  Using the newly developed 530 MeV positron beam from the Mainz Microtron MAMI
and employing a bent silicon crystal, we demonstrate the first successful
manipulation with high efficiencies of the trajectories of positrons through
planar channeling and volume reflection. This uncovered the presence of fine
structure within the angular distribution of charged particles when they are
channeled between the planes of bent crystals. The alignment of our
experimental findings with simulation results not only demonstrates a deeper
understanding of the interactions between charged particle beams and bent
crystals but also signals a new phase in the development of innovative
methodologies for slow extraction in circular accelerators operating in the GeV
range, with implications for worldwide accelerators. Our results also mark a
considerable progression in the generation of advanced x-ray sources through
the channeling process in periodically bent crystals, rooted in a comprehensive
understanding of the interactions between positron beams and such crystals.
