Linear acceleration emission: 2 Power spectrum

TL;DR

This paper develops a detailed theory of linear acceleration emission for highly relativistic particles in electrostatic waves, deriving the power spectrum and discussing its implications for pulsar high-energy emissions.

Contribution

It provides a new derivation of the power spectrum for linear acceleration emission, showing differences from the generalized Larmor formula and addressing mathematical inconsistencies.

Findings

Power spectrum increases as frequency to the 4/3rd power at low frequencies.

Power spectrum falls off exponentially above a characteristic frequency.

Linear acceleration emission cannot explain gamma-ray emission in pulsars but may aid in secondary pair creation.

Abstract

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.