Superluminal spectral densities of ultra-relativistic electrons in intense electromagnetic wave fields

Superluminal radiation from electrons accelerated in electromagnetic waves is investigated. The radiation field is a Proca field with negative mass-square, minimally coupled to the electron current. The spectrum is continuous in the ultra-relativistic regime, where steepest-descent asymptotics can be used to evaluate the power coefficients. The time averaging of Lissajous orbits in polarized wave fields is discussed, and the tachyonic spectral densities of electrons orbiting in intense laser beams are derived. In the ultra-relativistic limit, realized by high injection energy or high field intensity, the spectral functions are evaluated in closed form in terms of Airy integrals. In contrast to electromagnetic radiation, there is a longitudinal polarization component, and oscillations emerge at high beam intensity in the longitudinal and transversal spectral slopes, generated by the negative mass-square of the tachyonic quanta. The thermal ultra-relativistic electron plasma of two active galactic nuclei is analyzed in this regard, based on TeV spectral maps obtained with imaging air Cherenkov detectors. Specifically, tachyonic cascade fits are performed to γ-ray flares of the TeV blazars RGB J0152+017 and 3C 66A, and the transversal and longitudinal radiation components are disentangled in the spectral maps. The curvature of the spectral slopes is shown to be intrinsic, caused by the Boltzmann factor of the electronic source plasma radiating the tachyonic cascades.