83 research outputs found

### Absence of a consistent classical equation of motion for a mass-renormalized point charge

The restrictions of analyticity, relativistic (Born) rigidity, and negligible
O(a) terms involved in the evaluation of the self electromagnetic force on an
extended charged sphere of radius "a" are explicitly revealed and taken into
account in order to obtain a classical equation of motion of the extended
charge that is both causal and conserves momentum-energy. Because the
power-series expansion used in the evaluation of the self force becomes invalid
during transition time intervals immediately following the application and
termination of an otherwise analytic externally applied force, transition
forces must be included during these transition time intervals to remove the
noncausal pre-acceleration and pre-deceleration from the solutions to the
equation of motion without the transition forces. For the extended charged
sphere, the transition forces can be chosen to maintain conservation of
momentum-energy in the causal solutions to the equation of motion within the
restrictions of relativistic rigidity and negligible O(a) terms under which the
equation of motion is derived. However, it is shown that renormalization of the
electrostatic mass to a finite value as the radius of the charge approaches
zero introduces a violation of momentum-energy conservation into the causal
solutions to the equation of motion of the point charge if the magnitude of the
external force becomes too large. That is, the causal classical equation of
motion of a point charge with renormalized mass experiences a high acceleration
catastrophe.Comment: 13 pages, No figure

### Antimagnets: Controlling magnetic fields with superconductor-metamaterial hybrids

Magnetism is very important in science and technology, from magnetic
recording to energy generation to trapping cold atoms. Physicists have managed
to master magnetism - to create and manipulate magnetic fields- almost at will.
Surprisingly, there is at least one property which until now has been elusive:
how to 'switch off' the magnetic interaction of a magnetic material with
existing magnetic fields without modifying them. Here we introduce the
antimagnet, a design to conceal the magnetic response of a given volume from
its exterior, without altering the external magnetic fields, somehow analogous
to the recent theoretical proposals for cloaking electromagnetic waves with
metamaterials. However, different from these devices requiring extreme material
properties, our device is feasible and needs only two kinds of available
materials: superconductors and isotropic magnetic materials. Antimagnets may
have applications in magnetic-based medical techniques such as MRI or in
reducing the magnetic signature of vessels or planes.Comment: 14 pages, 4 figure

### Electrically Small Supergain Arrays

The theory, computer simulations, and experimental measurements are presented
for electrically small two-element supergain arrays with near optimal endfire
gains of 7 dB. We show how the difficulties of narrow tolerances, large
mismatches, low radiation efficiencies, and reduced scattering of electrically
small parasitic elements are overcome by using electrically small resonant
antennas as the elements in both separately driven and singly driven
(parasitic) two-element electrically small supergain endfire arrays. Although
rapidly increasing narrow tolerances prevent the practical realization of the
maximum theoretically possible endfire gain of electrically small arrays with
many elements, the theory and preliminary numerical simulations indicate that
near maximum supergains are also achievable in practice for electrically small
arrays with three (and possibly more) resonant elements if the decreasing
bandwidth with increasing number of elements can be tolerated.Comment: 10 pages, 11 figures, submitted to IEEE Transactions on Antennas and
Propagation (December 2006

### Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation

The Lorentz law of force is the fifth pillar of classical electrodynamics,
the other four being Maxwell's macroscopic equations. The Lorentz law is the
universal expression of the force exerted by electromagnetic fields on a volume
containing a distribution of electrical charges and currents. If electric and
magnetic dipoles also happen to be present in a material medium, they are
traditionally treated by expressing the corresponding polarization and
magnetization distributions in terms of bound-charge and bound-current
densities, which are subsequently added to free-charge and free-current
densities, respectively. In this way, Maxwell's macroscopic equations are
reduced to his microscopic equations, and the Lorentz law is expected to
provide a precise expression of the electromagnetic force density on material
bodies at all points in space and time. This paper presents incontrovertible
theoretical evidence of the incompatibility of the Lorentz law with the
fundamental tenets of special relativity. We argue that the Lorentz law must be
abandoned in favor of a more general expression of the electromagnetic force
density, such as the one discovered by A. Einstein and J. Laub in 1908. Not
only is the Einstein-Laub formula consistent with special relativity, it also
solves the long-standing problem of "hidden momentum" in classical
electrodynamics.Comment: 7 pages, 1 figur

### Resonant transmission of light through finite chains of subwavelength holes

In this paper we show that the extraordinary optical transmission phenomenon
found before in 2D hole arrays is already present in a linear chain of
subwavelength holes, which can be considered as the basic geometrical unit
showing this property. In order to study this problem we have developed a new
theoretical framework, able to analyze the optical properties of finite
collections of subwavelength apertures and/or dimples (of any shape and placed
in arbitrary positions) drilled in a metallic film.Comment: Accepted for publication in Phys. Rev. Let

### characteristic wave velocities in spherical electromagnetic cloaks

We investigate the characteristic wave velocities in spherical electromagnetic cloaks, namely, phase, ray, group and energy-transport velocities. After deriving explicit expressions for the phase and ray velocities (the latter defined as the phase velocity along the direction of the Poynting vector), special attention is given to the determination of group and energy-transport velocities, because a cursory application of conventional formulae for local group and energy-transport velocities can lead to a discrepancy between these velocities if the permittivity and permeability dyadics are not equal over a frequency range about the center frequency. In contrast, a general theorem can be proven from Maxwell's equations that the local group and energy-transport velocities are equal in linear, lossless, frequency dispersive, source-free bianisotropic material. This apparent paradox is explained by showing that the local fields of the spherical cloak uncouple into an E wave and an H wave, each with its own group and energy-transport velocities, and that the group and energy-transport velocities of either the E wave or the H wave are equal and thus satisfy the general theorem

### Radiative damping: a case study

We are interested in the motion of a classical charge coupled to the Maxwell
self-field and subject to a uniform external magnetic field, B. This is a
physically relevant, but difficult dynamical problem, to which contributions
range over more than one hundred years. Specifically, we will study the
Sommerfeld-Page approximation which assumes an extended charge distribution at
small velocities. The memory equation is then linear and many details become
available. We discuss how the friction equation arises in the limit of "small"
B and contrast this result with the standard Taylor expansion resulting in a
second order equation for the velocity of the charge.Comment: 4 figure

### Finite size corrections to the radiation reaction force in classical electrodynamics

We introduce an effective field theory approach that describes the motion of
finite size objects under the influence of electromagnetic fields. We prove
that leading order effects due to the finite radius $R$ of a spherically
symmetric charge is order $R^2$ rather than order $R$ in any physical model, as
widely claimed in the literature. This scaling arises as a consequence of
Poincar\'e and gauge symmetries, which can be shown to exclude linear
corrections. We use the formalism to calculate the leading order finite size
correction to the Abraham-Lorentz-Dirac force.Comment: 4 pages, 2 figure

### On the Solutions of the Lorentz-Dirac Equation

We discuss the unstable character of the solutions of the Lorentz-Dirac
equation and stress the need of methods like order reduction to derive a
physically acceptable equation of motion. The discussion is illustrated with
the paradigmatic example of the non-relativistic harmonic oscillator with
radiation reaction. We also illustrate removal of the noncasual
pre-acceleration with the introduction of a small correction in the
Lorentz-Dirac equation.Comment: 4 eps figs. to be published in GR

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