Radio pulsars resonantly accelerating electrons

Based on the recently demonstrated resonant wave-wave process, it is shown that electrons can be accelerated to ultra-relativistic energies in the magnetospheres of radio pulsars. The energization occurs via the resonant interaction of the electron wave (described by a Klein-Gordon (KG) equation) moving in unison with an intense electromagnetic (EM) wave; the KG wave/particle continuously draws energy from EM. In a brief recapitulation of the general theory, the high energy (resonantly enhanced) electron states are investigated by solving the KG equation, minimally coupled to the EM field. The restricted class of solutions, that propagate in phase with EM radiation (functions only of $\zeta=\omega t-kz$), are explored to serve as a possible basis for the proposed electron energization in the radio pulsars. We show that the wave-wave resonant energization mechanism could be operative in a broad class of radio pulsars with periods ranging from milliseconds to the normal values ($\sim 1$ sec); it could drive the magnetospheric electrons to acquire energies from $100$s of TeVs (millisecond pulsars) to $10$ ZeVs (normal pulsars).