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Electrostatics of Granular Material (EGM): Space Station Experiment

Aggregates were observed to form very suddenly in a lab-contained dust cloud, transforming (within seconds) an opaque monodispersed cloud into a clear volume containing rapidly-settling, long hair-like aggregates. The implications of such a "phase change" led to a series of experiments progressing from the lab, to KC-135, followed by micro-g flights on USML-1 and USML-2, and now EGM slated for Space Station. We attribute the sudden "collapse" of a cloud to the effect of dipoles. This has significant ramifications for all types of cloud systems, and additionally implicates dipoles in the processes of cohesion and adhesion of granular matter. Notably, there is the inference that like-charged grains need not necessarily repel if they are close enough together: attraction or repulsion depends on intergranular distance (the dipole being more powerful at short range), and the D/M ratio for each grain, where D is the dipole moment and M is the net charge. We discovered that these ideas about dipoles, the likely pervasiveness of them in granular material, the significance of the D/M ratio, and the idea of mixed charges on individual grains resulting from tribological processes --are not universally recognized in electrostatics, granular material studies, and aerosol science, despite some early seminal work in the literature, and despite commercial applications of dipoles in such modern uses as "Krazy Glue", housecleaning dust cloths, and photocopying. The overarching goal of EGM is to empirically prove that (triboelectrically) charged dielectric grains of material have dipole moments that provide an "always attractive" intergranular force as a result of both positive and negative charges residing on the surfaces of individual grains. Microgravity is required for this experiment because sand grains can be suspended as a cloud for protracted periods, the grains are free to rotate to express their electrostatic character, and Coulombic forces are unmasked. Suspended grains will be "interrogated" by applied electrical fields. In one module, grains will be immersed in an inhomogeneous electric field and allowed to be attracted towards or repelled from the central electrode of the module: part of the grain's speed will be a function of its net charge (monopole), part will be a function of the dipole. Observed grain position vs. time will provide a curve that can be deconvolved into the dipole and monopole forces responsible, since both have distinctive radial dependencies. In a second approach, the inhomogeneous field will be alternated at low frequency (e.g., every 5-10 seconds) so that the grains are alternately attracted and repelled from the center of the field. The resulting "zigzag" grain motion will gradually drift inwards, then suddenly change to a unidirectional inward path when a critical radial distance is encountered (a sort of "Coulombic event horizon") at which the dipole strength supersedes the monopole strength --thus proving the presence of a dipole, while also quantifying the D/M ratio. In a second module, an homogeneous electric field eliminates dipole effects (both Coulombic and induced) to provide calibration of the monopole and to more readily evaluate net charge statistical variance. In both modules, the e-fields will be exponentially step-ramped in voltage during the experiment, so that the field "nominalizes" grain speed while spreading the response time --effectively forcing each grain to "wait its turn" to be measured. In addition to rigorously quantifying M, D, and the D/M ratio for many hundreds of grains, the experiment will also observe gross electrometric and RF discharge phenomena associated with grain activity. The parameter space will encompass grain charging levels (via intentional triboelectrification), grain size, cloud density, and material type. Results will prove or disprove the dipole hypothesis. In either case, light will be shed on the role of electrostatic forces in governing granular systems. Knowledge so gained can be applied to natural clouds such as protostellar and protoplanetary dust and debris systems, planetary rings, planetary dust palls and aerosols created by volcanic, impact, aeolian, firestorm, or nuclear winter processes. The data are also directly applicable to adhesion, cohesion, transport, dispersion, and collection of granular materials in industrial, agricultural, pharmaceutical applications, and in fields as diverse as dust contamination of space suits on Mars and crop spraying on Earth.

Marshall, J.↗

On Geomagnetism and Paleomagnetism

A statistical description of Earth's broad scale, core-source magnetic field has been developed and tested. The description features an expected, or mean, spatial magnetic power spectrum that is neither "flat" nor "while" at any depth, but is akin to spectra advanced by Stevenson and McLeod. This multipole spectrum describes the magnetic energy range; it is not steep enough for Gubbins' magnetic dissipation range. Natural variations of core multipole powers about their mean values are to be expected over geologic time and are described via trial probability distribution functions that neither require nor prohibit magnetic isotropy. The description is thus applicable to core-source dipole and low degree non-dipole fields despite axial dipole anisotropy. The description is combined with main field models of modem satellite and surface geomagnetic measurements to make testable predictions of: (1) the radius of Earth's core, (2) mean paleomagnetic field intensity, and (3) the mean rates and durations of both dipole power excursions and durable axial dipole reversals. The predicted core radius is 0.7% above the 3480 km seismologic value. The predicted root mean square paleointensity (35.6 mu T) and mean Virtual Axial Dipole Moment (about 6.2 lx 1022 Am(exp 2)) are within the range of various mean paleointensity estimates. The predicted mean rate of dipole power excursions, as defined by an absolute dipole moment <20% of the 1980 value, is 9.04/Myr and 14% less than obtained by analysis of a 4 Myr paleointensity record. The predicted mean rate of durable axial dipole reversals (2.26/Myr) is 2.3% more than established by the polarity time-scale for the past 84 Myr. The predicted mean duration of axial dipole reversals (5533 yr) is indistinguishable from an observational value. The accuracy of these predictions demonstrates the power and utility of the description, which is thought to merit further development and testing. It is suggested that strong stable stratification of Earth's uppermost outer core leads to a geologically long interval of no dipole reversals and a very nearly axisymmetric field outside the core. Statistical descriptions of other planetary magnetic fields are outlined.

Voorhies, Coerte V.↗

PROBING THE DARK FLOW SIGNAL IN WMAP 9 -YEAR AND PLANCK COSMIC MICROWAVE BACKGROUND MAPS

The “dark flow” dipole is a statistically significant dipole found at the position of galaxy clusters in filtered maps of Cosmic Microwave Background (CMB) temperature anisotropies. The dipole measured in WMAP 3-, 5-, and 7- year data releases was (1) mutually consistent, (2) roughly aligned with the all-sky CMB dipole, and (3) correlated with clusters’ X-ray luminosities. We analyzed WMAP 9 -year and Planck 1st- year data releases using a catalog of 980 clusters outside of the Kp0 mask to test our earlier findings. The dipoles measured on these new data sets are fully compatible with our earlier estimates, are similar in amplitude and direction to our previous results, and are in disagreement with the results of an earlier study by the Planck Collaboration. Furthermore, in the Planck data sets dipoles are found to be independent of frequency, ruling out the thermal Sunyaev–Zeldovich as the source of the effect. In the data of both WMAP and Planck we find a clear correlation between the dipole measured at the cluster location in filtered maps and the average anisotropy on the original maps, further proving that the dipole is associated with clusters. The dipole signal is dominated by the most massive clusters, with a statistical significance that is better than 99%, slightly larger than in WMAP. Since both data sets differ in foreground contributions, instrumental noise, and other systematics, the agreement between the WMAP and Planck dipoles argues against them being due to systematic effects in either of the experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

Manipulating transmission and reflection properties of a photonic crystal doped with quantum dot nanostructures

The transmission and reflection properties of incident light in a defect dielectric structure is studied theoretically. The defect structure consists of donor and acceptor quantum dot nanostructures embedded in a photonic crystal. It is shown that the transmission and reflection properties of incident light can be controlled by adjusting the corresponding parameters of the system. The role of dipole–dipole interaction is considered as a new parameter in our calculations. It is noted that the features of transmission and reflection curves can be adjusted in the presence of dipole–dipole interaction. It is found that the absorption of weak probe light can be converted to the probe amplification in the presence of dipole–dipole interaction. Moreover, the group velocity of transmitted and reflected probe light is discussed in detail in the absence and presence of dipole–dipole interaction. Our proposed model can be used as a new all-optical devices based on photonic materials doped with nanoparticles.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Magneto‐Photoluminescence Based on Two‐Photon Excitation in Lanthanide‐Doped Up‐Conversion Crystal Particles

Experimental studies on magneto‐photoluminescence based on two‐photon excitation in up‐conversion Y 2 O 2 S:Er, Yb crystal particles are reported. It is found that the up‐conversion photoluminescence generated by two‐photon excitation exhibits magnetic field effects at room temperature, leading to a two‐photon excitation‐induced magneto‐photoluminescence, when the two‐photon excitation exceeds the critical intensity. By considering the spin selection rule in electronic transitions, it is proposed that spin‐antiparallel and spin‐parallel transition dipoles with spin mixing are accountable for the observed magneto‐photoluminescence. Specifically, the two‐photon excitation generates spin‐antiparallel electric dipoles between 4 S 3/2 – 4 I 15/2 in Er 3+ ions. The antiparallel spins are conserved by exchange interaction within dipoles. When the photoexcitation exceeds the critical intensity, the Coulomb screening can decrease the exchange interaction. Consequently, the spin–orbital coupling can partially convert the antiparallel dipoles into parallel dipoles, generating a spin mixing. Eventually, the populations between antiparallel and parallel dipoles reach an equilibrium established by the competition between exchange interaction and spin–orbital coupling. Applying a magnetic field can break the equilibrium by disturbing spin mixing through introducing spin precessions, changing the spin populations on antiparallel and parallel dipoles and leading to the magneto‐photoluminescence. Therefore, spin‐dependent transition dipoles present a convenient mechanism to realize magneto‐photoluminescence in multiphoton up‐conversion crystal particles.

Xu, Hengxing↗

Quantum optimal control of multiple weakly interacting molecular rotors in the time-dependent Hartree approximation

In this work we perform quantum optimal control simulations, based on the Time-Dependent Hartree (TDH) approximation, for systems of three to five dipole-dipole coupled OCS rotors. A control electric field is used to steer all of the individual rotors, arranged in chains and regular polygons in a plane, toward either identical or unique objectives. The goal is to explore the utility of the TDH approximation to model the field-induced dynamics of multiple interacting rotors in the weak dipole-dipole coupling regime. A stochastic hill climbing approach is employed to seek an optimal control field that achieves the desired objectives at a specified target time. We first show that multiple rotors in chain and polygon geometries can be identically oriented in the same direction; these cases do not significantly depend on the presence of the dipole-dipole interaction. Additionally, in particular geometrical arrangements, we demonstrate that individual rotors can be uniquely manipulated toward different objectives with the same field. Specifically, it is shown that for a three rotor chain, the two end rotors can be identically oriented in a specific direction while keeping the middle rotor in its ground state, and for an equilateral triangle, two rotors can be identically oriented in a specific direction while the third rotor is oriented in the opposite direction. These multirotor unique objective cases exploit the shape of the field in coordination with dipole-dipole coupling between the rotors. Comparisons to numerically exact calculations, utilizing the TDH-determined fields, are given for all optimal control studies involving systems of three rotors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Equivalent source modeling of the core magnetic field using magsat data

Experiments are carried out on fitting the main field using different numbers of equivalent sources arranged in equal area at fixed radii at and inside the core-mantle boundary. In fixing the radius for a given series of runs, the convergence problems that result from the extreme nonlinearity of the problem when dipole positions are allowed to vary are avoided. Results are presented from a comparison between this approach and the standard spherical harmonic approach for modeling the main field in terms of accuracy and computational efficiency. The modeling of the main field with an equivalent dipole representation is found to be comparable to the standard spherical harmonic approach in accuracy. The 32 deg dipole density (42 dipoles) corresponds approximately to an eleventh degree/order spherical harmonic expansion (143 parameters), whereas the 21 dipole density (92 dipoles) corresponds to approximately a seventeenth degree and order expansion (323 parameters). It is pointed out that fixing the dipole positions results in rapid convergence of the dipole solutions for single-epoch models.

Mayhew, M. A.↗

"Coulombic Viscosity" In Granular Materials: Planetary and Astrophysical Implications

The term "Coulombic viscosity" is introduced here to define an empirically observed phenomenon from experiments conducted in both microgravity, and in ground-based 1-g conditions. In the latter case, a sand attrition device was employed to test the longevity of aeolian materials by creating two intersecting grain-circulation paths or cells that would lead to most of the grain energy being expended on grain-to-grain collisions (simulating dune systems). In the areas in the device where gravitationally-driven grain-slurries recycled the sand, the slurries moved with a boundary-layer impeded motion down the chamber walls. Excessive electrostatic charging of the grains during these experiments was prevented by the use of an a.c. corona (created by a Tesla coil) through which the grains passed on every cycle. This created both positive and negative ions which neutralized the triboelectrically-generated grain charges. When the corona was switched on, the velocity of the wall-attached slurries increased by a factor of two as approximately determined by direct observation. What appeared to be a freely-flowing slurry of grains impeded only by intergranular mechanical friction, had obviously been significantly retarded in its motion by electrostatic forces between the grains; with the charging reduced, the grains were able to move past one another without a flow "viscosity" imposed by the Coulombic intergranular forces. A similar phenomenon was observed during microgravity experiments aboard Space Shuttle in USML-1 & USML-2 spacelabs where freely-suspended clouds of sand were being investigated for their potential to for-m aggregates. In this environment, the grains were also charged electrostatically (by natural processes prior to flight), but were free from the intervention of gravity in their interactions. The grains were dispersed into dense clouds by bursts of air turbulence and allowed to form aggregates as the ballistic and turbulent motions damped out. During this very brief (30-60 sec) damping period, motion of the grains was observed to be retarded by the electrostatic interactions. The fact that the grains almost instantly formed aggregates was evidence that their ballistic motions had been constrained and redirected by the dipole-dipole interactions that led to filamentary aggregate development. Undoubtedly, the "Coulombic viscosity" of the cloud assisted in damping grain motion so rapidly. The electrostatically-induced grain-cloud viscosity or drag exerted on grain motion, is a complex function of three major parameters: charge magnitude, charge sign, and mean intergranular distance. The above experiments illustrate one particular type of granular behavior. The discussion here will therefore be restricted to drag relationships: (a) between grains that are naturally charged triboelectrically and thus exhibit dipole-dipole attractions between one another even if there are slight net charges present (which can be overwhelmed by dipole coupling at short distances), and (b) between grains that are densely spaced where the intergranular distance varies between zero and some value (usually tens or hundreds of grain diameters) that permits each grain to detect the dipole moment of another grain -- the distance is not so great that other grains appears as neutral electrical "singularities. I. Aeolian transport: During motion of grains in a saltation cloud (on Earth, Mars, or Venus), triboelectric charging must occur as a result of multiple grain contacts, and by friction with the entraining air. A situation might develop that is similar to the one described above in the attrition device: grain motion becoming significantly retarded (reduced flux) as grains find it increasingly difficult to either separate from the surface, or to pass one another without Coulombic retarding forces. A "Coulombic drag" will exist at flux initiation and increase with time to work in direct opposition to the aerodynamic drag that drives the grain motion. It is predicted that this will lead to an increase with time of both the aerodynamic and bed-dilatancy thresholds (3). Because of Paschen discharge effects in the martian atmosphere, the electrostatic charging in a saltation cloud may be partially abated, but this will lead to greater grain mobility, more charging, and thus to a charge-discharge steady state mediated by mechanical interactions. II. Dry colluvial systems: Sand avalanches on dunes, dry debris flows, talus flows, avalanches, and pyroclastic surges are examples of gravity-driven, dense granular flows where rock/grain fragmentation and grain-to-grain interactions cause triboelectrification (sometimes augmented by other electrical charging processes), and where the grain densities of the systems are such that strong dipole-dipole interactions between grains might be expected to be present. Because it is expected that the Coulombic forces between grains will cause a sluggishness or enhanced granular-flow viscosity, the motion of a grain mass will be retarded or damped so that this will assist, ultimately, in terminating the flow. The greatest Coulombic viscosity will be created in the most highly charged systems, which will also be the most energetic. Thus, grain flows have some tendency to be self-limiting by internal energy partitioning; gravitational potential is converted to Coulombic potential, which manifests itself as a drag force between the grains. III. Volcanic eruption plumes and impact ejecta curtains: The violence of these systems leads to powerful electrical charging of particulates. Lightning storms emanating from volcanic plumes are a testimony to the levels of charging. As pyroclastic grains interact forcefully and frequently within eruption plumes, it is reasonable to predict that the internal turbulent motions of the plume will be significantly damped by the Coulombic viscosity exerted by grain charges. Additional information is contained in the original.

Marshall, J. R.↗

Force law in material media, hidden momentum and quantum phases

We address to the force law in classical electrodynamics of material media, paying attention on the force term due to time variation of hidden momentum of magnetic dipoles. We highlight that the emergence of this force component is required by the general theorem, deriving zero total momentum for any static configuration of charges/currents. At the same time, we disclose the impossibility to add this force term covariantly to the Lorentz force law in material media. We further show that the adoption of the Einstein–Laub force law does not resolve the issue, because for a small electric/magnetic dipole, the density of Einstein–Laub force integrates exactly to the same equation, like the Lorentz force with the inclusion of hidden momentum contribution. Thus, none of the available expressions for the force on a moving dipole is compatible with the relativistic transformation of force, and we support this statement with a number of particular examples. In this respect, we suggest applying the Lagrangian approach to the derivation of the force law in a magnetized/polarized medium. In the framework of this approach we obtain the novel expression for the force on a small electric/magnetic dipole, with the novel expression for its generalized momentum. The latter expression implies two novel quantum effects with non-topological phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field. These phases, in general, are not related to dynamical effects, because they are not equal to zero, when the classical force on a dipole is vanishing. The implications of the obtained results are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The effect of an offset polar cap dipolar magnetic field on the modeling of the vela pulsar's γ-ray light curves

We performed geometric pulsar light curve modeling using static, retarded vacuum, and offset polar cap (PC) dipole B-fields (the latter is characterized by a parameter ϵ), in conjunction with standard two-pole caustic (TPC) and outer gap (OG) emission geometries. The offset-PC dipole B-field mimics deviations from the static dipole (which corresponds to ϵ=0). In addition to constant-emissivity geometric models, we also considered a slot gap (SG) E-field associated with the offset-PC dipole B-field and found that its inclusion leads to qualitatively different light curves. Solving the particle transport equation shows that the particle energy only becomes large enough to yield significant curvature radiation at large altitudes above the stellar surface, given this relatively low E-field. Therefore, particles do not always attain the radiation-reaction limit. Our overall optimal light curve fit is for the retarded vacuum dipole field and OG model, at an inclination angle α=78{sub −1}{sup +1{sup {sup ∘}}} and observer angle ζ=69{sub −1}{sup +2{sup {sup ∘}}}. For this B-field, the TPC model is statistically disfavored compared to the OG model. For the static dipole field, neither model is significantly preferred. We found that smaller values of ϵ are favored for the offset-PC dipole field when assuming constant emissivity, and larger ϵ values favored for variable emissivity, but not significantly so. When multiplying the SG E-field by a factor of 100, we found improved light curve fits, with α and ζ being closer to best fits from independent studies, as well as curvature radiation reaction at lower altitudes.

79 ASTRONOMY AND ASTROPHYSICS↗

Reasonable Beam Deviation Envelope for Ray-tracing

At NSLS-II the unused dipole radiation is intercepted by the photon absorbers installed inside the vacuum chamber. The water-cooled absorbers are designed to take away the heat therefore the temperature is kept within the safety limit. However, if the beam orbit is severely perturbed, the radiation fan could pass through the geometry and strikes on the vacuum chamber components. This ray-leakage is a possible reason of the accelerator component temperature rise observed during the high-current operations. The goal of this work is to find the maximum beam deviation at the dipole hence ray-tracing can be re-examined under the operational constraints. The beam is confined to the orbit by the bending and focusing magnets. At NSLS-II the orbit is further controlled by a real time orbit feedback loop. Beam could be lost in any unpredictable direction if the magnet malfunctions. Consequently reasonable assumptions must be made to define the deviation envelope. It was determined that the dipole radiation is not powerful enough to cause damage within 10 ms, for example, if the rf power is shut off and the beam deviates from the orbit. Therefore we consider the radiation produced by the stored beam only; temporarily processes, such as unstable oscillating beam, should not be a concern. The orbit of the stored beam can be altered during magnet failures. The dipole current is interlocked to a small range of ±2% from the nominal value. If the dipole current changes slowly the beam energy automatically adjusts and the orbit remains the same. If the dipole current changes rapidly the beam will not be stable. Therefore dipole variation need not to be considered. For the other magnets we consider one magnet failure at a time because it is unlikely that two fail at the same time. It was found that the beam lifetime drops dramatically if one quadrupole power supply is turned off; therefore this scenario does not meet the stable beam condition. The current of one quadrupole could drop but will not result in orbit change with the feedback on. Beam could survive if one sextupole power supply is turned off, but the orbit will not be changed. Magnet could partially fail, for example, one or part of the coil shorts due to break-down. This is a low probability event and will not be considered. During daily operations the orbit is changed by the correctors and the rf frequency. In this work the correctors and the rf frequency are varied to explore the deviation envelope.

36 MATERIALS SCIENCE↗

Partition function corrections

The vibration-rotation interaction coupling in diatomic molecules is analyzed and first-order expressions for the energy levels are deduced. Corrections to the partition function to account for this coupling are derived. The effects of long-range intermolecular forces due to induced dipole-induced dipole interactions, dipole-induced dipole interactions, charge-dipole interactions, and charge-charge interactions are considered. London's quantized oscillator model of the induced dipole-induced dipole interaction is developed. The partition function including effects of such dispersion forces is derived and is shown to lead to the virial equation of state. For a model combining the hard sphere and long-range attractive type potentials, this is found to lead to the van der Waals equation of state. The equation of state near the critical point is presented in reduced form (thermodynamic variables expressed in units of critical point values). Finally, approximate corrections to the electronic partition functions are derived to account for perturbations of excited electronic states induced by neighboring neutral particles, heavy ions, and fast electron collisions.

Source record↗

Equivalent source modeling of the main field using MAGSAT data

An iterative least squares estimation algorithm with the capability for including a priori statistical information was implemented to recover multiple magnetic dipole models of the Earth's main magnetic field. The dipoles are fixed to a specified radius at or below the core-mantle boundary and centered on equal area blocks. The algorithm can solve for dipole magnitudes only (fixed orientations), or allow full freedom of orientation and solve for vector components. External field parameters and observatory anomaly biases can also be estimated simultaneously. Time dependence is modeled using first time derivatives for dipole vector components. Single-epoch and time dependent dipole models are derived using MAGSAT and observatory annul means data. Equivalent spherical harmonic representation are computed in closed form from the dipole models and compared with truncated spherical harmonic models estimated in the standard way from the same data sets. In particular, a 21 deg spatial resolution model based on 93 dipoles was computed based on observatory annual means data and a selected MAGSAT data set and was compared with candidate IGRF 1975 models and their 1980 secular variation.

Mayhew, M. A.↗

Low-degree Structure in Mercury's Planetary Magnetic Field

The structure of Mercury's internal magnetic field has been determined from analysis of orbital Magnetometer measurements by the MESSENGER spacecraft. We identified the magnetic equator on 531 low-altitude and 120 high-altitude equator crossings from the zero in the radial cylindrical magnetic field component, Beta (sub rho). The low-altitude crossings are offset 479 +/- 6 km northward, indicating an offset of the planetary dipole. The tilt of the magnetic pole relative to the planetary spin axis is less than 0.8 deg.. The high-altitude crossings yield a northward offset of the magnetic equator of 486 +/- 74 km. A field with only nonzero dipole and octupole coefficients also matches the low-altitude observations but cannot yield off-equatorial Beta (sub rho) = 0 at radial distances greater than 3520 km. We compared offset dipole and other descriptions of the field with vector field observations below 600 km for 13 longitudinally distributed, magnetically quiet orbits. An offset dipole with southward directed moment of 190 nT-R-cube (sub M) yields root-mean-square (RMS) residuals below 14 nT, whereas a field with only dipole and octupole terms tuned to match the polar field and the low-altitude magnetic equator crossings yields RMS residuals up to 68 nT. Attributing the residuals from the offset-dipole field to axial degree 3 and 4 contributions we estimate that the Gauss coefficient magnitudes for the additional terms are less than 4% and 7%, respectively, relative to the dipole. The axial alignment and prominent quadrupole are consistent with a non-convecting layer above a deep dynamo in Mercury's fluid outer core.

magnetometer↗

Dual-band GPS antenna with horizontal polarization

An antenna array is described herein that is suitable for dual-band GPS reception. The antenna array includes a plurality of dipole antennas arranged in a circular pattern. The antenna array further includes a feed network, separated from the dipole antennas by an insulating plate, and that passes electrical signals output by the dipole antennas to a feed line. The feed network comprises a central plate in contact with the feed line, and a plurality of arms aligned with the dipoles and extending from the center plate toward the outer edges of the circular pattern. The arms cross over slots in each of the dipole antennas. Electromagnetic waves that impinge on the dipoles induce signals that travel down the slots in the dipoles and couple to the arms of the feed network where the arms cross over the slots. The signals then travel along the feed network to the feed line.

42 ENGINEERING↗