Project Icarus is indeed furthering this goal. In retrospect, certain portions of the Daedalus report seem optimistic and should be updated:
Daedalus proposed the use of relativistic electron beams to compress the fuel pellets, but subsequent research has shown that electron beams could never provide the necessary punch. More recent research into inertial confinement fusion (ICF) has used lasers or ion beams instead. Nevertheless, the recent failure of the 20-year, $4 billion National Ignition Facility (NIF) to achieve break-even fusion has highlighted the difficulty of mastering ICF, even under ideal conditions.
The use of He3 to fuel Daedalus is a major hurdle, because He3 is unavailable on Earth, and so must be mined from the gas giants. Such mining operations would be prohibitively complex and expensive at present, and will likely remain so for (many) decades to come.
The limited availability of declassified information on nuclear technology at the time led the Daedalus team to make some unrealistically optimistic assumptions about the ability of the engine core to prevent damaging neutron and x-ray radiation from impacting the vessel.
Tritium cores were used in the fuel pellets to help spark ignition, but the heat generated in the fuel tanks by tritium decay (half-life 12 years) would have ruptured the pellets without a significantly beefier cryogenic system.
Pellet rupture would also have occurred as the tanks emptied, unless a substantial additional mass of tank pressurant were provided to maintain tank pressurization.
Finally, Daedalus imagined two R2D2-like droids -- with diagnostic capabilities advanced by even today's standards -- to identify and repair all failures aboard the vessel while it was en-route.
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