Confinement of antiprotons in the electrostatic space charge of positrons in a model of the ALPHA antihydrogen trap

The equilibrium of a positron plasma in a model of the ALPHA apparatus is computed using a finite-difference method. The positron plasma in the model extends to axial magnetic mirrors in absence of an octupole field. Formation of a three-dimensional electrostatic potential well is found to occur self-consistently. Well depths under various conditions are evaluated. Also, the equilibrium with an antiproton plasma confined in the potential well is computed. Conditions from the two species case are used to estimate timescales associated with three-body recombination, antiproton loss, and temperature equilibration. An equilibrium where the three-body recombination timescale is the smallest of the three is identified. (paper)