Abstract
Finite-element methods along with Monte Carlo simulations were used to design a magnetic storage device for ultracold neutrons (UCN) to measure their lifetime. A setup was determined which should make it possible to confine UCN with negligible losses and detect the protons emerging from β-decay with high efficiency: stacked superconducting solenoids create the magnetic storage field, an electrostatic extraction field inside the storage volume assures high proton collection efficiency. Alongside with the optimization of the magnetic and electrostatic design, the properties of the trap were investigated through extensive Monte Carlo simulation.