  The Galactic halo contains a complex ecosystem of multiphase
intermediate-velocity and high-velocity gas clouds whose origin has defied
clear explanation. They are generally believed to be involved in a Galaxy-wide
recycling process, either through an accretion flow or a large-scale fountain
flow, or both. We examine the evolution of these clouds in light of recent
claims that they may trigger condensation of gas from the Galactic corona as
they move through it. We measure condensation along a cloud's wake, with and
without the presence of an ambient magnetic field, using two- (2D) and
three-dimensional (3D), high-resolution simulations. We find that 3D
simulations are essential to correctly capture the condensation in all cases.
Magnetic fields significantly inhibit condensation in the wake of clouds at $t
\gtrsim 25$ Myr, preventing the sharp upturn in cold gas mass seen in previous
non-magnetic studies. The magnetic field suppresses the Kelvin-Helmholtz
instability responsible for the ablation and consequent mixing of a cloud with
halo gas which drives the condensation. This effect is universal across
different cloud properties (density, metallicity, velocity) and magnetic field
properties (strength and orientation). Simple convergence tests demonstrate
that resolving the gas on progressively smaller scales leads to even less
condensation. While condensation still occurs in all cases, our results show
that an ambient magnetic field drastically lowers the efficiency of
fountain-driven accretion and likely also accretion from condensation around
high-velocity clouds. These lower specific accretion rates are in better
agreement with observational constraints compared to 3D, non-magnetic
simulations.
