Fast Breeder Reactors

Uranium contains a fissile isotope 235U, as 0.7% of the naturally mined and chemically refined metal. Current commercial power plant designs, which are remarkably successful and reliable, use only the fissile isotope, and in the USA they essentially throw away the rest. Indeed, since the fuel rods do not contain all of the fissile isotope from the enrichment process, and fail to sustain the nuclear reaction when half of it is consumed, they only use about 0.3% of the raw, natural uranium. A fast breeder reactor (actually it's a fast-neutron, breeder, reactor) uses neutrons which have not been slowed down by a moderator, to turn some of its non-fissile isotope 238U into 239Pu, a fissile isotope of plutonium. This plutonium is a neutron-capture product. In a fast breeder reactor, the fuel atoms which have not yet split may capture more neutrons, forming americium, curium, and perhaps more. These elements are also called transuranic.
Strictly speaking, this is not the only possible design.
232Th --thorium --can be made into 233U, a different fissile isotope of uranium, in the same way, only it doesn't need fast neutrons.

In the long run, therefore, a fast breeder reactor can extract about 200 times as much energy from a ton of fuel as the non-recycling designs. This is pretty impressive, considering that about 50 tons of uranium suffice to provide as much energy in today's reactors as 1.25 million tons of coal in coal burning plants.

There have been several designs tried for constructing a viable breeder reactor for civilian use.
The most successful was at Argonne National Labs., twenty years ago. It was called the Integral Fast Reactor, IFR for short. It worked, and in the very month that the Chernobyl reactor failed, the project's EBR II (Experimental Breeder Reactor II) had already proven itself immune, by deliberate test, to that kind (and the TMI and Fukushima-Daiichi kind) of failure. It was cancelled in 1994 in response to people who think themselves environmentalists. There exists now (July 2010) a proprietary plan to build packaged 100 MWe reactors using the proven technology of the EBR II reactor.

How the IFR differs from current nuclear reactor designs

How the ARC 100 Differs from the IFR

Uranium Enrichment

is the process which separates natural uranium into depleted uranium and enriched uranium.
Enriched uranium is uranium with enough of the fissile isotope that it can sustain a nuclear chain reaction. The fissile isotope 235U differs from the non-fissile 238U only by three neutrons in its nucleus, and the mass difference is all that the enrichment operation can use. Two exceedingly tedious methods can work. Both work with uranium hexafluoride, UF6, whose molecules have molecular 'weights' of 349 and 352, depending upon the uranium isotope.
A centrifuge makes use of this mass difference. At the huge pseudo-gravitational force of the centrifuge, the heavier gas collects on the outside, and the lighter enriched gas in the center.
A gas diffusion apparatus can force the gases through porous membranes (brick-like) through which the gases diffuse at speeds proportional to the square root of the molecular weight.
Gradually, the isotopes become somewhat segregated.
As I said, the process is tedious. It is far more energy-intensive than mere chemical refining. Before this, the fluorine is combined with, and after is dissociated from, the uranium. Reactor-grade enriched uranium for Pressurised Water Reactors (PWRs) is 3.6% 235U. At, there is an example of the enrichment results which starts with 8.05 tonnes natural uranium, producing 1.0 tonne of reactor grade (3.6% U-235) uranium and 7.05 tonnes uranium depleted to 0.3% fissile U-235. In 1999, the USA had stocks of depleted uranium amounting to about 480,000 tonnes.
Note that if ARC100 can produce 20 years' worth of 100 MW from 8% of 20.7 tonnes, that's 100 MW for 1.656 tonnes of depleted U, or 20 GW-yr for 16.56 tonnes, so for 455,400 tonnes of that reserve stock, we'd have enough for 5500 GW-yrs of energy
Suppose we wanted an additional 55 GW of nuclear power. That's 550 such ARC100 reactors. Initial loading requires 20.7 tons each of uranium, at an enrichment of "less than 20%", actually three zones of 10.1, 12.1, 17.2 percent. Taking the average, 13.13, call it 14% means we'd need 550 x 20.7 x 0.14 tons of fissile isotope to start up. That's 11385 tons of uranium, containing just under 1600 tons of fissile U-235 or Pu-239. There's probably enough plutonium in the civilian spent fuel dumps to supply all that, and without actually separating it entirely from the U-238.

Fission Products

When a nucleus responds to collision with a neutron by splitting, this is called nuclear fission, and there are usually two fragments of about half the atomic weight of the nucleus that was split, and some more neutrons. These are called fission products. Many of them are so unstable that they decay in under a second to become another atomic nucleus and a small particle such as a helium nucleus or an electron, these being also called alpha and beta radiation. The radioactivity of an unstable isotope is inversely proportional to its half-life. It should be noted that at ten times the half-life, one 1024th of the original is all that is left. You could call it the one-thousandth-life.
So a freshly removed spent fuel rod is vastly more radioactive than one that is a day old! After a year, the radioactivity of fission products, if they were separated from the long-lived plutonium, is quite small.
Even in terms of its radioactivity, the statement that plutonium is the most toxic substance known is utter rubbish. It's twenty times less radioactive than radium, and a microgram of radium is nothing compared with a microgram of radon, because radon decays in days, not thousands of years. The fission products and further decay products are correctly called nuclear waste. Neutron capture products, being usable as fuel, should not be so classified.