Clean Nuclear Energy? A German Dr. Rudolf Schulten solved the problem in the 1950s. He invented the Pebble Bed Reactor (PBR). However, his research program was closed down by the German Government after Chernobyl due to political reasons.
it's called Pebble Bed because the fuel elements used are called pebbles. it uses an inert gas (helium) to act as the heat transfer agent. the helium gets heated up inside the reactor, which in turn runs a low pressure turbine to generate power. Helium has a low neutron cross-section, so it hardly gets radioactive despite exposure to the fuel elements. This allows the helium to directly power the generators instead of using heat exchangers (eg. sodium loop in fastbreeder reactors and heat exchangers in light-water reactors). This minimises the overall energy loss.
LWR has steam explosion point. This places an operational temperature limit on LWR. Helium, being a noble gas, has no explosion point. It can operate safely under high temperature. The high temperatures also let the turbine to extract mroe mechanical energy from the same amount of thermal energy. In another words, the pebble bed reactor uses less fuel per kilowatt-hour.
As the reactor gets hotter, the rate of neutron capture by U-238 increases, reducing the number of neutrons available to cause fission. This places a natural limit on the power produced by the reactor. In fact, the reactor is designed such that the cooling rate exceeds the heat generation rate. Even if the neutron moderators are removed, the idle temperature remains low. the case of a meltdown is thus very very unlikely.
Some designs of the pebble bed reactor allow it to be throttled by temperature, ie. by controlling the flow of helium, the energy generation can be increased or decreased, if the need arises. In another words, control rods are not necessary to moderate the reactor. Still then, it uses carbon rods as moderators (for maintenance sake).
PBRs are intentionally operated above the annealing temperature of graphite, so that Wigner energy is not accumulated. This solves a problem discovered in a famous accident, the Windscale fire. One of the reactors at the Windscale site in England (not a PBR) caught fire because of the release of energy stored as crystalline dislocations (Wigner energy) in the graphite. The dislocations are caused by neutron passage through the graphite. At Windscale, a program of regular annealing was put in place to release accumulated Wigner energy, but since the effect was not anticipated during the construction of the reactor, the process could not be reliably controlled and led to a fire.