Measurement of beam transverse emittance via measurement of the x-ray source size in a wakefield accelerator

We propose and use a new 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 $p_{\perp}/p_{\parallel}$, the measured longitudinal spectrum $p_\parallel$ 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. These so-called betatron x-rays $\left[ 1 \right]$ have also shown to be spatially coherent and as bright as currently existing 3rd generation Synchrotrons $\left[ 2 \right]$. We measure a normalized beam transverse emittance as small as 0.6~$\pi$~mm$\:$mrad for a monoenergetic electron beam with 400~MeV energy.\\ $\left[ 1 \right]$ A. Rousse, et. al. Phys. Rev. Lett. \textbf{93}, 135005 (2004)\\ $\left[ 2 \right]$ S. Kneip, et. al. Nature Physics, submitted (2010)