The waste issue (as well as inherent safety) is part of the reason that there's so much research on ADSRs right now (note: the article says that an ADSR "would use thorium as a fuel", but it's not actually limited to thorium, it can use any subcritical fissile core). Spallation can rip apart the long-lived actinides that don't have a sufficient (n, gamma) cross section to prevent their accumulation in nuclear waste. And of course, since the core is inherently subcritical by design, simply not enough neutronicity under any condition to sustain a chain reaction on its own, when you shut the beam off, fission ceases instantly (though you still have decay heat like with any other nuclear power plant). Spallation source provides no more than about 10% or so of the neutronicity, but it's the amount needed to push the core over the edge.
I have my own very radical variant on the concept of an accelerator driven fission that I'm working on simulating now in Geant4 (although that was probably a poor choice of software, apparently their thermal scattering codes are really immature... as far as CERN is concerned, once particles get down below the MeV range they're usually not particularly interesting). But anyway the concept is to have a core with literally zero neutronicty - a lithium-burning reactor. The basic concept is as such:
1. A planar proton beam is delivered by one or more high power linac beamlines. Commercial-scale linac costs - without any improvements in technology - are expected to cost $5-20 per watt. The particular design would call for very high voltage (~16MV) klystrons to drive it - and not simply to reduce size (more in this shortly)
2. The proton beam bombards a fragment emitting target inside an axial magnetic field in a vacuum. The estimation of deceleration efficiency is estimated at over 90% in fragment reactors due to the lack of Carnot losses (according to the published research on the subject). The resultant HVDC will be direct converted to the klystron voltage in producing the electron beam that drives the linac. About 60% of the energy of spallation goes into fragment production. Fragments will be drawn away from the fragment target en route to the collector via a slightly expanding axial magnetic field. Fragment collection allows for automatic isotope separation.
3. The maximum power output of a fragment reactor is limited by its surface area and its ability to radiate heat. Fragment-emitting targets can be either electrostatically suspended dust or rapidly rotating with thin fibers or planes of target material, in order to radiatively cool without melting. Spallation targets, for efficiency, need to be high-Z materials, such as lead, tungsten, mercury, etc. Tungsten is particularly attractive due to its high melting point of 3695K. High-Z metal-rich ceramics are also possible targets, with very high melting points. The temperature of the chamber's beryllium walls being radiated to will be around 1050K. This means heat exchange between a ~3000K emitter (4.6e7W/m) and a 1050K receiver (6.8e4W/m), or about 4.5MW per square meter. In short, this allows for a surprisingly compact core, limited more by the length necessary to ensure a sufficient proton spallation cross section.
4. Neutrons emitted by spallation (at a cost of 30-40 MeV per neutron) are heavily biased by energy level. High energy neutrons are biased in the forward direction, while lower energy neutrons scatter with less of a forward bias. As a result, the high energy neutrons (>8 MeV) predominantly continue forward in the high-Z target where they receive a better neutron multiplication ratio than they would in beryllium, while the lower energy (2,5-8MeV) neutrons are predominantly multiplied in the beryllium walls, which is the only effective multiplier for such an energy range. The net neutron yield after multiplication should be around one neutron per 20 MeV of input energy.
5. The beryllium walls, being the recipient of about 2/3rds of the proton beam's energy, are effectively a giant array of cooling channels. As the neutrons are still relatively high energy at this point, the neutron cross sections are not huge and the choice of coolant not critical. The coolant temperature should reach about 1000K and thus allow for around 50% efficient power generation.
6. The neutrons continue scattering outwards past the beryllium and need to be thermalized. This is done in stages to progressively lower their temperature as well as to insulate each section from the next. The first stage would likely be ideally loose-fill graphite. The stage would operate at a minimum temperature of 500-600K to prevent the accumulation of Wigner energy. The still fairly high neutron temperature means that there's some degree of options on wall material based on whether one wants to keep the neutron losses to a small fraction of a percent (say, carbon-carbon or 90-Zr) up to a percent or so (steel).
7. The next neutron cooling stage is a little more sensitive to neutron loss. There are many moderator possibilities. I like the possibility of supercritical CO2 under around 100 ATM (roughly the same pressure that one would want the cooling channels in the beryllium), although lower pressure moderators are certainly an option. A sparse fibrous or porous insulation poor in metallic cations and rich in carbon, nitrogen, and/or oxygen would limit thermal heat flow without offering significant neutron capture. (Wigner energy is not as much of a concern in fibrous materials and carbon-carbon). The outer wall should ideally have a low neutron cross section - plastic, composites, carbon-carbon, and zirconium (natural or 90Zr) are all options to keep the neutron losses at a fraction of 1% percent. The neutron temperature would be lowered to about 200K.
8. The third neutron cooling stage is rather sensitive to neutron loss. It can be heavy water ice, dry ice, or compressed helium, with sparse carbon and oxygen-rich insulation as needed. The temperature is lowered down to near the coolant temperature, which may be ~80K in the case of liquid nitrogen, ~55K in the case of isobutane, or lower in the case of compressed helium. This region begins to become somewhat sensitive to incidently captured radiation, such as gamma, as it takes a dozen-ish joules of energy to remove one joule of heat from it. The outer wall needs be made of a low cross-section material - materials like aluminum and steel are not options at this point.
9. The fourth and final neutron cooling stage is liquid helium. There are no other options with realistically low neutron cross sections except for extremely expensive materials like 15N and tritium. The temperature should be as low as reasonably possible without requiring expensive 3He-based refrigeration systems - 1,5-2K. However, it should be kept it from forming a superfluid, due to the extreme thermal conductivity superfluids present. Helium has a rather low thermal conductivity on its own, so additional insulative material is probably not needed. While conductive inflow of heat to this stage should be minimal due to the great thickness of insulation formed by the prior stages, incident capture of nuclear energy absolutely must be minimized (this is where accurate simulations become critical) - in particular, gamma from a wide range of nuclear processes elsewhere in the reactor. While helium is a very poor gamma absorber, every joule of energy captured in it equates to having to spend hundreds of joules of cooling energy. If gamma capture proves too great, additional periodic gamma absorbers can be placed (more on this shortly).
10. Periodically breaking up this stage are the reason for all of this neutron cooling: the 7-lithium capture assembly. We have to cool the neutrons to boost the lithium (n,gamma) cross section sufficiently. Each assembly consists of an extremely low neutron capture, low scattering cross sections, high gamma cross section, thermally resistive wall capable of maintaining a vacuum. There is unfortunately only a rather short list of candidates meeting this spec - namely, 90-Zr and 208-Pb foams. Fortunately, processes for foaming both metals already exist - foamed lead and zirconium are available on the open market. 90Zr is estimated to cost about $300 per kilogram - which would be affordable in this context. 208-Pb - is more uncertain. It can be found naturally enriched up to about 90% in thorium ores, but as far as I have been able to find there are no estimates as to what it would cost to produce. One paper estimates that 99% pure 208-Pb produced from ordinary lead would cost about $7000 per kilogram from normal lead, but probably significantly less from naturally enriched lead. Regardless of the choice of material, their interior surface would contain cooling channels. The coolant would be gaseous helium, possibly multiple channels different temperatures to optimize cooling efficiency.
11. Inside each assembly would be a series of thin (100um) 7-Li foils. To help maintain structural integrity, increase heat tolerance, and decrease flammability during maintenance, they can be alloyed with 90-Zr (maintenance should not be commonly needed, more on that later). The (n, gamma) capture cross section is about 1/8th of the scattering cross section, so a lot of neutrons will scatter, increase in energy, and many will leave the assembly. However, they will overwhelmingly be re-cooled in the helium (depositing an irrelevantly trivial amount of energy) and return to the foils for repeated passes, as the scattering distance at such low neutron energies is so small. The spacing of the foils will need to be proportional the axial magnetic field strength - for a 10T field, it works out to about 3 centimeters. Heat captured by incident betas or gammas will be radiated to the assembly walls
12. Any (n, gamma) reactions in the lithium would produce 8Li, which decays in about 0,8 seconds by releasing an incredibly powerful 16 MeV beta. The byproduct is helium. The very thin foils provide a poor beta capture target; the betas are collimated by the magnetic field and drawn away from the foils by the field's gradual expansion. The result is a monoenergetic 16MeV electron beam leaving the reactor. This 16MeV beam is fed straight into the linac klystrons.
Let's look at the overall energy picture. A good superconducting linac achieves around 85% efficiency, all associated hardware systems included. By starting with HVDC for beam production, and especially an already-produced electron beam of the desired energy, we only stand to improve this number. Let's say an average of 88% efficiency and a beam energy output of 100MW, meaning 113MW consumed. Each 20 MeV of proton energy, after multiplication, gives us a neutron. The vast majority of those neutrons (we'll say 90%) give us 16 MeV of 7Li beta energy, making up all but 6.2 MeV of the initial proton energy. So 113MW in, 69MW out. However, that's only the start of it. 60% of the beam's energy used to make those neutrons goes into fission fragments, and we capture that energy to electricity at 90% efficiency. So that's 54MW more for our accelerator, for a total of 123MW. But we're not done - that's only our non-Carnot energy. Virtually all of the energy of thermalizing these neutrons happened at high temperatures and is captured in the cooling channels in the beryllium and graphite, turning into electricity at around 50% efficiency. And while neutron multiplication is an endothermic process, the resulting tungsten fragments both from spallation and proton capture will yield more energy via decay than they consumed (splitting up nuclei heavier than iron yields a net release of energy), thus adding more heat to the system. Furthermore, energy lost to heat in our ion deceleration grids, our klystrons, and other components of our linac also goes toward electricity production; altogether, the thermal energy production should add perhaps 35MW more electricity generation.
In short, our 16MeV 7Li betas and our spallation fragments power our accelerator with a little bit to spare, and all of the waste heat from all processes is net yield. The losses in all of our accelerator components are already accounted for in the accelerator's efficiency, athough we have to spend a (currently unknown) amount of energy on keeping our third and especially fourth neutron cooling stages cold. And this is where there's no substitute for accurate simulations, unfortunately.
Let us guess that our cooling costs eat up the beta/fragment surplus energy and thus we have the 35MW thermally-generated electricity for sale, at near 100% capacity factor (more on that shortly - for now let's say 95% to be pessimistic). Our 100MW beam, as described previously, will cost $500M-$2B. The plant would produce 290 million kWh per year. Over a nuclear-typical 50 year lifespan, that's 14.6 billion kilowatt hours. It's easy to see scenarios where this could be cost effective, esp. if accelerator technology advances over this time period. The electricity is high availability and carbon free, which commands a premium. Our fragments are isotopically sorted, which means not only simple waste handling, but the ability to sell valuable isotopes, for example for medical needs. Having a very high flux cold neutron source yields many options for production of difficult-to-produce isotopes, allowing one to sacrifice a bit of electricity generation for very valuable side revenue streams. Nuclear waste can be burned in the spallation target - not only adding another revenue stream (waste disposal), but increasing the neutron flux at the same time (fissile materials release more evaporation neutrons upon spallation).
The fuel is cheap and abundant. 7Li makes up 93% of natural lithium, versus U235 making up 0.7% of natural uranium. Lithium can be enriched (which may not even be necessary here) by cheap chemical processes, versus uranium which is much more difficult. Raw lithium is far cheaper than uranium, and many orders of magnitude more abundant, being one of the most common elements in the universe. Earth's oceans contain 2,4e14 kilograms of lithium; scaled by 16 MeV per 7Li, that works out to 9.6e22 watt hours, or about 5 million years of our current electricity consumption; about half that amount (as per the numbers above) would be sellable, or 2.5 million years. It's actually similar to that of D-T fusion, since the tritium for D-T fusion is bred from lithium, yields 17 MeV per fusion, and since that energy is captured thermally, only about half of it is turned into sellable electricity.
As mentioned, while a uranium-fuelled reactor reactor uses a fuel that's found in only 0.7% concentrations, enriched to several times higher, and then burns though only half of that, a lithium reactor uses a fuel found in a mostly pure state and can burn through almost all of it. And while uranium fission releases more energy per reaction - ~200 MeV per fission versus about 16, or 12.5 times as much - a U235 atom is 33.6 times heavier than a 7Li atom. So even versus pure U235 fuel burned up completely, 7Li contains far more energy potential for release. Compared to real-world situations, per unit mass, the 7Li needs refuelling in the ballpark of a hundredth as often per unit energy sold (rather than replacement due to burnthrough reasons, it would need periodic annealing or meltdown / reproduction for structural reasons). Now, of course the 7-Li targets are only part of the reactor to which neutrons are having an effect - but the same is true with conventional fission reactors as well as fusion reactors.
The high energy density of 7Li also raises possibilities for spaceflight applications as an intermedite stage between fission and fusion - although probably in a different form (rather than a spallation neutron source, the ideal would probably be a highly enriched plutonium fission neutron source, with all of the neutrons not needed to keep the chain reaction going being used toward 7Li bombardment)
There would be no more reason for people to NIMBY a 7Li reactor than a D-T fusion reactor. Both produce only incident radiation and shut down instantly (excepting delayed decay heat). Unlike D-T fusion, there's no proliferation risk (no tritium to divert).
So, that's the basic concept. But to iron it down more - where the neutrons actually get absorbed, how much energy gets deposited in what layer and what is the generation potential / cooling costs, what's the optimal neutron production geometry and how efficient is it, and so forth, requires an accurate simulation. With thermal scattering. So hopefully I'll be able to get that working in Geant4 sooner or later. :)