We study the feasibility of storing cold neutron beams in a strong focusing synchrotron. We also propose an alternating-current (ac) dipole magnet to be used as a neutron acceleration device and a pulsed quadrupole as a neutron beam kicker for injection and extraction. The ac acceleration device can provide adiabatic capture, acceleration, or deceleration of neutron beams. It seems feasible to design a high-quality neutron synchrotron for many future neutron beam applications, such as neutron life time measurements, monoenergetic neutron scattering experiments, and pencil neutron beam applications. This synchrotron can also be used as an injector for a neutron accumulator ring. Published by the American Physical Society 2024