Narrowband <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi></mml:math>-ray radiation generation by acoustically driven crystalline undulators

In this paper, we present a novel scheme for the controlled generation of tunable narrowband <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>γ</a:mi></a:math>-ray radiation by ultrarelativistic positron beams inside acoustically driven periodically bent crystals. A novel acoustic crystalline undulator is presented, in which the excitation of a silicon single crystal along the (100) planar direction by a piezoelectric transducer periodically modulates the crystal lattice in the [100] axial direction. An ultrarelativistic positron beam is directed diagonally into the crystal and propagates along the (110) planes. The lattice modulation forces the positrons to follow periodic trajectories, resulting in the emission of undulator radiation in the MeV range. A computational methodology for the design and development of such acoustically based light sources is presented together with the results of simulations demonstrating the favorable properties of the proposed technology. The longitudinal acoustic strains induced in the crystal by high-frequency piezoelectric elements are calculated by finite element simulations. The resulting bending profiles of the deformed crystal planes are used as geometrical conditions for the relativistic molecular dynamics simulations that calculate the positron trajectories and the spectral distribution of the emitted radiation. The results show a strong enhancement of the emitted radiation within a narrow spectral band defined by the bending period, demonstrating the feasibility and potential of the proposed technology.