  In the near future there will be the request for very large liquid Xenon
(LXe) detectors for Dark Matter (DM) searches in the 50-ton range. To avoid an
impractically long, single drift space of a dual-phase detector, it seems
beneficial to use the single-phase technique. Since electrons then can drift in
any direction, we can segment the homogeneous medium and thus avoid an
excessive maximum drift path of order 4 m. The shorter detector length has
several benefits, e.g. requiring a lower cathode voltage for the same drift
field. We can easily split the TPC into two regions with the cathode in the
center and two anodes at the top and bottom. One also can use multiple TPCs
stacked on top of each other in the same liquid volume to reduce the maximum
drift length even further.
  A further division of the drift space by installing an additional anode in
the center would require S2 photons to traverse the liquid for several times
the Rayleigh scattering length in LXe, which is only 30 - 40 cm. This seems to
be excessive for good x - y localization. We therefore suggest a geometry of
two independent TPCs with two drift spaces each.
  Despite earlier publications concerns persisted about the effect of
shadowing. A detailed FEM model of the anode regions shows that with an aligned
wire arrangement the drifting electrons impinge sideways on the anode in a
narrow angular range of width 15$^{\circ}$ - 20$^{\circ}$. Most S2 photons are
emitted in full view of the close-by PMT array. About 37% of the S2 photons are
shadowed by the anode wire out of which 30\% will be reflected back again on
the gold plating of the wires. Thus we can observe 74% of the total S2 light.
Compared to a dual-phase detector, however, we do not suffer from the
extraction efficiency, sometimes reported as low as 50%.
