  We extend our investigation of magnetic field evolution in three-dimensional
flows driven by the stationary accretion shock instability (SASI) with a suite
of higher-resolution idealized models of the post-bounce core-collapse
supernova environment. Our magnetohydrodynamic simulations vary in initial
magnetic field strength, rotation rate, and grid resolution. Vigorous
SASI-driven turbulence inside the shock amplifies magnetic fields
exponentially; but while the amplified fields reduce the kinetic energy of
small-scale flows, they do not seem to affect the global shock dynamics. The
growth rate and final magnitude of the magnetic energy are very sensitive to
grid resolution, and both are underestimated by the simulations. Nevertheless
our simulations suggest that neutron star magnetic fields exceeding $10^{14}$ G
can result from dynamics driven by the SASI, \emph{even for non-rotating
progenitors}.
