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.