A Magnetic Recoil Spectrometer (MRSt) has been conceptually designed for time-resolved measurements of the neutron spectrum at the National Ignition Facility. Using the MRSt, the goals are to measure the time-evolution of the spectrum with a time resolution of ∼20-ps and absolute accuracy better than 5%. To meet these goals, a detailed understanding and optimization of the signal and background characteristics are required. Through ion-optics, MCNP simulations, and detector-response calculations, it is demonstrated that the goals and a signal-to background >5-10 for the down-scattered neutron measurement are met if the background, consisting of ambient neutrons and gammas, at the MRSt is reduced 50-100 times.