Continued development of nuclear fission as a source of energy is blocked by three main fears: potential reactor meltdown, proliferation of weaponizable fuel, and unsolved buildup of nuclear waste. As it turns out, the least progress has been made on addressing the waste issue! The concern with nuclear waste is its radioactivity - radioactive elements are unstable and can decay into other elements, releasing energy in the process. In some cases this energy can be threatening to humans or other life close enough to be exposed to the radiation. Waste is categorized according to two metrics - the danger it poses, and the lifetime over which it remains dangerous. Some radioactive waste is a byproduct of medical and research efforts, but the majority is produced through nuclear fission in reactors. 
The fuel in a nuclear reactor consists of heavy elements, most often U-235 and U-238. This fuel is constantly bombarded by neutrons during the reactor's operation, which can generate new elements through two mechanisms. The first is nuclear fission - a 'fissionable' element may split after it is hit by a neutron. This process, which occurs for the U-235, releases energy and some more neutrons as the nucleus divides into several (often two) smaller nuclei. The resulting elements are called 'fission products' (FP). However, neutrons colliding with U-238 will not split the nucleus, and are instead absorbed to create a new isotope of the element with one more neutron. Elements created through absorption rather than fission therefore have a much higher nuclear mass, and are known as actinides, or 'transuranics' (TRU) if heavier than uranium. Over the course of a reactor's lifetime, many fissions and absorptions occur in various combinations so that the fuel contains an incredible diversity of elements when removed from the reactor core. Many elements created through fission or absorption are very unstable and will quickly decay into more benign species, but a few pose a serious threat over longer timescales, even though produced in small quantities. These products make a solution to long-lived radioactive waste integral to any nuclear energy proposal.
Several solutions have been proposed and enacted for dealing with nuclear waste. In a 'closed' fuel cycle, the spent fuel from a reactor is reprocessed to extract the remaining usable elements. The unusable radioactive waste is left behind in a more concentrated (usually liquid) form.  In contrast, the 'open' fuel cycle does not reprocess spent fuel so while it contains much the same spectrum of radioactive elements, they constitute only a small amount of the total mass, and the fuel is left solid. In either form, the waste produced contains the same radioactive elements that have to be dealt with. Initially, the waste is so highly radioactive that it can kill in minutes and some of the radioactivity heats it to high temperatures.  It is usually put in 'interim' storage, often in sealed containers that are kept underwater to cool it down. While this isn't ideal and the storage must be kept under surveillance, simply waiting for a few years will decrease the waste's potency. By then, the most radioactive 'short-lived' elements will have mostly decayed, and the truly problematic elements remain. They include both long-lived fission products and actinides, seen in Table 1. [1,3] In waste that hasn't been reprocessed, there is also a considerable amount of plutonium (a TRU) in different isotopes, all radioactive.
|Table 1: - The most concerning elements in nuclear reactor waste (spent fuel)|
There are two options to avoid the threat of the longer-lived radioactive elements. One is to wait until they decay into stability, the same strategy as is used during the interim storage. However, current interim storage isn't suitable for the much longer timescales necessary for waste to become safe. As a result, the concept of 'geologic' storage has been proposed, in which large amounts of waste are stockpiled and sealed away for millions of years, with a thick layer of rock (hence the name) separating them from us.  With thousands of tons of nuclear waste, the United States has investigated storage in Yucca Mountain since 1982, but little progress has been made and in the meantime the waste remains in interim situations that weren't meant to be used for decades.  Geologic storage promises a very long wait, however, and the prospect of continually searching for and filling new repositories as more waste is produced. The other option is to accelerate the change of dangerous waste into more benign elements by transmuting it with more neutrons. A fission reactor is unsuitable for this purpose because the waste acts as a 'poison' preventing chain reactions from occuring. Other sources of neutrons are possible, however, including those from nuclear fusion and created by particle accelerators. The last is known as 'accelerator transmutation of waste' (ATW) and is being investigated as an alternative to the geologic storage solution.
The basic concept of ATW is simply to 'finish the job' of burning or transmuting the radioactive waste through intense neutron flux, thereby drastically reducing its radioactivity. Again, bombardment with large numbers of neutrons is considered as a way to either fission the heavier elements into less dangerous species or convert the lighter ones through absorption. A particle accelerator can be used as a source of high-energy protons, which can then be used to create neutrons through a process known as 'spallation.' This occurs when a proton collides with a heavy nucleus in the spallation target, after which the nucleus ejects a large number of neutrons proportional to the energy of the original proton.  However, advances both in the technology needed to accelerate the protons and the understanding of spallation physics have prompted investigation of accelerator-created neutrons for waste treatment.  While doing so may create further radioactive elements both in the spallation target and in the bulk of the waste, by eliminating the long-lived ones from Table 1 above ATW can theoretically change the nature and the timescale of the problem considerably.
The question is, how many and what kind of neutrons are necessary for effective transmutation? The answer depends on the cross sections of the waste elements, where cross section relates to the probability to absorb or fission when hit by a neutron of a given energy. For a low cross section, one must generate more neutrons and use more energy to transmute the offending element. The TRU elements remaining in the waste are generally fairly easy to fission, but the threatening FP's usually have much lower cross sections for the desired neutron absorption that can transmute them into a more benign state.  These elements present a greater concern than the TRUs because they can easily contaminate water and so leaks of radioactive waste can spread much more quickly if they include long-lived FP's. To transmute them effectively, ATW systems propose using a large flux - about 1016 cm-2 sec-1 - of relatively low-energy 'thermal' neutrons that can also fission the TRUs. [5,6] To acheive the desired flux, ATW proposals usually include an accelerator that can produce 1 GeV protons. One problem is that, with a goal of waste reduction in mind, the most effective system will be one that bombards the most concentrated waste. A target with a high proportion of non-waste elements (like the leftover uranium in 'open' cycle spent fuel) will have a lower chance of hitting an FP or TRU with a given neutron, thus lowering the 'effective' neutron flux. Of course, one could process the spent fuel to separate the uranium and plutonium, but the US and some other countries have chosen the open cycle specifically to avoid reprocessing, which they claim increases proliferation risk. Instead, proponents of ATW have largely turned to an attractive alternative that takes advantage of the large amount of usable fuel mixed in with the waste.
The proposal that now dominates work in ATW is to combine it with the concept of the Accelerator Driven System (ADS). An ADS is a kind of nuclear reactor that is 'driven' by neutrons from a particle accelerator. The rate of reactions in a nuclear plant is determined by the flux of neutrons within the fuel, so by using an external source of neutrons the ADS is proposed as a way to control the rate more effectively. The accelerator doesn't provide all of the neutrons used for fission, only a fraction that can then set off chain reactions and thereby create more neutrons for reactor operation. Instead of the single goal of transmuting the waste, which can be prohibitively expensive in the unprocessed form, we now have added the goal of generating energy through fission of usable fuel. Such a combination has been suggested both by the Los Alamos National Lab and the former director of CERN, Carlo Rubbia, who calls it an 'Energy Amplifier' or EA.  While a traditional ADS might use fuel similar to a nuclear reactor, the EA relies more on 'fertile' elements that can be transmuted or 'bred' into fissionable fuel, like the high proportion of U238 which can be bred into Pu-239.
A large number of energy-producing ATW designs have been proposed varying by type of fuel, processing required, accelerator and spallation technology, and neutron spectrum. Transmuting the long-lived TRUs seems to be acheivable in such a scenario, but dealing with the fission products falls by the wayside.  This is partly because the fission products are what cause regular reactors to stop working in the first place, acting as a 'poison' that consumes too many neutrons and slows the reaction down. To really deal with the waste economically, all scenarios assume some kind of processing - otherwise, far too many neutrons would be required because so many would be wasted in useless capture processes. The scheme is to use reprocessing technology that is 'proliferation resistant' in that it avoids generating a stream of pure weapons-grade plutonium, and run an ADS using TRUs and only the most dangerous FPs from Table 1. The TRUs are used as fissionable fuel, thereby reducing their danger as waste and extracting the extra energy that makes them dangerous in the first place. Fission products like iodine and technetium are separated during processing and included either in the fuel or near it to absorb some of the neutrons and be transmuted.  Originally, producing energy was proposed as a way to offset cost and work with open cycle spent fuel, but in recent ATW proposals it has taken over as the priority, so that actual treatment of the waste isn't optimized. Energy generation may help with costs, but it makes the solution of the waste problem less complete and requires reprocessing and new technologies that haven't yet been tested.
Much testing needs to be done to demonstrate the feasibility of ATW. It relies on advanced accelerator and spallation technology, and energy production would require new processing methods that also haven't been used yet.  For a facility proposed to transmute U.S. Waste, the theoretical prediction is that "after 60 years of operation, nearly all of the transuranics will have been fissioned, most of the technetium will have been converted to stable isotopes of ruthenium, and most of the iodine will have been transmuted to stable isotopes of xenon."  GeV-scale proton accelerators have been demonstrated, but no existing versions have the reliability, energy efficiency, and high throughput (or current) that is assumed - often a linear accelerator - in ATW models. As a result, the type of long-term spallation targets needed, which often consist of a lead-bismuth (LBE) alloy, also haven't been tested to the extent that they would be used. The processing technology, combinations of pyroprocessing and fluorination have been considered, have also not been implemented on the scale necessary. 
Although these issues of technological implementation are important, the biggest questions are whether energy can actually be generated, and how effectively the FPs will be transmuted. Among a wide range of accelerator parameters, a popular choice seems to be a 1.6 GeV proton linear accelerator with a 250 mA current - the best existing linear accelerators achieve about 1 mA of current.  This means that the beam energy would be 400 MW with a total of 1.6 × 1018 protons per second hitting the spallation target. At existing levels of accelerator technology, the most economical equipment might be 30-50% efficient: a Los Alamos paper on this design suggested a figure of 900 MW of electricity used to run the accelerator.  Another proposal, based on a U.S. 'Roadmap' for the ATW program, claims to use the accelerator much more sparsely, with a 90 mA beam of protons at 1GeV consuming around 300 Mwe.  It purports to generate around 1500 Mwe with such a beam by fissioning TRUs using several ideal assumptions: high thermodynamic efficiency (37%), negligible processing costs, high neutron multiplication (~33), and the accelerator supplying a constant flux of neutrons.  None of these assumptions are guaranteed or demonstrated in current systems; moreover, the report claims to use .65 neutrons per fission event to transmute the FPs iodine and technetium! While it's easy to say that the long-lived fission products will be burned, the fact is that they have much lower cross sections than the TRUs so that it is ridiculous to assume that their absorption rate will be comparable to the fission rate, unless a much larger volume of FPs is placed in the reactor. 
Essentially, current ATW proposals sacrifice effective transmutation for energy, and require several unproven technologies combined with concepts used in Generation IV breeder reactors like advanced processing and molten coolants. The idea of using accelerator neutrons to manipulate the reactor's neutron economy is a nice one, and indeed energy might plausibly be produced through burning the TRUs, but it is not a complete waste solution (especially in the case of long lived fission products) and requires significant engineering advances in accelerator, spallation, cooling, and reprocessing technology. Even if energy can be produced, there is little evidence that a combined system would be more effective than simply burning the TRUs in an ADS and then using the energy for a separate, dedicated ATW system. Even this scenario would require detailed processing of the wastes to high purities that hasn't been demonstrated.
© Jamie Ray. 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.
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