Non-invasive characterization of transverse beam emittance of electrons from a laser-plasma wakefield accelerator in the bubble regime using betatron x-ray radiation

We propose and use a technique to measure the transverse emittance of a laser-wakefield accelerated beam of relativistic electrons. The technique is based on the simultaneous measurements of the electron beam divergence given by $v_{perp}/v_{parallel}$, the measured longitudinal spectrum $gamma_parallel$ and the transverse electron bunch size in the bubble $r_{perp}$. The latter is obtained via the measurement of the source size of the x-rays emitted by the accelerating electron bunch in the bubble. We measure a textit{normalised} RMS beam transverse emittance $<0.5$ $pi$ mm$:$mrad as an upper limit for a spatially gaussian, spectrally quasi-monoenergetic electron beam with 230 MeV energy in agreement with numerical modeling and analytic theory in the bubble regime.