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We report on an indirect and non-invasive method to simultaneouslycharacterise the energy-dependent emittance and source size ofultra-relativistic positron beams generated during the propagation of alaser-wakefield accelerated electron beam through a high-Z converter target.The strong correlation of the geometrical emittance of the positrons with thatof the scattered electrons allows the former to be inferred, with highaccuracy, from monitoring the latter. The technique has been tested in aproof-of-principle experiment where, for 100 MeV positrons, we infergeometrical emittances and source sizes of the order of $\epsilon_{e^+}\approx$ 3 $\mu$m and $D_{e^+} \approx$ 150 $\mu$m, respectively. This isconsistent with the numerically predicted possibility of achieving sub-$\mu$mgeometrical emittances and micron-scale source sizes at the GeV level.

Non-invasive characterisation of a laser-driven positron beam