The Manhattan Project Read online

  The Manhattan Project

  A very brief introduction to the physics of nuclear weapons

  B Cameron Reed

  Alma College, MI, USA

  Morgan & Claypool Publishers

  Copyright © 2017 Morgan & Claypool Publishers

  All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher, or as expressly permitted by law or under terms agreed with the appropriate rights organization. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency, the Copyright Clearance Centre and other reproduction rights organisations.

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  ISBN 978-1-6817-4605-0 (ebook)

  ISBN 978-1-6817-4604-3 (print)

  ISBN 978-1-6817-4607-4 (mobi)

  DOI 10.1088/978-1-6817-4605-0

  Version: 20170501

  IOP Concise Physics

  ISSN 2053-2571 (online)

  ISSN 2054-7307 (print)

  A Morgan & Claypool publication as part of IOP Concise Physics

  Published by Morgan & Claypool Publishers, 40 Oak Drive, San Rafael, CA, 94903 USA

  IOP Publishing, Temple Circus, Temple Way, Bristol BS1 6HG, UK

  This work is dedicated to Laurie.

  Again.

  Contents

  Preface

  A note on units

  Acknowledgements

  Author biography

  1 The background

  1.1 The physics

  1.2 The Manhattan Project

  References

  2 Nuclear fission

  2.1 Energy release in fission

  2.2 Chain reaction timescale

  2.3 Temperature equivalent of fission fragments

  2.4 A first glimpse of the efficiency issue

  2.5 Neutron pairing energy, the fission barrier, and plutonium

  2.6 Decay mechanisms and the (α, n) problem

  2.7 Spontaneous fission

  References

  3 Criticality and efficiency

  3.1 Bare criticality

  3.2 Supercriticality and the radius-density effect

  3.3 Tamped criticality

  3.4 Efficiency

  References

  4 Obtaining fissile material

  4.1 U-235: the electromagnetic method

  4.2 U-235: the gaseous diffusion method

  4.3 Pu-239: The Hanford reactors

  References

  5 Los Alamos, Little Boy, Fat Man, Trinity, Hiroshima and Nagasaki

  5.1 Predetonation probability

  5.2 Little Boy

  5.3 Implosion and Fat Man

  5.4 Yield probability

  5.5 Trinity

  5.6 Hiroshima and Nagasaki

  References

  6 Effects of nuclear weapons

  6.1 Brightness and thermal radiation

  6.2 Shock wave

  6.3 Neutron scattering

  6.4 A brief tutorial on radioactivity and radiation exposure units

  6.5 Prompt radioactivity from a nuclear weapon

  References

  7 Legacy

  7.1 Postwar proliferation, tests, and deployments

  7.2 Nuclear arms treaties and the baggage of the Cold War

  7.3 Final thoughts

  References

  8 Bibliography

  Glossary of Symbols

  Preface

  No student of physics can resist learning about nuclear weapons. Whether you consider these devices a blessing which helped end the most brutal war in history and subsequently deterred further large-scale conflicts, or regard them as a curse which should never have been released upon the world, the power that they bestow on their holders and the influence they have in global affairs cannot be overstated. The science which underpins them is fascinating; learning anything about them gives one a sense of being close to their power and of being privy to otherwise forbidden knowledge.

  Nuclear weapons are now nearly 75-year-old technology. First developed by the United States Army in World War II in an effort which came to be known as the Manhattan Project, they represented the fruition of discoveries that dated back to the beginnings of nuclear physics in the decade before World War I. Yet, the physics of nuclear weapons is not normally part of the syllabus of most college and university-level science courses; even most physics majors likely have only a vague notion of how they work. I have written this book for physics students who wish to apply some of the scientific concepts and mathematical techniques they have encountered to understanding something of ‘first generation’ fission weapons: what principles underlie them, how they are made, how they function, and what are some of their effects.

  This book is not a conventional text. My purpose is not to develop concepts or derivations from first principles; there exist many very good and very comprehensive treatments of the history and physics of the Manhattan Project for readers who wish to explore the details (see the Bibliography). Rather, my intent is to whet your appetite to learn more about the Project from such sources by describing some of the relevant background discoveries, and by presenting some key equations and showing how they can be used to carry out approximate but informative calculations. It may come as a surprise to learn that much of the ‘forbidden knowledge’ surrounding nuclear weapons is quite accessible to a reader armed with an undergraduate-level understanding of physics.

  I have written this book assuming a fairly substantial background on the part of its readers. Ideally, you will have had classes in modern physics and basic nuclear physics. You should know that nuclei are comprised of protons and neutrons, what is meant by ‘atomic number’ (Z) and ‘mass number’ (A), that chemical elements come in a variety of isotopic forms, what ‘alpha decay’ and ‘beta decay’ mean, what abbreviations like U-235, Pu-239, , and mean, that energies in nuclear physics are measured in millions of electron-volts (MeVs), that nuclear physicists quantify the probability of a reaction by a ‘cross-section’ measured in ‘barns’, what nuclear fission involves, and the basic idea of how a reactor operates by maintaining a chain reaction of fissioning uranium-235 nuclei while simultaneously ‘breeding’ plutonium-239 via neutron-capture by U-238 nuclei. I also assume that you know something of the basic history and accomplishments of the Manhattan Project. Chapter 1 offers a brief qualitative refresher on some of the background physics, and an equally brief description of how the Project came to be organized. For a more thorough treatment, the companion volume to this book, Atomic Bomb: The Story of the Manhattan Project, is recommended reading. In essence, my goal here is to fill in some of the physics details that were skipped over in Atomic Bomb. Occasional exercises are scattered throughout the text so that you can try some calculations for yourself: you will get the most out of this book if you do them.

  This book covers five main topics, one in each of chapters 2–6. Nuclear weapons derive their destructive power by initiating a fast-neutron fission chain reaction in any material which is known to suffer fission under neutron bombardment; for practical purposes, only uranium-235 (U-235) or plutonium-239 (Pu-239) or a combination of the two can be used to fuel a fission bomb. Chapter 2 quantifies the energy released in fission and the remarkable brevity of chain reactions, and explores why, out of over 2000 isotopes known to nuclear physicists, only U-235 and Pu-239 are practicable for use as fission-bomb materials. Particularly important in this latter context is an examination of how natural decay processes, specifically a
lpha-decay and spontaneous fission, limit the number of bomb-fuel candidates.

  Chapter 3 addresses the intertwined issues of ‘criticality’ and ‘efficiency’. Perhaps the single most important number one needs to know to develop a nuclear weapon is the so-called critical mass of fissile material necessary. Phrased loosely, the critical mass is the minimum mass of fissile material that can sustain a chain reaction, at least until it blows itself apart. If the critical mass should prove to be, say, 500 kg of a very rare or hard-to-synthesize isotope, it may not be practical to attempt to develop a nuclear weapon. The critical masses of U-235 and Pu-239 are on the order of tens of kilograms, but even these amounts are very hard to acquire from scratch. Related to this is the question of efficiency. A nuclear bomb blows itself apart over the course of mere microseconds, and it proves essentially impossible to fission all of the core material before this happens. Thus, even if a critical mass is within practical reach, one needs to have an idea of the expected efficiency to judge if making a nuclear bomb will be worth the effort—or not.

  Nuclear weapons would not exist if we were not able to isolate naturally-occurring fissile isotopes or artificially synthesize non-naturally-occurring ones in sufficient quantity. Chapter 4 examines some of the physics behind isolating U-235 by two processes, one electromagnetic and the other based on results from kinetic theory, and of synthesizing Pu-239 by the process of neutron capture within a reactor. Estimates of the scales of time and number of processing steps involved in producing kilogram-level quantities of these substances explain why the industrial facilities of the Manhattan Project grew to such gargantuan proportions.

  The end results of the Manhattan Project were two types of nuclear bombs. These were the so-called ‘gun’ design which employed uranium and was used in the Little Boy bomb detonated over Hiroshima, and the very complex ‘implosion’ design utilized in the Fat Man plutonium-based bomb, one of which was tested in New Mexico on July 16, 1945—the Trinity test—and another of which was soon thereafter used at Nagasaki. The uranium bomb contained about 65 kg of U-235, and the plutonium bomb contained about 6.4 kg of Pu-239; when making order-of-magnitude estimates I will often round these numbers to 60 kg and 10 kg. The need to develop the implosion design was a consequence of an initially only loosely-anticipated property of reactor-produced plutonium, its propensity to suffer spontaneous fission. Had this design not been developed, the plutonium bomb would have been extremely inefficient. Chapter 5 describes the designs of the two weapons, elaborates further upon some of the ramifications of the fissile-candidates issues raised in chapter 2, and describes the Hiroshima and Nagasaki bombing missions.

  Chapter 6 addresses some of the effects of nuclear weapons. The energy released in fission reactions proves to be millions of times as much as that released by the same mass of a chemical explosive, and when a large amount of energy is released into the atmosphere over a short time, the result is a destructive high-pressure shock wave that propagates outward from the point of the explosion. In addition to this, nuclear explosions release fantastic amounts of light and heat radiation which can vaporize people and structures close to the explosion, cause blindness, and start fires even kilometers away. Another hazard is the immense flux of fission-generated neutrons which can cause cellular damage out to distances of hundreds of meters from the explosion. Finally, exposure to radioactivity, by either prompt mechanisms such as gamma-rays and neutrons or by longer-term ‘fallout’, can cause serious health effects up to the level of death. There is a multiplicity of very unpleasant ways to be harmed by a nuclear weapon.

  Finally, chapter 7 presents a very brief summary of current worldwide nuclear weapons deployments, and the Bibliography lists a number of print and electronic sources for readers who wish to explore the Manhattan Project and nuclear weapons in more detail. The Glossary summarizes definitions of mathematical symbols used in the text.

  A note on units

  At the time of the Manhattan Project, customary United States units such as pounds, feet, and miles were still in widespread use in American scientific and engineering circles. Most original Project documentation uses such units, and I follow this pattern, giving SI equivalents for some of the more important quantities. Readers must be comfortable in translating between these different systems.

  Acknowledgements

  When I began researching the Manhattan Project over 20 years ago, I never dreamed that it would become such a significant part of my professional career. Even after several dozen papers and articles, presentations at conferences, and this, my fourth book on the subject, the well seems inexhaustible. The most rewarding part of this journey has been interacting with other Manhattan aficionados I have met along the way. For conversations, correspondence, helpful suggestions, gentle corrections, comments on draft material, and continual encouragement, I am grateful to John Abelson, Joseph-James Ahern, Dana Aspinall, Jeremy Bernstein, Alan Carr, David Cassidy, Thomas Cochran, Pierce Corden, John Coster-Mullen, Steve Croft, Gene Deci, Eric Erpelding, Patricia Ezzell, Charles Ferguson, Edward Gerjuoy, Dennis Giangreco, Chris Gould, Robert Hayward, Dave Hafemeister, Siegfried Hecker, Dieter Hoffmann, Cindy Kelly, William Lanouette, Irving Lerch, Jeffrey Marque, Heather McLenahan, Albert Menard, Tony Murphy, Ed Neuenschwander, Stan Norris, Sean Prunty, Klaus Rohe, Frank Settle, Ruth Sime, Ray Smith, Roger Stuewer, Michael Traynor, Alex Wellerstein, John Yates, and Pete Zimmerman. Jeanine Burke and Nicki Dennis at IoP and Joel Claypool of Morgan & Claypool Publishers deserve thanks for suggesting this project and encouraging me to see it through.

  But above all is Laurie, who understands my obsession.

  Author biography

  B Cameron Reed

  Bruce Cameron Reed is the Charles A. Dana Professor of Physics at Alma College, Alma, Michigan. He holds a PhD in Physics from the University of Waterloo in Canada. In addition to a quantum mechanics text and three other books on the Manhattan Project (including the IOP Concise Physics volume Atomic Bomb: The Story of the Manhattan Project), he has published over 100 papers in peer-reviewed scientific journals on research in the fields of astronomy, data analysis, quantum physics, mathematics, nuclear physics, the history of physics, and the physics of nuclear weapons. In 2009 he was elected a Fellow of the American Physical Society ‘For his contributions to the history of both the physics and the development of nuclear weapons in the Manhattan Project’. In 2016 he was elected a Fellow of the Institute of Physics. He lives in Michigan with his wife Laurie.

  IOP Concise Physics

  The Manhattan Project

  A very brief introduction to the physics of nuclear weapons

  B Cameron Reed

  * * *

  Chapter 1

  The background

  1.1 The physics

  Neutron-induced fission of uranium was discovered in Berlin in late 1938 by Otto Hahn and Fritz Strassmann. Physicists soon realized that this phenomenon released a tremendous amount of energy, nearly 200 MeV per reaction. This is dramatically more than the few eVs typical of a chemical reaction. Such a great energy release immediately hinted at the possibility of developing a very powerful but compact bomb in which millions of pounds of conventional explosive could be replaced with a few pounds of a nuclear explosive.

  The fact that the bombarding particles in fission are neutrons is a key point. Fission cannot be induced by attempting to strike one uranium nucleus with another uranium nucleus; the repulsive forces between the protons in the nuclei are so great that they will not be able to closely approach each other unless the incoming nucleus is given very great kinetic energy. But neutrons are electrically neutral and thus experience no such repulsion; there is nothing to stop them from coming into contact with a target nucleus and disrupting it. In the process of fission, the struck nucleus loses a small amount of mass, but this corresponds to a great amount of energy in accordance with Albert Einstein’s famous equation E = mc2. A few weeks after the discovery of fission, it was found that a by-product of each fission was the simul
taneous liberation of two or three neutrons from the disrupted nucleus. These ‘secondary’ neutrons, if they can be prevented from escaping from the sample of uranium, can go on to induce fission in other nuclei and so initiate a chain reaction which, in theory, can continue until all of the uranium has been fissioned.

  These discoveries raised a number of questions. Could any other elements undergo fission? Were both of the known isotopes of uranium (U-235 and U-238) fissile? Was some minimum amount of uranium necessary to create a chain reaction? Could the process be controlled by human intervention to create a power source, or would any attempt to initiate fission on a large scale result in a violent, uncontrolled explosion?

  By the time of the outbreak of World War II in September, 1939, it had been theoretically predicted that only the rare U-235 isotope would fission under neutron bombardment; in contrast, nuclei of the much more common U-238 isotope would likely capture incoming neutrons without fissioning. These predictions were confirmed experimentally in early 1940. Since most natural uranium is U-238 (>99%), this capture effect meant that it looked as if it would be impossible to achieve a chain reaction using natural-abundance uranium. To obtain a chain reaction, it would be necessary to isolate a sample of U-235 from its sister isotope, or at least process a sample of uranium in some way as to isolate a sub-sample with a dramatically increased percentage of U-235. Such processing is known as enrichment. Since isotopes of any element behave identically so far as their chemical properties are concerned, no chemical process can be employed to achieve enrichment; only a technique that depends on the slight mass difference between the two isotopes (∼1%) could be a possibility.