  We study the magnetic response of a superconducting double strip, i.e., two
parallel coplanar thin strips of width $2w$, thickness $d \ll w$ and of
infinite length, separated by a gap of width $2s$ and subject to a
perpendicular magnetic field $H$. The magnetic properties of this system are
governed by the presence of a geometric energy barrier for vortex penetration
which we investigate as a function of applied field $H$ and gap parameter $s$.
The new results deal with the case of a narrow gap $s \ll w$, where the field
penetration from the inner edges is facilitated by large flux focusing. Upon
reducing the gap width $2s$, we observe a considerable rearrangement of the
screening currents, leading to a strong reduction of the penetration field and
the overall magnetization loop, with a suppression factor reaching $\sim
(d/w)^{1/2}$ as the gap drops below the sample thickness, $2s < d$. We compare
our results with similar systems of different shapes (elliptic, rectangular
platelet) and include effects of surface barriers as well. Furthermore, we
verify that corrections arising from the magnetic response of the Shubnikov
phase in the penetrated state are small and can be omitted. Extending the
analysis to multiple strips, we determine the specific sequence of flux
penetrations into the different strips. Our studies are relevant for the
understanding of platelet shaped samples with cracks or the penetration into
layered superconductors at oblique magnetic fields.
