The emission of superluminal quanta (tachyons) by ultra-relativistic electrons gyrating in magnetic fields is investigated. The tachyonic Liénard–Wiechert potentials of helically orbiting charges are derived, as well as the superluminal energy flux and the transversal and longitudinal spectral densities. We calculate the tachyonic synchrotron power, its angular dependence, the mean energy of the superluminal quanta radiated, tachyonic emission rates, the spectral maxima, critical and break frequencies, and we identify the Stokes parameter of the longitudinal radiation. The tachyonic energy densities are averaged with electronic power-law distributions, and the spectral indices are determined. Quantitative estimates are given for superluminal synchrotron radiation generated in storage rings, the Jovian magnetosphere, and supernova remnants. The spectral density of Jupiter's tachyonic X-ray emission is inferred from radio fluxes obtained from SL9 pre-impact observations and the Cassini fly-by, and we identify the tachyonic spectral peak at 2keV in the ROSAT and Einstein spectral maps. We scrutinize multiwavelength observations of galactic supernova remnants, pointing out evidence in their wideband spectra for the TeV γ-radiation to be tachyonic rather than a consequence of inverse Compton scattering or pion decay. In the Crab Nebula, the electronic source population generating this radiation extends beyond the ‘knee’ of the cosmic ray spectrum.
