  Yukawa potentials are often used as effective potentials for systems as
colloids, plasmas, etc. When the Debye screening length is large, the Yukawa
potential tends to the non-screened Coulomb potential ; in this small screening
limit, or Coulomb limit, the potential is long ranged. As it is well known in
computer simulation, a simple truncation of the long ranged potential and the
minimum image convention are insufficient to obtain accurate numerical data on
systems. The Ewald method for bulk systems, i.e. with periodic boundary
conditions in all three directions of the space, has already been derived for
Yukawa potential [cf. Y., Rosenfeld, {\it Mol. Phys.}, \bm{88}, 1357, (1996)
and G., Salin and J.-M., Caillol, {\it J. Chem. Phys.}, \bm{113}, 10459,
(2000)], but for systems with partial periodic boundary conditions, the Ewald
sums have only recently been obtained [M., Mazars, {\it J. Chem. Phys.}, {\bf
126}, 056101 (2007)]. In this paper, we provide a closed derivation of the
Ewald sums for Yukawa potentials in systems with periodic boundary conditions
in only two directions and for any value of the Debye length. A special
attention is paid to the Coulomb limit and its relation with the
electroneutrality of systems.
