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To formation of the longitudinal electromagnetic wave at discrete change of a charge density for normal and inclined falling of the accelerated point charge particle
Abstract
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.
... Possible existence and physical relevance of longitudinal electromagnetic waves from quantum electrodynamic point of view was studied in [15]. Formation of transient longitudinal electromagnetic wave at the instant when a point charge crosses the perfectly conducting half-space and annihilates with its image was theoretically shown in [19]. ...
... This current, similar to its classical counterpart (18), satisfies the charge conservation law for the upper charge. In effect, (19) represents AC current wave in space and in time, "flowing" or traveling in the direction of positive charge. As a result, here we consider traveling wave antenna (dipole). ...
... This means that velocity factor of the wire connecting the point charges is taken to be 100%. We note that the non-constant (time-varying) currents, similar to the one in (19), are considered in almost any textbook about linear antenna theories or transmission line theories. For example, dipole antenna with standing wave current consisting of four traveling constant current waves was considered in [29], triangular and sine standing wave currents in the small and finite dipole antenna were considered in [1], sine wave current in linear antenna was considered in [24]. ...
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.
... Possible existence and physical relevance of longitudinal electromagnetic waves from quantum electrodynamic point of view was studied in [7]. Formation of transient longitudinal electromagnetic wave at the instant when a point charge crosses the perfectly conducting half-space and annihilates with its image was theoretically shown in [11]. ...
... We note that even though the results for electric and magnetic fields given in (42) and (43) are generalized cases of the classical solution, they are strictly valid only for the case d λ = N ∈ N, where N is non-negative integer (N = 0, 1, 2, ..., ∞). This is due to the specific form of scalar potential taken in (11). ...
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 nonnegligible; (c) total radiated power is proportional to the fourth degree of frequency and to the second degree of the charge separation distance; and (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; and (d) most of the power is emitted in a narrow beam along the dipole axis; thus, emission of waves is focused as with lasers.
The induced charge and current distribution along the transverse orientation linear antenna, while its surface is intersected by the relativistic point charge, has been calculated. The wave packet of the current with a step and delta-shaped fronts extends along the antenna. A normal component of the transition-radiation electric field is calculated. The normal component of the electric field, having a maximum along the normal to the antenna axis, is distributed in the form of a diverging spherical wave with a delta-shaped front. The uncompensated normal component of the transitionradiation electric field strength in the wave zone is a wave packet of different-polarity delta-shaped pulses. The delta-shaped pulses are related to the relativistic charge radiation itself and to the relativistic charge radiation reflected from the target. The relativistic charge radiation reflected from the target is much higher than the radiation of the relativistic charge itself.
Transition radiation is a process of a rather general character. It occurs when some source, which does not have a proper frequency (for example, a charge) moves at a constant velocity in an inhomogeneous and (or) nonstationary medium or near such a medium. The simplest type of transition radiation takes place when a charge crosses a boundary between two media (the role of one of the media may be played by vacuum). In the case of periodic variation of the medium, transition radiation possesses some specific features (resonance transition radiation or transition scattering). Transition scattering occurs, in particular, when a permittivity wave falls onto an nonmoving (fixed) charge. Transition scattering is closely connected with transition bremsstrahlung radiation. All these transition processes are essential for plasma physics.
Transition radiation and transition scattering have analogues outside the framework of electrodynamics (like in the case of Vavilov–Cherenkov radiation). In the present report the corresponding range of phenomena is elucidated, as far as possible, in a generally physical aspect.
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Development in a space and in a time of the process of relativistic electron transition radiation, " Herald of the Kharkov University, physics series "Kernels, particles, fields
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N.F. Shulga, S.V. Trofimenko, V.V. Syshchenko, " Development in a space and in a time of the process of relativistic electron transition radiation, " Herald of the Kharkov University, physics series "Kernels, particles, fields ", №916, pp. 23 -41, Ed. 3. 2010. (in Russian).
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