Prompted by plans for a free neutron oscillation experiment at the European Spallation Source (ESS), we consider issues associated with the magnetic fields that must be present. To this end, we introduce a stochastic model of the residual magnetic field within the propagation region which draws on features of magnetic profiles measured during the last free oscillation experiment at the Institut Laue-Langevin (ILL). A perturbative analysis, which relates the antineutron probability to the power spectral density of the magnetic field sampled, suggests that deviations from the quasifree result will increase quadratically with the length l of the propagation region. However, with inclusion of averaging over representative spectra of neutron speeds, departures from the quasifree result are found to be approximately linear in l. As regards the large spikes in the magnetic field at, for example, joints in the magnetic shielding of the propagation region (despite compensating currents and magnetic idealization of the shield), we demonstrate that their effect scales as l/D-3/2, where D is the diameter of the cylindrical magnetic shielding, and identify conditions under which they can be neglected. We also establish that any large magnetic field encountered after the propagation region is exited will not diminish the probability for antineutron detection. For the range of values of l of most interest to the ESS experiment, it should suffice to improve on the level of magnetic suppression achieved at the ILL by a factor of 2.
