Field Energies Research Articles

Evaluating the Transmission Type Reference Chamber for Small Field Dosimetry

AbstractTo assess the efficacy of a transmission‐type parallel plane reference chamber (T‐REF) for small‐field percentage depth dose (PDD) measurements using two high‐resolution detectors. The study utilizes microSilicon and microDiamond detectors for small‐field measurements, both with and without a T‐REF reference chamber. TrueBeam linear accelerator provides various photon energies (6X, 6XFFF, 10X, 10XFFF) for depth dose measurements. A sun‐nuclear 3D water tank is used to measure the PDD up to a depth of 15 cm. Analysis of the data includes a 1D gamma passing rate calculated using an in‐house MATLAB program. The study compares the PDD measurements obtained with and without the T‐REF. The T‐REF exhibits negligible beam perturbations across different field sizes and energies. The overall maximum mean PDD differences are 0.31 ± 0.16% for microSilicon and 0.33 ± 0.17% for microdiamond. The overall mean 1D gamma passing rate is 99.6 ± 0.2%. This study demonstrates that the T‐REF is a reliable and effective reference detector for small‐field radiation dosimetry.

Study of half-metallic ferromagnetism and transport properties of Cs2XI6 (X = transition metals) for spintronic and energy harvesting applications

The double perovskites (DPs) are an emerging applicant for spintronic devices. In the present paper, the ferromagnetism, Curie temperature, and transport characteristics of Cs2XI6 (X = Ta, W, Re, Os) are controlled by the 5d-electrons of transition metal ions. The optimization curves indicate the stability of ferromagnetic states because the energy released in ferromagnetic states is greater than in antiferromagnetic states. The formation energy and phonons dispersion calculations confirmed thermodynamic and dynamic stabilities, while the Goldsmith tolerance factor ensured structural stability. The Heisenberg model and polarization density findings ensure ferromagnetism at high temperatures and 100 % spin polarization. Furthermore, the analysis of the band structures and density of states shows that half-metallic ferromagnetism has a major contribution from 5d-X and 5p-I states. The hybridization, double exchange model, exchange constants, and crystal field energies are also reported for the comprehensive study of the origin of ferromagnetism. Finally, the Seebeck coefficients, electrical and thermal conductivities, and thermoelectric power are illustrated comprehensively. The significant values of the figure of merit make these materials potential candidates for energy harvesting applications.

Substrate‐Free Terahertz Metamaterial Sensors With Customizable Configuration and High Performance

AbstractMetamaterials based on quasi‐bound states in the continuum (qBICs) with manipulable resonance quality (Q) factors have provided a standout platform for cutting‐edge terahertz (THz) sensing applications. However, most so far have been implemented as conventional metal patch structures with adjacent substrate layers, incurring the limitation of insufficient light‐matter interaction due to substrate effects. Here, qBIC‐driven metamaterials with substrate‐free metallic aperture structures for tailoring light‐matter interactions and exhibiting near‐ideal sensing performance is introduced. Specifically, it is incorporated ultrafast femtosecond laser processing technology to fabricate H‐type metallic aperture metamaterials with accessible high‐contrast Q factor resonances allowed by in‐plane symmetry breaking. Correspondingly, stronger light field energies are applied to the interactions due to completely eliminating the confinement of the substrate effect, enabling experimental sensitivity of up to 0.86 THz RIU−1 for the qBIC resonance, 1.9 times that of the conventional dipole resonance. Moreover, a high Q qBIC resonance achieved by optimized asymmetry parameter is exploited for detecting ultrathin layers of L‐proline molecules as low as 0.87 nmol. It is envisioned that this approach will deliver insights for real‐time, precise, and high‐performance detection of trace biomolecules, and open new perspectives for realizing ideal performance metadevices.

Ab initio analysis of structural, electronic, magnetic, thermodynamic, and elastic properties of Half Heusler alloys ZMnAs (Z = Be, Mg) for spintronics applications

In this study, the structural, electronic, magnetic, thermodynamic, and elastic attributes of ZMnAs (Z = Be, Mg) have been investigated. These Half-Heusler alloys exhibit stability in the ferromagnetic state (FM), as demonstrated by optimization-related energy release. The half-metallicity (HM) of these compounds is examined through the band structures and density of states (DOS). In addition, the crystal field and exchange energies are reported to confirm the control of electron spin. Additionally, the double exchange process and exchange constants were premeditated. In this case, ferromagnetism (FM) is caused by the quantum exchange of electrons, as evidenced by the negative pd exchange energy and the exchange constants, rather than being a result of clustering effects. The quasi-harmonic Debye model, included within the Gibbs code, was utilized to calculate the thermodynamic properties. These two compounds are mechanically stable and show ductile nature confirmed by the value of Poisson's ratio (v), Pugh's ratio (B/G), and Cauchy pressure (CP), which demonstrates the ability to withstand substantial plastic deformation before fracturing. Based on our calculations, the half-metallic (HM) nature, thermodynamic, ferromagnetic, ductile, and high inherent magnetic moment have been evaluated. These alloys are crucial in the advancement of spintronics and renewable energy systems.

A novel method to solve analytically the non-linear Poisson equation in the inversion layer of a MOSFET

Abstract Despite the enormous importance that the metal oxide semiconductors (MOS) and the field effect transistors (MOSFETs) have in the actual semiconductor technology, the task of finding the analytical solution of the Poisson equation in the inversion layer was not fully accomplished for more than half a century. It is a well-known fact that due to the non-linear nature of this equation, the attempts to solve it got stuck after the first integration. Nevertheless, experimental and applied researchers found ways to characterize, control, and develop MOSFET devices based on approximate models, and numerical calculations. Here I present a new method to analytically solve the nonlinear Poisson equation, in principle, for any charge distribution in the inversion layer of a MOS, and for the charge density of the original Shockley model, in particular. To this purpose, a physical argument related to the charge and field energies in the transient population-inversion process is introduced and a new nonlinear but solvable second order differential equation is obtained, whose solution also solves the original Poisson equation. The analytical results presented here allow us to derive explicit expressions for the electrical potential distribution and, very importantly, for the charge distribution, the inversion layer width and the effective impurity concentration in the depletion layer. The quantum Hall effect and other physical phenomena were discovered in the inversion layer of a MOS. The Hall effect was explained under the assumption that the charge distribution is a two-dimensional electron gas, we show here however that the 2D limit is reached only at high gate voltages. When applied to MOSFET structures, we obtain new expressions for the drain currents in the inversion and depletion layers, as functions of the impurity concentration and the gate voltage for single and double-gate MOSFETs, and we give an insight for multi-gate MOSFETs.

Influences of densities and thermal temperatures of electron and beam fluids on the characteristics of the electron acoustic electrostatic fields and fluid energies

A model of nonlinear electron acoustic electrostatic plasma waves having electron beams has been investigated. The structure of Korteweg–de Vries soliton energy and the corresponding electrostatic field have been discussed. The parametric regimes for wave existence of compressive and rarefactive structures have been examined via auroral zone data. The effects of densities and thermal temperature of electrons and beams on the nature of the electrostatic field and fluid energies have been taken into account.

Dual-energy lattice-tip ablation system for persistent atrial fibrillation: a randomized trial

Clinical outcomes of catheter ablation for atrial fibrillation (AF) are suboptimal due, in part, to challenges in achieving durable lesions. Although focal point-by-point ablation allows for the creation of any required lesion set, this strategy necessitates the generation of contiguous lesions without gaps. A large-tip catheter, capable of creating wide-footprint ablation lesions, may increase ablation effectiveness and efficiency. In a randomized, single-blind, non-inferiority trial, 420 patients with persistent AF underwent ablation using a large-tip catheter with dual pulsed field and radiofrequency energies versus ablation using a conventional radiofrequency ablation system. The primary composite effectiveness endpoint was evaluated through 1 year and included freedom from acute procedural failure and repeat ablation at any time, plus arrhythmia recurrence, drug initiation or escalation or cardioversion after a 3-month blanking period. The primary safety endpoint was freedom from a composite of serious procedure-related or device-related adverse events. The primary effectiveness endpoint was observed for 73.8% and 65.8% of patients in the investigational and control arms, respectively (P < 0.0001 for non-inferiority). Major procedural or device-related complications occurred in three patients in the investigational arm and in two patients in the control arm (P < 0.0001 for non-inferiority). In a secondary analysis, procedural times were shorter in the investigational arm as compared to the control arm (P < 0.0001). These results demonstrate non-inferior safety and effectiveness of the dual-energy catheter for the treatment of persistent AF. Future large-scale studies are needed to gather real-world evidence on the impact of the focal dual-energy lattice catheter on the broader population of patients with AF. ClinicalTrials.gov identifier: NCT05120193.

Tunable quantized spin Hall effect of light in graphene

The spin Hall effect of light is an appealing toolset for metrology that holds incredible potential for precision measurements due to its high sensitivity to the refractive index and nanostructure physical parameters. Here, we theoretically examine the quantized spin Hall effect of light on the surface of a monolayer graphene–substrate system subjected to an external perpendicular magnetic field. We discuss the impact of Landau levels induced by the external magnetic field B and the photon energy on magneto-optical conductivities and Fresnel reflection coefficients. We find that the spin-dependent splittings in graphene exhibit quantized characteristics due to the Landau levels quantization of the magneto-optical conductivities and Fresnel’s reflection coefficients near the Brewster angle. Moreover, the spin-dependent shifts are quantized and show oscillatory behavior with changes in the magnetic field and the photon energy. Our results manifest that the quantized photonic spin-dependent separations are sensitive to variations in the incidence angle, magnetic field, and incident photonic energies. The quantized spin-dependent splitting opens a promising route to find the quantized Hall conductivity and discrete Landau levels in the monolayer graphene by a direct optical weak measurement.

The extended resonant modal theory and its applications

AbstractThe authors extend the resonant modal theory (RMT) developed previously for a metal object to an arbitrary source region consisting of metals, dielectrics, or a combination of both. The influences of dielectrics on the fields are replaced by equivalent volume sources through the use of the compensation theorem in electromagnetic theory. The resonant frequencies can be determined by finding the roots of the determinant of the matrix resulted from the discretisation of the real homogeneous volume–surface integral equation derived from the requirement that the difference of stored field energies in the source region vanishes. As applications of the extended RMT, three examples have been investigated. The first example is a dielectric resonator antenna and is designed by exciting the first resonant mode of the composite structure in which the dielectric cylinder is combined with a conformal metallic strip. The second example is a dual‐band dielectric‐coated metallic wire antenna. The third example studies the resonant modes of a rectangular patch antenna.

Small-scale dynamo in cool stars

Context. Some of the quiet solar magnetic flux could be attributed to a small-scale dynamo (SSD) operating in the convection zone. An SSD operating in cool main-sequence stars is expected to affect the atmospheric structure, in particular, the convection, and should have observational signatures. Aims. We investigate the distribution of SSD magnetic fields and their effect on bolometric intensity characteristics, vertical velocity, and spatial distribution of the kinetic energy (KE) and magnetic energy (ME) in the lower photosphere of different spectral types. Methods. We analyzed the SSD and purely hydrodynamic simulations of the near surface layers of F3V, G2V, K0V, and M0V stars. We compared the time-averaged distributions and power spectra in SSD setups relative to the hydrodynamic setup. The properties of the individual magnetic fields are also considered. Results. The probability density functions with a field strength at the τ = 1 surface are quite similar for all cases. The M0V star displays the strongest fields, but relative to the gas pressure, the fields on the F3V star reach the highest values. In all stars, the horizontal field is stronger than the vertical field in the middle photosphere, and this excess becomes increasingly prominent toward later spectral types. These fields result in a decrease in the upflow velocities and a slight decrease in granule size, and also lead to formation of bright points in intergranular lanes. The spatial distribution of the KE and ME is also similar for all cases, implying that important scales are proportional to the pressure scale height. Conclusions. The SSD fields have rather similar effects on the photospheres of cool main-sequence stars: a significant reduction in convective velocities, as well as a slight reduction in granule size and a concentration of the field to kilogauss levels in intergranular lanes that is associated with the formation of bright points. The distribution of the field strengths and energies is also rather similar.

Physical properties of vacancy-ordered double perovskites K2TcZ6 (Z = Cl, Br) for spintronics applications: DFT calculations.

Vacancy-ordered double perovskites (DPs) are emerging materials for spintronics due to their stable structures and non-toxic properties. In this study, we conducted a comprehensive investigation into the role of 4d electrons in Tc to understand their impact on the ferromagnetic properties of K2TcY6 (Y = Cl, Br). We have employed a modified Back and Johnson potential to assess electronic and magnetic characteristics and utilized the BoltzTraP code to investigate thermoelectric effects. Experimental lattice constants confirmed the presence of stable structures and formation energy estimates affirmed their thermodynamic stability. The Heisenberg model and density of electron states (DOS) at the Fermi level provides insights into Curie temperature and spin polarization. The presence of ferromagnetism is evident in the density of states, reflecting the transition of electron spins that support the exchange mechanism. The study delves into how electron functionality influences the control of ferromagnetism, considering exchange constants, exchange energies, hybridization process and the crystal field energies. Moreover, the exploitation of magnetic moments from Tc to K and Cl/Br sites takes precedence in driving ferromagnetism by exchanging electron spins rather than forming magnetic clusters. Additionally, to explore the optical characteristics of the compounds, we investigated their optical absorption, dielectric constants and refractive index within the energy range of 0-10 eV, ensuring absorption across both the visible and ultraviolet regions. Finally, we delve into the impact of the thermoelectric effect on both thermoelectric performance and spin functionality, taking into account factors such as the Seebeck coefficient, power factor, and electronic conductivity.

Cosmological solutions of chameleon scalar field model

We investigate cosmological solutions of the chameleon model with a non-minimal coupling between the matter and the scalar field through a conformal factor with gravitational strength. By considering the spatially flat FLRW metric and the matter density as a non-relativistic perfect fluid, we focus on the matter-dominated phase and the late-time accelerated-phase of the universe. In this regard, we manipulate and scrutinize the related field equations for the density parameters of the matter and the scalar fields with respect to the e-folding. Since the scalar field fluctuations depend on the background and the field equations become highly non-linear, we probe and derive the governing equations in the context of various cases of the relation between the kinetic and potential energies of the chameleon scalar field, or indeed, for some specific cases of the scalar field equation of state parameter. Thereupon, we schematically plot those density parameters for two different values of the chameleon non-minimal coupling parameter, and discuss the results. In the both considered phases, we specify that, when the kinetic energy of the chameleon scalar field is much less than its potential energy (i.e., when the scalar field equation of state parameter is ≃-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\simeq - 1 $$\\end{document}), the behavior of the chameleon model is similar to the ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda CDM$$\\end{document} model. Such compatibility suggests that the chameleon model is phenomenologically viable and can be tested with the observational data.

Shadow area growth with increasing of charge and angular momentum in the Kerr-Newman metric with irreducible mass

The standard form of the Kerr-Newman (KN) metric contains the total mass of a charged rotating source, which includes the mass of the neutral non-rotating source (the "irreducible" mass), as well as the mass equivalents of the rotational and electric field energies. According to the Christodolou-Ruffini mass formula, at a constant irreducible mass, the total mass increases with increasing angular momentum and charge. However, ignoring this fact, at studying the dependence of the effects of gravity on parameters, the total mass was assumed to be constant with varying angular momentum and/or charge, and this error led to physically absurd results, as if an increase in charge and/or angular momentum, by increasing the energy of the source, weakens the effects of gravity. Recently, the author introduced the concept of metrics with independent parameters and formulated a new method for describing the effects of gravity based on it, leading to physically correct results (Z. Zakir 2022). The KN metric was also expressed through independent parameters, in particular through the irreducible mass, independent of charge and angular momentum (Z. Zakir 2023). It was shown that in the KN metric with irreducible mass, an increase in charge and angular momentum does not weaken the effects of gravity, as was previously accepted, but, on the contrary, enhances all these effects, as it should be when the source energy increases. This letter presents results for the shadow in the KN metric with irreducible mass. In the figures 9 shadow contours with three values of each of parameters are presented. It is shown that, as for other gravity effects, an increase in charge and/or angular momentum, increasing the source’s gravity, enhances this effect also, which is expressed in an increase in the shadow area.

Universality of the Buchdahl sphere

Buchdahl sphere, the limiting stable isotropic stellar structure without exotic matter, plays a very important role in our understanding of how compact an astrophysical object can be. Here, we show certain universal properties associated with the Buchdahl sphere, in the sense that these properties will not change with the inclusion of electric charge in the stellar structure, or, will hold good in the pure Lovelock theories of gravity as well. Using these universalities, we have proposed a Buchdahl limit for a slowly-rotating stellar configuration, for the first time. Finally, the universality of the Buchdahl sphere in terms of the gravitational and non-gravitational field energies, as well as for the photon sphere have also been discussed.

Study of spin control on half metallic ferromagnetism and thermoelectric properties of MgEu2(S/Se)4 for spintronic and energy harvesting devices

Spintronic is the emerging technology for next generation electronic devices that can improve memory and computing capability by use of electrons spin degree of freedom. The electronic, magnetic, and transport properties of MgEu2(S/Se)4 spinels are explored systematically. These spinels are stable in ferromagnetic state (FM) confirmed by energy release in optimization, phonons band structures, and enthalpy of formation (ΔHf). The Curie temperature and spin polarization signify spin polarization at high temperature. The hybridization of p-S/Se and f-Eu states have been discussed from Band structure, and density of states which explain the nature of ferromagnetism. The crystal field and exchange energies are also reported for the verification of control of electrons spin. Furthermore, the exchange constants, and double exchange mechanism also premeditated. The double exchange model is satisfied by the negative Δx (pf) and constant Noβ. Moreover, the Seebeck coefficient, conductivities, and power factor (PF) for spin (↑) and spin (↓) are investigated separately and collectively by BoltzTraP code. The high values of PF and ultralow values of thermal conductivity make the potential materials for thermoelectric generators.

First-principles calculations to investigate role of 4d electrons spin (Mo/Tc) in half metallic ferromagnetism, and thermoelectric characteristics of Rb2(Tc, Mo)X6 (X =Cl, Br)

The absolute spin polarization, stable structures, and non-toxic nature of vacancy-ordered double perovskites (DPs) make them merging materials for spintronic. Therefore, in the present study, the role of 4 d electrons of Mo/Tc has been focused comprehensively to monitor the ferromagnetism in Rb2(Tc, Mo)X6 (X = Cl, Br). The electronic and magnetic behaviors have been analyzed by modified Back and Johnson potential and thermoelectric effect by BoltzTrap code. The tolerance and octahedral factor show the existence of structures, while formation energy calculations ensure thermodynamic stability. The density of electron states at the Fermi level and the Heisenberg model report the spin polarization and Curie temperature. The density of states exposed half-metallic ferromagnetism and the transition of electrons spin to endorse the exchange mechanism. The control of ferromagnetism by electron functionality has been analyzed regarding exchange energies, crystal field energies, double exchange model, exchange constants, and hybridization process. Furthermore, shifting a magnetic moment from Mo/Tc to Rb and Cl/Br sites dominates the ferromagnetism due to the exchange of electrons spin instead of magnetic clusters. Finally, the Seebeck coefficient, conductivity of electrons, and power factor have discussed the thermoelectric effect on spin functionality and thermoelectric performance.

Particle-in-Cell Modeling of Omega Experiments on Ablation of Plasmas

The large electric fields due to charge separation generated by a laser pulse propagating in a plasma can accelerate the electrons to very high energies. The hydrodynamics models that are based on the local thermodynamic equilibrium assuming a Maxwellian distribution of velocities cannot describe the evolution of groups of hot electrons of different energy ranges and kinetic particle-in-cell (PIC) simulations are required. The SMILEI PIC code is used to investigate the generation of hot electrons in plasmas produced by laser pulses in the Omega extended performance (EP) experiments. In 2-D PIC simulation using SMILEI code, a Gaussian-shaped laser pulse of 100-ps duration with the intensity of 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{15}$</tex-math> </inline-formula> W/cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{2}$</tex-math> </inline-formula> and a wavelength of 351 nm impinges onto a plasma with the electron density and temperature profiles. The electromagnetic field, electron, and total energies of a plasma as a function of time are evaluated. The evolution of number density, electromagnetic fields, and energy spectra of electrons is studied. The time evolution of hot electrons in a plasma is investigated. These PIC results provide insights into the contribution and importance of the kinetic effects in the expansion dynamics of ablated plasmas, thereby helping to analyze and explain the Omega experimental data and computational fluid dynamics results.

Metrics with irreducible mass leading to a correct parameter dependence of gravitational effects around charged and rotating bodies

The standard metrics outside of charged and rotating sources (Kerr-Newman in general, Reissner-Nordström and Kerr in particular) contain the total mass at infinity, which includes both the mass of a neutral non-rotating body and the mass equivalents of rotational and electric field energies. Therefore, the total mass is related to other parameters of the metric - angular momentum and charge. However, at studying the dependence of gravitational effects on parameters, this relationship was ignored, assuming total mass to be constant at varying angular momentum and charge. This error led to physically absurd predictions about the weakening of gravity and its effects with increasing the rotational and electric field energies. To eliminate such errors, the total mass must be expressed in terms of independent parameters - the mass of the neutral non-rotating matter of the source, charge and angular momentum. Recently this has been done using as an independent parameter the mass determined from the gravitational radius at the pole when the charge is only on the surface (Zakir, 2022). In the present paper it is used “irreducible mass”, earlier defined heuristically as the remainder of total mass after the removal of angular momentum and charge. Earlier, mass formulas expressing total mass in terms of irreducible mass were proposed by Florides (1960) (improved by the author (2022)) for charged bodies and then by Christodolou (1970) for rotating and Christodolou-Ruffini (1971) for charged rotating sources. In the paper, the standard metrics are transformed to metrics with independent parameters by substituting the expression for the total mass according to these mass formulas. It is shown that the metrics in this form lead to a physically correct dependence of the effects of gravity on the parameters, in particular, the growth of the rotation and electric field energies strengthens gravity and its effects, such as time dilation and redshifts, increases radii of orbits and the area of shadow.

Crystal host engineering for transition metal lasers

Much progress has been made in the power and energy scaling of mid-infrared lasers based on transition metal ions, such as Cr2 + , Co2 + , and Fe2 + , in zinc and cadmium chalcogenides. Still, the exploration of the physics of these devices is incomplete. In this work, we analyze absorption spectra collected from Fe2 + ions in several binary, ternary, and quaternary host crystals at temperatures from a few degrees Kelvin to room temperature. We use the zero-phonon lines of the low-temperature spectra to calculate the value of the crystal field energy of Fe2 + ions in these hosts. We plot these crystal field energies with respect to the anion–cation distance of the host crystal and show that their crystal field strengths deviate somewhat from the trend predicted by crystal field theory. We use a model which we previously developed to describe the upper state lifetime of Fe2 + ions to predict the steady-state radiative efficiency of Fe:II–VI materials with respect to temperature. The impact of relative crystalline disorder on the output characteristics of lasers based on Cr:ZnS, Cr:ZnSe, Fe:ZnSe, and Fe:CdMnTe is explored. The effect of decreased long-range order of the host crystal is observed in the broadening of the absorption spectra of Fe2 + -doped ternary and quaternary alloys, the broadening of the spectral linewidth of continuous-wave Fe:II–VI lasers, and a reduction in the portion of the Cr:ZnSe emission spectrum accessible for modelocked lasing. This survey provides a richer picture of the tradespaces that can be leveraged when producing laser devices based on transition metal chalcogenides.

Concerning classical forces, energies, and potentials for accelerated point charges

Although expressions for energy densities involving electric and magnetic fields are exactly analogous, their connections to forces and electromagnetic potentials are vastly different. For electrostatic situations, changes in the electric energy can be related directly to electric forces and to the electrostatic potential. In contrast, discussions of magnetic forces and energy changes involve two fundamentally different situations. For charged particles moving with constant velocities, the changes in both electric and magnetic field energies are provided by the external forces that keep the particles' velocities constant; there are no Faraday acceleration electric fields in this situation. However, for particles that change speed, the changes in magnetic energy density are related to acceleration-dependent Faraday electric fields. Current undergraduate and graduate textbooks deal only with highly symmetric situations, where the Faraday electric fields are easily calculated from the time-changing magnetic flux. However, in situations that lack high symmetry, such as the magnetic Aharonov–Bohm situation, the back (Faraday) acceleration electric fields of point charges may seem unfamiliar. In this article, we present a simple unsymmetric example and analyze it using the Darwin Lagrangian. In all cases involving changing velocities of the current carriers, it is the work done by the back (Faraday) acceleration electric fields that balances the magnetic energy changes.