  A novel cold neutron source employing chess-board or staircase assemblies of
high-aspect ratio rectangular \hpara moderators is proposed. It is demonstrated
that this design can generate neutron beams with higher intensity and
brightness, up to approximately 2.5 times more than any para-hydrogen-based
cold neutron source with an equal cold neutron beam cross-section made of a
single moderator (flat or voluminous). Two limiting factors for this gain are
identified: the limited volume of the high-density thermal neutron region
surrounding the reactor core or spallation target, which imposes constraints on
the total length of the moderator assembly, and the finite width of moderator
walls. Moreover, the relatively large length of moderator assemblies makes
their application for short pulse neutron sources very problematic. An analytic
approach for calculating the brightness of para-hydrogen moderators is
introduced. Because brightness gain originates from a near-the-surface effect
resulting from the prevailing single collision process during thermal-to-cold
neutron conversion, high-aspect ratio rectangular cold moderators offer a
significant increase, up to a factor of 10, in cold neutron brightness. The
obtained results are in excellent agreement with MCNP calculations. The concept
of 'low-dimensionality' in moderators is explored, demonstrating that achieving
a substantial increase in brightness necessitates moderators to be
low-dimensional both geometrically, implying a high aspect ratio, and
physically, requiring the moderator's smallest dimension to be smaller than the
characteristic scale of moderator medium (about the mean free path for thermal
neutrons). This explains why additional compression of the moderator along the
longest direction, effectively giving it a tube-like shape, does not result in
a significant brightness increase comparable to the flattening of moderator.
