Newsletters

World Energy Transformation

G.P. Yeh, Fermilab

Sustainable energy can reduce challenges concerning energy, economy, environment, water, food, health, education, security and peace. The world energy consumption is equivalent to 15,000 Giga Watts (GW), by the world’s 7 billion people. The global carbon emission is 10 billion tons per year, or 1 million tons per hour [1]. More than 1 billion people in the world have no electricity. Solar, Wind, and other renewable energies and energy efficiencies will continue their tremendous recent progress. Countries including Saudi Arabia and United Arab Emirates are significantly investing in renewable energies. The 400 nuclear reactors in the world, with an average age of 30 years, provide 2.3% of the world’s energy. To significantly provide sustainable energy and help reduce carbon emissions, nuclear power needs fundamental changes. US laboratories, universities, and companies can lead the world towards sustainable nuclear energy. Sustainable Energy is the greatest human challenge, responsibility, opportunity, andendeavor.

Scientists and Public Forums

Alvin Saperstein

Two of the major concerns expressed at the Business Meeting of the Forum on Physics and Society, held at the recent Columbus, Ohio meeting of the APS, were the growing lack of support for science on the part of the present American government and the apparently swelling disinterest of the American public in the processes and results of science as they relate to public policy. Both of these concerns, are, of course, strongly coupled. Traditionally, the professional bodies of science have concentrated on lobbying governmental bodies for support, assuming that enhanced governmental interest would filter down to the general public. For the most part these scientific groups have ignored direct interactions with the “man in the street.” This “filtering down” has apparently not been very successful recently. Thus, it seems important at this time for individual scientists, or small groups of them, to endeavor to interact locally with groups of fellow citizens, emphasizing process, results, and public and private implications of their science.

As an illustration of what can be productively done, a small group of us have created a traveling “road show” for the Detroit metropolitan area. This panel includes a physicist and political scientist from Wayne State University, a political scientist and an ethicist from Henry Ford College, and a physicist from the University of Detroit Mercy. (The real world is not easily divided into the traditional academic disciplines and this interdisciplinary panel approach recognizes different disciplinary approaches and concerns but connects them together for the public — and for each other!)

We have put on panel discussions — roughly 20 minutes by each presenter, some with power-point slides — followed by audience questions and response — on the subject “Nukes in Your Future”. We have presented at area Colleges, Senior Citizen complexes and Community Centers, with audiences ranging from about a dozen to well over 100 people in the audience. We continue to seek further venues, especially in the “out-county” areas. We have found the senior audiences concerned about the prospects of nuclear conflict though with little factual basis for their concerns, the youthful audiences oblivious to this problem. We think we have buttressed the concern of the “seniors” and awakened the “juniors”. The younger audiences are mostly used to interactions with academics and so remain quiet on the whole; the elders find it novel to being addressed by professors and so respond very actively. Hopefully the knowledge and concerns we impart will have some immediate effect on voting behavior and eventual impact on public policy.

There is no need for FPS members to struggle through the creation of an interdisciplinary colloquial traveling group. There are many community groups — churches, synagogues, mosques, alumni groups, book and discussion clubs, community centers — made of up senior and/or middle-aged citizens who would welcome scientific insight into current important public issues from locally based professional scientists. (They are more likely to think about and/or accept local expertise than public expertise from distant sources.) Many colleges have such knowledge within their ranks — active and retired faculty, students, alumni — and should be strongly encouraged to publicly announce their availability to their communities. The political aspects of the issues cannot be avoided, but the presenting scientist should be careful to avoid the appearance of being partisan.

I have given a number of well-received talks at a Detroit area group called SOAR (Society Of Active Retirees). This group was initially an off-shoot of Wayne State University, known as the “Society of Alumni Retirees”. It became an independent organization as alumni of other educational institutions indicated that they too wanted to participate in such informational presentations. The group offers a wide variety of “courses”, ranging from history, politics, arts, cinema and theater, humanities, social, biological and physical sciences. The “courses” range from single one-or-two-hour sessions to multiple sequential sessions over several weeks. People in the area, mostly seniors, sign up in advance, upon receipt of the course catalogue which is published twice a year. I have given Power-Point slide presentations on two separate topics: The “science of climate change” and the “science of nuclear weapons and their use”. I do not claim to be an “expert” on either of these topics, but I am much more informed about the basics and their applications than most of my audiences, which usually number about 50 people. My talks usually go for about an hour-and-a half, and there is never any difficulty filling the scheduled two-hour sessions with audience questions and responses – even from those on the opposite side of the “political fence.”. My talks are strictly neutral, presenting the history, technology, and strategy of all sides of each issue. If asked during the question period, I will briefly give my own opinion (and make sure it is clear that it is a personal opinion, albeit based on the facts and information I presented earlier in the session.)

There are many other important topics which can be similarly productively addressed: climate, population, public health, natural resources, ground, air and water pollution, general matters of environment, war and peace. Science and scientists can greatly aid the public in reaching productive rational decisions on these pressing matters. They should strive to be actively involved in the public discussions. The public policy “theater” takes place on a physical stage whose pitfall can best be elucidated — and thus avoided — by the scientific community. These public presentations are one more way to do this interactively — and also for the scientists to learn from the public what they, and the public, need and want to know.

Alvin Saperstein

Wayne State University

U.S. Nuclear Weapons Modernization∗

Roy F. Schwitters

Department of Physics

The University of Texas at Austin

Introduction
The United States conducted the last of its more than 800 underground1 nuclear tests (UGTs) on September 23, 1992. Codenamed “Divider”, that test produced a yield reported[1] as less than 20 kt (kilotons TNT equivalent), compared to 21 kt for the world’s first nuclear test, “Trinity”, in 1945. Coincidentally, the Rocky Flats plutonium fabrication facility, which produced most of the pits — primary fission triggers — for today’s U.S. nuclear weapon stockpile, was permanently closed in 1992; its capabilities have since been partially reconstituted at Los Alamos National Laboratory (LANL). Underground testing and the capability to produce large quantities of plutonium pits (along with other components) were, by then, established cornerstones of the U.S. nuclear deterrent at the same time the Cold War with the Soviet Union and its emphasis on nuclear weapons was ending. In response, the U.S. launched the science-based Stockpile Stewardship Program (SSP) in 1995 under the Department of Energy (DOE) to ensure the safety, security, and effectiveness of whatever nuclear weapons stockpile it would require in the post Cold War world without nuclear testing.

Today, a generation after the cessation of underground testing, the U.S. nuclear stockpile is assessed annually and meets requirements for safety, security, and effectiveness. Particular stockpile systems are being or will be modernized through “lifetime extension programs” (LEPs) to address changes in requirements and component aging, informed by advances in scientific understanding and engineering practice since they entered the stockpile. DOE’s SSP responsibilities are conducted through its National Nuclear Security Administration (NNSA)2 and associated facilities comprising national scientific and engineering laboratories, production plants, and assembly operations located at ten major sites around the United States.

Of particular importance to SSP, was the early and sustained priority assigned to developing new computer modeling and simulation capabilities for comparing archived results of UGTs with modern predictions of weapon performance. This talk describes technical advances made during the first generation of SSP, looking forward to what comparable scientific opportunities and corresponding investments can be expected over the next generation of SSP to better understand the U.S. stockpile and respond to new requirements.

For context, the number of nuclear warheads in the U.S. stockpile since Trinity through the first generation of science-based Stockpile Stewardship is shown in Figure 1. Notice that since the end of the cold war and closing of Rocky Flats, the average age of the U.S. stockpile has increased essentially by one year per year to the present.

All warheads in today’s U.S. stockpile are two-stage devices, which function through similar physical processes, but which are tailored to meet different military requirements depending on delivery system and other operational considerations. The primary stages of U.S. stockpile weapons employ: 1) chemical high explosives to implode a hollow plutonium (Pu) pit filled with deuterium-tritium (D-T) gas to achieve the critical density where: 2) neutrons initially supplied by timed neutron generators, are multiplied through Pu fission, heating the compressing gas: 3) to the temperature where D-T nuclei fuse, forming an intense burst of neutrons that: 4) causes most of the Pu nuclei from the pit to fission rapidly in a process called “boost.” The net result is an efficient release of the energy stored in Pu nuclei of the primary in the form of energetic electromagnetic radiation—x-rays and gamma rays. This radiation is transported to the secondary stage of the weapon where it compresses and heats that stage, creating a thermonuclear “burn” that provides most of the explosive energy — yield — of the device.

The science and arts of nuclear weapon design, engineering, construction, and underground testing advanced substantially during the cold war, resulting in the science and technology base on which today’s stockpile and SSP are based, with a strategic focus on the Soviet/Russian threat of limited anti-ballistic missile (ABM) defenses coupled with a massive offensive or retaliatory capacity.

An annual series of Stockpile Management plans prepared for Congress by NNSA [2] form an unclassified, historical picture of SSP, including its developments of new scientific tools and methods to better understand the performance of U.S. nuclear weapons and to modernize them accordingly. Technical reports available through websites at the NNSA national laboratories, Lawrence Livermore (LLNL), Los Alamos (LANL), and Sandia (SNL) also provide information on technical developments achieved through SSP.

U.S. nuclear weapons policy for the stockpile is outlined in periodic “posture” reviews; today’s stockpile follows closely the 2010 Nuclear Posture Review [3] and the new administration’s policy is outlined in the 2018 Nuclear Posture Review [4]. Much of the content related to U.S. stockpile requirements are similar, but their descriptions of current threats are different: the 2010 review stresses terrorist threats and aging infrastructure of the nuclear weapons complex, while the 2018 review describes an overall security situation more complex and demanding than anytime since the end of the cold war, in which significant modernization of U.S. nuclear forces is highlighted as being needed to preserve a credible nuclear deterrent.

I shall describe “modernization” of U.S. nuclear weapons in a more abstract way than the arguments, convincing to me, put forward for replacing delivery systems — ballistic missile submarines, ground-based ICBMs, and aircraft — when they reach the end of service life. Engineering expectations on service life, generally well understood before those systems come into service, truly determine the end of service life. In contrast, the lifetimes of nuclear weapons are known to be measured in decades, can be confirmed through surveillance and laboratory tests, but have uncertainties. Aside from special subsystems employing limited life components that are exchanged periodically, as long as today’s weapons are judged to continue to meet military requirements and our treaty obligations, they have remained in service and are refurbished as needed through LEPs. A more nuanced approach to address an apparent proliferation of non-strategic weapon types and inefficiencies in fielding different weapon designs among strategic missile warheads, called the ”3+2 Strategy” was approved by the Nuclear Weapons Council (NWC)3 in 2013 and adopted as a “program of record”, as described in DOE’s 2018 stockpile management plan.4

The 2018 NPR states:

The current threat environment and future uncertainties now necessitate a national commitment to maintain modern and effective nuclear forces, as well as the infrastructure needed to support them. Consequently, the United States has initiated a series of programs to sustain and replace existing nuclear capabilities before they reach the end of their service lives.

I wish to argue that when it comes to U.S. nuclear weapons, it is the knowledge base of nuclear weapon design and engineering, gained through testing and, now, by means of stewardship without nuclear testing, that constitutes the critical DOE/NNSA capability that must be continually modernized to maintain future confidence in the U.S. deterrent as threats evolve and weapons age.

Recent Statements On Future Threats and Responses
Before describing U.S. stockpile stewardship, we note two interesting commentaries reported in the press recently regarding nuclear modernization in Russia and the U.S., one by the Russian president and the other by a former U.S. Secretary of State. In a March 1, 2018 address [6] to “Citizens of Russia, members of the Federation Council and State Duma”, Vladimir Putin stated: “Todays Address is a very special landmark event, just as the times we are living in, when the choices we make and every step we take are set to shape the future of our country for decades to come.” He goes on:

Russia‘s advanced arms are based on the cutting-edge, unique achievements of our scientists, designers and engineers. One of them is a smallscale heavy-duty nuclear energy unit that can be installed in a missile like our latest X-101 air-launched missile or the American Tomahawk missile a similar type but with a range dozens of times longer, dozens, basically an unlimited range. It is a low-flying stealth missile carrying a nuclear warhead, with almost an unlimited range, unpredictable trajectory and ability to bypass interception boundaries. It is invincible against all existing and prospective missile defense and counter-air defense systems. I will repeat this several times today.

In late 2017, Russia successfully launched its latest nuclear-powered missile at the Central training ground. During its flight, the nuclear-powered engine reached its design capacity and provided the necessary propulsion.

Now that the missile launch and ground tests were successful, we can begin developing a completely new type of weapon, a strategic nuclear weapons system with a nuclear-powered missile.

Roll the video, please. (Video plays.)5

Putin also describes a doomsday nuclear powered torpedo that “enabled us to begin developing a new type of strategic weapon that would carry massive nuclear ordnance.”

Significantly, the 2018 NPR calls for new types of nuclear weapons to be added the the U.S. nuclear stockpile for non-strategic missions:

Additionally, in the near-term, the United States will modify a small number of existing SLBM warheads to provide a low-yield option, and in the longer term, pursue a modern nuclear-armed sea-launched cruise missile (SLCM). ... a low-yield SLBM warhead and SLCM will not require or rely on host nation support to provide deterrent effect. They will provide additional diversity in platforms, range, and survivability, and a valuable hedge against future nuclear “break out” scenarios.

Large numbers of “low-yield” nuclear weapons have been a mainstay of the Soviet, now Russian arsenal. In testimony[7] on Global Challenges before the Senate Armed Services Committee on January 25, 2018, former Secretary of State George Shultz addressed current nuclear challenges relevant to Putin’s threats and new low-yield weapons described in the 2018 U.S. NPR. In part, Secretary Shultz observed:

A nuclear weapon is a nuclear weapon. You use a small one, then you go to a bigger one. Nuclear weapons are nuclear weapons, and we need to draw the line there. One of the alarming things to me is this notion we can have something called a small nuclear weapon, which I understand the Russians are doing, and somehow that is usable. Your mind goes to the idea that nuclear weapons become usable, and then we are really in trouble... And we need to get rid of them. Personally, I think the way to get rid of them is on the one hand, maintain the strength of our arsenal, but then we need to somehow get rearranged with Russia.

Today's Stockpile
Today’s U.S. nuclear weapons and associated delivery systems are listed in Table 1. The W78 and W87 are reentry vehicle warheads carried by Minuteman III ICBMs that comprise the ground leg of the U.S. strategic triad; W76-0/1, W88 are reentry body warheads carried by Trident II submarine-launched ballistic missiles, comprising the sea leg of the triad; and B61-7,11 and B83-1 are strategic bombs carried by various long-range bombers, which along with the W80-1, a air-launched cruise warhead, comprise the air leg. The remaining B61 variants would be employed in non-strategic roles.

Table 1: Current U.S. nuclear weapons and associated delivery systems.

It is instructive to note the “tail numbers” that identify stockpile weapon-types. The two-digit number following the warhead (W) or bomb (B) designator approximately — to various degrees — represent the year in which the weapon family first came into service. The most recent addition occurred in 1988. This is not to say that these devices are relics from distant cold war design. They are continually being “touched” by SSP through annual assessments, surveillance where units are disassembled and inspected on a regular basis, maintenance where limited-life components are exchanged, and modernization by means of alterations, modifications, and lifetime extension programs. Furthermore, their designs are based on established scientific and engineering principles that were tested extensively in laboratory experiments and underground explosions before 1992; the data from large numbers of these UGTs have been captured on modern media forming an invaluable resource that is used extensively within the SSP to compare with and challenge computer models of stockpile systems.

Selected Highlights of Stockpile Stewardship

1995 to the Present

The founder of SSP at DOE (Reis) and two scientists who joined DOE/NNSA to help manage the enterprise (Hanrahan and Levidahl) wrote a knowledgeable overview of the first generation of SSP that was published in 2016 in the American Physical Society’s magazine, Physics Today [8]. I will try not to repeat their descriptions of some of the many important ongoing technical efforts supporting SSP, but do want to highlight some, which I consider to be most significant:

• The central accomplishment during this period — certifying the U.S. nuclear deterrent without explosive nuclear testing—was accomplished in large part by means of new computing capabilities developed under the Accelerated Strategic Computing Initiative (ASCI) and its follow-on, Advanced Simulation and Computing program (ASC). The impetus provided by science-based stockpile stewardship rejuvenated high performance computing through adoption of massively parallel hardware and associated software, largely developed at the NNSA national laboratories, that could be applied efficiently to SSP problems. The resulting computing power — hardware and software — available to SSP grew by an astonishing factor of 200 per decade over the first generation of SSP.
• Knowledge of physical properties of materials employed in stockpile systems is essential to accurate modeling and simulation of weapon performance; new and improved measurements of such properties are regularly conducted under SSP science campaigns and are incorporated into simulation codes as they become validated.
• Archival UGT data are of strategic importance to U.S. SSP. ASC computer codes describing weapon performance are evolving to “common” models that can be applied to any type of weapon in the stockpile, drawing on the same algorithms to simulate the relevant physics and common libraries of relevant material properties. Earlier generations of simulation codes relied on weapon-dependent ad hoc “knobs” to manage transitions among the different physical stages — for example, from initiation of high explosive detonation in a weapon primary, to fissioning and boost of a primary pit, to radiation flow to the weapon secondary, etc. — involved in the functioning of a U.S. stockpile weapon. Common models are challenging because they enforce common physics constraints that are inherant in weapons (and everything else), enabling better understanding of all stockpile systems. Last year, FY17,[9] teams from LANL and LLNL successfully completed a “Level-1 milestone” by simulating one to two dozen different UGTs, involving different weapon types and “anomalies” where pre-shot predictions differed significantly from the actual test result. Such results demonstrate that not only do ASC simulations agree with UGT data, but they do so for the right reasons!
• Quantifying performance margins M and associated uncertainties U, generally referred to as QMU, has become the lingua franca of SSP and the broader nuclear weapons enterprise. QMU is important because it is useful in communicating complex issues in simple ways among the large and diverse community responsible for maintaining the U.S. nuclear deterrent. NNSA requested the JASON group of national security consultants6 examine the pit assessment programs of Los Alamos and Livermore national laboratories as they approached a Level-1 Milestone in 2006 to estimate pit lifetimes with associated uncertainties. Concern had been prompted, in part, by the closure of the Rocky Flats plutonium facility in 1992. The JASON report is classified, but NNSA released unclassified sections, one of which provides a simple, but useful operational description of QMU:
  
  The basic idea is to compute a ratio of the margin M to the total uncertainty U. The higher this ratio, the higher the level of confidence in the weapon’s operation, and, in general, a central goal of Stockpile Stewardship is to continually monitor and assess this ratio and to perform mitigation to increase it should the ratio tend close to 1.
• Surveillance of our nuclear stockpile is a most important function of SSP — it is the only way we can actually see how the parts are standing up to their years of readiness. Every year, a small number of weapons are dismantled and inspected for problems or changes. In addition, instruments providing non-destructive inspection have been developed and employed. Given the complexity of modern nuclear weapons, it is not surprising that problems are revealed in inspection of individual weapons and they are. Any anomaly discovered that could affect performance initiates a “significant finding investigation” (SFI) to understand it and respond as needed. The numbers of SFIs opened and resolved by calendar year since 2000 are shown in Figure 2. The point of this figure is to highlight the considerable effort that goes into examining the stockpile for potential surprises. The data show no obvious trends in the numbers of SFIs discovered on this decadal time scale.

Future Directions
NNSA’s 2018 stockpile management plan reveals some qualitatively different experimental initiatives aimed at discovering new knowledge about nuclear weapons science through integrated experiments rather than comparing simulations with archival UGT data. They go by the acronyms NDSE and ECSE which mean Neutron-Diagnosed Subcritical Experiment and Extended-Capability Subcritical Experiment, respectively. The focus is on primary stage performance — basically understanding margins and uncertainties for primaries to achieve boost, including effects of aged materials. The experiments will use plutonium in sub-scale replicas of weapon components and measure the time-development of their hydrodynamic behavior and neutron reactivity with pulsed neutron or electron sources. An important early goal would be to compare the behaviors of “fresh” plutonium with aged material with sensitivity meaningful to stockpile performance requirements. Computer simulation cannot capture the small physical scales thought to be relevant to aging effects in weapons.

These experiments function like other large, integrated experiments common, say, in high energy physics, where simulations link detector responses to physics of interest through “forward computer modeling,” In these experiments, one can determine accurately the connections between physics observables — e.g., detection rates, locations, and angular distributions of detected particles — through simulation. The experimental observations are then “unfolded” using the simulated connections to reveal the actual important physics processes present in the experiment, with manageable understanding of statistical and other sources of uncertainty. Thus definitive results are expected, which can be repeated if needed, an option not available from the UGT data.

One can speculate that as experience is gained with the new integrated experiments, it might be possible to reduce the uncertainty, U, in our stockpile assessments, to below today’s estimates arising from limitations of simulation tools and the use of UGT data alone. In situations, where a system’s margin M may be limited by other constraints, reducing U has value by increasing the ratio M/U, thus increasing confidence.

Concluding Remarks
Science-based stockpile stewardship has succeeded to date in validating the safety, security, and effectiveness of the U.S. nuclear stockpile and promises to continue to do so for the foreseeable future. We have discussed how the knowledge base provided by SSP has been continuously modernized through implementation of new scientific tools and methods, notably high performance computing and the rich experimental data collected from U.S. nuclear tests is continuing to be used in new ways, such as the common software model studies. We can look forward to the next generation of SSP with modernized approaches to dynamic, subcritical experiments that may provide better understanding and reduced uncertainty in aspects of weapon performance not accessible since the end of underground testing.

Would that NNSA and DoD might find ways to modernize their management practices that project today the production schedules shown in Figure 3. LEPs are scheduled over the next 3-4 decades, but without clearly demonstrating a continuity in workloads for the various types of expertise needed to accomplish the different demanding tasks! LEPs take the products of SSP and apply them to the actual stockpile! They require intensive involvement of weapon scientists and engineers with production managers and workers to actually create the complex devices modeled in ASC simulations. Fitting such long and intricate schedules into budget reality can and does lead to delays in critical work, say design, for one example, that cannot necessarily be made up later if the designers must work on multiple weapon types simultaneously for a few years and then be furloughed during gaps in design work.

Related management issues plagued efforts to establish a pit production capability with a known production rate at LANL. The Secretary of Energy decision to produce a small number of weapon quality pits annually at LANL was made in December 1996. [11] It was more than a decade later that a small quantity of weapon quality pits were produced at LANL for stockpile use. However, sustained production did not follow and efforts languished, a classic case of “use it or lose it”. Today, there is a much better organized effort at LANL that is having some success producing 3-5 pits per year, but to what purpose? Unless the teams needed to build these demanding and crucial components see their work contributing to national needs in efficient ways, it will be difficult to establish stable production. Congress demands rates of 30-80 pits be produced per year by 2030, as reflected in the most recent NNSA Management Plan Report. Why not consider taking a different tack and begin producing pits continuously in batches for all weapon types in the stockpile under stable work-load conditions and build up a reserve that would serve several upcoming LEPs, when needed? Similarly, particular weapon system LEPs could be produced in interleaved batches to balance the load, sustain, and, even, grow expertise over all critical production capabilities and the design and engineering support needed for them to succeed. The present long blocks of effort shown in the NNSA’s production schedules do not guarantee continuity of critical knowledge and skills for several reasons: 1) the schedules tend to be notional beyond the normal DoD/DOE 5-year budget horizon; 2) LEPs do not necessarily replace all components in the weapon, so multi-year gaps in exercising critical capabilities can occur at individual sites. Consideration should be given to a more holistic approach to stockpile modernization based on continuous productive use of critical capabilities not found elsewhere in the U.S. economy.

schwitters@physics.utexas.edu

∗Invited talk at the 2018 Annual Meeting of the American Physical Society in Columbus, OH

¹ The U.S. also conducted 210 atmospheric nuclear tests[1] until stopped under the 1963 Limited Test Ban Treaty.

² NNSA is directed by Presidential and DOE policy documents and performance requirements established by the U.S. Department of Defense (DoD).

³ From its charter: “The NWC is a joint DoD-DOE activity responsible for facilitating cooperation and coordination, reaching consensus, and establishing priorities between the two Departments as they fulfill their dual-agency responsibilities for U.S. nuclear weapons stockpile management.”

⁴ An independent, unclassified analysis of the 3+2 Strategy was conducted by the Union of Concerned Scientists [5].

⁵ Actually, a computer animation.

⁶ The author was chair of JASON at the time of the pit lifetime study.

References

1. U.S. Department of Energy, National Nuclear Security Adminsitration Nevada Field Office, United States Nuclear Tests July 1945 through September 1992, DOE Nevada Site Office - 209 Rev 16, https://www.nnss.gov/docs/ docs_LibraryPublications/DOE_NV-209_Rev16.pdf, September 2015.
2. National Nuclear Security Administration, U.S. Department of Energy, Fiscal Year 2018 Stockpile Stewardship and Management Plan Report to Congress, https://www.energy.gov/downloads/stockpile-stewardship-and-management-plan, November, 2017.
3. U.S. Department of Defense, 2010 Nuclear Posture Review,
4. https://www.defense.gov/Portals/1/features/defenseReviews/NPR/2010_Nuclear_Posture_Review_Report.pdf, April 2010.
5. U.S. Department of Defense, 2018 Nuclear Posture Review,
6. https://www.defense.gov/News/SpecialReports/2018NuclearPostureReview.aspx, February, 2018.
7. Union of Concerned Scientists, Bad Math on Nuclear Weapons (2015)
8. https://www.ucsusa.org/nuclear-weapons/us-nuclear-weapons-policy/ 3-plus-2#.WxNNS1Mvz_8
9. http://en.kremlin.ru/events/president/news/56957
10. https://www.c-span.org/video/?439996-1/
11. Victor Reis, Robert Hanrahan, and Kirk Levedahl, The Big Science of stockpile stewardship, Physics Today 69, 8, 46 (2016); https://doi.org/10.1063/PT.3.3268
12. Michael Bernardin, LANL, private communication (2018).
13. R.J. Hemley, et al, Pit Lifetimes, JASON report JSR-06-335, January 2007,
14. https://fas.org/irp/agency/dod/jason/pit.pdf.
15. Stephen Guidice, private communication (2018).