General Theory of Coherent Curvature Radiation

We develop a general formalism for coherent emission by a relativistic plasma whose particles move along curved trajectories. A plane wave of wave number k and coherence length s0 causes particle bunching along the particle trajectory. When ks0 ⪢ 1 the emitted radiation peaks strongly at the plasma wave frequency. Only when the plasma wave is at rest in the plasma frame, i.e. the wave is not convective, does the coherent spectrum factor into a product of the single particle spectrum and a resonance function in ks0. When the plasma wave is convective, as is the case for streaming instabilities, no simple functional form emerges. Transverse dimensions of the plasma also can have a dramatic effect on the radiated spectrum. In general, the formalism for coherent radiation is quite different from that of single particle emission.