  We study the development of high energy (E_in < 1TeV) cascades produced by a
primary electron of energy E_in injected into the intergalactic medium (IGM).
To this aim we have developed the new code MEDEA (Monte Carlo Energy DEposition
Analysis) which includes Bremsstrahlung and Inverse Compton (IC) processes,
along with H/He collisional ionizations and excitations, and electron-electron
collisions. The cascade energy partition into heating, excitations and
ionizations depends primarily on the IGM ionized fraction, x_e, but also on
redshift, z, due to IC on CMB photons. While Bremsstrahlung is unimportant
under most conditions, IC becomes largely dominant at energies E_in > 1MeV. The
main effect of IC at injection energies E_in < 100MeV is a significant boost of
the fraction of energy converted into low energy photons (h\nu < 10.2eV) which
do not further interact with the IGM. For energies E_in > 1GeV CMB photons are
preferentially upscattered within the X-ray spectrum ($h\nu > 10^4eV) and can
free stream to the observer. Complete tables of the fractional energy
depositions as a function of redshift, E_in and ionized fraction are given. Our
results can be used in many astrophysical contexts, with an obvious application
related to the study of decaying/annihilating Dark Matter (DM) candidates in
the high-z Universe.
