Coherent radiation of ultrashort electron-bunches from linear acceleration

We consider the radiation emitted by a purely longitudinally accelerated relativistic electron bunch and find, contrary to the usual expectation of negligible emission, that for ultrashort compact bunches within reach of current experiments, a significant and measurable radiation pulse is produced. The underlying mechanism for the enhanced emission is coherence in the single-electron emission over O ( 10 8 ) electrons. We derive analytic descriptions of the emission spectrum and energy for acceleration fields and bunch conditions encountered in rf-driven particle accelerators, and in the extreme high-gradient conditions of plasma-driven acceleration. Both the bunch duration and the duration of the acceleration have a role in describing a phase-matching limitation to the coherence, with the latter dependent on the acceleration field strength and the initial energy of the electrons. In extremely compact bunches, just beyond those currently realized in the laboratory, the radiation losses approach the Larmor radiation for a massively charged particle ( Q ∼ 10 9 e ). In such conditions, the implied energy of the longitudinal acceleration radiation may approach the energy available from the electric field driving the acceleration, raising questions about a connection to mechanisms of field depletion.