Possible Quantum Mechanical Effect on Beam Echo

The echo effect in charged particle beams provides a link between macroscopic measurable beam parameters and microscopic phase space motion of the beam. Since quantum mechanics dictates a granularization of the phase space, it influences how the phase space behaves microscopically, and thus potentially affect how the echo effect behaves macroscopically. In this study, we propose to examine the possible measurable macroscopic effects of quantum mechanics on beams through its echo effect