  We investigate several theoretical possibilities for the suppression in a
c-axis magnetic field of the magnetic resonance recently observed in inelastic
neutron scattering experiments on YBCO_{6.6}. We find that neither the Doppler
shift of the quasiparticle states caused by supercurrents outside the vortex
core, nor an assumed spatially uniform suppression of the coherence factors or
spectral gap due to the applied field, can account for the observed effect. In
contrast, suppressing the gap or the coherence factors in the vortex core to
zero is consistent with the data. We demonstrate that an even simpler
description of the data can be achieved by assuming that the resonance is not
supported within an effective radius xi_{eff} around each vortex, where
xi_{eff} is the sum of the superconducting and spin-spin correlation lengths.
We use this simple idea to predict the doping dependence of the field
suppression.
