The theory of linear acceleration emission is developed for a large amplitude
electrostatic wave in which all particles become highly relativistic in much
less than a wave period. An Airy integral approximation is shown to apply near
the phases where the electric field passes through zero and the Lorentz factors
of all particles have their maxima. The emissivity is derived for an individual
particle and is integrated over frequency and solid angle to find the power
radiated per particle. The result is different from that implied by the
generalized Larmor formula which, we argue, is not valid in this case. We also
discuss a mathematical inconsistency that arises when one evaluates the power
spectrum by integrating the emissivity over solid angle. The correct power
spectrum increases as the 4/3rd power of the frequency at low frequencies, and
falls off exponentially above a characteristic frequency.
We discuss application of linear acceleration emission to the emission of
high frequency photons in an oscillating model for pulsars. We conclude that it
cannot account for gamma-ray emission, but can play a role in secondary pair
creation.Comment: 25 pages; Accepted for publication in Ap