Longitudinal Dynamics of Positron Beams in the ALPHA Antihydrogen Experiment

The CERN ALPHA experiment studies trapped antihydrogen atoms, produced by slowly merging cold plasmas of positrons and antiprotons. ALPHA's ability to produce antihydrogen depends on our ability to efficiently transport positrons around the experiment in the form of a low-energy ($<$100 eV) pulsed beam. In this report, we develop a model for the longitudinal dynamics of positron beams in transit around the ALPHA apparatus. We solve the longitudinal beam envelope equation for a range of beam parameters, and use COMSOL to accurately account for the defocusing effect of space charge. We show that this semi-analytical model reproduces experimental measurements taken at ALPHA in 2019, and extend our model to study how shorter bunch lengths could be achieved in the future using time-dependent electric potentials.