Prospects for a Third Generation ACME Search for an Electron Electric Dipole Moment

The observation of an electron electric dipole moment (eEDM) would reveal new sources of time-reversal symmetry violation and indicate physics beyond the Standard Model. The most stringent upper limit on the eEDM, \textbar d$_{\mathrm{e}}$\textbar \textless 9.4 x10$^{\mathrm{-29}}$~e\textbullet cm, was set by the first generation of the ACME experiment by means of measuring electron spin precession in a beam of thorium monoxide (Science 343 (2014), 269-272). Here, we present studies for further improvements to the ACME experiment, with the eventual goal of sensitivity at the 10$^{\mathrm{-30}}$ e\textbullet cm level, roughly 1 order of magnitude smaller than the currently running second generation experiment. The methods we discuss focus primarily on improving statistics, and include a magnetic lens to focus the molecular beam and optical cycling to improve detection.