The radiation from an electric current distribution, the cylindrical components of whose density depend on the azimuthal angle phi and time t in only the combination phi - omegat (with a constant angular frequency omega), is considered. It is shown that in cases where such a current also flows outside the light cylinder r=c/omega, and so has a rotating distribution pattern that attains superluminal linear phase speeds, a broad-band coherent radiation is emitted that is, in all its salient features, similar to the radiation received from pulsars (r and c stand for the cylindrical radius and the speed of light in vacuo, respectively). The emitted radiation is beamed into a finite solid angle that depends on the extent of the source distribution and that points in a direction normal to the axis of rotation. At any given observation point within this solid angle, the electromagnetic field arises almost exclusively from those volume elements of the source whose positions at the retarded time match the positions of the set of rigidly rotating points that approach the observer with the wave speed and zero acceleration in the radiation direction. These are the points - collectively forming a space curve - at which the Green function for the problem is most singular. Because the signals received at two neighbouring instants in time thus arise from distinct filamentary parts of the source which have both different extents and different strengths, the resulting overall waveform in the far zone consists of the superposition of a (continuous) set of narrow micropulses with uneven amplitudes. Each micropulse embodies a caustic and hence has an amplitude that does not obey the spherical spreading law: its flux density falls off like R(P)-1, rather than like R(P)-2, with distance R(P) from the source. That this is not incompatible with the conservation of energy is mainly due to the fact that the micropulses are narrower the larger the distance at which they are observed. The radiation therefore has a brightness temperature that is, by a factor of the order of R(P)omega/c, greater than the kinetic temperature of the plasma that generates it. The spectrum of this radiation in general extends over a wide range of frequencies from radio waves to gamma-rays: since it entails caustics, at which the wavefronts crowd together to such an extent that the wavelength of the radiation is Doppler-shifted to zero, the Green function for the present problem has a Fourier transform that, in contrast to that of the Green function for a subluminally moving source, falls off algebraically rather than exponentially at high frequencies. Throughout this wide range of frequencies, the emission is generated by the same set of source points and is beamed into essentially the same solid angle. Furthermore, this radiation consists of two concurrent elliptically polarized modes whose position angles are approximately orthogonal and individually vary across the waveform in the course of each rotation: the phase shift that is generally present between the waves on opposite sides of a caustic in this case endows the polarization state of each micropulse with two distinct values of the position angle, values that directly depend on the average orientation of the electric current density along the filamentary site of emission.
