|Fig. 1: Chart of nuclides. Heavier elements become neutron rich.  (Source: Wikimedia Commons).|
One person's waste may be another person's treasure - this is especially true when it comes to nuclear waste. Nuclear waste has carries an otherworldly stigma as a dangerous contaminant and has lead to protests against the construction of nuclear power plants. The U.S. alone has generated over 75,000 metric tons of waste and is adding 2,000 more every year while waste storage facilities such as Yucca Mountain, Nevada remain political hot potatoes. [1,2] Failing to find a long-term storage solution is estimated to cost $56 billion, but when we get right down to it, we find that nuclear waste is not really "waste" at all - it is fuel.  When most of the fissionable uranium is used up after 3 years, the "spent fuel" contains 95% of its original energy. Moreover, only 1/10 of the mined uranium ore is turned into fuel during the enrichment process where the concentration of fissionable U-235 is increased via gaseous diffusion or centrifuge. [3,4] Nuclear waste can kill you: even after 50 years, the gamma radiation one meter away from light water reactor fuel rod waste delivers a deadly dosage in less than an hour.  But by using more efficient reactor designs and reprocessing techniques, the amount of long-term waste, and therefore the risks associated with it, can be significantly reduced.
Transatomic Power Corporation, a Cambridge, MA company founded in 2011 by MIT nuclear engineering students Leslie Dewan and Mark Massie, claims to have designed a nuclear reactor that "can consume the spent nuclear fuel generated by commercial light water reactors" and be significantly more efficient than current designs making it profitable and scalable.  While they have not built a proof-of-concept reactor, we would like to put their claims and proposed design in the larger context of nuclear reactor technology. This requires a review of nuclear waste, the currently used light water reactor, and the molten salt reactor.
The U.S. Environmental Protection Agency (EPA) sorts nuclear waste into six categories: (1) spent nuclear fuel, (2) uranium mill tailings from mining ore, (3) high-level waste from fuel reprocessing, (4) low-level waste, (5) transuranic waste from defense programs, and (6) naturally occurring and accelerator-produced radioactive materials. [7,8] High level nuclear waste refers to the radioactive elements left over from after the fission process of fissile uranium nuclei has occurs; these can be divided into low-Z waste fission products and heavy "actinide waste" such as Pu and Am with a half-life of 24,000 years (Pu-239). [1,5] The fission products make up about 5% of the waste; after a decade, the two strongest isotopes are strontium Sr-90 and Cs-137, which remain problematic for about 300 years. Fertile uranium makes up 94% of the waste and transuranic actinide waste makes up the remaining 1%.  The low-Z elements are distributed around two peaks with atomic numbers between A = 90 - 100 and A = 130 - 140. The bending of the nuclides (see Fig. 1) towards neutron-rich nuclei means that after a fission, the low-Z elements will be very neutron rich, enough so to give off neutrons and generate a chain reaction.  The energy spectrum of the neutrons is given by the empirical distribution: 
|P(E) = (0.4865) sinh( √ 2E ) e-E||(1)|
This distribution says the probability a neutron created from the fission of U-235 has an energy between E and E+dE that is P(E)dE. The neutron flux is proportional to the velocity
and is given by
|Φ(E) = v(E) P(E)||(3)|
This is plotted in arbitrary units in Fig. 2. The reaction rate Γ is then given by Γ = ∫ Φ(E)σ(E) dE where σ(E) is the energy-dependent cross-section. Beyond this, the low-Z nuclei beta decay and give off high-energy electrons until they reach the line of stability shown in Fig. 1 as the black isotopes. High-Z nuclei may alpha-decay and give off a high-energy Helium nucleus. While these particles are moving near the speed of light, they are not capable of traveling very far. Alpha particles can be stopped by paper. Beta particles can be stopped by a piece of aluminum foil. Gamma rays can be stopped by lead. Materials with high neutron absorption cross sections (see Table 1) can be used to stop neutrons. It is therefore not these high-energy particles that will fly away from the reactor and do damage, but rather the spread of radioactive emitters themselves into the air or water supply that is dangerous. This can be caused by failures in the reactor core such as loss of coolant, but can also occur if nuclear waste is not properly maintained.
|Fig. 2: Neutron flux Φ(E) calculated using Eqs. (1) - (3), expressed in arbitrary units.  (Source: J. Dodaro).|
As previously mentioned, spent nuclear fuel consists of 94% fertile uranium. Uranium ore such as uranium oxide UO2 from the ground is not pure fissile material; the amount of fissile U-235 is only 0.71% while the rest consists of the fertile U-238 (with trace amounts of other isotopes).  After enriching the uranium by increasing the concentration of fissile fuel up to 3-5% for light water reactors, the majority of uranium, and hence waste, is still fertile. The reactor naturally creates fissile Pu-239 when U-238 absorbs a neutron. The U-238 therefore does not just act as a neutron sink, but it is generating fuel in the process or breeding. By the time of fuel replacement due to neutron-eating fission product waste buildup, more than half of the reactor's energy is coming from the burning of plutonium.  This breeding process can similarly be done for fertile thorium to produce fissile U-233 which, like plutonium, can be separated by chemical means and burned.
Waste reprocessing coupled with fast breeder reactors can use over 99% of energy in uranium ore to reduce the amount of waste from a 1 GW(th) plant from 100 tons per year to 1 ton per year of fission products with trace amounts of long-lived transuranic waste.  Fast breeder reactors are designed to maximize the production of Pu-239 through U-238 transmutation and Pu-239 chain reactions, making it possible to run the reactor on plutonium while breeding more plutonium than is consumed.  Fast (MeV) neutrons can induce fission in U-238 and are not absorbed as rapidly as slow neutrons giving U-238 the opportunity to absorb the neutron in the resonances between eV and MeV energies.  This maximizes the burning of the high concentration of fertile uranium isotope as bred plutonium in addition to actinide waste at the expense of increased damage by fast neutrons. By surrounding the reactor core with a blanket of fertile uranium (or thorium), the neutrons leaving the core can breed additional fissile material that can be separated by chemical means. Since water slows neutrons, it cannot be used in fast breeder reactors; instead, liquid metal such as sodium is used to carry heat away at atmospheric pressure. The spent fuel from both fast breeders and light water reactors can then be reprocessed to remove the fission product waste via electroplating from the uranium, plutonium, and heavy actinides which are then cast into new fuel rods.  This pyroprocessing of the waste doesn't remove plutonium alone as in the PUREX (plutonium uranium extraction) method and therefore may be somewhat less dangerous in terms of proliferation since the plutonium is never cleanly separated from other transuranic elements. [1,4] While reprocessing with breeders may be more efficient in dealing with waste, the most common nuclear reactor is the light water reactor.
Light water reactors are a type of "thermal" reactor that use H2O as a neutron moderator to slow the neutrons down to thermal energies where the fission cross section is large. The H2O has a mass much closer to the neutron than that of the uranium nuclei which results in fewer collisions to reach lower energy. As can be seen in Table 1, hydrogen has the largest neutron scattering cross section but absorbs the neutron population faster than other elements such as carbon and zirconium. When the average neutron population is constant in time, the reactor is said to be critical and the fission chain reaction is self-sustaining. While the light water moderator increases the fission cross section by slowing down the neutrons to thermal energies, it can also absorb neutrons and decrease the population. Deuterium can similarly be used in a "heavy water" D2O moderator that takes advantage of deuterium's low neutron absorption coefficient (about 1000 times smaller than for hydrogen, see Table 1). Even though the scattering cross section is lower than that of hydrogen such that the number of collisions to thermalize is larger, the reduction in neutron population loss is significant enough to eliminate the need to enrich making it possible to burn uranium ore as is done in Canadian Deuterium Uranium (CANDU) reactors.
The fuel consists of solid uranium oxide pellets encased in metal "cladding" and submerged in water to control the fuel volume density.  The metal cladding is thin to minimize neutron absorption, but leaves it more susceptible to radiation damage. Additionally, built up nuclear waste such as krypton and argon gas gets trapped in the fuel rods and eats the neutron population. These effects require replacement of the rods about every four years. A 1,000 MW light water reactor produces 20 metric tons (44,000 lbs) of waste per year. The waste then needs to be stored safely for 100,000 years due to long-lasting transuranics. For a 1 GW(e) light water reactor with thermal efficiency of 33%, the amount of uranium used over a 30 year lifetime is roughly:
|W||=||30 years × 365 days/year ×
24 hours/day × 3600 sec/hour × 2.02 ×
215 MeV/atom × 1.6 × 10-13 J/MeV × 6.022 × 1023 atoms/mole × 0.007 moles/mole (U-235/U)
|× 0.270 kg/mole × 10-3 tonnes/kg||=||5337 tonnes UO2|
|Fig. 3: Molten salt nuclear reactor schematic. (Source: Wikimedia Commons).|
In a light water reactor, the fuel rods' cladding becomes irradiated and weak, requiring the rods to be discarded and replaced (about every four years) after only using about 5% of the available energy inside of them. Rather than using fuel rods housing solid uranium oxide pellets, molten salt reactors (MSR) dissolve uranium tetrafluoride UF4 into salts kept liquid by the heat from the fission reactions. This heat, generated in the critical reactor core containing a neutron moderator, is carried by the liquid salt and transferred through an intermediate heat exchanger to non-fissile molten salt coolant (such as NaBF4-NaF) and then to water to power a steam turbine as shown in Fig. 3.  There are a number of advantages to this design. The boiling point of molten salt is higher than water such that the salt remains liquid at the reactor's higher operating temperature (700°C - 750°C) resulting in a greater thermal efficiency. [12,13] Eutectic "flibe" 7LiF and BeF2 mixtures are common carrier salts due to low neutron capture and effective moderation. [11,13] More quantitatively, the fluorides offer a high average log energy loss per collision (0.10).  As a coolant, molten fluoride salts have a 25% higher heat capacity per unit volume than pressurized water (4.184 MJ/m3K) and 5 times higher than liquid sodium used in fast breeder reactors. This results in a smaller volume of salt in the primary loop and a more compact design.  Unlike in high-pressure light water reactors, the molten salt can operate at atmospheric pressure allowing for low pressure piping and vessels to be used.  Noble gases (such as Kr or Xe-135 from the decay of I-135) that eat the neutron population bubble out rather than remain trapped in the rods while other insoluble fission products can be continuously removed or plated out. [11,15]
MSR technology is by no means new and has been demonstrated to function as intended. In 1954, the U.S. Aircraft Reactor Experiment operated a molten salt reactor from going critical to shutdown for 221 hours at powers up to 2.5 MW(th).  Thermal megawatts MW(th) refers to the thermal power produced. This must be converted to MW(e) electrical power with a steam cycle efficiency around 40%. The reactor required highly enriched uranium at 93.4% U-235, used blocks of beryllium oxide (BeO) to moderate neutrons, and employed sodium fluoride and zirconium tetrafluoride NaF-ZrF4 coolant salt. [11,14] The fuel salt mixture consisted of 53.09 mole % NaF, 40.73 mole % ZrF4, and 6.18 mole % UF4 with a temperature gradient of 180°C through the reactor reaching a maximum operating temperature of 860°C.  The removal of volatile fission products was also tested, and over 95% of Xe bubbled out of the fuel salt in a 25 hour run at 2.12 MW.  Also at Oak Ridge National Laboratory, the Molten Salt Reactor Experiment (MSRE) operated a 7.4 MW(th) test reactor with molten salt at 648°C and graphite moderator from 1965 to 1969. [11,13,16] The high operating temperature resulted in a higher thermal efficiency, but required all metal in contact with molten salt to be made of a Ni(68)-Mo(17)-Cr(7)-Fe(5) alloy "Hastelloy-N" due to its corrosion resistance to high-temperature fluoride salts; by measuring the fuel salt's chromium content leached from the alloy surface every week for three years, the estimated depth of corrosion was less than 67 micrometers/year.  The "flibe" fuel salt also contained 5.0 mole % ZrF4 which is the first to oxide and form ZrO2 in the presence of moisture or oxygen; this prevents uranium in the fuel salt from precipitating as UO2 due to salt contamination.  The "single fluid" reactor design ran for the equivalent of 9,006 full-power hours on 33% enriched U-235 and subsequently on 15% enriched UF4, with a lower delayed neutron fraction, for 2,549 full-power hours.  While not utilized in the MSRE, a "two fluid" design for breeding has a separate blanket salt containing ThF4 surrounding the fuel salt containing fissile UF4 to capture neutrons. The generated U-233 is removed by fluorination whereby fluorine gas is bubbled through the blanket turning UF4 to volatile UF6. [11,12] The UF6 is then collected and turned back into UF4 which is added to the liquid fuel salt to undergo fission. While the two-fluid design requires a more complicated (sphere within a sphere) vessel to separate the fluids, it has the advantage of separating the collection of thorium from the removal of chemically-similar rare earth fission products that absorb neutrons and inhibit breeding. This is accomplished by removing the UF4 and evaporating off the carrier salt by vacuum distillation to leave most of the fission product waste behind. The capital cost of a MSR continuous vacuum distillation system was originally estimated at (inflation adjusted) $40 million with an annual operating cost of about $5.8 million for a 1 GW(e) reactor. [11,17]
One safety feature of the liquid fuel MSR is the strong negative temperature coefficient of reactivity: thermal expansion decreases the fissile fuel density thereby slowing down the rate of reactions to create a self-regulating negative feedback loop. [12,16] Unlike light water reactors, MSRs lack the moderator evaporation failsafe since fuel salt becoming critical in the core also serves as coolant. While the salt's negative temperature reactivity stabilized the reactor as intended, it is not clear that thermal expansion would be as sufficient in responding to a runaway supercritical reaction. In over 15,000 hours of the MSRE running at criticality, there was no need to scram the reactor and drop control rods into the core.  Additionally, the salt can be continuously processed to remove some of the neutron-eating fission products (as shown in Fig. 3) by pyroprocessing as mentioned above, and the fissile concentration can be adjusted continuously. [11,16] This allows for most of the fissile fuel to be broken down and reduces the amount of long-lived transuranic waste. This then decreases the risk of spent fuel in water accidentally becoming critical if the density is too high.  In the event of a power outage, a freeze valve of electrically cooled salt melts and the molten salt fuel drains into an auxiliary containment tank where it remains subcritical due to lack of moderation from the graphite core. [11,15] The disadvantages of the molten salt reactor included high cost, a bulky reactor core (90%) made of graphite moderator resulting in a low-power density, lower effective delayed neutron fraction due to loss of delayed neutrons in fuel salt outside of the reactor core, and high enrichment levels of 33-93%. This is not feasible for commercial reactors since uranium is only commercially available below 20%. Above 90% is weapons-grade, raising proliferation issues.
|Table 1: Neutron scattering/absorption cross-sections in barns = 100 fm2 = 10-28 m2. |
With an understanding of the history and advantages of the MSR, we can now review Transatomic Power's proposed design. The proposed power cycle is similar to the MSRE, but incorporates spent nuclear fuel as follows: the waste from light water reactors is removed, and the uranium oxide pellets are dissolved into molten salt in the primary loop at criticality. The salt transfers energy by a heat exchanger with a secondary loop of LiF-KF-NaF salt (without uranium) which is connected to a third (power production) loop with steam generator. Volatile fission products are continuously removed by an off-gassing system and new fuel is added to maintain reactor criticality.  Transatomic makes two important material changes over the previous MSR designs: the moderator and the salt. The graphite moderator and LiFBe + UF4 salt required enrichment of 33%-93%, since only a small amount of uranium could be dissolved in the salt. The resulting power density was 4 MW(th)/m3. Instead, the Transatomic design incorporates a zirconium hydride moderator and LiF + UF4 salt. The LiF + UF4 salt at 650°C can hold about 27 times as much uranium and therefore requires a lower enrichment of 1.8% to maintain criticality (with the additional salt in the core). The LiF-based salt has a higher melting point than "flibe" salt which could freeze at cold spots and reduce flow if not designed properly.  While this high temperature offers a thermal efficiency advantage (estimated at 44%), it requires the pumps, tanks, and piping to be made of Hastelloy-N as in the MSRE. [6,16] The reactor can run on the actinide waste in spent fuel from light water reactors in addition to freshly mined and enriched uranium.
Zirconium has a low neutron absorption cross-section, and hydrogen acts as an effective moderator due to its large scattering cross section (see Table 1). Transatomic's neutron energy spectrum has a stronger peak at thermal energies (with high fission cross-section) and a reduction in the spectrum across the "epithermal" region with absorption resonances. This results in a smaller (and cheaper) core consisting of 50% moderator rather than 90% of graphite moderator as in the MSRE. Fitting 5 times the amount of salt in the core yields a higher power density of 86 MW(th)/m3 and therefore a more compact design. [6,18] There is a concern about hydrogen in the moderator under radiation stress and the possibility of an explosion, but zirconium hydride has been tested in similar environments and hydrogen can be outgassed if necessary.  There is additionally stronger peak for fast neutrons (compared to graphite) with their choice of moderator which helps break down the heavy actinide waste. By continuously removing fission products from the fuel salt and avoiding the buildup of neutron eaters, Transatomic claims to be able to break up spent nuclear fuel from light water reactors and burn up to 96% when running on fresh fuel. At 1.8% enrichment, this amounts to an estimated 75 times more electricity per ton of mined uranium than commercial light water reactors with 5% burn up at 5% enrichment - through the combination of lower enrichment, higher burn up, and higher thermal efficiency. 
As far as nuclear waste goes, Transatomic Power predicts that a 520 MW(e) plant would remove 500 kg of fission product waste per year which is replaced with fresh fuel.  Waste removal is accomplished through a combination of off-gassing Kr and Xe, plating out noble metals, and salt/liquid-metal extraction of lanthanides; it remains to be seen if these reprocessing methods are commercially feasible for the MSR. By running off waste produced by light water reactors, Transatomic Power claims their reactor design could turn 270,000 metric tons of high-level nuclear waste (worldwide) into electricity to power the world for 72 years (even taking into account increasing demand). They claim the reactors are small enough to run at the site of light water reactors to consume the waste as it is produced.
The company has yet to build a functional prototype; all their estimates are based on computer models that may hide certain engineering difficulties such as salt freezes or unforeseen problems such as long-term lanthanide waste buildup that wouldn't have to be dealt with in light water reactors which continuously discard fuel rods. Transatomic hopes to build a 20 MW demonstration reactor by 2020 and eventually a 520 MW(e) capacity plant from a 1250 MW(th) reactor for $2 billion. The technological foundation of their reactor, based on the MSRE, is established science; it remains to be seen if their proposed improvements, among them the choice of moderator and salt, can overcome the costs and political hurdles to making the Transatomic Power reactor a reality.
© John Dodaro. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 N. Barnett, "Nuclear Waste Storage at Yucca Mountain," Physics 241, Stanford University, Winter 2014.
 J. Ahearne et al., "Consolidated Interim Storage of Commercial Spent Nuclear Fuel: A Technical and Programmatic Assessment," American Physics Society, February 2007.
 "Nuclear Fuel Cycle Simulation System (VISTA)," International Atomic Energy Agency, IAEA-TECDOC-1535, February 2007.
 W. Hannum, G. E. Marsh and G. S. Stanford, "Smarter Use of Nuclear Waste," Scientific American 293, 85 (2005).
 F. N. von Hippel, "Plutonium and Reprocessing of Spent Nuclear Fuel," Science 293, 2397 (2001).
 Technical White Paper," Transatomic Power, March 2014.
 L. Sjöberg, "Explaining Individual Risk Perception: The Case of Nuclear Waste," Risk Management 6, 51 (2004).
 Th. Briggs, P. L. Kunsch and B. Mareschal, "Nuclear Waste Management: An Application of the Multicriteria PROMETHEE Methods," Eur. J. Oper. Res. 44, 1 (1990).
 A. Sonzogni, "NNDC Chart of Nuclides," in 2007 Proceedings of the International Conference on Nuclear Data for Science and Technology, ed. by F. Gunsing et al. (EDP Sciences, 2008).
 B. E. Watt, "Energy Spectrum of Neutrons from Thermal Fission of U235," Phys. Rev. 87, 1037 (1952).
 D. LeBlanc, "Molten Salt Reactors: A New Beginning For an Old Idea," Nucl. Eng. Des. 240, 1644 (2010).
 J. Serp et al., "The Molten Salt Reactor (MSR) in Generation IV: Overview and Perspectives," Prog. Nucl. Energy 77, 308 (2014).
 Y. Kelaita, "Molten Salt Reactors," Physics 241, Stanford University, Winter 2015.
 S. Omar, "The Aircraft Reactor Experiment," Physics 241, Stanford University, Winter 2012.
 W. B. Cottrell et al., "Operation of the Aircraft Reactor Experiment," Oak Ridge National Laboratory, ORNL-1845, August 1955.
 P. N. Haubenreich and J. R. Engel, "Experience with the Molten-Salt Reactor Experiment," Nucl. Appl. Technol. 8, 118 (1970).
 C.D. Scott and W.L. Carter, "Preliminary Design Study of a Continuous Fluorination-Vacuum- Distillation System for Regenerating Fuel and Fertile Streams in a Molten Salt Breeder Reactor," Oak Ridge National Laboratory, ORNL-3791, January 1966.
 M. Khalaf, "A Nuclear Renaissance," Physics 241, Stanford University, Winter 2015.
 V.F. Sears, "Neutron Scattering Lengths and Cross Sections," Neutron News 3, No. 3, 26 (1992).