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Long-Range Longitudinal Electric Wave in Vacuum Radiated by Electric Dipole: Part I
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Abstract
In this work by using the assumptions that wavelength is much smaller than charge separation distance of an electric dipole, which in turn is much smaller than a distance up to the point of observation, the new results for radiation of an electric dipole were obtained. These results generalize and extend the standard classical solution, and they indicate that under the above assumptions the electric dipole emits both long-range longitudinal electric and transverse electromagnetic waves. For a specific values of the dipole system parameters the longitudinal and transverse electric fields are displayed. Total power emitted by electric and electromagnetic waves are calculated and compared. It was shown that under the standard assumption of charge separation distance being much smaller than wavelength: a) classical solution correctly describes the transverse electromagnetic waves only; b) longitudinal electric waves are non-negligible; c) total radiated power is proportional to the fourth degree of frequency and to the second degree of the charge separation distance; d) transverse component of our solution reduces to classical solution. In case wavelength is much smaller than charge separation distance: a) the classical solution is not valid and it overestimates the total radiated power; b) longitudinal electric waves are dominant and transverse electromagnetic waves are negligible; c) total radiated power is proportional to the third degree of frequency and to the charge separation distance; d) most of the power is emitted in a narrow beam along the dipole axis, thus emission of waves is focused as with lasers.
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The observation of an electroscalar signal during the eclipse of the Sun by the Moon in 2008 was a starting point for the development and creation of the electroscalar field theory. This observation shows that such radiation has a long wavelength, and is longitudinal and extremely penetrating. The properties of the electroscalar and electromagnetic dynamics of a massive charged particle have been studied. An analogy between the linear theory of elasticity and Maxwell electrodynam-ics is made. The observed spectrum of radiation clarifying peculiar properties. Real sources of electroscalar radiation are determined. In accordance with the principle of least action, the La-grangian of the electroscalar field and the field force acting on the particle are defined. The spectral expansion of the electroscalar field allowed us to establish that the field is longitudinal and aligned with the wave vector. At the heart of the electroscalar theory, which is compliant with the experimental data, is the four-dimensional scalar potential that describes radial vibrations of the electroscalar field source. The four-vector Maxwell electromagnetic potential and four-scalar potential neither form a single object in the Minkowski space nor interfere and, as a consequence, prove to be independent and unrelated differential relations. Moreover, a strong correlation between the spatial position of the particle and the field components allows and demonstrates a new degree of freedom in the electrodynamics of charged particles.
The theory of electrodynamics can be cast into biquaternion form. Usually Maxwells’ equations are invariant with respect to a gauge transformation of the potentials and one can choose freely a gauge condition. For instance, the Lorentz gauge condition yields the potential Lorenz inhomogeneous wave equations. It is possible to introduce a scalar field in the Maxwell equations such that the generalized Maxwell theory, expressed in terms of the potentials, automatically satisfy the Lorentz inhomogeneous wave equations, without any gauge condition. This theory of electrodynamics is no longer gauge invariant with respect to a transformation of the potentials: it is electrodynamics with broken gauge symmetry. The appearence of the extra scalar field terms can be described as a conditional current regauge that does not violate the conservation of charge, and it has several consequences: the prediction of a longitudinal electroscalar wave (LES wave) in vacuum; superluminal wave solutions, and possibly classical theory about photon tunneling; a generalized Lorentz force expression that contains an extra scalar term; generalized energy and momentum theorems, with an extra power flow term associated with LES waves. A charge density wave that only induces a scalar field is possible in this theory.
It is well understood that various alternatives are available within EM theory for the definitions of energy density, momentum transfer, EM stress-energy tensor, and so forth. Although the various options are all compatible with the basic equations of electrodynamics (e.g., Maxwell's equations, Lorentz force law, gauge invariance), nonetheless certain alternative formulations lend themselves to being seen as preferable to others with regard to the transparency of their application to physical problems of interest. Here we argue for the transparency of an option based on use of the EM potentials alone. Comment: 11 pages
A vacuum test campaign evaluating the impulsive thrust performance of a tapered radio-frequency test article excited in the transverse magnitude 212 mode at 1937 MHz has been completed. The test campaign consisted of a forward thrust phase and reverse thrust phase at less than 8×10−6 torr vacuum with power scans at 40, 60, and 80 W. The test campaign included a null thrust test effort to identify any mundane sources of impulsive thrust; however, none were identified. Thrust data from forward, reverse, and null suggested that the system was consistently performing with a thrust-to-power ratio of 1.2±0.1 mN/kW.
A hypothesis for the possibility of longitudinal electromagnetic waves in arbitrary media is discussed.
A charge-image model was applied to solve the problem concerning the space-time formation of an electromagnetic field when the boundary between the vacuum and the perfectly conducting half-space is crossed by the point charge particle with a final velocity and acceleration. The cases of normal and oblique incidence of a charge at the boundary are under consideration. In the case of oblique incidence, unlike the normal one, the magnetic dipole “annihilation” at the boundary is observed. The longitudinal electromagnetic wave is formed in the far-field region. This wave has strength component of the potential electric field being normal to the wave front.
In a vacuum the scalar field 4 and vector field A of electromagnetic radiation satisfy wave equations. Certain mathematically natural measures of energy density and power flux arise for any solutions of any wave equation, and, as components of a conservation law, these measures are utilized like Lyapunov functions in an associated PDE stability theory [Hahn, Stability of Motion, Springer-Verlag, New York, 1967, pp. 216’217], [Walker, Dynamical Systems and Evolution Equations, Plenum, New York, 1990, p. 106], [Zachmanoglov and Thoe, Introduction to Partial Differential Equations with Applications, Dover, New York, 1986, p. 283]. But energy conservation in electrodynamics is conventionally accounted for with the Poynting equation, another mathematical conservation law. The purpose of this paper is to compare the contending measures and conservation laws.A consequence of the new measures is that power flux vanishes if the scalar and vector potentials are constant with respect to time, in contrast to the Poyn...
Although Poynting's theorem receives general acceptance in the treatment of electromagnetic energy, an alternative theorem, Macdonald's, has equal claim to validity at the present state of our knowledge. In a comparison of many results derived from the two, Macdonald's theorem exhibits sufficient superiority to warrant its consideration more generally in electromagnetics.
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Theoretically scalar potential Φ waves with a longitudinal electric field in the direction of propagation must exist. A centrally fed ball antenna, 6 cm diameter, producing a pulsating 433.59 MHz spherical source charge, generated such a wave, that was detected by an identical ball antenna. The longitudinality of was demonstrated by intervening a cubic array of 9 half-wavelength wires, that absorbed the wave when the wires were parallel (but not when perpendicular) to the direction of propagation. The signal from the ball antenna source, placed 4.0 m above ground and receiver 4.4 m above ground, was measured as a function of distance, yielding satisfactory agreement with theory, including 2 expected interference minima produced by an image source induced in the Earth. Only waves can yield such an interference and can be reflected from the Earth's surface and vary as the inverse square of distance.
The radiation field is quantized by introducing four types of photons - two transverse, one longitudinal, and one scalar. The scalar photons are treated by using an indefinite metric, and it is found necessary to modify the usual supplementary condition slightly. The present theory offers a justification for the symmetrical treatment of the four components of the electromagnetic potential, recently applied by a number of authors, and proves to be very convenient in applications. The results of physical interest, however, are the same as obtained from the ordinary formulation.
It has been observed in the far radiating zone that at a certain receiver antenna position and orientation the transit time of the arriving pulse-modulated microwaves in open space was constant regardless of the distance between the receiver and the transmitter. The apparent phase velocity exceeded the intrinsic velocity. Calibration techniques employed and repeated time-domain measurements done at different frequencies and distances confirmed this phenomenon.
The Ampere electrodynamics of metallic conductors and experiments supporting it predict that the interaction of a current‐carrying wire with its own magnetic field should produce longitudinal mechanical forces in the conductor, existing in addition to the transverse Lorentz forces. The longitudinal forces should stretch the conductor and have been referred to as Ampere tension. In 1964 it was discovered that a current pulse would break a straight copper wire into many fragments without visible melting. A metallurgical examination of the pieces confirmed that the metal parted in the solid state. The same observation has now been made with aluminum wires. In the latest experiments the wire was bent into a semicircle and arc‐connected to a capacitor discharge circuit. The arc connections ruled out rupture by Lorentz hoop tension and indicated that longitudinal forces may also arise in circular magnet windings. Explanations of wire fragmentation by thermal shock, longitudinal stress waves, Lorentz pinch‐off, bending stresses, and material defects have been considered and found unconvincing. Computed Ampere tensions would be sufficient to fracture hot wires. The Ampere tension would double the hoop tension normally expected in dipole magnets. This should be borne in mind in the design of large dipole magnets contemplated for MHD power generators and railgun accelerators.
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