I don't have the time at the moment but I'll come back and fill in more details later, I wanted to inject a few important facts into this thread first though.

One thing a lot of people have misconceptions about is that Thorium reactors (like the LFTR design) would be easy to build and have far fewer problems than existing reactor designs. Thorium reactors would have some advantages but a lot of the hype around them comes from a very good sales job which ignores a lot of the fundamental problems. A Thorium fuel cycle means breeding U-233 which means producing lots of U-232 as a byproduct. U-232 is nasty stuff, it's an extremely active gamma emitter. Humans can't be near the stuff, and gamma rays aren't easily blocked by water so you need special shielding and you need a robotic/waldo based fuel handling and processing infrastructure, negative pressure glove boxes won't cut it. Also, gammas are extremely bad for both electronics and the materials commonly used for seals and joints. So that's a huge engineering nightmare trying to come up with special materials and systems that won't degrade quickly in a Thorium reactor environment. Add to that othe fuel cycle worries and the reactor design defecit (Uranium reactors are on their 4th major generation, LFTRs are on their zeroeth) and it's a daunting development challenge.

Also, the claim that the Thorium fuel cycle is immune to weapons proliferation issues is sort of bunk. The ordinary byproducts of reactor operations wouldn't be useful in weapons, but that's mostly true for existing reactors too. In practice the fact that any fission power plant, regardless of fuel, is a prodigious neutron source means that you can breed U-238 into Plutonium as easy as baking a cake (leave samples in the neutron flux for a set period of time, remove and chemically separate the Plutonium, then continue until you have enough for bombs).

Only one has been built so far, the Molten Salt Reactor Experiment at Oak Ridge. Lots of old photos there.

It worked. People are still trying to figure out how to fully clean it up though. Check that out; the preface is written by one of the people who first worked on it.

It is safe in the sense that the reaction cannot run out of control and the plutonium you could get out of it would be too hot and too contaminated to be used in a bomb. However, it is unsafe because the contents of the tank are the stuff of materials science nightmares.

The FLiBe solution is very hot, rapidly poisonous, bitingly radioactive and intensely corrosive molten salts that continually evolves gaseous fluorine and tritium. Fluorine is the most reactive element known and has the potential to slowly eat through almost every material known to man. Tritium is valuable (especially if you want a hydrogen bomb) and is produced in small amounts by all reactors, but it enters and accumulates within the lattices of metals and slowly makes them more and more brittle.

Oh, and the unattended partly decomissioned fuel nearly had a criticality incident because uranium hexafluoride gas was building up in the top of the salt storage space.

So it's "safe," but not necessarily safe to work on, safe to keep mothballed with no attention paid to it, or inherently safe for the local water supply. Be careful what you wish for.

(I'm posting this as another top level reply instead of editing my original)

OK, so first let's start with a whirlwind tour of nuclear technology and fission physics.

Some isotopes can be fissioned when struck with a neutron, and some such isotopes will release additional neutrons when fissioning. This enables a neutron mediated fission chain reaction where a neutron induces a fission reaction which releases neutrons (and produces fisson byproducts) which induce additional fission reactions, and so forth. Isotopes capable of such are called "fissile". Now, if you have an assembly which contains fissile materials and if the product of the statistical probability of a neutron being released from within the assembly resulting in a fission reaction (vs. simply escaping or being absorbed by non fissile isotopes) multiplied by the average number of neutrons generated during a fission reaction is in total equal to or greater than 1 then that assembly is said to be "critical" (e.g. 50% * 2 neutrons per fission = 1). In a sub-critical assembly the number of neutrons and fission reactions will decrease from "generation" to generation. In a precisely critical assembly the neutrons and fission reactions are kept at a steady state. In a critical assembly the fission reactions will increase over time, allowing an increase in energy produced. In a super-critical assembly (as in a bomb) the energy released will rapidly increase from generation to generation in a runaway process.

That brings us to moderators. Fission reactions normally release very high energy (fast) neutrons. However, the propensity (or "cross section") of a fissile nucleus to fission varies based on neutron speed, and by several orders of magnitude. For an isotope like U-235 the cross section is much higher for "thermal" (room-temperature-ish kinetic energy) neutrons. Neutrons can be screened through various materials which can slow them down from their inate fast speeds to thermal speeds, this is called moderation. Common moderators include water, deuterated (heavy) water, and graphite. By controlling the insertion or removal of these materials, as well as neutron absorbers and other elements, in a reactor the level of criticality and power production can be precisely controlled, making fission power reactors practical systems.

And that brings us to acquisition of fissile materials. Rather fortunately it's very difficult to use natural materials to create nuclear reactors, and impossible to make bombs. The main fissile isotopes are U-235 and Pu-239. U-235 exists as 0.7% of natural Uranium, which means that in order to get sizable amounts of it you have to painstakingly isotopically seperate Uranium. Which uses lots of advanced equipment, lots of energy, and lots of raw materials. Plutonium can be bred using any neutron source, like a reactor, from natural Uranium (U-238). Normally you put U-238 in a reactor for a while then take it out and chemically separate out the bred Plutonium, which can be used for fuel or bombs, depending on how long it spent in the reactor. If it spent a long time in the reactor then significant quantities of Pu-240 and other Plutonium isotopes will also exist, and these basically make it impossible to make bombs out of the Plutonium due to "pre-detonation" issues which we won't go into. That's how you get weapons grade Plutonium (mostly Pu-239, from short periods in a reactor) and reactor grade Plutonium (a mixture of Plutonium isotopes, from long periods in a reactor).

So, what does this have to do with Thorium and where's the history? Trust me, I'll get there.

First, some history of conventional nuclear reactors. The nuclear industry started with nuclear weapons. The Manhattan project developed several technologies for isotope separation which were used to produce highly enriched Uranium for bombs. It also developed breeder reactors for producing Plutonium. These systems gave an early start to the Uranium/Plutonium nuclear fuel cycle, by creating the infrastructure necessary to produce fuel rods for power reactors developed down the road. There was early development of very small-scale research reactors but the first power reactors were developed by the Navy. At the time there was a very significant initial development cost to power reactors, but the advantage of nuclear power for aircraft carriers, capital ships, and especially submarines was too tremendous to pass up. It took less than a decade from the end of WWII for nuclear reactors as a source of power for submarines to be realized.

The demands of a reactor for a submarine drove the design toward a pressurized light water (solid core) design fueled by enriched Uranium. Such reactors can be compact with a high power density, and they use fuel that can be provided by the same processing infrastructure used for nuclear weapons, which made them a near-term feasible technology in the 1950s. The Navy's work helped jump start civil power reactor research in the '50s and '60s which ended up focusing heavily on solid core light water reactors.

Molten salt reactor interest began in the 1940s, as various folks, especially the US military, sought various applications of nuclear reactor technology. The Navy had their program which bore fruit in reactors for powering submarines, aircraft carriers, and potentially other vessels. The Army had their program in the form of land-based power reactors of different sorts, with the idea of being able to provide power to remote bases. The Air Force also got into the act, with the idea of developing nuclear powered aircraft. NASA got into the act too with the concept of nuclear powered rockets (project NERVA and ORION).

Nuclear powered aircraft concepts took several forms: a ramjet concept which passed ram compressed air directly through a high temperature reactor and a turbojet concept which replaced the heating of turbine compressed air with either direct heating from a reactor or with indirect heating via a heat exchanger. These concepts were, to say the least, incredibly ambitious, risky, and unconventional. The nuclear ramjet evolved into an unmanned cruise missile concept, due to the radiation exposure issues. The nuclear powered turbojet concept evaluated several possible power sources, including a molten salt reactor, due to the possibility of extremely high temperature operation. In such a design a reactor would use a fissile actinide (e.g. Uranium) salt as a fuel which would be dissolved in a larger volume of another salt. The salt and fuel would be held at hundreds of degrees Celsius during operation, keeping the salt molten. The fuel would be cycled through the reactor core where it would flow through a moderation apparatus and experience fission criticality, then it would flow through a series of heat exchanger loops where it would provide heat to either a power generator (e.g. steam turbine) or, in the nuclear aircraft concept, to the compressed air in a modified turbojet engine.

In the early 1950s this research gave rise to the first molten salt reactor experiment, the "Aircraft Reactor Experiment" conducted by the US Air Force. A small-scale molten salt reactor powered by U-235 fuel was operated for a few days in 1954 to prove the concept. Additionally, solid core reactor experiments were also conducted to explore the feasibility of nuclear powered aircraft. These included fully operational turbojet engines powered by nuclear reactors and nuclear reactors flown on conventional jets to evaluate shielding requirements. It should be noted that few of the scientists working on the nuclear powered aircraft project thought it was actually feasible, and many thought it was actually rather daft. Though many were intrigued by the unique reactor concept and its potential in other applications.

In the first few months of President Kennedy's administration, in 1961, most of the research on nuclear aircraft was cancelled, with the nuclear ramjet powered cruise missile concept living on for a few years longer (being cancelled in 1964). Ultimately such designs proved impractical due to the heavy shielding requirements for manned aircraft or the extreme radiological contamination problems of unmanned vehicles.

But despite the impracticality of nuclear powered aircraft the molten salt concept gained a lot of attention due to several rather unique features. High temperature operation at low pressure (which promised high efficiency while maintaining good safety margins) and inherent controllability due to a high negative temperature coefficient of reactivity. Solid core reactors can be designed with a negative temperature coefficient as well, but that's not always the case (the Chernobyl disaster being the poster child of badly designed positive temperature coefficient reactors).

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