  Positron acceleration in plasma wakefield faces significant challenges since
the positron beam must be pre-generated and precisely coupled into the
wakefield, and most critically, suffers from defocusing issues. Here we propose
a scheme that utilizes laser-driven electrons to produce, inject and accelerate
positrons in a single set-up. The high-charge electron beam from wakefield
acceleration creates copious electron-positron pairs via the Bethe-Heitler
process, followed by enormous coherent transition radiation due to the
electrons' exiting from the metallic foil. Simulation results show that the
coherent transition radiation field reaches up to 10's GV m-1, which captures
and accelerates the positrons to cut-off energy of 1.5 GeV with energy peak of
500 MeV and energy spread is about 24.3%. An external longitudinal magnetic
field of 30 T is also applied to guide the electrons and positrons during the
acceleration process. This proposed method offers a promising way to obtain GeV
fast positron sources.
