Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit (L=0) by explicitly including the effect of the second, L=1, Landau level and arbitrary spin polarization. The inclusion of the L=1 level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for L=0 and complete spin polarization. We identify and explain two distinct regimes separated by a critical density n(c). Below n(c), the per particle exchange energy is lowered by the contribution of L=1, whereas above n(c) it is increased. As special cases of our general equation we recover various known more limited results for higher fields, and we identify and correct a few inconsistencies in some of these earlier expressions.

Calculating current densities and fields due to shielded bi-planar radio-frequency coils

A method for the accurate computation of the current densities produced in a wide-runged bi-planar radio-frequency coil is presented. The device has applications in magnetic resonance imaging. There is a set of opposing primary rungs, symmetrically placed on parallel planes and a similar arrangement of rungs on two parallel planes surrounding the primary serves as a shield. Current densities induced in these primary and shielding rungs are calculated to a high degree of accuracy using an integral-equation approach, combined with the inverse finite Hilbert transform. Once these densities are known, accurate electrical and magnetic fields are then computed without difficulty. Some test results are shown. The method is so rapid that it can be incorporated into optimization software. Some preliminary fields produced from optimized coils are presented.

On a possible mechanism for peripheral nerve stimulation during magnetic resonance imaging scans

When patients undergo a magnetic resonance imaging scan, they are subject to both strong static and temporal magnetic fields. The temporal fields are designed to vary at each point in the region being imaged. This is achieved by the use of gradient coils. However, when the gradient coils are switched very rapidly, the strongly time-varying magnetic fields produced can be responsible for stimulating nerves in the peripheral regions of the body. This paper gives a somewhat novel explanation for this phenomenon. The physical mechanism suggested is supported by an illustrative theoretical calculation.

An investigation of magnetic antennas for ground penetrating radar

For ground penetrating radar (GPR), smaller antennas would provide considerable practical advantages. Some of which are: portability; ease of use; and higher spatial sampling. A theoretical comparison of the fundamental limits of a small electric field antenna and a small magnetic field antenna shows that the minimum Q constraints are identical. Furthermore, it is shown that only the small magnetic loop antenna can be constructed to approach, arbitrarily closely, the fundamental minimum Q limit. This is achieved with the addition of a high permeability material which reduces energy stored in the magnetic fields. This is of special interest to some GPR applications. For example, applications requiring synthetic aperture data collection would benefit from the increased spatial sampling offered by electrically smaller antennas. Low frequency applications may also benefit, in terms of reduced antenna dimensions, by the use of electrically small antennas. Under these circumstances, a magnetic type antenna should be considered in preference to the typical electric field antenna. Numerical modeling data supports this assertion.

Winding patterns for actively shielded shim coils with asymmetric target-fields

A method is presented for calculating the currents and winding patterns required to design independent zonal and tesseral shim coils for magnetic resonance imaging. Both actively shielded and unshielded configurations are considered, and the region of interest can be located asymmetrically with respect to the coil's length. Streamline, target-field and Fourier-series methods are utilized. The desired target-field is specified at two cylindrical radii, on and inside a circular conducting cylinder of length 2L and radius a. The specification is over some asymmetric portion pL < z < qL of the coil's length (-1 < p < q < 1). Arbitrary functions are used in the outer sections, -L < z < pL and qL < z < L, to ensure continuity of the magnetic field across the entire length of the coil. The entire field is then periodically extended as a half-range cosine Fourier series about either end of the coil. The resultant Fourier coefficients are then substituted into the Fourier-series expressions for the internal and external magnetic fields, and current densities and stream functions on both the primary coil and shield. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis and shielding analysis on field calculations from a ZX shim coil indicate that example designs and theory are well matched.

Calculation of electric fields induced by body and head motion in high-field MRI

In modern magnetic resonance imaging (MRI), patients are exposed to strong, nonuniform static magnetic fields outside the central imaging region, in which the movement of the body may be able to induce electric currents in tissues which could be possibly harmful. This paper presents theoretical investigations into the spatial distribution of induced electric fields and currents in the patient when moving into the MRI scanner and also for head motion at various positions in the magnet. The numerical calculations are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic, full-body, male model. 3D field profiles from an actively shielded 4T magnet system are used and the body model projected through the field profile with a range of velocities. The simulation shows that it possible to induce electric fields/currents near the level of physiological significance under some circumstances and provides insight into the spatial characteristics of the induced fields. The results are extrapolated to very high field strengths and tabulated data shows the expected induced currents and fields with both movement velocity and field strength. (C) 2003 Elsevier Science (USA). All rights reserved.

Influence of magnetically-induced E-fields on cardiac electric activity during MRI: A modeling study

In modern magnetic resonance imaging (MRI), patients are exposed to strong, time-varying gradient magnetic fields that may be able to induce electric fields (E-fields)/currents in tissues approaching the level of physiological significance. In this work we present theoretical investigations into induced E-fields in the thorax, and evaluate their potential influence on cardiac electric activity under the assumption that the sites of maximum E-field correspond to the myocardial stimulation threshold (an abnormal circumstance). Whole-body cylindrical and planar gradient coils were included in the model. The calculations of the induced fields are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic, whole-body model. The potential for cardiac stimulation was evaluated using an electrical model of the heart. Twelve-lead electrocardiogram (ECG) signals were simulated and inspected for arrhythmias caused by the applied fields for both healthy and diseased hearts. The simulations show that the shape of the thorax and the conductive paths significantly influence induced E-fields. In healthy patients, these fields are not sufficient to elicit serious arrhythmias with the use of contemporary gradient sets. However, raising the strength and number of repeated switching episodes of gradients, as is certainly possible in local chest gradient sets, could expose patients to increased risk. For patients with cardiac disease, the risk factors are elevated. By the use of this model, the sensitivity of cardiac pathologies, such as abnormal conductive pathways, to the induced fields generated by an MRI sequence can be investigated. (C) 2003 Wiley-Liss, Inc.

Reversible current power supply for fast-field cycling nuclear magnetic resonance equipment

The Fast Field-Cycling Nuclear Magnetic Resonance (FFC-NMR) is a technique used to study the molecular dynamics of different types of materials. The main elements of this equipment are a magnet and its power supply. The magnet used as reference in this work is basically a ferromagnetic core with two sets of coils and an air-gap where the materials' sample is placed. The power supply should supply the magnet being the magnet current controlled in order to perform cycles. One of the technical issues of this type of solution is the compensation of the non-linearities associated to the magnetic characteristic of the magnet and to parasitic magnetic fields. To overcome this problem, this paper describes and discusses a solution for the FFC-NMR power supply based on a four quadrant DC/DC converter.

Correction of spatial distortion in magnetic resonance imaging

Dissertation to Obtain the Degree of Master in Biomedical Engineering

Tailored magnetic and magnetoelectric responses of polymer-based composites

The manipulation of electric ordering with applied magnetic fields has been realized on magnetoelectric (ME) materials, however, their ME switching is often accompanied by significant hysteresis and coercivity that represents, for some applications, a severe weakness. To overcome this obstacle, this work focus on the development of a new type of ME polymer nanocomposites that exhibits tailored ME response at room temperature. The multiferroic nanocomposites are based on three different ferrite nanoparticles, Zn0.2Mn0.8Fe2O4 (ZMFO), CoFe2O4 (CFO) and Fe3O4 (FO), dispersed in a piezoelectric co-polymer poly(vinylindene fluoride-trifluoroethylene), P(VDF-TrFE), matrix. No substantial differences were detected on the time-stable piezoelectric response of the composites (≈ -28 pC.N−1) with distinct ferrite fillers and for the same ferrite content of 10wt.%. Magnetic hysteresis loops from pure ferrite nanopowders showed different magnetic responses. ME results of the nanocomposite films with 10wt.% ferrite content revealed that the ME induced voltage increases with increasing DC magnetic field until a maximum of 6.5 mV∙cm−1∙Oe−1, at an optimum magnetic field of 0.26 T, and 0.8 mV∙cm−1∙Oe−1, at an optimum magnetic field of 0.15T, for the CFO/P(VDF-TrFE) and FO/P(VDF-TrFE) composites, respectively. On the contrary, the ME response of the ZMFO/P(VDF-TrFE) exposed no hysteresis and high dependence on the ZMFO filler content. Possible innovative applications such as memories and information storage, signal processing, ME sensors and oscillators have been addressed for such ferrite/PVDF nanocomposites.

Metallic glass/PVDF magnetoelectric energy harvester working up to the radiofrequency range

Companies and researchers involved in developing miniaturized electronic devices face the basic problem of the needed batteries size, finite life of time and environmental pollution caused by their final deposition. The current trends to overcome this situation point towards Energy Harvesting technology. These harvesters (or scavengers) store the energy from sources present in the ambient (as wind, solar, electromagnetic, etc) and are costless for us. Piezoelectric devices are the ones that show a higher power density, and materials as ceramic PZT or polymeric PVDF have already demonstrated their ability to act as such energy harvester elements. Combinations between piezoelectric and electromagnetic mechanism have been also extensively investigated. Nevertheless, the power generated by these combinations is limited under the application of small magnetic fields, reducing the performance of the energy harvester [1]. In the last years the appearance of magnetoelectric (ME) devices, in which the piezoelectric deformation is driven by the magnetostrictive element, enables to extract the energy of very small electromagnetic signals through the generated magnetoelectric voltage at the piezoelectric element. However, very little work has been done testing PVDF polymer as piezoelectric constituent of the ME energy harvester device, and only to be proposed as a possibility of application [2]. Among the advantages of using piezopolymers for vibrational energy harvesting we can remember that they are ductile, resilient to shock, deformable and lightweight. In this work we demonstrate the feasibility of using magnetostrictive Fe-rich magnetic amorphous alloys/piezoelectric PVDF sandwich-type laminated ME devices as energy harvesters. A very simple experimental set-up will show how these laminates can extract energy, in amounts of μW, from an external AC field.

Desenvolvimento e teste de um sistema para caracterização de materiais magnetoelétricos

Dissertação de mestrado integrado em Engenharia Eletrónica Industrial e Computadores

Optimization of magnetoelectric composites based on electroactive polymers for energy harvesting and sensor application

Tese de Doutoramento em Engenharia de Materiais.

Quantification of in vivo short echo-time proton magnetic resonance spectra at 14.1 T using two different approaches of modelling the macromolecule spectrum

Reliable quantification of the macromolecule signals in short echo-time H-1 MRS spectra is particularly important at high magnetic fields for an accurate quantification of metabolite concentrations (the neurochemical profile) due to effectively increased spectral resolution of the macromolecule components. The purpose of the present study was to assess two approaches of quantification, which take the contribution of macromolecules into account in the quantification step. H-1 spectra were acquired on a 14.1 T/26 cm horizontal scanner on five rats using the ultra-short echo-time SPECIAL (spin echo full intensity acquired localization) spectroscopy sequence. Metabolite concentrations were estimated using LCModel, combined with a simulated basis set of metabolites using published spectral parameters and either the spectrum of macromolecules measured in vivo, using an inversion recovery technique, or baseline simulated by the built-in spline function. The fitted spline function resulted in a smooth approximation of the in vivo macromolecules, but in accordance with previous studies using Subtract-QUEST could not reproduce completely all features of the in vivo spectrum of macromolecules at 14.1 T. As a consequence, the measured macromolecular 'baseline' led to a more accurate and reliable quantification at higher field strengths.

Oscillatory magnetic tweezers based on ferromagnetic beads and simple coaxial coils

We report the design and validation of simple magnetic tweezers for oscillating ferromagnetic beads in the piconewton and nanometer scales. The system is based on a single pair of coaxial coils operating in two sequential modes: permanent magnetization of the beads through a large and brief pulse of magnetic field and generation of magnetic gradients to produce uniaxial oscillatory forces. By using this two step method, the magnetic moment of the beads remains constant during measurements. Therefore, the applied force can be computed and varies linearly with the driving signal. No feedback control is required to produce well defined force oscillations over a wide bandwidth. The design of the coils was optimized to obtain high magnetic fields (280 mT) and gradients (2 T/m) with high homogeneity (5% variation) within the sample. The magnetic tweezers were implemented in an inverted optical microscope with a videomicroscopy-based multiparticle tracking system. The apparatus was validated with 4.5 ¿m magnetite beads obtaining forces up to ~2 pN and subnanometer resolution. The applicability of the device includes microrheology of biopolymer and cell cytoplasm, molecular mechanics, and mechanotransduction in living cells.