Electromagnetic field diffusion, θ-functions,and image solutions

Contents We discuss some initial and boundary value problems of one-dimensional electromagnetic field diffusion. The solutions can be given by infinite series in two essentially different (however equivalent) forms, one being the usual Fourier-expansion and the other one being an infinite series of Gaussian exponentials or related functions (as for instance error-functions). The second form can be obtained by using infinitely many images to fulfill initial and boundary conditions. Finally the mathematical relations between the two equivalent types of solutions are discussed in terms of -functions and their transformation properties. The existence of the solutions in these two different forms is very interesting from a numerical point of view also.

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Die Diffusion elektromagnetischer Felder, -Funktionen und Spiegelungsmethoden

Übersicht Es werden einige Anfangs- und Randwertprobleme eindimensionaler elektromagnetischer Felddiffusion erörtert. Die Lösungen können in zwei wesentlich verschiedenen (jedoch gleichwertigen) Formen angegeben werden, erstens in Form üblicher Fourier-Reihen und zweitens in Form unendlicher Reihen von Gaußschen Exponentialfunktionen oder damit verwandter Funktionen (z.B. Fehlerfunktionen). Diese zweite Form der Lösungen läßt sich durch die Anwendung unendlich oft wiederholter Spiegelung zur Erfüllung der Rand- und Anfangsbedingung anschaulich interpretieren. Abschließend werden die beiden Lösungstypen mit Hilfe von -Funktionen und deren Transformationseigenschaften erläutert. Die Verfügbarkeit der Lösungen in beiden Formen ist auch numerisch sehr interessant.

     

DC field test for medium-voltage cables: why can no one agree?

Industry standards for shielded medium-voltage cables (5-46 kV) have been revised, changing the DC test voltages for field tests and test durations and limiting tests to newly installed cables. The following industry groups' specifications and standards provide different guidelines for DC field tests for cross-linked polyethylene and ethylene propylene rubber insulated cables: IEEE, Insulated Cable Engineers Association (AEIC), and the Association of Edison Illuminating Companies (AEIC). These specifications and standards are discussed, showing the differences in the recommendations and why the differences exist. The conclusion provides a guide for DC field testing shielded medium-voltage cables based on these industry standards     

Monitoring and correcting spatio-temporal variations of the MR scanner’s static magnetic field

The homogeneity and stability of the static magnetic field are of paramount importance to the accuracy of MR procedures that are sensitive to phase errors and magnetic field inhomogeneity. It is shown that intense gradient utilization in clinical horizontal-bore superconducting MR scanners of three different vendors results in main magnetic fields that vary on a long time scale both spatially and temporally by amounts of order 0.8–2.5 ppm. The observed spatial changes have linear and quadratic variations that are strongest along the z direction. It is shown that the effect of such variations is of sufficient magnitude to completely obfuscate thermal phase shifts measured by proton-resonance frequency-shift MR thermometry and certainly affect accuracy. In addition, field variations cause signal loss and line-broadening in MR spectroscopy, as exemplified by a fourfold line-broadening of metabolites over the course of a 45 min human brain study. The field variations are consistent with resistive heating of the magnet structures. It is concluded that correction strategies are required to compensate for these spatial and temporal field drifts for phase-sensitive MR protocols. It is demonstrated that serial field mapping and phased difference imaging correction protocols can substantially compensate for the drift effects observed in the MR thermometry and spectroscopy experiments.     

Electromagnetic field calculation inside a conducting cylinder of finite length using the T-Ω method

Contents The solution of a 3-dimensional problem is, almost in all cases, a quite difficult task, since a great computational effort is required. AT- method accompanied by a boundary element technique is presented for the evaluation of the field inside a conducting cylinder of finite length. The excitation is a current dipole with harmonic time variation (electric Hertzian dipole), located somewhere inside the cylinder. According to the method the problem is split into smaller independent successive problems, requiring much less computational effort.

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Berechnung des elektromagnetischen Feldes innerhalb eines leitenden Zylinders endlicher Länge mit Hilfe der T--Methode

Übersicht Die Lösung des dreidimensionalen Problems ist, fast in allen Fällen, wegen der großen Mühe, die bei den Computerberechnungen erforderlich ist, sehr schwierig. EineT--Methode kombiniert mit einer Randelementtechnik für die Berechnung des Feldes innerhalb eines leitenden Zylinders endlicher Länge wird präsentiert. Ein Hertzscher Dipol an einer beliebigen Stelle innerhalb des Zylinders stellt die Felderregung dar. Entsprechend der Methode wird das Problem in mehrere kleinere, unabhängige sukzessive Probleme, die viel weniger Mühe bei der Computerberechnung erfordern, unterteilt.

     

Coupled circuit–field formulation for analysis of parallel operation of converters with interphase transformer

This paper deals with the coupled circuit–field analysis of an interphase transformer (IPT) required for two three-pulse controlled converters operating in parallel for the typical low voltage high current electrolysis application. Two-dimensional nonlinear transient finite element (FE) model of the IPT is coupled with external power electronic circuit comprised of switching thyristors. Output current is maintained constant at 6000 A by implementing current feedback control system. The resulting system of transient nonlinear equations is solved by backward Euler and Newton–Raphson methods, and analyzed under balanced, unbalanced and short circuit conditions. The results obtained from short circuit condition are verified with experimental results and design values, making them helpful for design purpose.     

Microwave magnetoelectric effects in ferrite—piezoelectric composites and dual electric and magnetic field tunable filters

Magnetoelectric (ME) effects at ferromagnetic resonance (FMR) in ferrite—piezoelectric layered structures have been investigated in lithium zinc ferrite (LZFO)-lead zirconate titanate (PZT) and yttrium iron garnet (YIG)-PZT. When an electric field E is applied to PZT, the piezoelectric deformation is transmitted to the ferrite and results in a shift in FMR. Data on the field shift caused by E are presented and compared with theory. Although the strength of ME coupling is weaker in YIG-PZT than in LZFO-PZT, the E-assisted field shift in YIG-PZT is much higher than the resonance line width and is potentially useful for filter applications. An electric field tunable YIG-PZT microwave band-pass filter based on ME effects at FMR is designed and characterized. The device can be tuned over a wide frequency band with a bias magnetic field and over a narrow band with a voltage applied across PZT. Data on tuning range, insertion loss, and device characteristics are presented.     

Quantum kinetics approach to calculation of the low field mobility in the hole inversion layers of silicon MOSFET’s

Analytic expressions for low field mobility have been obtained in the quantized p-type inversion layers. The confining potential is approximated by a triangular quantum well. Main attention is paid to study the dependence of the hole mobility on transverse effective field at different temperatures and concentrations of the ionized impurities. Acoustic and optical phonons, charged impurities, and surface roughness have been adopted as scattering system. Theoretical considerations are based on the quantum kinetic equation and special form of the non-equilibrium distribution function (shifted Fermi distribution). Calculations show that the acoustic phonon limited mobility does not depend on the transverse effective electrical field \(E_\mathrm{eff} \) and has a temperature dependence closer to experiment than known expression for the universal mobility. At the same time, the mobility limited by scattering with optical phonons and surface roughness is proportional to \(E_\mathrm{eff} ^{-1/3}\) and \(E_\mathrm{eff} ^{-2}\), respectively. The mobility limited by scattering by ionized impurities is a weak function of the transverse effective field. Results of the calculations are compared with known experimental data.     

Magnetic field analysis of a 9–6 without permanent magnet brushless DC motor by using 3-D finite element method

This paper presents characteristic analysis of without permanent magnet brushless DC (WPMBLDC) motor by using three-dimensional (3-D) finite element method (FEM). The paper describes the complex magnetic structure and principle of the presented WPMBLDC motor in detail. The magnetic field distribution of the presented motor is numerically computed by 3-D FEM. The primary characteristics of the motor including magnetic flux density, flux linkage and inductance profile are obtained. A prototype WPMBLDC machine has also been built and tested; additionally, the accuracy of 3-D FE analysis is verified by comparing the calculated results with the experimental measured values.     

Effect of the variation of the charge distribution along multi-overhead transmission lines’ conductors on the calculation method of ground surface electric field

This paper presents a new methodology to calculate the ground surface electric field, produced by overhead transmission lines (OHTLs), taking into account the effect of the variation of the charge distributions along the conductors of multi-overhead transmission lines. In this paper, the effects of the conductors sag, the presence of the tower, replacing the sub-conductors of each phase with an equivalent conductor, the presence of the ground wires, and the presence of another overhead transmission line (OHTL) circuit on the electric charge distribution along the OHTL conductors and hence on the calculation of the ground surface electric fields are extensively studied. The suggested technique is verified by comparing its results with a measurement by the other. The suggested technique is based on both the Charge Simulation Method (CSM) and the Image Method (IM).     

Minimizing the effects of magnetization transfer asymmetry on inhomogeneous magnetization transfer (ihMT) at ultra-high magnetic field (11.75 T)

Objectives

The recently reported inhomogeneous magnetization transfer technique (ihMT) has been proposed for specific imaging of inhomogeneously broadened lines, and has shown great promise for characterizing myelinated tissues. The ihMT contrast is obtained by subtracting magnetization transfer images obtained with simultaneous saturation at positive and negative frequency offsets (dual frequency saturation experiment, MT ^+/?) from those obtained with single frequency saturation (MT ⁺) at the same total power. Hence, ihMT may be biased by MT-asymmetry, especially at ultra-high magnetic field. Use of the average of single positive and negative frequency offset saturation MT images, i.e., (MT ⁺+MT ^?) has been proposed to correct the ihMT signal from MT-asymmetry signal.

Materials and methods

The efficiency of this correction method was experimentally assessed in this study, performed at 11.75 T on mice. Quantitative corrected ihMT and MT-asymmetry ratios (ihMTR and MTRasym) were measured in mouse brain structures for several MT-asymmetry magnitudes and different saturation parameter sets.

Results

Our results indicated a “safe” range of magnitudes (/MTRasym/<4 %) for which MT-asymmetry signal did not bias the corrected ihMT signal. Moreover, experimental evidence of the different natures of both MT-asymmetry and inhomogeneous MT contrasts were provided. In particular, non-zero ihMT ratios were obtained at zero MTRasym values.

Conclusion

MTRasym is not a confounding factor for ihMT quantification, even at ultra-high field, as long as MTRasym is restricted to ±4 %.