Tachyonic cyclotron radiation

Abstract

We study superluminal cyclotron emission by electrons and muons in semiclassical orbits. The tachyonic line spectra of hydrogenic ions such as $\mbox{H}$ , ${}^{56}\mbox{Fe}^{25 + }$ , and ${}^{238} \mbox{U}^{91 + }$ , as well as their muonic counterparts ${p}\mu^-$ , ${}^{56}\mbox{Fe}^{26 + }\mu ^-$ and ${}^{238} \mbox{U}^{92 + }\mu^-$ are calculated, in particular the tachyonic power transversally and longitudinally radiated, the total intensity, and the power radiated in the individual harmonics. We also investigate tachyonic continuum radiation from electrons and protons cycling in the surface and light cylinder fields of $\gamma$ -ray and millisecond pulsars, such as the Crab pulsar, PSR B1509-58, and PSR J0218 + 4232. The superluminal spectral densities generated by non-relativistic, mildly relativistic and ultra-relativistic source particles are derived. We study the parameters determining the global shape of the transversal and longitudinal densities and the energy scales of the broadband spectrum. The observed cutoff frequency in the $\gamma$ -ray band of the pulsars is used to infer the upper edge of the orbital energy, and we conclude that electrons and nuclei cycling in the surface fields can reach energies beyond the "ankle" of the cosmic ray spectrum. This suggests $\gamma$ -ray pulsars as sources of ultra-high energy cosmic rays.