  We obtained high-resolution VLT and FUSE spectra of the quasar HE2347-4342 to
study the properties of the intergalactic medium between redshifts z=2.0-2.9.
The high-quality optical spectrum allows us to identify approximately 850 HeII
absorption components with column densities between N~5X10^11 and $ 10^18
cm^-2. The reprocessed FUSE spectrum extends the wavelength coverage of the
HeII absorption down to an observed wavelength of 920 A. Approximately 1400
HeII absorption components are identified, including 917 HeII Ly-alpha systems
and some of their HeII Ly-beta, Ly-gamma, and Ly-delta counterparts. The
ionization structure of HeII is complex, with approximately 90 components that
are not detected in the hydrogen spectrum. These components may represent the
effect of soft ionizing sources. The ratio Eta=N(HeII)/N(HI) varies
approximately from unity to more than a thousand, with a median value of 62 and
a distribution consistent with the intrinsic spectral indices of quasars. This
suggests that the dominant ionizing field is from the accumulated quasar
radiation, with contributions from other soft sources such as star-forming
regions and obscured AGN, which do not ionize helium. We find an evolution in
Eta toward smaller values at lower redshift, with the gradual disappearance of
soft components. At redshifts z>2.7, the large but finite increase in the HeII
opacity, Tau=5+/-1, suggests that we are viewing the end stages of a
reionization process that began at an earlier epoch. Fits of the absorption
profiles of unblended lines indicate comparable velocities between hydrogen and
He^+ ions. At hydrogen column densities N<3X10^12 cm^-2 the number of forest
lines shows a significant deficit relative to a power law, and becomes
negligible below N=10^11 cm^-2.
