Electron microscopes have been widely used by material scientists, biologists, and industrial scientists to study the composition and chemical structure of materials with high spatial resolution. Aberration-corrected instruments can image individual defects and interfaces at atomic resolution, and continued advances in electron energy-loss spectroscopy (EELS) have made elemental analysis possible down to the atomic level. Low energy electron microscopes (LEEM) provide an exquisitely sensitive surface imaging technique, capable of imaging single atomic layers with high contrast. Commonly used electron sources limit the performance of these techniques: electrons are emitted with a relatively large energy spread (0.25-1 eV), which limits the energy resolution of spectroscopic techniques like EELS and makes techniques like LEEM susceptible to chromatic aberrations. Monochromators have been developed to reduce the energy spread to as low as 5-10 meV; however, the filtering of the energy distribution also dramatically reduces the beam current to below 1 pA. As a result, these instruments suf- fer from long acquisition times, which constrain their practical applications to niche areas. Furthermore, there is great interest in reducing the energy spread further, down to 1 meV, which would open up new opportunities in the spectroscopic characterization of materials. The monochromator proposed in this Phase I project is based on a recently developed and proven concept that combines an energy-dispersive, magnetic beam separator with an electrostatic electron mirror and a knife-edge aperture to filter electrons with energies that are lower or higher than the nominal beam energy. The design exploits the symmetry inherent in reversing the electron trajectory in order to monochromatize the original beam. The new monochromator design will be optimized to achieve 1 meV energy resolution and accept a novel coherent electron gun (CSEG) that is currently being developed in a collaborative effort with researchers at Lawrence Berkeley National Laboratory (LBNL) and Kimball Physics, a Wilton, N.H. based manufacturer of electron guns and electron and ion beam equipment. Initial results have shown that the CSEG equipped with a superconducting Nb electron emitter can produce a beam of electrons with an energy spread as low as 19 meV. Our novel electron monochromator will reduce the energy spread of emitted electrons to 1 meV while delivering a beam current exceeding 10 pA, and to 5 meV while delivering a beam current of more than 200 pA. A detailed electron-optical analysis of the key monochromator components, such as the magnetic beam separator, the mirror, and the CSEG gun, will be performed using state-of-the-art simulation software. A detailed analysis of the trade-offs between the achievable beam current, energy, and monochromator geometry will be carried out. The goal of the phase I research is to provide a detailed opto-mechanical design of a monochromator that can be prototyped in phase II. During phase II, the monochromator will be built and its performance will be characterized in collaboration with the research group developing the electron source at LBNL.