  Sub-micron defects represent a well-known fundamental problem in
manufacturing since they can significantly affect performance and lifetime of
virtually any high-value component. Positron annihilation lifetime spectroscopy
is arguably the only established method capable of detecting defects down to
the sub-nanometer scale but, to date, it only works for surface studies, and
with limited resolution. Here, we experimentally and numerically show that
laser-driven systems can overcome these well-known limitations, by generating
ultra-short positron beams with a kinetic energy tuneable from 500 keV up to 2
MeV and a number of positrons per shot in a 50 keV energy slice \color{black}
of the order of $10^3$. Numerical simulations of the expected performance of a
typical mJ-scale kHz laser demonstrate the possibility of generating MeV-scale
narrow-band and ultra-short positron beams with a flux exceeding $10^5$
positrons/s, of interest for fast volumetric scanning of materials at high
resolution.
