We consider the nonspherically decaying radiation field that is generated by a polarization current with a superluminally rotating distribution pattern in vacuum, a field that decays with the distance R(P) from its source as R(P)(-1/2), instead of R(P)(-1). It is shown (i) that the nonspherical decay of this emission remains in force at all distances from its source independently of the frequency of the radiation, (ii) that the part of the source that makes the main contribution toward the value of the nonspherically decaying field has a filamentary structure whose radial and azimuthal widths become narrower (as R(P)(-2) and R(P)(-3), respectively) the farther the observer is from the source, (iii) that the loci on which the waves emanating from this filament interfere constructively delineate a radiation subbeam that is nondiffracting in the polar direction, (iv) that the cross-sectional area of each nondiffracting subbeam increases as R(P), instead of R(P)(2), so that the requirements of conservation of energy are met by the nonspherically decaying radiation automatically, and (v) that the overall radiation beam within which the field decays nonspherically consists, in general, of the incoherent superposition of such coherent nondiffracting subbeams. These findings are related to the recent construction and use of superluminal sources in the laboratory and numerical models of the emission from them. We also briefly discuss the relevance of these results to the giant pulses received from pulsars.

No abstract

We present a theoretical study of the emission from a superluminal polarization current whose distribution pattern rotates (with an angular frequency ω) and oscillates (with a frequency Ω) at the same time, and which comprises both poloidal and toroidal components. This type of polarization current is found in recent practical machines designed to investigate superluminal emission. We find that the superluminal motion of the distribution pattern of the emitting current generates localized electromagnetic waves that do not decay spherically, i.e. that do not have an intensity diminishing like RP −2 with the distance RP from their source. The nonspherical decay of the focused wave packets that are emitted by the polarization currents does not contravene conservation of energy: the constructive interference of the constituent waves of such propagating caustics takes place within different solid angles on spheres of different radii (RP ) centred on the source. For a polarization current whose longitudinal distribution (over an azimuthal interval of length 2π) consists of m cycles of a sinusoidal wave train, the nonspherically decaying part of the emitted radiation contains the frequencies Ω ± mω; i.e. it contains only the frequencies involved in the creation and implementation of the source. This is in contrast to recent studies of the spherically decaying emission, which was shown to contain much higher frequencies. The polarization of the emitted radiation is found to be linear for most configurations of the source.

The mechanism by which the radiation received from obliquely rotating neutron stars is generated remains an open question half a century after the discovery of pulsars. In contrast, considerable progress has recently been made in determining the structure of the magnetosphere that surrounds these objects: numerical computations based on the force-free, magnetohydrodynamic and particle-in-cell formalisms have now firmly established that the magnetosphere of an oblique rotator entails a current sheet outside its light cylinder whose rotating distribution pattern moves with linear speeds exceeding the speed of light in vacuum. However, the role played by the superluminal motion of this current sheet in generating the multi-wavelength focused pulses of radiation that we receive from neutron stars is unknown. Here we insert the description of the current sheet provided by the numerical simulations in the classical expression for the retarded potential and thereby calculate the radiation field generated by this source in the time domain. We find a radiation consisting of highly focused pulses whose salient features (brightness temperature, polarization, spectrum and profile with microstructure and a phase lag between the radio and gamma-ray peaks) are strikingly similar to those of the emission received from pulsars. In addition, the flux density of this radiation diminishes with the distance D from the star as D−3/2 (rather than D−2) in certain latitudinal directions: a result that suggests that the high energetic requirements normally attributed to magnetars and the sources of fast radio bursts and gamma-ray bursts could be artefacts of the assumption that the radiation fields of all sources necessarily decay as predicted by the inverse-square law.

We investigate the spectral features of the emission from a superluminal polarization current whose distribution pattern rotates with an angular frequency ω and oscillates with an incommensurate frequency Ω > ω. This type of polarization current is found in recent practical machines designed to investigate superluminal emission. Although all of the processes involved are linear, we find that the broadband emission contains frequencies that are higher than Ω by a factor of the order of (Ω/ω)2 . This generation of frequencies not required for the creation of the source stems from mathematically rigorous consequences of the familiar classical expression for the retarded potential. The results suggest practical applications for superluminal polarization currents as broad-band radiofrequency and infrared sources.