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A new methodology able to model and reconstruct the transverse trace space of low-emittance electron beams accelerated in the bubble regime of laser-plasma interaction is presented. The single-shot measurement of both the electron energy spectrum and the betatron radiation spectrum is shown to allow a complete measurement of the transverse emittance, including the correlation term. A novel technique to directly measure the betatron oscillation amplitude distribution is described and tested at the SPARC-LAB test facility through the interaction of the ultrashort ultraintense Ti:Sa laser FLAME with a He gas-jet target. Via the exposed technique the beam transverse profile is also retrieved. From the study of the electron transverse dynamics inside the plasma bubble, the nonlinear correlation between the betatron amplitude and the divergence, i.e. the angle with respect the acceleration axis, is found. The angular distribution of the electron beam inside the bubble is retrieved. The knowledge of the trace-space density allows a more accurate measurement of the transverse emittance with respect to previous paradigms.

Trace-space reconstruction of low-emittance electron beams through betatron radiation in laser-plasma accelerators