  In this paper we study the Casimir energy of a sample made by N cavities,
with N >> 1, across the transition from the metallic to the superconducting
phase of the constituting plates. After having characterized the energy for the
configuration in which the layers constituting the cavities are made by
dielectric and for the configuration in which the layers are made by plasma
sheets, we concentrate our analysis on the latter. It represents the final step
towards the macroscopic characterization of a "multi cavity" (with N large)
necessary to fully understand the behaviour of the Casimir energy of a YBCO (or
a BSCCO) sample across the transition. Our analysis is especially useful to the
Archimedes experiment, aimed at measuring the interaction of the
electromagnetic vacuum energy with a gravitational field. To this purpose, we
aim at modulating the Casimir energy of a layered structure, the multi cavity,
by inducing a transition from the metallic to the superconducting phase. After
having characterized the Casimir energy of such a structure for both the
metallic and the superconducting phase, we give an estimate of the modulation
of the energy across the transition.
