  The presence of magnetic field is crucial in the transport of energy through
the solar atmosphere. Recent ground-based and space-borne observations of the
quiet Sun have revealed that magnetic field accumulates at photospheric
heights, via a local dynamo or from small-scale flux emergence events. However,
most of this small-scale magnetic field may not expand into the chromosphere
due to the entropy drop with height at the photosphere. Here we present a study
that uses a high resolution 3D radiative MHD simulation of the solar atmosphere
with non-grey and non-LTE radiative transfer and thermal conduction along the
magnetic field to reveal that: 1) the net magnetic flux from the simulated
quiet photosphere is not sufficient to maintain a chromospheric magnetic field
(on average), 2) processes in the lower chromosphere, in the region dominated
by magneto-acoustic shocks, are able to convert kinetic energy into magnetic
energy, 3) the magnetic energy in the chromosphere increases linearly in time
until the r.m.s. of the magnetic field strength saturates at roughly 4 to 30 G
(horizontal average) due to conversion from kinetic energy, 4) and that the
magnetic features formed in the chromosphere are localized to this region.
