The electromagnetic radiation whose decay violates the inversesquare law: detailed mathematical treatment of an experimentally realized example
Abstract
I analyse and numerically evaluate the radiation field generated by an experimentally realized embodiment of an electric polarization current whose rotating distribution pattern moves with linear speeds exceeding the speed of light in vacuum. I find that the flux density of the resulting emission (i) has a dominant value and is linearly polarized within a sharply delineated radiation beam whose orientation and polar width are determined by the range of values of the linear speeds of the rotating source distribution, and (ii) decays with the distance from the source as in which the value of lies between and (instead of being equal to as in a conventional radiation) across the beam. In that the rate at which boundaries of the retarded distribution of such a source change with time depends on its duration monotonically, this is an intrinsically transient emission process: temporal rate of change of the energy density of the radiation generated by it has a timeaveraged value that is negative (instead of being zero as in a conventional radiation) at points where the envelopes of the wave fronts emanating from the constituent volume elements of the source distribution are cusped. The difference in the fluxes of power across any two spheres centred on the source is in this case balanced by the change with time of the energy contained inside the shell bounded by those spheres. These results are relevant not only to longrange transmitters in communications technology but also to astrophysical objects containing rapidly rotating neutron stars (such as pulsars) and to the interpretation of the energetics of the multiwavelength emissions from sources that lie at cosmological distances (such as radio and gammaray bursts). The analysis presented in this paper is selfcontained and supersedes my earlier works on this problem.
 Publication:

Journal of Plasma Physics
 Pub Date:
 June 2019
 DOI:
 10.1017/S0022377819000382
 arXiv:
 arXiv:1907.10715
 Bibcode:
 2019JPlPh..85c9004A
 Keywords:

 astrophysical plasmas;
 plasma applications;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 91 pages, 38 figures