: a universal generalized free-field sector, and a chiral current sector analogous to edge modes in Chern-Simons theory. In a similar setup, we also revisit the twist fields attached to non-invertible line defects in the 2d compact boson CFT. We discuss a defect ’t Hooft anomaly involving a chiral O (2) symmetry, highlighting its dynamical implications.

Abstract This article investigates the Lie-algebraic properties of a Davey–Stewartson type system of differential equations in three space dimensions. We determine that, the invariance algebra includes an infinite-dimensional Kac–Moody algebra. In addition, we obtain several analytical solutions in explicit form.

Artificial composite materials that focus on electromagnetic waves are known as metamaterials. Metamaterials are artificial materials engineered by human technology, possessing a geometric structure built from microscopic, engineerable materials. The goal is for the new material to be able to direct light, sound, and waves, making it useful. Metamaterials are known as left-handed materials (LHMs), but the concept of metamaterials is broader than LHM. The purpose of this research is to solve the transverse electric (TE) and transverse magnetic (TM) electromagnetic wave equations in left-handed materials (LHMs) using the Nikiforov-Uvarov approach and to analyze the results of the energy spectrum equation from the solution of the transverse electric (TE) and transverse magnetic (TM) electromagnetic wave equations in left-handed medium (LHM). This research was conducted using Matlab software. The material being studied is the positive-negative gradient profile in an LHM medium thru variations in dielectric permittivity and/or magnetic permeability. Energy and wave equations were obtained with their visualization.

By solving Maxwell's equations the exact dispersion equation for electromagnetic waves propagating in a layered coaxial ferrite line is obtained. In particular the analytical consideration is carried out for a simpler case of complete filling of the coaxial line with ferrite (i.e. gomogeneous ferrite line). The behavior of dispersion curves of TEM-electromagnetic waves, as well as E- and H-waveguide electromagnetic waves, is investigated.

We present a closed-form solution for the electromagnetic wave equation that governs propagation in a spatially unbounded, linear time-varying gaseous plasma. Using a proper change of variable, the wave equation is converted into the Lommel's transformed version of the Bessel differential equation. The analytical wave functions in time are then expressed in terms of Bessel functions of the first kind with complex orders, which appears to be a very rare case in physical problems. Unlike previous analytical treatments of the problem, such as the use of adiabatic and Laplace transform approximations, which deal with slow and fast rise times of the plasma, respectively, the solution presented here imposes no constraints on the rise time relative to the time period of the source wave.

It has been a common view that electromagnetic wave equation in vacuum cannot be obtained with Weber’s electrodynamics. With a polarizable vacuum postulate, an electric wave equation was recently derived from Weber’s electrodynamics. However, this wave equation only applies to longitudinal wave propagation. It does not work for transverse wave since it requires non-zero divergence of electric field. In this paper, we try to derive a wave equation for transverse wave propagation using the curl component of electric field with zero divergence.

Until now, we do not know whether elementary particles have structure, but we cannot assert that elementary particles do not have structure, because all experiences tell us that the properties of non-living and living things are closely related to their structure. As their foundation, can the microscopic particles be excluded? Do photons and charged fermions have structure? What structure? We study the key to the Schrödinger computation that accurately reproduce the energy levels of the Bohr model and the general solution of Schrödinger equation mathematically; we found to satisfy Schrödinger equation the charged fermions must possess a double helix structure of mass density. Such structures plus partial self-rotation make them quantized and a fixed value spin or . We prove that the Maxwell wave equation is simultaneously the Klein-Gordon equation for electromagnetic waves. Then we prove that photons have a double helix structure of EH-energy that makes photons quantized and a fixed value spin or . There is a charge in the electron (and charged fermions); a pair of charges in the photons, they distribute double helically along their side boundaries; these charges produce and carry a circular polarized E-wave and EH-wave respectively. They form two traveling-wave-particle hybrid structures. It is such hybrid structures give them traveling-wave-particle duality. Such dualities can exhibit their wave property and particle property simultaneously in the same experiments. At last, we prove that the electron cloud photo not only exhibits the probability distribution of electrons but also proves the existence of electrons’ trajectories around the nucleus; the electrons’ motions make the probability distribution. The electron probability distribution around the nucleus is causal. At last we prove that the electron in the main shells (the Eigen states) of a multi-electron atom does not radiate pure EM energy, not fall to the nucleus.

After studying null geodesics in the equatorial plane in NUT spacetime, we show that there are unstable photon rings in this plane. Next, we transform the metric of this plane to the isotropic coordinates and introduce its equivalent two-parameter index of refraction. Utilizing the analog gravity concepts, we assign this index of refraction to a metamaterial analog of this plane, and by ray-tracing simulation find its photon rings. Furthermore, we extend our analysis to the charged NUT spacetime and employ wave optics to numerically solve Maxwell's equations for electromagnetic waves within an inhomogeneous medium assigned with this spacetime's three-parameter index of refraction. We investigate the optical properties of such metamaterial analogs for designing enhanced and fine-tuned optical devices.

Momentary analysis of the electromagnetic radiation of gabbro rock under compressive stress

Due to its low symmetry, $\ensuremath{\beta}$-${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ exhibits a strongly anisotropic optical response. As a result, the absorption spectra change with the polarization state of the incoming photons. To understand this phenomenon, here we calculate the complete electromagnetic wave equation solutions as a function of linear polarization angle and photon energy for $\ensuremath{\beta}$-${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ using its previously measured complex dielectric function tensor. The significant off-diagonal terms in this tensor can result in a nonexponential decay in the photon flux, indicating that the Beer-Lambert law is not generally valid in this anisotropic material. However, for above-band-gap spectral regions that depend on crystallographic orientations [>5.8 eV (001-plane) and >5.2 eV (010-plane)], an effective absorption coefficient closely approximates the photon flux decay with depth. On the other hand, near the optical absorption edge [4.9--5.8 eV (001-plane) and 4.65--5.2 eV (010-plane)], the photon flux decay exhibits a sum of two exponential decays, such that two effective absorption coefficients are necessary to model the loss behavior versus the absorption depth. This behavior manifests from the presence of dichroism in $\ensuremath{\beta}$-${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. A single effective absorption coefficient can only be recovered for this energy range by augmenting the isotropic Beer-Lambert law with a critical penetration depth and polarization dependence. Using these results, we calculate the polarization-dependent photoresponsivity spectra for light polarized along different crystallographic directions.

The current response of a hot magnetized plasma to a radio-frequency wave is non-local, turning the electromagnetic wave equation into an integro-differential equation. Non-local physics gives rise to wave physics and absorption processes not observed in local media. Furthermore, non-local physics alters wave propagation and absorption properties of the plasma. In this work, an iterative method that accounts for parallel non-local effects in 2D axisymmetric tokamak plasmas is developed, implemented, and verified. The iterative method is based on the finite element method and Fourier decomposition, with the advantage that this numerical scheme can describe non-local effects while using a high-fidelity antenna and wall representation, as well as limiting memory usage. The proposed method is implemented in the existing full wave solver FEMIC and applied to a minority heating scenario in ITER to quantify how parallel non-local physics affect wave propagation and dissipation in the ion cyclotron range of frequencies (ICRF). The effects are then compared to a reduced local plane wave model, both verifying the physics implemented in the model, as well as estimating how well a local plane wave approximation performs in scenarios with high single pass damping. Finally, the new version of FEMIC is benchmarked against the ICRF code TORIC.

An optimized design of a spintronic terahertz emitter has been developed, based on a bilayer Co/Pt structure with an integrated distributed Bragg reflector. The incorporation of the Bragg mirror between the Co/Pt structure and the silicon substrate enhances optical absorption in the ferromagnetic layer, thereby amplifying spin current generation and, consequently, THz signal. A model was developed for calculating the optical absorption in the ferromagnetic layer of the spintronic emitter, taking into account the parameters of the Bragg mirror (layer thicknesses, period) based on the superlattice structure [TiO2/SiO2]N. This model is grounded on the solution of Maxwell's equations for electromagnetic waves using the COMSOL Multiphysics software. The effect of anti-reflective dielectric coatings on the level of optical absorption in the ferromagnetic layer was also analyzed. The study confirmed that using the optimized Bragg mirror is sufficient for achieving optimal absorption.

Maxwell’s equations and the Dirac equation are the first-order differential relativistic wave equation for electromagnetic waves and electronic waves respectively. Hence, there is a notable similarity between these two wave equations, which has been widely researched since the Dirac equation was proposed. In this paper, we show that the Maxwell equations can be written in an exact form of the Dirac equation by representing the four Dirac operators with 8×8 matrices. Unlike the ordinary 4×4 Dirac equation, both spin–1/2 and spin–1 operators can be derived from the 8×8 Dirac equation, manifesting that the 8×8 Dirac equation is able to describe both electrons and photons. As a result of the restrictions that the electromagnetic wave is a transverse wave, the photon is a spin–1 particle. The four–current in the Maxwell equations and the mass in the electronic Dirac equation also force the electromagnetic field to transform differently to the electronic field. We use this 8×8 representation to find that the Zitterbewegung of the photon is actually the oscillatory part of the Poynting vector, often neglected upon time averaging.

This paper presents a new theory of gravity, called here Ashtekar-Kodama (AK) gravity, which is based on the Ashtekar-Kodama formulation of loop quantum gravity (LQG), yields in the limit the Einstein equations, and in the quantum regime a full renormalizable quantum gauge field theory. The three fundamental constraints (hamiltonian, gaussian and diffeomorphism) were formulated in 3-dimensional spatial form within LQG in Ashtekar formulation using the notion of the Kodama state with positive cosmological constant Λ. We introduce a 4-dimensional covariant version of the 3-dimensional (spatial) hamiltonian, gaussian and diffeomorphism constraints of LQG. We obtain 32 partial differential equations for the 16 variables Emn (E-tensor, inverse densitized tetrad of the metric) and 16 variables Amn (A-tensor, gravitational wave tensor). We impose the boundary condition: for large distance the E-generated metric g(E) becomes the GR-metric g (normally Schwarzschild-spacetime). The theory based on these Ashtekar-Kodama (AK) equations, and called in the following Ashtekar-Kodama (AK-) gravity has the following properties. • For Λ = 0 the AK equations become Einstein equations, A-tensor is trivial (constant), and the E-generated metric g(E) is identical with the GR-metric g. • When the AK-equations are developed into a Λ-power series, the Λ-term yields a gravitational wave equation, which has only at least quadrupole wave solutions and becomes in the limit of large distance r the (normal electromagnetic) wave equation. • AK-gravity, as opposed to GR, has no singularity at the horizon: the singularity in the metric becomes a (very high) peak. • AK-gravity has a limit scale of the gravitational quantum region 39 μm, which emerges as the limit scale in the objective wave collapse theory of Gherardi-Rimini-Weber. In the quantum region, the AK-gravity becomes a quantum gauge theory (AK quantum gravity) with the Lie group extended SU(2) = ε-tensor-group(four generators) as gauge group and a corresponding covariant derivative. • AK quantum gravity is fully renormalizable, we derive its Lagrangian, which is dimensionally renormalizable, the normalized one-graviton wave function, the graviton propagator, and demonstrate the calculation of cross-section from Feynman diagrams.

This paper investigates discrete symmetries for dyon and the invariance of Maxwell’s field equations in the macroscopic media (material medium). Using advanced mathematical approaches, the paper derived electromagnetic duality and a unique form of Poynting theorem for dyon in macroscopic media. Here, we demonstrate that the combination of parity [Formula: see text], charge conjugation [Formula: see text], and time reversal [Formula: see text] symmetry: [Formula: see text], is an exact symmetry for dyon in macroscopic media. Furthermore, a comprehensive analysis of the electromagnetic wave equation for dyons in conducting media is also derived. These findings contribute significantly to the understanding of dyon behavior in electromagnetic fields.

Frequency response analysis offers an insight about the integrity of machine windings, when employed as a tool for condition monitoring. To ensure that, an electromagnetic wave is injected from one terminal of winding, and the power of the wave at the receiving terminal is measured. The power at the terminals is measured in terms of either voltage or current. This difference in power at the two terminals can be attributed to the medium's permittivity, permeability and conductivity, through which the signal is being transmitted. This paper offers an explanation for the behavior of the voltage gain frequency response of induction motor winding and propagating medium parameters by employing the fundamental electromagnetic wave equations. Their explanation illustrates how these parameters can affect the response. The correlation established using Maxwell's equation and these parameters with frequency response analysis is evident while identifying open winding fault and issue with machine core inductance. The results are analyzed and interpreted with the new correlation.

Optical metamaterials manipulate light through various confinement and scattering processes, offering unique advantages like high performance, small form factor and easy integration with semiconductor devices. However, designing metasurfaces with suitable optical responses for complex metamaterial systems remains challenging due to the exponentially growing computation cost and the ill‐posed nature of inverse problems. To expedite the computation for the inverse design of metasurfaces, a physics‐informed deep learning (DL) framework is used. A tandem DL architecture with physics‐based learning is used to select designs that are scientifically consistent, have low error in design prediction, and accurate reconstruction of optical responses. The authors focus on the inverse design of a representative plasmonic device and consider the prediction of design for the optical response of a single wavelength incident or a spectrum of wavelength in the visible light range. The physics‐based constraint is derived from solving the electromagnetic wave equations for a simplified homogenized model. The model converges with an accuracy up to 97% for inverse design prediction with the optical response for the visible light spectrum as input, and up to 96% for optical response of single wavelength of light as input, with optical response reconstruction accuracy of 99%.

"Combinations of three pairs of contacting media with linear, exponential, and parabolic profiles of dielectric permittivity are described theoretically. Three new types of narrowly localized transverse electric waves propagating along the interfaces between the considered graded-index media are found. The exact dispersion equations for each type of the waves determining the effective refractive index in dependence on optical and geometric characteristics are obtained. The influence of the thicknesses of the graded-index layers on dispersion equation solutions is analyzed. It is found that the effective refractive index increases with an increase in the thickness of the gradedindex layers in all considered combinations of the contacting media. The thickness of the parabolic graded-index profile has the least significant effect on the effective refractive index, compared to the linear and exponential ones. "

We re-examined the four-dimensional spacetime formulation of invariance of electromagnetic fields between two inertial frames under Lorentz transformation, which predicts a pure electric (magnetic) field in one inertial frame is composed the Cartesian components of a pure both electric and magnetic fields in another inertial frame. This contradicts the Lorentz invariance condition which requires that the vector quantities in one inertial frame must have the same form in another inertial frame. In this work, we introduce a three-dimensional quasi-time vector to modify the classical four-dimensional spacetime (3+1) to a new six-dimensional spacetime (3+3) and derive spacetime metric equation and relativistic velocity. We use the classical vector transformation theory to derive expressions for Cartesian components of relativistic velocity and net electromagnetic force vectors. Considering two massive inertial frames form a closed system, we integrated the transformed relativistic velocity with the law of conservation of energy to prove that contrary to the common belief, the electromagnetic field that appears as a purely electric (magnetic) field in one massive inertial frame, it also appears as a pure electric (magnetic) field in another massive inertial frame under Lorentz transformation. As an application of the proposed six-dimensional spacetime theory, we prove Lorentz invariance of Maxwell’s equations with and without charge and current source. We also prove the scalar electromagnetic wave equations with and without charge and current source and the conservation laws of the continuity equations of current and densities of electromagnetic energy and linear and angular momentums between two massive inertial frames under Lorentz transformation.