Current Sheet as an Optimal Synchrotron Maser on a Radio Pulsar

Using a relativistic plasma with an isotropic monoenergetic distribution of electrons and positrons as an example, we show that in the maser regime the maximum possible amplification of synchrotron radiation at a distance of one wavelength is achieved in a medium where the magnetic energy density is of the order of the particle energy density. This ratio of the energy densities corresponds to a (Harris-type) current sheet. We have obtained an electron Lorentz factor of 350 and a magnetic field strength of 10 kG in the maser radio emission region for the Crab pulsar. Our estimate suggests that the optical and coherent radio emissions of the object originate from one synchrotron source in the form of a current sheet. The diameter of the source must exceed the light-cylinder radius approximately by a factor of 6 for the maser wave field to interact with particles in the linear regime, in particular, to keep its phase velocity higher than the speed of light in a vacuum—a necessary condition for the synchrotron instability.