Magnetic Permeability Functions Research Articles

Compensation of the Skin Effect in Low-Frequency Potential Drop Measurements

Potential drop measurements are routinely used in the non-destructive evaluation of component integrity. Potential drop measurements use either direct current (DC) or alternating current (AC), the latter will have superior noise performance due to the ability to perform phase sensitive detection and the reduction of flicker noise. AC measurements are however subject to the skin effect where the current is electromagnetically constricted to the surface of the component. Unfortunately, the skin effect is a function of magnetic permeability, which in ferromagnetic materials is sensitive to a number of parameters including stress and temperature, and consequently in-situ impedance measurements are likely to be unstable. It has been proposed that quasi-DC measurements, which benefit from superior noise performance, but also tend to the skin-effect independent DC measurement, be adopted for in-situ creep measurements for power station components. Unfortunately, the quasi-DC measurement will only tend to the DC distribution and therefore some remnant sensitivity to the skin effect will remain. This paper will present a correction for situations where the remnant sensitivity to the skin effect is not adequately suppressed by using sufficiently low frequency; the application of particular interest being the in-situ monitoring of the creep strain of power station components. The correction uses the measured phase angle to approximate the influence of the skin effect and allow recovery of the DC-asymptotic value of the resistance. The basis of the correction, that potential drop measurements are minimum phase is presented and illustrated on two cases; the creep strain sensor of practical interest and a conducting rod as another common case to illustrate generality. The correction is demonstrated experimentally on a component where the skin effect is manipulated by application of a range of elastic stresses.

An adaptive finite element method in reconstruction of coefficients in Maxwell’s equations from limited observations

We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary observations of the electric field in 3D. We derive a posteriori error estimates in the Tikhonov functional to be minimized and in the regularized solution of this functional, as well as formulate the corresponding adaptive algorithm. Our numerical experiments justify the efficiency of our a posteriori estimates and show significant improvement of the reconstructions obtained on locally adaptively refined meshes.

Optimization approach for the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions from limited observations

We consider the inverse problem of the simultaneous reconstruction of the dielectricpermittivity and magnetic permeability functions of the Maxwell's system in3D with limited boundary observations of the electric field. Thetheoretical stability for the problem is provided by the Carleman estimates.For the numerical computations the problem is formulated as anoptimization problem and hybrid finite element/difference method isused to solve the parameter identification problem.

Adjusted oscillator strength matching for hybrid magnetic and electric excitations in Dy3Fe5O12garnet

Far-infrared spectra of magneto-dielectric Dy3Fe5O12 garnet were studied between 13 and 100 cm-1 and at low temperatures between 5 and 80 K. A combination of transmission, reflectivity, and rotating analyzer ellipsometry was used to unambiguously identify the type of the dipole activity of the infrared modes. In addition to purely dielectric and magnetic modes, we observed several hybrid modes with a mixed magnetic and electric dipole activity. These modes originate from the superexchange between magnetic moments of Fe and Dy ions. Using 4x4 matrix formalism for materials with Mu=/=1, we modeled the experimental optical spectra and determined the far-infrared dielectric and magnetic permeability functions. The matching condition Mu(Wh)*Se=Eps(Wh)*Sm for the oscillator strengths Se(m) explains the observed vanishing of certain hybrid modes at Wh in reflectivity.

Modified frequency-domain method for simulating the electromagnetic properties in periodic magnetoactive systems

In this work, we develop a numerical simulation method to characterize the photonic properties of photonic crystals made of either dielectric or magnetic materials. Due to the magnetic materials in the photonic crystals, not only the dielectric but also the magnetic permeability functions vary periodically with position. Thus, a master equation is needed. The simulation method based on the existing algorithm developed for periodic media with uniform magnetic permeability [Johnson and Joannopoulos, Opt. Express 8, 173 (2001)] is further modified for the present case. We then use the modified numerical simulation method to investigate the photonic properties, such as the dispersion relation, photonic band gap, and electromagnetic field distribution, of some typical photonic crystals which possess analytic expression or well-known photonic properties. A good match between the simulated and the analytic results is obtained. This fact shows that the modified numerical simulation method can be used to explore electromagnetic waves in both dielectrically and the magnetically periodic media.

Resonant electromagnetism in photonic crystals composed of triangular-arrayed rods with both dielectric constant and magnetic permeability functions

The modified frequency-domain method was used to simulate the photonic properties of triangular-arrayed rods surrounded by air and possessing nonunity dielectric and magnetic permeability functions. It was found that the photonic bandgap becomes broader for the TE mode when material with higher magnetic permeability and lower dielectric constant is used for rods as compared with that of purely dielectric rods with the same refractive index, whereas the gap is reduced for the TM mode. We further examined the photonic characteristics of the photonic-crystal cavity formed when a point defect is introduced into the rod array. With a fixed refractive index of the rods, the resonant frequency of the TE mode in the first band gap is lower and the electromagnetic energy concentration at the point defect is higher when material with higher magnetic permeability and lower dielectric constant is used for the rods. The opposite was found for the TM mode.

Field quantization in dielectric media and the generalized multipolar Hamiltonian.

Canonical quantization of the electromagnetic (EM) field is carried out for the situation where the total charge and current densities are the sum of contributions from neutral dielectric atoms whose effect is to be described purely classically in terms of spatially dependent electric permittivity and magnetic permeability functions, and neutral, stationary radiative atoms whose interaction with the EM field is to be treated quantum mechanically. The coefficients for the expansion of the vector potential in terms of mode functions determined from a generalized Helmholtz equation are chosen as independent generalized coordinates for the EM field. The spatially dependent electric permittivity and magnetic permeability appear in a generalized Helmholtz's equation and the former also occurs in the mode function orthogonality and normalization conditions. The quantum Hamiltonian is derived in a generalized multipolar form rather than the minimal coupling form obtained in other work. The radiative energy is the sum of quantum harmonic oscillator terms, one for each mode. The modes are independent in the present case of exact mode functions associated with the spatially dependent electric permittivity and magnetic permeability, there being no direct mode-mode coupling terms. In the electric dipole approximation the electric interaction energy contribution for each mode and radiative atom is proportional to the scalar product of the dipole operator with the mode function evaluated at the atom, times the annihilation operator, plus the Hermitian adjoint. This form has been widely used in studies of radiative processes for atomic systems in dielectric media, and it is justified here via the canonical quantization procedure. The results apply to the theoretical treatment of numerous quantum optical experiments involving such interactions in the presence of passive, lossless, dispersionless, linear classical optics devices such as resonator cavities, lenses, beam splitters, and so on. An illustrative application of the theory for atomic decay in a one-dimensional Fabry-Perot cavity is given. \textcopyright{} 1996 The American Physical Society.