We present the endpoint formalism for the calculation of electromagnetic radiation and illustrate its applications in astroparticle physics. We use the formalism to explain why the coherent radiation from the Askaryan effect is not in general Cherenk
ov radiation, as the emission directly results from the time-variation of the net charge in the particle shower. Secondly, we illustrate how the formalism has been applied in the air shower radio emission code REAS3 to unify the microscopic and macroscopic views of radio emission from extensive air showers. Indeed, the formalism is completely universal and particularly well-suited for implementation in Monte Carlo codes in the time- and frequency-domains. It easily reproduces well-known classical mechanisms such as synchrotron radiation, Vavilov-Cherenkov radiation and transition radiation in the adequate limits, but has the advantage that it continues to work in realistic, complex situations, where the classical mechanisms tend to no longer apply and adhering to them can result in misleading interpretations.
We present a new methodology for calculating the electromagnetic radiation from accelerated charged particles. Our formulation --- the `endpoint formulation --- combines numerous results developed in the literature in relation to radiation arising fr
om particle acceleration using a complete, and completely general, treatment. We do this by describing particle motion via a series of discrete, instantaneous acceleration events, or `endpoints, with each such event being treated as a source of emission. This method implicitly allows for particle creation/destruction, and is suited to direct numerical implementation in either the time- or frequency-domains. In this paper, we demonstrate the complete generality of our method for calculating the radiated field from charged particle acceleration, and show how it reduces to the classical named radiation processes such as synchrotron, Tamms description of Vavilov-Cherenkov, and transition radiation under appropriate limits. Using this formulation, we are immediately able to answer outstanding questions regarding the phenomenology of radio emission from ultra-high-energy particle interactions in both the Earths atmosphere and the Moon. In particular, our formulation makes it apparent that the dominant emission component of the Askaryan Effect (coherent radio-wave radiation from high-energy particle cascades in dense media) comes from coherent `bremsstrahlung from particle acceleration, rather than coherent Vavilov-Cherenkov radiation.
