Material unaccounted for (MUF), in the context of nuclear material, refers to any discrepancy between a nuclear-weapons state's physical inventory of nuclear material, and the book inventory. The difference can be either a positive discrepancy (an apparent gain of material) or a negative discrepancy (an apparent loss of material). Nuclear accounting discrepancies are commonplace and inevitable due to the problem of accurately measuring nuclear materials. This problem of inaccurate measurement provides a potential loophole for diversion of nuclear materials for weapons production. In a large plant, even a tiny percentage of the annual through-put of nuclear material will suffice to build one or more nuclear weapons.
MUF is a term used within nuclear material monitoring, the organisational and physical tests used in the monitoring of fissile material and the detection of any impermissible removal. An associated term is limit of error for the material unaccounted for (LEMUF), meaning the associated statistical limits of error possible for the MUF. In a civilian context, MUF is also sometimes referred to as the inventory difference (ID).
A 2014 report by the United States Army War College's Strategic Studies Institute states that although the quantity of MUF globally is unknown, it is "significant." They add that "U.S. nuclear weapons MUF alone is pegged at nearly six tons—i.e., enough to fashion at least 800 low-tech, multi-kiloton bombs," with Russian MUF numbers assumed to be as large. "As for Chinese, Indian, Pakistani, Israeli, and North Korean MUF figures, though, we have only a general idea of what they might be […] The civilian production of nuclear weapons-usable plutonium in the United States, United Kingdom (UK), Japan, France, and India also is a worry. We know that specific accounting losses in the case of civilian plutonium reprocessing and fuel making in the UK and Japan have been significant—measured in scores of bombs worth. What they might be elsewhere, again, is unknown."
Definition The International Atomic Energy Agency define MUF as the "difference between the book inventory and the physical inventory. This definition may be with respect to either the element or isotope weight." A more exact definition is represented by the following equation: MUF = I - 0 + B - E where I designates inputs, 0 designates outputs (which are sometimes subdivided into product and waste streams), B refers to beginning inventory, and E to ending inventory. The three terms in (eq. 3.4.1), I, 0, and B, collectively represent the book inventory, while E represents the physical inventory. Note that the physical inventory for one accounting period becomes a part of the book inventory for the subsequent period.
The IAEA also notes that the "definition of MUF implicitly assumes that the material balance is based completely on measured data. The use of by-difference accounting results in a meaningless MUF. For example, if the contents of waste streams are calculated as the differences between the measured amounts entering a process step and those exiting the step, it is clear that the calculated MUF would be zero over that particular material balance area, i.e., it would be meaningless as a performance index."
History
Cold War United States The Center for Public Integrity (CPI) reported that during the Cold War nuclear weapons production was so frantic that approximately six tons of nuclear material, enough to fuel "hundreds of nuclear explosives", has been declared as MUF by the government. They add that "most of it [is] presumed to have been trapped in factory pipes, filters, and machines, or improperly logged in paperwork." A Defense Nuclear Facilities Safety Board report highlights, “On at least one occasion, in trying to determine the cause of a MUF in excess of 40 kg in 1969, all of the vessels, sumps, and catchbasins were flushed and inspected: total plutonium yield was less than 10% of the MUF."
Charles D. Ferguson, former president of the Federation of American Scientists, writes that this "was due to an emphasis […] on fast production rather than accurate accounting." He adds that "Given the history of U.S. production of enriched uranium […] one has to realize that tens of thousands of tons of uranium hexafluoride gas were pumped through these plants to produce the approximately 750 metric tons of HEU for military purposes. It is not surprising then that a few metric tons are considered MUF." Ferguson's assessment of the whereabouts differs from that of the CPI's, stating "discharges of nuclear material in waste streams and the environment were most likely the major reasons why the MUF values were 2.4 metric tons for plutonium and 3.2 metric tons for HEU." Elmer B. Staats stated, in a 1978 report, "For the most part, MUF is attributed by DOE and NRC to such things as inaccurate measurements and difficult to measure material held up in pipes, filters and machines used in processing special nuclear material." The other main reason given was "clerical errors."
In 1974, Karen Silkwood, a lab technician at Kerr-McGee, revealed to the Atomic Energy Commission that among many others irregularities, 40 pounds of plutonium was missing from the company's inventory. In 1977, The New York Times reported that 8,000 pounds of HEU and plutonium was unaccounted for across nuclear plants in the U.S.
Soviet Union Soviet figures are unknown, as, unlike Western producers of plutonium, Soviet Russia did not use the 'MUF' accounting system (or an equivalent) to track its physical inventory of nuclear materials. Instead, it simply relied on the physical security of its plants. However, as stated above, Russian figures are presumed to be as large as the United States counterpart.
Post-Cold War Worries that weapons-grade nuclear material could perhaps leak onto the black market following the collapse of the Soviet Union at the end of 1991 grabbed headlines at the time. However, several reported deals involving the sale of nuclear material turned out to be hoaxes. Nonetheless, of the approximately 20 known seizures of nuclear weapons materials since the dissolution of the Soviet Union, all have been made in former Soviet states. Thomas Cochran, formerly of the Natural Resources Defense Council stated that "The Russian problem is by far the most serious. People have an incentive to make money. There is clear evidence that stuff is leaking out." The CPI also notes that "although roughly two dozen countries have enough nuclear explosives to make a bomb, Russia's materials have long been the chief Western concern." The main threat about a potential nuclear explosion on Western soil post-cold war, as perceived by the United States, "[has] always been centered around the risk that explosive materials — more than a bomb's mechanical workings — could fall into the wrong hands." In 2005, Porter Goss warned that "There is sufficient material unaccounted for so that it would be possible for those with know-how to construct a nuclear weapon."
The CPI also reports that the United States government has spent "$4 billion over the past 25 years to help [Russia] tighten control of the weapons-usable materials inside its vast nuclear complex." In the same report, a US intelligence official alleges that former Russian military and intelligence personnel have been suspects in Nuclear trafficking. However, Russia has dismissed allegations of a leakage of nuclear materials as a smear campaign. Under Vladimir Putin, who first came to power in 1999, Russia has slowly reduced its nuclear security cooperation with the United States, stating that it has no further need of financial or technical assistance from Washington. Michael McFaul states it became a "tertiary issue" under Putin. In his 2007 memoir, George Tenet stated that upon hearing Al-Qaeda were attempting to purchase Russian nuclear devices in 2003, a Department of Energy intelligence official was sent to Moscow seeking information about "reports we had received of missing material," but the Russian government refused to provide details.
In 2018, the CPI also reported that two United States Department of Energy nuclear specialists "drove to San Antonio to pick up nuclear material from a research lab and transport it to an Idaho lab." However, "before they were able to complete the mission, radioactive material that they brought with them to calibrate radiation detectors was stolen from their vehicle while they stayed at a hotel." Over a year later, the CPI found that the nuclear materials in question, plutonium and cesium, have not been located, "and are now among an unknown amount of military-grade nuclear materials that have gone missing over the years." The same report also found "gaps" in the amount of plutonium manufactured by weapons companies and the amount that the government can account for.
Causes
Charles D. Ferguson writes that the "biggest concern is statistically significant positive MUF values bigger than the LEMUF, because this could indicate diversion, loss, or theft. The inventory difference also has to reconcile losses of uranium and plutonium through radioactive decay and transmutations of an element to a different element in a nuclear reactor or accelerator. Other losses or consumptions of nuclear material occur in nuclear explosives or reactors via fission. The Department of Energy (DOE) has tried to take into account these natural and manmade losses and consumptions in its historical assessment of uranium and plutonium stockpiles."
As stated by the Office for Nuclear Regulation (ONR), however, the primary cause of MUF is uncertainties "inherent in measurement systems." They elaborate, "[a] finished product such as Plutonium Oxide, can be more accurately weighed and the uncertainty will be smaller." For materials that cannot be easily handled due to dangerous levels of radioactivity, or material in large quantities, "measurements may be more difficult and the associated uncertainties higher. Such measurement uncertainties are a major cause of [MUF] figures, and their existence does not mean that material has been found or lost." For example, according to a DOE report dated September 1996, "Most of the HEU in waste has been removed from the U.S. inventory as ‘normal operating losses’ because it is technically too difficult or uneconomical to recover." The ONR also note that "The magnitude of [the MUF] due to measurement uncertainty will depend strongly on the throughput of material at the plant concerned […] This is particularly the case in bulk processes such as reprocessing, where large volumes of material (hundreds of Tonnes per annum) pass through the plant, often in liquid solution form."
Residual holdup, which refers to the nuclear material remaining in and around the process equipment and handling areas after operation, is also a problem. The NRC write that "Uranium accumulates in cracks, pores, and zones of poor circulation within and around process equipment. The walls of process vessels and associated plumbing often become coated with uranium during processing of solutions. Uranium also accumulates in air filters and associated ductwork. The absolute amounts of uranium holdup must be small for efficient processing and proper hazards control. However, the total amount of uranium holdup may be significant in the context of the plant MUF."