Radiation by charged particles in nonuniform acceleration:The inapplicability of Larmor's formula

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Abstract
A recent work which explained synchrotron radiation as an inverse Compton effect [R. Lieu and W. I. Axford, Astrophys. J. 416, 700 (1993)] highlighted the importance of coherence in characterizing the radiation from a relativistic electron. In this paper we demonstrate explicitly that the well-known Larmor formula for the classical radiative loss rate of a circulating charge is only valid in the limit of constant acceleration. When the acceleration varies significantly over a ``radiation formation length,'' the radiation properties are determined by coherent interference in an orbit-dependent way, and spectra and total loss rates are modified nontrivially. We illustrate these effects by considering a representative trajectory where analytical results are available.