Information about the absolute charge radius of nuclei is a critical ingredient for theoretical models of the atomic structure, including the ongoing search for violations to parity conservation and physics beyond the Standard Model. This observable is best measured experimentally using the elastic electron scattering technique in which the angular dependence of the nuclear response is proportional to the charge distribution. Such information is scarce for nuclei beyond bismuth and almost non-existent for radioactive isotopes. Several worldwide facilities are either in the process of or have already coupled electron \acf{linac} systems to ion storage rings or ion traps for the possibility to extend scattering experiments from stable to exotic nuclei, such as SCRIT - RIKEN in Japan, and ELISE - FAIR and DERICA - Dubna in Europe. This thesis investigates the development of an electron gun, acceleration system, and ion trap that could be coupled to a beamline like the ones at the \acf{FRIB} to perform scattering experiments along with laser spectroscopy to probe rare isotopes. We first benchmark our simulation by modeling the electron \acf{ATF} at \acf{BNL} and compare our results to measurements of the electron transverse profile. We also extracted the parameters of an ion trap (e.g, trapping potential) that a linac with the desired properties could achieve, and estimated the achievable luminosity of the system. This preliminary study provides some baseline for a possible coupling of a new electron acceleration system to \ac{FRIB} that could enhance the scientific reach of this facility and expand our knowledge of the nuclear structure.
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