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 ${v}_{\ensuremath{\perp}}/{v}_{\ensuremath{\parallel}}$, the measured spectrum $\ensuremath{\gamma}$, and the transverse electron bunch size in the bubble ${r}_{\ensuremath{\perp}}$. 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 normalized rms beam transverse emittance $<0.5\ensuremath{\pi}\text{ }\text{ }\mathrm{mm}\text{ }\mathrm{mrad}$ as an upper limit for a spatially Gaussian, spectrally quasimonoenergetic electron beam with 230 MeV energy in agreement with numerical modeling and analytic theory in the bubble regime.