  We describe the application of displaced, or misaligned, beams in a
mirror-based magneto-optical trap (MOT) to enable portable and miniaturized
atom chip experiments, where optical access is limited to a single window. Two
different geometries of beam displacement are investigated: a variation on the
well-known 'vortex-MOT', and the other a novel 'hybrid-MOT' combining
Zeeman-shifted and purely optical scattering force components. The beam
geometry is obtained similar to the mirror-MOT, using a planar mirror surface
but with a different magnetic field geometry more suited to planar systems.
Using these techniques, we have trapped around 6$\times 10^6$ and 26$\times
10^6$atoms of $^{85}$Rb in the vortex-MOT and hybrid-MOT respectively. For the
vortex-MOT the atoms are directly cooled well below the Doppler temperature
without any additional sub-Doppler cooling stage, whereas the temperature of
the hybrid-MOT has been measured slightly above the Doppler temperature limit.
In both cases the attained lower temperature ensures the quantum behaviour of
the trapped atoms required for the applications of portable quantum sensors and
many others.
