Coherence properties and diagnostics of betatron radiation emitted by an externally-injected electron beam propagating in a plasma channel

A 3-dimensional time-domain simulation of X-ray produced by a laser wakefield accelerated electron beam was performed in order to know its properties like intensity, spectrum, divergence and coherence. Particular attention was paid to the coherence around the acceleration axis. The broad spectrum of betatron radiation (1-10 keV) leads to a short coherence length. Nevertheless we observe that under particular detection condition the spatial coherence has a characteristic enlargement. We give a simplified interpretation of this effect in terms of phase shift of the electric field on a virtual detector. Moreover we describe a near field scattering technique to characterize the betatron radiation. This diagnostics will be used to map the transverse spatio-temporal coherence of X-ray radiation in the laser wakefield accelerator under development at Frascati National Laboratories (LNF).