A study on the performance of an electrostatic focusing mirror for Rydberg positronium

Recently, we demonstrated an electrostatic mirror that focuses a beam of Rydberg positronium atoms over a 6 m path to a 32 ± 1 mm FWHM diameter spot on a position sensitive detector. The mirror is comprised of 360 wires arranged in the shape of a nearly-cylindrical revolved truncated ellipse ~96 mm in radius, with potentials of equal and opposite magnitude applied to alternating wires to create a short-ranged electric field that decreases in magnitude exponentially with e-folding length = 0.53 mm. Here, we explore in detail the observed resolution and discuss the factors contributing to its broadening from the ideal point focus of a perfect embodiment of the mirror. Improvements to the design are considered, with the aim to achieve a mirror with a resolution of <0.5 mm, which is necessary for a proposed measurement of the gravitational deflection of positronium.