  Positronium (Ps) has emerged as a promising test particle within the QUPLAS
collaboration for investigating the gravitational effect. In this work, we
present a novel approach to generate a monoenergetic and highly coherent Ps
beam by creating a negative Ps ion (Ps$^-$, consisting of two electrons and one
positron). The necessary positron beam is formed by using a high flux electron
LINAC. Subsequently, we utilize a Fabry-Perot IR laser cavity operating at a
wavelength of 1560 nm to selectively remove the extra electron. An alternative
pulsed laser operating at a 3600 nm wavelength was studied to reduce broadening
due to recoil and excitation. Here, we provide a Monte Carlo simulation to
estimate the characteristics of the Ps beam, including its energy distribution
and intensity profiles. The results obtained from this study will provide
essential groundwork for future advancements in fundamental studies as Ps
gravity measurements by using a Mach-Zehnder interferometer.
