Current Sheet Approximation Research Articles

Efficient Transfer of the Medium Frequency Magnetic Field Using Anisotropic Metamaterials

This paper introduces a novel waveguide intended for the spatial transfer of alternating magnetic fields. Instead of ferromagnetic material, an air core was proposed, while the cladding was realized using anisotropic metamaterial, built of the resonators and a paramagnetic composite. Since prior works regarding magnetic field transfer concentrated on static or high frequency fields, the proposed device complements the range of medium frequencies (several to hundreds of kilohertz). The three-dimensional model of the 50 cm long and 20 cm wide rectangular structure with metamaterial cladding was made in COMSOL and computed using the finite element method. Multi-turn inductors were considered and homogenized by the current sheet approximation, while an optimization solver was used to identify an optimal design of the waveguide. The analysis was made with respect to different resonators and permeability of the paramagnetic material. Additionally, the frequency response of the structure was determined. On these bases, the dependencies of the mean energy density and magnetic field intensity at the output of the waveguide were characterized. It was shown that discussed structure was able to provide an efficient transfer of the magnetic field between two ports. Thus, this device can be used to extend the distance of the wireless power transfer, especially between devices isolated by a thick barrier (e.g., wall), in which the meta-structure may be embodied.

Homogenization of the vertically stacked medium frequency magnetic metamaterials with multi-turn resonators

The paper presents a homogenization method of the magnetic metamaterials, made of perpendicularly oriented resonators consisting of multi-turn planar coils. A resulting composite, in the form of parallel stripes with metamaterial cells, exhibits extraordinary properties in the medium frequency magnetic field, such as zero permeability. To identify an effective permeability of this metamaterial, two models were presented, i.e., a three-dimensional numerical model with current sheet approximation as well as Lorentz oscillator model, where individual coefficients are based on the lumped circuit parameters and directly related with a geometry of the unit cell. The accuracy of the second approach is improved by taking into account mutual inductances in a metamaterial grid. Then, a comparison is made with numerical model results to show adequacy of the adopted analytical attempt, and properties of this type of metamaterial are discussed. It is shown that discussed metamaterial structure can achieve negative permeability as well as its values, at identical resonant frequency, are dependent on number of turns of the planar coil.

Numerical and Circuit Modeling of the Low-Power Periodic WPT Systems

This article presents a method for analysis of the low-power periodic Wireless Power Transfer (WPT) system, using field and circuit models. A three-dimensional numerical model of multi-segment charging system, with periodic boundary conditions and current sheet approximation was solved by using the finite element method (FEM) and discussed. An equivalent circuit model of periodic WPT system was proposed, and required lumped parameters were obtained, utilizing analytical formulae. Mathematical formulations were complemented by analysis of some geometrical variants, where transmitting and receiving coils with different sizes and numbers of turns were considered. The results indicated that the proposed circuit model was able to achieve similar accuracy as the numerical model. However, the complexity of model and analysis were significantly reduced.

New method to design magnetic channels with 2D optimization tools and using permendur vanadium

Magnetic channels are used in almost all cyclotrons to focus radially the beam along the extraction path through the coils and yoke region, where the rapid fall off of the magnetic field produces a strong vertical focusing and radial defocusing of the beam. These magnetic channels consist generally of three iron bars. The current sheet approximation has been generally used to evaluate quickly the performance of magnetic channels.For the new magnetic channels to be used in the upgrade of the LNS-INFN k800 Superconducting Cyclotron, a new method was developed to investigate complex configurations and to achieve higher magnetic gradients in a larger area. The optimization procedure is based on a genetic algorithm implemented on MATLAB code and using the COMSOL code to perform the 2D magnetic field simulations.Moreover, the use of permendur vanadium in alternative to iron allows to reduce the volume of the bars and mainly the magnetic force.The results of our simulations are here presented.

A Scalable, Broadband, and Physics-Based Model for On-Chip Rectangular Spiral Inductors

A scalable, broadband, and physics-based compact model for on-chip spiral inductors with rectangular outline shape is demonstrated for the first time in this paper. A simple dc inductance model is developed based on the current sheet approximation. The reduction in inductance due to the flow of eddy current in a back metal plate is considered using the method of images. A three-ladder network is shown to be sufficient to accurately model skin effect caused due to the magnetic field setup at high frequencies. Geometry-dependent expression suitable for rectangular cross-sectional metal strips is presented to predict the proximity effect. Physics-based expression for the substrate capacitance is derived. The proposed model is also shown to have a good correlation in the presence of a patterned ground shield. The proposed model is verified across CMOS process parameters that affect the inductor performance, such as metal thickness, substrate resistivity, and substrate thickness. Furthermore, model accuracy is also validated across design parameters such as spiral width, spacing between turns, number of turns, and diameter. The model is shown to have a good agreement with both EM simulations and measurements.

The Design and EM-Simulation of Square Spiral Inductor Using Simple Equations

The RF/Microwave circuits are very much essential in communication and broadcasting fields. The important requirement of such a circuit is to be miniaturized and integrate planar passive components. The design of passive on chip capacitor and inductor are key components for RFIC/MMIC design technique such as filters and oscillators. In this work consider RT/Duriod substrate material and planar microstrip line to design square spiral inductor. In this paper we propose design of square spiral inductor using simple equations and compare the calculated results with obtained EM simulated results. The verification is done by varying the conductor width (W), space between the conductor (S), number of turns (N) and inner diameter (din) of the square spiral inductor structure. The observed electromagnetic simulated results gives better agreement with standard simple equations like modified wheeler (MW), current sheet Approximation (CSA) and data fitted monomial equation (DFME) at 600MHZ operating frequency. The design and simulation is carried out using NI/AWR microwave office tool.

Study of the new return yoke for the upgraded Superconducting Cyclotron of INFN-LNS

The LNS Superconducting Cyclotron (CS) has been working for 20 years making a wide range of ions and energies available. Many experiments are performed each year. In the near future a major upgrade is planned. This will allow to overcome the major limitation of the CS, which is the beam power delivered to the users, that at present does not exceed 100 W. In the new version of the CS, the extracted beam power will be increased up to a factor 100. This improvement will be reached extracting by stripping a specific set of light ions and energies extracted by stripping. Nevertheless, the extraction through the two electrostatic deflectors, providing a beam power limited to 100 W, will be also maintained to fulfil the users requests. The new design could strongly affect the beam dynamics. The iron yoke penetrations do not respect the three folds symmetry of our cyclotron and have a complex shape, due to the double extraction methods and all services entrances. This inhomogeneity produces unwanted field harmonics, which have to be reduced as much as possible to avoid beam precession or second order effects. Here the study accomplished to minimize the perturbation of the non- three fold field symmetry using the current sheet approximation (CSA) is presented, along with the state-of-art configuration of the updated cyclotron.

OPTIMIZATION OFSPIRAL INDUCTOR WITH DIFFERENT INNER DIAMETERS

A scalable and highly accurate RF/Microwave symmetricalinductor has been designed using microstrip line. The 18 circular and 18 square structures are optimized with 600MHz operating frequency. The characteristic interest on high frequency operating circuits is inductance value and quality factor of the spiral inductor. The value of the spiral inductor is depends on conductor width (W) space between the conductor (S), turns (n) outer diameter and inner diameter of the spiral inductor. In this design change the distribution of an inner diameter from 5mil to 10milfor 3 to 5 turns of spiral inductors. The optimization of inner diameter distribution is done by keeping space (1mil)between the conductor and width (2mil) of the conductor as constant. The changing inner diameter will effect to change in magnitude of the inductance and quality factor due passive capacitive and inductive reactance effect. These spiral inductors are designed using aluminum (Al) substrate material with 15mil height from the ground plane. The cupper material is used as a conductor of thickness 0.302mm. The aim of this paper is to compare the electromagnetic simulated results with simple equations of modified wheeler (MW), current sheet Approximation (CSA) and monomial equation (ME). The passive component effect the spiral inductor is examines the variation of inductance and quality factor. The observed electromagnetic field simulated results gives better agreement with standard simple mentioned equations with 600MHz operating frequency. The validation of spiral inductor is done with different inner diameter (5mil to 10mil) and number of turns (3turns to 5 turns) of the spiral inductor.

Space Technology 5 multipoint observations of transpolar arc-related field-aligned currents

[1] We present two transpolar arc events where for the first time we are able to analyze changes in field-aligned currents associated with high-latitude transpolar auroral arcs on time scales of a few minutes. This is accomplished through the use of highly accurate multipoint magnetic field measurements provided by the Space Technology 5 mission, which consists of three microsatellites in low-Earth orbit. In the first event we examine measurements of an arc that is part of a highly dynamic auroral pattern, that of a hook-shaped arc. In the second event, a more stable dusk oval-aligned arc is analyzed. These events illustrate the dynamic nature of arc formation and show the usefulness of high-resolution multipoint measurements. Minimum variance analysis is used to determine the appropriateness of the infinite current sheet approximation and to calculate arc alignment angles which are then compared with those estimated from UV images or precipitating particle data.

Current carriers near dipolarization fronts in the magnetotail: A THEMIS event study

[1] We study current carriers observed within thin current sheets ahead of and during the passage of earthward moving dipolarization fronts in the near‐Earth plasma sheet using Time History of Events and Macroscale Interactions During Substorms (THEMIS) multipoint measurements. The fronts are embedded within flow bursts at the initial stage of bursty bulk flow events. Simultaneous north‐south and radial separations between probes P3, P4, and P5 and the planar current sheet approximation enable estimation of cross‐tail current density in the current sheet ahead of and within the fronts, respectively. The cross‐tail current density increase ahead of the fronts, a substorm growth phase signature, is predominantly due to the ion diamagnetic current; at times, however, the electron pressure gradient may contribute up to 60% of the total current density. Note that in this paper we refer to the horizontal (vertical) current sheet as the cross‐tail current sheet (current sheet associated with dipolarization fronts). At the dipolarization fronts, the horizontal cross‐tail current sheet (with a current density of several nA/m 2 ) relaxes, and a vertical current sheet (with a current density of several tens of nA/m 2 ), consistent with the thin interface of the front, appears. Thus, the cross‐tail current at longitudes adjacent to the flow burst feeds into the dipolarization front’s current sheet and may be extended to higher latitudes. The vertical current density also decreases after passage of the front. The pressure gradient of 1–10 keV electrons is a dominant contributor to the current in the dipolarization fronts. In the event studied, probes P1 and P2, which were several Earth radii downtail, reveal a tailward expansion of the current reduction process at a propagation velocity ∼50 km/s, even as the bulk flow carrying the magnetic flux remains earthward. This study shows how dipolarization fronts and their current systems are building blocks of the large‐scale substorm current wedge.

On the limitation of the current sheet approximation in estimation of the northward Bz associated field‐aligned currents

This paper calls attention to the limitation of the current sheet approximation, which has commonly been used in deducing the field‐aligned currents (FACs) from the field‐perpendicular components of magnetic field disturbances detected from low‐altitude/midaltitude (below a few Earth radii) satellites. We focus our study on the current system involved in the northward interplanetary magnetic field associated FAC (so‐called northward Bz (NBZ)). Assuming a numerical model for the total system of the region 1, region 2, and NBZ FACs, plus the associated ionospheric currents, the dusk‐to‐dawn and sunward components of the resulting magnetic disturbance δBx and δBy are calculated. In contrast to the commonly adopted hypothesis that the field‐perpendicular magnetic disturbances as observed from the low‐altitude (a few hundred kilometers) satellites are attributed primarily to the FACs, it is found that the ionospheric currents can make a significant contribution to those disturbances. Particularly, in the central part of the region of NBZ FACs, δBx from the ionospheric currents dominates δBx from the FACs. Next, for a simple discussion on the limit of the current sheet approximation we consider the magnetic disturbances at altitudes higher than several hundred kilometers where the contribution (to δBy) from the ionospheric currents can be neglected. It is found that in general, the FAC intensities based on the current sheet model are significantly different from those actually given in the FAC distribution. Specific points to be noted are as follows: (1) On the dusk‐dawn lines passing the central part of the NBZ region the intensity of NBZ under the current sheet approximation is considerably smaller than the actual value, and the intensity ratio between region 1 and NBZ can be overestimated, by >50%, under that approximation. (2) On the dusk‐dawn lines near the edges (but just inside) of the NBZ region, the current sheet model breaks down even qualitatively; the current sheet model cannot infer the right locations of region 1 and NBZ FACs. (3) On the dusk‐dawn lines just outside of the NBZ region the so‐called “W”‐shaped profile in δBy, which can commonly be interpreted as a signature of the presence of NBZ FACs, emerges in the region where actually no NBZ FAC exists.

Interpretation of the Observed Plasma ``Turbulent'' Velocities as a Result of Magnetic Reconnection in Solar Flares

view Abstract Citations (13) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Interpretation of the Observed Plasma ``Turbulent'' Velocities as a Result of Magnetic Reconnection in Solar Flares Antonucci, Ester ; Benna, Carlo ; Somov, Boris V. Abstract One of the distinctive features of magnetic reconnection in current sheets, which has been proposed as the primary energy source in solar flares, is the presence of fast plasma outflows, or jets, whose velocities are nearly equal to the Alfvén speed and depend mainly on the electron and ion temperatures inside the current sheet. We briefly discuss the outflows that originate during the reconnection process in the high-temperature turbulent current sheet (HTTCS) approximation, both for preflare and "hot" phase conditions. Outflows can give rise to plasma velocity distributions with equal and opposite components along the line of sight, and therefore they can, in this way, create a symmetric, nonthermal broadening in the soft X-ray lines observed during solar flares. A comparison of the nonthermal profiles of the Fe xxv emission lines observed at flare onset with the predictions of the HTTCS model suggests that the observed nonthermal broadenings are consistent with the presence in the flare region of several small-scale or one (or a few) curved, large-scale reconnecting current sheets with internal temperature ≤8 x 107 K. The velocities of the outflows at the emergence of the reconnecting current sheets are inferred to be ≤ 1100 km s-1. Publication: The Astrophysical Journal Pub Date: January 1996 DOI: 10.1086/176700 Bibcode: 1996ApJ...456..833A Keywords: MAGNETOHYDRODYNAMICS: MHD; SUN: FLARES; TURBULENCE full text sources ADS |

A model for X-ray bright points due to unequal cancelling flux sources

A recent discovery from the Big Bear Solar Observatory has linked the cancellation of opposite polarity magnetic fragments in the photosphere (i.e., so-called cancelling magnetic features) to X-ray bright points and has stimulated the setting up of a converging flux model for the process. Cancelling magnetic features can occur between magnetic fragments of differing strengths in many different situations. Here, therefore, we model two opposite polarity fragments of different strengths in the photosphere by two unequal sources in an overlying uniform field. Initially in thepre-interaction phase these sources are assumed to be unconnected, but as they move closer together theinteraction phase starts with an X-type neutral point forming, initially on the photosphere, then rising up into the chromosphere and corona before lowering back down to the photosphere. Thecapture phase then follows with the sources fully connected as they move together. Finally, after they come in to contact, during thecancellation phase the weaker source is cancelled by part of the stronger source. The height of the X-type neutral point varies with the separation of the sources and the ratio of the source strengths, as do the positions of the neutral points before connection and after complete reconnection of the two sources. The neutral point is the location of magnetic reconnection and therefore energy release which is believed to power the X-ray bright point in the corona. By using a current sheet approximation, where it is assumed no reconnection takes place as the two sources move together, the total amount of energy released during reconnection may be estimated. The typical total free magnetic energy is found to be of the order of 1020–1021 J, which is as required for an X-ray bright point. It is also found that, as the ratio of the source strengths increases, the height of the X-type neutral point decreases, as do the total energy released, and the lifetime of the bright point.

Three-dimensional eddy current analysis of induction melting in cold crucibles

In order to reduce computer resources for the analysis of the eddy current distribution of cold crucible models, the authors used a current sheet approximation for the eddy current distribution because the penetration depth of the eddy current is relatively small in comparison with the dimension of the conducting bodies. The eddy current distributions approximated by current sheets are solved by an integrodifferential method using an electric vector potential. Furthermore, the magnetic flux density, power loss, Lorentz force, and lifting force of the molten metals are obtained from the solved eddy current distribution. The calculated results for the power loss and the Lorentz force gave good agreement with experimental results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Finite geometry effects of field‐aligned currents

Traditionally, field‐aligned current densities calculated from gradients in the perturbation magnetic field measured from low‐altitude spacecraft have been based on the assumption that the current regions are infinite in length. However, many measurements clearly indicate that this assumption is invalid. We have performed model calculations of the magnetic field produced by finite current regions that would be measured by a spacecraft‐borne magnetometer. These calculations serve two purposes: (1) to assess the extent to which an infinite current sheet approximation is applicable in calculating field‐aligned current densities by comparing the current density computed from the model perturbation magnetic field assuming an infinite length current region to the model current density; and (2) to assist in the interpretation of the magnetometer signals when the infinite sheet current approximation is clearly inapplicable. For current regions with various aspect (length to width) ratios, we find that the perturbation magnetic fields within the current region more than one current element width from an end produce a calculated current density with less than a 10% departure from the model current density. Certain nonlinear patterns (e.g., V‐shaped signatures) in the correlation plots of the two horizontal components of the perturbation magnetic field can be explained in terms of the end field effects of field‐aligned current regions. Such signatures can be used to determine the configuration of the satellite track through the current region.

Response of the polar cap boundary and the current system to changes in IMF observed from the Magsat satellite in the southern hemisphere during summer

The magnetic field vector residuals observed from the Magsat satellite have been used to obtain the dependence of the polar cap boundary and the current system on IMF for quiet and mildly disturbed conditions ( K p ⩽ 3 +). The study has been carried out for the summer months in the Southern Hemisphere. “Shear reversals” (SRs) in vector residuals indicative of the infinite current sheet approximation of the field-aligned currents (FACs) indicate roughly the polar cap boundary or the poleward boundary of the plasma sheet. This is also the poleward edge of the region 1 FACs. The SR is defined to occur at the latitude where the vector goes to minimum and changes direction by approximately 180°. It is found that SRs mainly occur when the interplanetary magnetic field (IMF) has a southward-directed B z - component and in the latitude range of about 70°–80°. SRs in the dusk sector occur predominantly when the azimuthal component B y is positive and in the dawn sector when B y is negative, irrespective of the sign of B z These results agree with the known merging process of IMF with magnetopause field lines. When SRs occur on both dawn and dusk sectors, the residuals over the entire polar cap are nearly uniform in direction and magnitude, indicating negligible polar currents. Similar behaviour is observed during highly disturbed conditions usually associated with large negative values of B z . Forty-one Magsat orbits with such SRs are quantitatively modelled for preliminary case studies of the resulting current distribution. It is found that SRs, in the plane perpendicular to the geomagnetic field, for the current vectors and the magnetic vector residuals (perturbations relative to the unperturbed field) occur at almost the same latitudes. The electrojet intensities range from 1.2 × 10 4 to 6.5 × 10 5 A (amperes). A preliminary classification of polar cap boundary crossings characterized by vector rotations rather than SRs also shows that they tend to occur mainly for negative B z .

A simple model of auroral electrodynamics compared with HILAT measurements

Simultaneous measurements of cold plasma drift velocities, magnetic field perturbations, and precipitating electron fluxes with instrumentation on board the HILAT satellite provide an opportunity to correlate Birkeland current densities, electric fields, and ionospheric conductivities in the region of an auroral form. Typical plasma parameters such as ion density, temperature, and composition and electron density and temperature are also available. On July 17, 1983, the satellite crossed the northern auroral zone in the early morning, magnetic local time sector. As the satellite crossed a bright auroral form, recorded by the auroral imager‐mapper, the particle spectrometer detected a 2 orders of magnitude increase in the flux of &gt;10‐keV electrons. The precipitating electrons of this event produced a double inverted‐V structure embedded in the large‐scale, region 2 field‐aligned current sheet. This paper presents calculations of the component of the electric field along the satellite trajectory and perpendicular to the auroral form, given the Birkeland current feeding the auroral form and conductivities derived from particle precipitation data. This electric field component emerges as a solution to the current continuity equation j∥ = −▽ · (Σ · E) in the infinite current sheet approximation with appropriate boundary conditions. Emphasis is placed on accurately representing the Birkeland current density in the region of the bright auroral form. In general, large‐scale features are well represented by the calculations. Although small‐scale features are not well tracked, calculations of the auroral zone potential drop and the height‐integrated Joule heating varied by less than 2% from measured values. During this particular pass the ionospheric Joule heating exceeded the particle energy deposition along the satellite trajectory by a factor of 2.6.

Time‐dependent flows in the renovated model of the magnetosphere

A revised empirical model of the magnetosphere, based on observations of Birkeland currents, is presented with earthward flow in the plasma sheet confined to the duskside. Convection (E × B drift) carries tail‐associated features in the sunward direction. This competes with Birkeland‐current‐associated plasma depletion (divergence of ion drifts), which allows flux tubes to collapse to a more dipolar form, thereby moving tail‐associated features in the antisunward direction. In substorm intensifications, depletion dominates, and the taillike region recedes from the earth. The recession appears to be unstable. A quantitative relationship between Birkeland currents and convection is developed and is used on published results. It indicates that 4×1020 ions drift off a plasma sheet flux tube as it collapses from taillike to dipolar. Application of the quantitative relationship to a published set of presubstorm and expansion data raises the following points: (1) Consistency is high, suggesting that the assumptions of hot protons, cold electrons, and a pressure‐dominated equilibrium apply in the plasma sheet. (2) The breakup instability condition is that the taillike region is just beginning to recede. (3) The changes at breakup can be interpreted as either the breakdown of the Birkeland current sheet approximation or the formation of a near‐earth neutral line.