FISSION, FUSION AND STAGING

Chers Amis,

Nous avons l'honneur de publier le quatrième et dernier article du physicien Franco COZZANI, Chef du Département de Stratégie et Innovation auprès du Secrétariat de l'initiative EUREKA à la Commission européenne.

A universe of death, which God by curse

Created evil, for evil only good,

Where all life dies, death lives, and nature breeds

Perverse, all monstrous, all prodigious things,

Abominable, innumerable, and worse

Than fables yet have feigned, or fear conceived,

Gorgons and hydras, and chimeras dire.

 

John Milton, Paradise Lost, II, 623-628

The so-called hydrogen bomb saw the light of the day on November 1st, 1952. Supposedly relying upon "the fusion reactions which power the Sun", the Ivy Mike shot actually did light up the day around the Eniwetok atoll over a range of several miles. Ivy Mike achieved a yield of 10.4 megaton, about 700 times the energy released by the Hiroshima explosion and 20 times the yield of the most powerful fission device ever to be tested by the United States. Two weeks later, on November 16th, the King shot during the same Operation Ivy campaign of nuclear testing, reached half a megaton; an advanced, multi-point implosion boosted fission device, Ivy King had been designed as a fall-back option in case the idea behind Ivy Mike had failed. The weapon designers had no reason to worry, though, as the "new idea" had worked beautifully, with multi-megaton yields now fully within reach. The most powerful shots in the following Operation Castle series, two years later, achieved yields of 15, 11 and 13.5 megatons, respectively, and their weaponised versions that were soon developed and fielded by the U.S. Air Force were capable of yields in the same range. The United States later deployed a gravity bomb with a rated maximum yield of 25 megatons, the B-41, for delivery from its B-52 long range bomber and, in the 1960's, then Secretary of Defence Robert McNamara claimed that the United States was technically capable, with testing, of developing a 35 megaton warhead for the Titan II missile, and to deliver a 50 to 60 megaton bomb for delivery from a B-52 aircraft without the need for further testing.

Considering the yields of the first generation fission bombs, of the order of 20 kilotons, and the fact that the most powerful fission bombsⁱ were tested at a maximum yield of a few hundred kilotons, there could be no denying that the "hydrogen bomb" was visibly and immensely more powerful than any previous nuclear fission weapon. Laymen and self-proclaimed nuclear experts, therefore, could perhaps be forgiven for thinking that fusion reactions are intrinsically quite more powerful than fission reactions. A simple look at the basics, however, easily disproves this naïve myth.

Typical fission reactions - like the fissioning of one nucleus of uranium 235 or plutonium 239, the two best known fissionable isotopes and the firsts to have been used in the fabrication of practical nuclear weapons - produce just a little over 200 MeVⁱⁱ of energy in total. Of these 200 MeV, about 170 MeV go into the kinetic energies of the two daughter nuclei (for example, strontium and xenon, in the case of uranium fission) and a few other tens of MeV go into high energy electromagnetic radiation, mostly gamma and hard X-rays. Less than a few percent of the total fission energy go into neutrinos, which escape without appreciable interaction with the surrounding matter.

 

How much is 200 MeV? To put things in perspective, let us briefly recall that the most energetic chemical reactions, from conventional explosives for military applications like PBX, Baritol, Trinitol and WWII-class Torpexⁱⁱⁱ to modern plastic explosives like Semtex and C-4, to the more mundane - but still very much energetic! - burning of gasoline in internal combustion engines, release only up to about 5 eV of energy per reaction. Therefore, one nuclear fission reaction releases several ten million times the energy of an already quite energetic chemical reaction. This spectacular difference between the binding energies inside the nucleus of the atom and those relevant to the molecular bonds which make up most of chemistry is what lurks behind the tremendous destructiveness of all nuclear weapons and the impressive performance of nuclear reactors for energy production^iv.

 

That was fission. What about fusion, then? Is it even more powerful? Let us consider the most energetic and easiest to achieve fusion reaction, that of deuterium with tritium. Reacting the two heavy isotopes of hydrogen produces one neutron, one alpha particle (which is basically a helium nucleus) and 17.6 MeV of energy, of which 14.1 MeV go with the neutron and 3.52 MeV with the alpha particle. One sees immediately that, considering the energy released per reacting nucleus, fusion is actually much less energetic than fission! The balance swings back to the side of fusion, when one instead considers the amount of energy released per unit mass. Recalling that the atomic weight of the chain-reacting isotope of uranium is 235, and that of weapon-grade plutonium is 239, whereas the atomic weight of the resonant state briefly formed by the interacting nuclei of deuterium and tritium is 5^v we find that the nuclear energy released per nucleon^vi is four to five times higher in the fusion cases. Higher, but certainly not in the range of a thousand times higher! Furthermore, fourth-fifth of the fusion energy goes into the neutron channel in the case of D-T fusion, whereas most of the energy of a fission reaction goes into the kinetic energy of the two electrically charged daughter nuclei, which, together with the instantaneous X-rays, drive effectively the propagation of the fireball of a nuclear explosion. The escaping neutron from a deuterium-tritium fusion reaction, on the other hand, cannot directly produce heat and blast effects. This brings down the militarily directly useful energy release per nucleon of D-T fusion at precisely about the same level as that of fission, but the overall energy release per reaction, and per nucleus, is much higher in the case of fission: over 10 times in absolute terms, and some 50 times higher if one counts up only the energy released through charge particles and electromagnetic energy, the channels which can drive heat and blast effects from an explosion.

 

But the so-called hydrogen bombs, based on fusion reactions, did achieve much larger yields than fission weapons! What could be the possible explanation, then? Since as back as 1952, the "secret" behind thermonuclear devices lies in achieving multi-megaton yields by using the copious X-rays from a conventional fission-imploded device (called the "primary") to drive the compression and adiabatic heating of the fusion material contained in a separate device (the "secondary"). This heating and compression mechanism turns out to be much more powerful and efficient than direct driving by X-ray radiation pressure and much more powerful and efficient than the compression made available by conventional explosives in regular fission weapons. As a result, a larger quantity of material undergoes nuclear reactions than would be attainable without staging and radiation-driven implosion. As an added bonus, as we will see shortly, another kind of fission (each reaction releasing again the 200 MeV of energy typical of fission) becomes possible thanks to fusion reactions, and that multiplies the yield of a hydrogen bomb by a further factor of two to three. Fusion reactions are not more powerful than fission reactions; thermonuclear weapons can be made so much more powerful than regular fission weapons, because they employ a clever way to make a larger quantity of material undergoing both fission and fusion reactions at the same time.

 

Further, thermonuclear weapons do not work by using a fission bomb to heat up the fusion material to the extremely high temperatures, typical of the interior of the Sun, necessary to the onset of fusion reactions. In thermonuclear weapons, a "regular" fission bomb does not function as a nuclear match, lighting up the intense combustion of exotic fusion material. If sovereign States of dubious reputation and self-respecting would-be nuclear terrorists would not already know all too well, this would a very nice fairy tale to keep circulating, for it would provide years of frustration to the bad characters and of peace of mind for the rest of the world. This was precisely the original idea behind the concept of the so-called super-bomb, colloquially referred-to as the "Super" among physicists in the late 1940's, which did not work. Nuclear gossip has it that the super-bomb champion, Edward Teller, grew almost paranoid back then, trying one approach after the other to make the concept work, while a seraphim-like Hans Bethe produced one back-of-the-envelope calculation after the other only to argue that the Super would fizzle, as was confirmed immediately afterwards by John von Neumann with his brand new Eniac electronic computer^vii. Since the Super used no compression, any initial thermonuclear reaction would have cooled down too quickly because of electron irradiation, and this basically killed the concept. It is fairly amazing that well into the 1970's the not-working concept of the Super still was the one presented in the open literature and even more incredible that many people nowadays continue to believe this to be the basis of the “hydrogen bomb”!

 

In an even cleverer design, the secondary device needs only a small quantity of the tritium necessary to start the first fusion reactions, and then it goes on to manufacture more tritium by itself as the fusion reactions progress. The principle is, however, the same: because X-rays driven compression is so much more efficient than normal implosion, one is able to ignite a larger quantity of material undergoing fusion than the amount one is capable of compressing effectively in a fission bomb, starting from a non-critical mass arrangement. This fusion mixture of lithium deuteride and a small initial quantity of tritium is also cheaper and simpler to obtain than producing a larger quantity of tritium in a fission reactor dedicated to the purpose of course, but perhaps even more attractive to a weapon designer is its relative simplicity. Such an arrangement can be packed it into a weapon to be stored and delivered against its target in a bomb or missile warhead.

 

We are now ready to consider the issue of secondary fast fission. It is another widely- spread misconception to state that natural uranium (U-238) does not fission. It does, although there are two differences with respect to U-235 fission. Firstly, U-238 indeed does not fission with thermal-spectrum neutrons, nor with the neutrons normally emitted during a fission chain reaction; in other words, the fission cross section^viii for U-238 is vanishingly small for neutrons energies ranging from thermal to up to about 5 MeV. But U-238 fissions very happily, and it releases the same almost 200 MeV energy of its weapon-grade brethren, the U-235 isotope, when bombarded by the 14.1 MeV neutrons coming from D-T fusion. The second difference is that, even when it does fission, U-238 does not undergo a chain reaction, because it does not release secondary neutrons when it fissions. One says that U-238 is fissionable but is not a fissile material. Otherwise, the cross section of U-238 fast-fissioning from very high energy neutrons (above 5 MeV all the way to 14.1 MeV) is quite large, and enormous amounts of fission energy can be obtained by reacting large quantities of U-238, otherwise inert in an ordinary fission weapon. A tamper in a fission weapon has been used since the first-generation fission weapons, to introduces some inertia in the rapid expansion of the exploding fission material, making a bomb possible, but it is otherwise just an inert material whatever its composition. Choosing instead a tamper for the secondary stage of a thermonuclear device made of natural uranium, rather than lead or tungsten, increases the total yield of a thermonuclear weapon by a factor of two to three. Most of the energy release from the first thermonuclear explosions actually came from (very) fast neutron fission, not from fusion. There is nothing sinisterly magic in fusion reactions, and the so-called hydrogen bomb does not use a super powerful nuclear reaction, bringing the immense power of the sun to Earth, albeit in an "uncontrolled" manner. Thermonuclear bombs actually control quite well what they do. They employ a very clever way to fusion and fission much larger quantities of nuclear material than regular nuclear fission bombs are capable of: staging.

Staging

There is an additional degree of confusion, even among people who grasp the basic principles of radiation-imploding a secondary, about the proper concept of staging, as witnessed in many publications and Wikipedia entries alike. Many commentators call "third stage" the fast fission of the natural uranium (U-238) tamper in the secondary by the 14.1 MeV neutrons produced by deuterium-tritium fusion. Warheads which employ a fast fissionable tamper are usually referred to as "dirty" designs, because they are optimised for maximum total yield at the (ethical) price of heavy radioactive fallout. During the development of nuclear weapons in the era of atmospheric testing, actual testing of new designs was sometimes carried out with inert tampers, precisely to reduce strongly fall-out from the explosion^ix, but when high levels of radioactivity are not an issue^x, no warhead designer worth his name would forego fast fission in the secondary, as the simplest, most effective way to increase yield in a staged thermonuclear.

 

Let us now consider the basic principles of staging in some more detail.

 

Staging is usually defined as the concept of driving the implosion of a secondary by means of X-ray compression. In reality, X-rays from the primary stage do not actually compress the material in the secondary, the way conventional explosive "lenses" compress the plutonium pit in the primary (or in simple, first-generation fission weapons). Hard X-rays from the exploding primary are radiatively transported (this is one of the tricky parts in designing modern high-yield weapons) through a radiation channel to fill the cavity of the secondary stage and typically Compton-scatter off a low atomic number filler into a higher intensity, lower energy X ray radiation field. This fills the cavity further and more uniformly, smoothing out any anisotropy in the initial hard X-rays distribution. These “softer” but more intense X-rays finally heat up the external layer of the secondary, which ablates. By momentum conservation (the physical principle known to the layman as “rocket action”) the outward motion of the rapidly expanding ablating layer results in a strong compression of the inner core - the "payload" – which adiabatically heats up as a consequence. The small quantity of tritium in the payload starts fusing with the deuterium and the first 14 MeV neutrons breed more tritium from the lithium in the surrounding lithium-deuteride composite. Extensive fusion takes place then in the secondary stage. Although very early thermonuclears used a fission “spark plug” in the secondary, to help compressing the fusion mixture, it is generally believed this is not required any more. Apart from references on the public web, some evidence of this is provided by the fact that the design of modern pellets for inertial fusion experiments does not resort at all to such a mechanism. Using the rocket action of an ablative layer^xi provides a much more symmetric implosion of the payload, avoiding (or reducing to a minimum) the onset of Rayleigh-Taylor type instabilities in the imploding layer. This more than compensates for the loss of energy efficiency resulting from the radiative coupling of the X-ray to the ablating layer.

 

One can summarise the idea behind staging, therefore, by saying that it properly refers only to the concept of driving a physically separate part of the device to implosion, via ablative compression, using X-rays from a primary device. A second stage can be relatively "clean", deriving all of its yield from fusion reactions, by using a lead or tungsten tamper, or "dirty", using a cheaper natural uranium tamper. When secondary fast fission occurs, yield is easily increased by a factor of two or three, with significant more radioactivity and fall-out, as remarked. However, whether or not fast fission occurs, staging only pertains to radiatively compress the secondary; the fact that staged weapons with fast fission occurring in the secondary tamper are also called fission-fusion-fission devices only increased confusion in the definitions. A true three stage device is one in which the X-rays from the secondary are used to drive the implosion of a tertiary stage. It is reported that both the U.S. B-41 gravity bomb and the famous "Tsar Bomba" detonated by the Soviets in 1961 were true three-stage designs; namely, they featured a fission primary, which radiatively compressed a second stage, which in turn radiatively compressed an even larger third stage. The B-41 is reported in the open literature as having been deployed in a clean and dirty variants, depending on the nature of the tamper in the third stage. Tsar Bomba, which achieved between 50 and 58 megatons according to quoted values which followed different measured yields, was one of the cleanest shots ever, with some 97% of its yield from fusion in its secondary and tertiary stages. If fitted with a fissionable tamper, Tsar Bomba would have reached 100 megatons, or perhaps 150 megatons. That provided Nikita Khrushchev with the basis for his famous claim that the Soviet Union had a 100 megaton bomb in its arsenal. Testing Tsar Bomba at full design yield, including fast fission from a fissionable tamper, would also have resulted in an unprecedented level of fallout, absolutely unacceptable even during those acutely confrontational Cold War years, which followed the Berlin blockade and preceded the Cuban missile crisis.

 

How much large can bombs be made through staging? One often finds claims on the public Internet that multiple stages could be combined one after the other, in an arbitrary large number, and that therefore the in-principle yield of a thermonuclear could be increased without limit. Such authors usually conclude this argument with the wise statement that nuclear weapons were made already so destructive, that no one could possibly think of increasing their yield even further, or that their military use would be pointless. These statements remind this author of what the hagiography of nuclear weapons refers to as Teller's backyard weapon: a bomb so powerful that it needed not being delivered physically on its intended target. Its yield was so high that it could have been simply detonated in the garden behind Edward Teller's home (or less figuratively deployed in any U.S. Air Force base in the continental United States) and its blast would have obliterated every city, and killed every person, on our planet^xii. Of course, no one in the U.S. physicists community actually proposed a backyard bomb, but it was reportedly a concept often used in "scaling" arguments during the development of the different classical Super designs. The problem with a backyard weapon, however, was not so much comically ethical as it was physical: the classical Super, based on the idea that the nuclear combustion of fusion fuel could be ignited by a fission bomb, the way a gasoline fire of arbitrary strength could be lighted by a match, just did not work because, in the absence of compression, the fusing mixture cools off too rapidly, before meaningful quantities of energy could be released. Staging is original and clever, because it implements the breakthrough idea of separating the primary from the secondary stage, and to use ablation-driven compression of the secondary, but it still relies upon the basic idea of the first plutonium fission bomb: implosion and compression. The everyday thinking-defying concept, that X-rays from an exploding primary could drive compression of the secondary stage before everything blows up, stems from the fact that inertia does play a role, even on the microseconds scale of a working staged thermonuclear. This is essentially a more sophisticated version of the original concept of the tamper in a first generation implosion fission weapon, but, at some point, everything does blow up! The idea of adding four, ten, a hundred stages, in a disciplined and well orderly way, driving a larger radiation-driven implosion after the other sounds much more like a sheer nonsense than an in-principle design for an Armageddon-class weapon. It should be added that, to the best knowledge of this author, statements about the actual yield of the most powerful weapons in the U.S. nuclear arsenal, either deployed or envisaged at some stage, were declassified, but no detailed hints at triple staging were released in the open from official sources. Also, there are (convincing) well-known sketches and some reasonable-looking calculations in the open literature about two-stage weapons, but no similarly accurate descriptions of true three stages concepts.

 

Whether or not true three stages devices are indeed for real, and whether they were actually deployed, the conclusion which is most important to our discussion is that every stage in a thermonuclear device involves a fairly complex combination of different fission and fusion reactions. On the one hand, the fission primary uses typically a few grams of tritium to boost its fission yield by up to a factor of two, and basically all modern "pure fission" designs are in reality fusion-boosted. On the other hand, unless special reasons require so, the yield of the secondary stage is easily increased by a factor of two or three by adding a fissionable tamper to it. Even more to the point, the most advanced nuclear warheads in the U.S. nuclear arsenal, like for instance the W-88 warhead in the Trident II submarine-launched missile, reportedly use an oralloy (enriched fissile U-235 uranium alloy) in the tamper of their secondary stage. The oralloy tamper gets fissioned by all neutrons being generated during the many nuclear reactions, providing an even more efficient explosion than the use of a tamper made of natural or depleted uranium. Some commentators have even remarked that in most modern nuclear weapons, for which availability of fissile material is not a problem, and very high yield are shunned in place of low weight and compact size, staging is actually used mostly to implode with a greater efficiency the secondary, where most fission reactions take place, actually producing most of the weapon energy release, rather than generating that many fusion reactions per se. In other words, some of today's weapons might not be very much "thermonuclear" at all.

 

If this sounds surprising, one could perhaps remember that, when the Eureka moment of using staging dawned on Stan Ulam^xiii, he was actually investigating ways of making implosion of fission bombs more efficient than was up to that moment possible through the use of conventional high explosive lenses.

 

This, perhaps better than any other argument, provides convincing ground to the often ignored reality hidden in the physics behind nuclear weapons design: fission and fusion nuclear reactions do show a greater continuity and similarity. Any sharp distinguishing between the two - as for instance one often hears in elementary discussions about peaceful uses of nuclear fusion for energy production - may perhaps help in making a dialectic point, but sorely lacks a basic grasp of the theoretical foundation and practical consequences of the physics of nuclear reactions.

 

Conclusions

Fission and fusion reactions are not quite one the opposite of the other, as laymen and ill-informed "experts" all too often love to remark; in reality, both get to be relevant to all modern nuclear weapon designs. In particular, the so-called “hydrogen bomb” never did, and it happily continues not to, get its power simply from the energy reactions which power the Sun! For the record, future magnetic fusion reactors will involve quite different physics from the physics of nuclear weapons and of inertially confined fusion systems alike, but they as well will have very little to do with the physics in the interior of the stars^xiv! In reality, the so-called “hydrogen bomb” achieves its potentially very high yields from a clever combination of several fission and fusion reactions occurring in series at first, and later in parallel. By themselves, fission and fusion reactions produce comparable energy outputs: both are of course enormously higher than those in even the most energetic chemical reactions, but they are otherwise very similar to one another in terms of the range of the energy released.

 

The idea of staging a secondary implosion via its radiatively driven compression, and producing the tritium necessary for the fusion reactions during the detonation itself, was, in the words of Robert Oppenheimer, "technically sweet". It takes a theoretical physicist of some calibre to appreciate the sheer intelligence of the approach, before the ethical dimension associated with weapons of such potential destructiveness kicks in. Oppenheimer famously opposed the development of the hydrogen bomb and shivered about the prospect of armies fielding multi-megaton warheads, a class of weapons so different from fission weapons as those were from conventional explosives. The idea of staging, absolutely brilliant as it was, succeeded spectacularly in opening up the brave new world of much higher yields, up to the multi-megaton range. Man had become almost God-like in his capacity to master such an unprecedented force, but the risk and the potential consequences for the whole of Mankind were going to be nothing but all too humanely tragic.

About the author

Franco Cozzani is an Expert Scientific Administrator in the European Commission. He is the author of “Mal d’America” and lives in Brussels with his wife Nilla and daughter Linda Margherita.

Disclaimer

The opinions and the statements contained in this paper, either explicit or inferred, are solely the author's and should not be taken to reflect the views, nor involve the responsibility, of any person whose name appears in the present paper, of the European Commission or its Services.

The distribution and possible publication of this article, as the sole cultural endeavour of the author, has been kindly authorised by the European Commission, according to provisions of Art. 17 of the Statutes of the Officials and other Agents of the European Communities.

Copyright 2010, 2011 © Franco Cozzani

Perhaps the better-known fusion reaction, as it is the one which gave rise to the somewhat mythical attribute of future fusion reactors running on seawater, is the one which (for the most part, as we will see momentarily) fuelled Ivy Mike, the first staged thermonuclear test device ever. This is the D-D reaction, in reality a double process, with the two reaction channels having about comparable probabilities:

D+D --› T (1.01 MeV) + proton (3.03 MeV), and

D+D --› He-3 (0.82 MeV) + neutron (2.45 MeV).

It is easy to see that the most energetic of the two reactions, the first one, achieves an efficiency of converting mass into energy of about exactly one thousandth: about 4 GeV of rest mass (two reacting nuclei of deuterium, each with one proton and one neutron in their nuclei) give rise to 4.04 MeV of energy. This is only slightly better than fission - about 16% more efficient - and, as it is the case with fission, this energy goes all into electrically charged products, which can immediately release energy through the surrounding volume.

The most typical reaction for weapon designs in practice is instead the one involving deuterium and tritium, the two heavier isotopes of hydrogen:

D + T --› He-4 + neutron + 17.6 MeV.

A whole 14.1 MeV of the energy produced in the reaction goes into the kinetic energy of the neutron and “only” 3.52 MeV, or about one-fifth of the total energy, go with the alpha particle, which can directly drive the weapon fireball formation. The D-T reaction forms the basis of most thermonuclear weapons, starting with its use in boosting the yield of the fission primary, but mostly as it is the first reaction in a whole series of fusion processes which all occur in the course of a thermonuclear explosion.

In the so called hydrogen bomb, a very small quantity - typically a few grams - of pure deuterium and tritium are used to boost the yield of the fission primary and start the nuclear explosion, which, with staging, is really a complex process involving a number of different fission and fusion reactions. Then, the additional tritium necessary to fuel most of the fusion reactions in the secondary stage is bred on the spot, by both the fission neutrons from the primary and – when it was included in earlier designs - from the "spark plug" in the secondary, and from the neutrons produced by the initial (boosting) D-T fusion. The way to breed tritium on the spot is to use a lithium mixture in the bomb. Fusion textbooks^xv regularly report the two following core reactions involving lithium:

Li-6 + neutron --› T + He-4 + 4.8 MeV, and

Li-7 + neutron --› T + He-4 + neutron - 2.5 MeV.

Lithium-7 is the more abundant occurring isotope in nature but, since the lithium-6 reaction is exoenergetic, one would like to enrich natural lithium to a higher percentage of lithium-6 to obtain more energy from this breeding reaction and especially to get all neutrons (even those which slowed down below 2.5 MeV) to react with the lithium to breed more tritium. There is however another interesting reaction, unknown to the first American weapons scientists at the time the first "dry" thermonuclear was tested in 1954. This is the reaction:

Li-7 + neutron --› Li-6 + 2 neutrons.

The consequences of the existence of this additional cross section are recalled in the narrative history of nuclear weapon development in very suggestive terms^xvi. The first nuclear test employing a “dry” mixture of deuterium and lithium^xvii was the now sinisterly famous Castle Bravo shot. Originally foreseen to yield 5 megatons, it ran away and reached 15 megatons, endangering the scientists observing the blast from ships some 30 miles away^xviii and irradiating the crew of a Japanese fishing vessel cruising downwind from the blast, the Fukuryu Maru^xix. The entire crew got irradiation symptoms from the fallout and one fisherman eventually died of secondary infections. The much higher yield of Castle Bravo^xx was due to the fact that the lithium-7 in its core produced more lithium-6, via the (n,2n) reaction, which bred more tritium, which in turn, together with the deuterium, produced more fusion reactions. These reactions produced many more fusion 14.1 MeV neutrons than it was originally foreseen, leading to fast-fissioning a larger percentage of the natural uranium tamper of the Shrimp device. Also in this case, however, it is important to note that, just as the cryogenic D-D fuelled Ivy Mike two years before, Castle Bravo got most of its yield from fast-neutron fission in the secondary tamper, not from fusion!

Using a combination of the above three fusion reactions involving lithium, tritium is bred in the radiatively imploded secondary stage of a thermonuclear weapon. Then it fuses with the deuterium in the lithium deuteride compound and produces both energy and - especially - very high energy neutrons. However, also D-D reactions take place, as written down above, the first reaction producing more tritium, which fuses with deuterium and the second reaction breeding helium-3, which also fuses with the deuterium. In the high temperature and high energy density cauldron of a detonating fusion bomb, tritium also fuses with itself, producing helium-4, two neutrons and 11.27 MeV of energy.

In the secondary stage of a fusion bomb, therefore, the following fairly complicated mix of energy producing nuclear fusion reactions takes place, in part with the fusion products of the one feeding secondary and tertiary reactions through the others:

D + D --› T + proton + 4.04 MeV,

D + D --› He-3 + neutron + 3.27 MeV,

D + T --› He-4 + neutron + 17.6 MeV,

T + T --› He-4 + 2 neutrons + 11.27 MeV,

D + He-3 --› He-4 + proton + 18.34 MeV,

Li-6 + neutron --› T + He-4 + 4.8 MeV.

Of the reactions above, that of deuterium and helium-3, the isotope of helium with two protons and only one neutron in its nucleus, is quite interesting as it has been often touted as ideal for peaceful applications of fusion power. Annex 3 to this paper deals with this subject in some more detail.

If the tamper of the secondary is a non-fissionable material, tungsten for instance, there are no more esoenergetic nuclear reactions taking place in the second stage. If instead a fissionable material is chosen and fast fission in the secondary tamper occurs, probably a full page of text would not accommodate the host of nuclear transmutations occurring at such high neutron energies! Most of the know-how about transmutations in the civilian nuclear industry are limited to the fission spectrum of neutrons, which come out with energies up to a few MeV. But there are even more cross sections waiting to become dominant at neutron energies above 5 MeV! A detonating high yield thermonuclear with fast fission in the secondary (using neutron with an energy spectrum up to 14.1 MeV) basically creates almost all the elements in the Universe, up to atomic number 100. For instance, element 100 in the Periodic Table, fermium, which has an atomic weight of 255, was first isolated from the radioactive debris of the first staged test, Ivy Mike, in November 1952.

Inert tampers have been used in the secondary of a thermonuclear weapon essentially during the years of extensive atmospheric testing, before the signing of the atmospheric test ban by the United States and the Soviet Union in 1963. This allowed testing of different designs, minimising heavy fall-out from the fast-fissioning of the tamper in the secondary. During the late 1970's, a related design came to instant and negatively sinister notoriety, when the United States planned to develop a new warhead for deployment in Western Europe. This was called the “neutron bomb”, famously derided by pacifists and anti-nuclear activists alike as the bomb which killed people - notably inside Soviet tanks and armoured troop carriers - while leaving buildings intact. While this author hates to spoil a joke, a little reasoning leads one to conclude that the neutron bomb was nothing more than a secondary fission-suppressed thermonuclear, where beryllium (a strong neutron multiplier) replaced the fissionable uranium in the tamper. Since beryllium is light, its tamper still needed probably some heavy material, combined with beryllium. Guessing is free in such matters, of course, but one could imagine that bismuth could have had some advantages over tungsten, in view of the traditionally known stable and inert character of the former^xxi, when exposed to intense neutron bombardment. The beryllium in the tamper would produce copiously bursts of neutrons while, using a lower-yield primary, heat and blast effects would have been minimised; also, since neutrons have greater ranges than blast effects, a neutron bomb was probably going to be detonated high up above advancing Warsaw Pact troops, further minimising heat and blast effects. In this latter aspect, the neutron bomb was probably also as much a way to use the weapon as it was a specific design.

There is often a certain degree of confusion about the "efficiency" of nuclear weapon designs versus the "efficiency" of energy to mass conversion. We are now ready to examine this in somewhat more detail.

In the universally-known relation E = mc², E is the energy associated with a given quantity of matter, m, and c is the speed of light. c is is a very large number when expressed in the units which we use in our everyday experience: about 300,000 km per second, or about 3 x 10E8 meters per second. Now, c being such a large number, its square power is truly huge, c² = about 9 x 10E16 (meters per second)². Therefore, when converting mass into energy, even a small quantity of matter, m, produces a very large quantity of energy, E. This is quite well known to most people. What is often less realised, though, is that there is absolutely nothing "nuclear" about this relation! Chemical reactions converts mass into energy precisely according to the same relation, and the kinetic energies of the air molecules in the wind are transformed into the electrical energy output of wind turbines, again according to the same relation. In this latter case, the speeding molecules in the wind are "heavier" than the corresponding molecules at rest, by exactly the amount m = E/c², where E is their kinetic energy while they are moving. The difference, of course, is that nuclear reactions were the first occurrence where man could easily measure the differences in mass before and after a reaction, since nuclear energies are so large. In the case of chemical reactions, and even more so, in the case of wind energies, mass differences are truly infinitesimal. But how large exactly are the mass differences involved in nuclear reactions?

The plutonium isotope of most interest for weapon application is Pu-239. It has 94 protons, like all plutonium isotopes, of course, and 239 - 94 = 145 neutrons. For our back-of-the-envelope calculation, we will assume that protons and neutrons have the same rest mass, about 1 GeV in energy units. To fission one nucleus of Pu-239, one needs a neutron to be absorbed, bringing the total count to 240 nucleons (neutrons and protons) in a plutonium nucleus ready to fission. Upon fission, 207 MeV of energy are released in total, to be divided among the kinetic energies of the daughter nuclei, the two to three secondary neutrons, gamma and X-rays, and neutrinos. Therefore about 240 GeV of rest mass, when fissioning plutonium, give rise to 207 MeV of energy, a fraction of 8.63 10E-4: somewhat less than one thousandth of the reacting mass is converted into energy. In the case of reacting U-235, which produces some 202 MeV, we have the same proportion. This is fission. How much mass is converted in energy during a fusion reaction?

Considering the D-T reaction, we have, upon the "fusing" of deuterium (one proton and one neutron in its nucleus) and tritium (one proton and two neutrons in its nucleus), a resonant state of helium with five nucleons which instantaneously breaks apart into a regular helium nucleus (two protons and two neutrons in its nucleus) and one escaping neutron with a very high energy. Only about one-fifth of the energy of the reaction goes into the kinetic energies of the helium nucleus, 3.52 MeV, while the escaping neutron flies away with 14.1 MeV. The overall energy release of the D-T reaction is 17.6 MeV. Therefore, about 5 GeV of the rest mass of the initially reacting nuclei, in this case of fusing deuterium with tritium, give rise to 17.6 MeV of energy, a fraction of 3.52 10E-3: a little more than three thousandth of the reacting mass is converted into energy.

D-T fusion is indeed somewhat more efficient, as far as total energy is concerned, at converting mass into energy than fission: a fraction of 3.52 10E-3 as opposed to 8.63 10E-4 for fission, or about 4.4 times more efficient. In other terms, D-T fusion is about 4.4 times more energetic, per unit mass, than fission, when total energy is concerned.

However, as four-fifth of the D-T fusion energy output goes with the escaping neutron which carries away 14.1 MeV out of the total 17.6 MeV produced, these four-fifths cannot drive immediately the formation of a fireball in a nuclear explosion and are not directly able to generate heat in a reactor for peaceful energy production either, but will need instead a rather complex heat-exchanging blanket^xxii.

That was D-T fusion. How efficient are other typical fusion reactions?

The D-D reaction, as already noted, consists in reality of two different reactions, with about comparable probabilities :

D + D --› T (1.01 MeV) + proton (3.03 MeV), and

D + D --› He-3 (0.82 MeV) + neutron (2.45 MeV).

It is easy to see that the most energetic of the two reactions, the first one, achieves an efficiency of converting mass into energy of about exactly one thousandth: about 4 GeV of rest mass (two reacting nuclei of deuterium, each with one proton and one neutron in their nuclei) give rise to 4.04 MeV of energy. This is slightly better than fission, about 16% more efficient, and, as it is the case with fission, this energy goes all into electrically charged products, which immediately release energy through the surrounding volume for military applications and envisaged future peaceful energy production alike. Let us now consider the reaction involving deuterium and helium-3:

D + He-3 --› He-4 (3.67 MeV) + proton (14.67 MeV).

In this case, 18.34 MeV of energy are produced, with an efficiency slightly higher than is the case in the D-T reaction: about 5 GeV of rest mass, when fusing deuterium (one proton, one neutron in the nucleus) with helium-3 (two protons, one neutron in the nucleus), give rise to 18.34 MeV of energy. A fraction of 3.67 10E-3 of the reacting mass is converted into energy, about 4% more efficiently than is the case in D-T fusion. The main difference with D - He-3 fusion, with respect to the case of D-T fusion, is that all of the energy produced in the reaction comes out as electrically charged products, therefore all of the energy produced is immediately available to heat up the surrounding material air or water in a warhead explosion. In a future D - He-3 reactor, a direct energy conversion method will be feasible, dispensing it from relying upon a less efficient thermal cycle.

Considering the above results, one can easily see that, as far as total energy release per unit mass is concerned, nuclear fusion is at best about four times more efficient than fission! If one considers the fraction which is available to drive a fireball formation, the energy release per unit mass is typically one-to-one with fission, since this is the case pertaining to the most widely used reaction at the basis of all modern nuclear weapons: the D-T reaction. Also the (secondary) D-He-3 reaction taking place in the thermonuclear cauldron of an exploding two-stage thermonuclear is about only four times more efficient than fission. There is more, however, which will surprise people who believe that the nuclear reactions “which power the sun” must be so much more powerful, to give the hydrogen bomb its awesome power. Let us consider the total energy release per single neutron being produced in an exploding nuclear weapon: in this case, the energy balance is heavily tilted in favour of fission! Indeed, a neutron from the initial burning of D-T can breed more tritium via the reactions:

Li-6 + neutron --› T + He-4 + 4.8 MeV, and

Li-7 + neutron --› T + He-4 + neutron - 2.5 MeV.

The first reaction actually adds up more energy to the explosion but, for both reactions, their role is to breed more tritium “on-the-fly”. But at some point, when enough tritium is produced in the lithium-deuteride to sustain an effective thermonuclear burn, these 14.1 MeV neutrons produced by the D-T fusion reactions become much more useful to fast-fission cheap natural U-238, each neutron releasing about 200 MeV of energy, almost all of which is available to drive the fireball formation.

This is of course the same argument used by advocates of hybrid fusion-fission systems for future energy-producing nuclear reactors. From the point of view of simple energetics, it makes a lot more sense to use every available (very fast) neutron going around in a thermonuclear cauldron to drive secondary fast fission rather than using it to breed more tritium, at least after a certain quantity of tritium has been produced. The argument, applied to peaceful applications of thermonuclear fusion, is strengthened by the the fact that the physical parameters for the fusion part of a fusion-fission hybrid reactor would be easier to reach than they would be for a pure fusion reactor, even one based on the easiest reaction to use, that of deuterium and tritium. The idea of fusion-fission hybrids remains nowadays technically sound as it is socio-politically unwise, however. Politically speaking, a hybrid system would lack the emotionally attractive connotation – scientifically unfounded as it is, as we have amply argued in this paper – of a reactor based on the "power of the stars". Furthermore, safety and - especially – proliferation aspects would likely be quite complex for fusion-fission hybrids. Although not even magnetically confined D-T pure fusion systems would be intrinsically immune from potential proliferation risks^xxiii, it is true that pure fusion systems would make in practice for a simpler control of possible diversion of materials than is the case with conventional fission reactors. A hybrid-fission systems, like and possibly even more so than a breeder fast reactor, would instead be the mother of all worries as far as potential proliferation of materials is concerned.

On the other hand, one might perhaps surmise that it would be a rather particular scenario to imagine a world some fifty or sixty years from now, when pure fusion reactors based on the D-T reaction would have reached a significant energy penetration for baseload electricity production, where humanity would have not yet destroyed itself over a major war fought (with nuclear weapons) over dwindling resources and climate change, would have not found a wide-spread solution to providing ample and clean energy from sources other than fusion, but would still face the same problems of today with nuclear proliferation making breeder fast reactors and fusion-fission hybrids unacceptably dangerous.

Let us now focus on a different kind of efficiency, that related to the yield-weight relationship for nuclear warheads. Aside from Dr Strangelove-style, "backyard"-level devices, a nuclear weapon has no use until it can be effectively delivered on an enemy target. Although most scientists back in 1939 thought of delivering the then-envisaged new weapon by way of a ship^xxiv, meant to devastate an enemy harbour, the preferred mean of delivery soon became the airplane and, later in the 1970's, the ballistic missile. In both cases, bombs and warheads have often rather stringent size and especially weight limitations, thence the importance of maximising the yield to weight ratio of the weapons being deployed grew progressively more and more over the intervening years. In the open literature, one finds plenty of reference to - but scantly a proper analytical calculation of - a practical upper limit of about 6 kiloton per kilogram, or 6 megaton for metric tonne, for a working nuclear warhead. This is normally known as the "Taylor limit", in honour of former weapon designer, turned nuclear-propelled space travel visionary, Ted Taylor^xxv. The Taylor limit includes some essential structural parts of a warhead in its estimate, such as the aerodynamic casing or the fuse, but it does not include, for instance, the guidance system for a modern GPS-assisted gravity bomb.

The first multi-megaton bombs actively deployed by the United States in the mid-1950's, the large Mk-17 and Mk-24 carried by the turboprop-propelled B-36 long range bomber, were physically imposing weapons weighting in excess of 18 metric tonnes, which, despite their unprecedented yield, had fairly low efficiencies: both the Mk-17 and Mk-24 achieved an efficiency less than 1 megaton for metric tonne of weight. In comparison, the B-41 bomb, deployed some fifteen years later and carried by the B-52 bomber at the height of the Cold War, reached an high efficiency ratio of 5.2 megatons per metric tonne of weight. The B-41 bomb reportedly came with two yield, depending on whether an inert or fissionable tamper was used in its secondary stage. Some sources report that the B-41 was actually a three-stage design, where the second stage was used to drive a larger, third stage to radiative implosion. At its highest stated yield, the B-41 bomb reached 25 megaton, making it the highest-power nuclear weapon ever fielded by the United States, as well as the most efficient bomb or warhead actually deployed by any country during the Cold War and afterwards. A value of 5.2 was indeed the closest to the Taylor limit ever reached by any weapon reaching active duty. It is easy to see what aspects of a weapon design influence heavily its yield-to-weight efficiency: rudimentary designs requiring a thick heavy tamper were detrimental, whereas the benefits of more sophisticated radiative transport and implosion calculations appear equally clear. The Taylor limit should not be seen as derived from first principles, though, as the following example shows convincingly.

As noted earlier in this paper, Defence Secretary McNamara announced in his now famous interview with Time Magazine in the early 1960's that the United States was capable of developing, with testing, a 35 megaton warhead for the Titan II intercontinental missile. The warhead was never deployed in the end, but it is quite interesting to estimate the efficiency that it would have reached. Assuming its weight to have been the same as the deployed W-53^xxvi, in view of the weight requirement that it had to be delivered by a Titan II, a yield of 35 MT for such a warhead would have blown over the roof of the Taylor limit, reaching an unheard-of efficiency of about 9.5. No wonder such a warhead would have needed testing!

In comparison, the longest serving, multi-megaton warhead in the U.S. nuclear arsenal, the W53/B-53 design had a lower - but still very much multi-megaton! - yield: 9 megatons. The W53/B-53, with a weight of 3,690 kg, was slightly lighter than the B-41 bomb and had an efficiency ratio of 2.44, slightly less than half that of its mightier predecessor.

The McNamara speech marked however an interesting moment in the technological history of nuclear weaponry, in that it acted as a kind of separatrix between the run to develop maximum destructive efficiency from a nuclear weapon and the later tendency instead to reduce maximum yields as well as the quantity of fissile material required by weapons, to the price of a somewhat lower overall efficiency.

A comparison of efficiencies (yield/weight ratios) is indeed quite telling. Note that I dubbed "W-XX" the never-deployed 35 megaton warhead in the table below:

Warhead	Yield	Weight	Efficiency
	kiloton	kg
Mk-17	12500	18600	0.7
Mk-24	15000	18600	0.8
B-41	25000	4810	5.2
W-53 for the Titan II	9000	3690	2.4
W-XX for the Titan II	35000	3690	9.5
W-88	475	400	1.2

The W-53 / B-53 was also known for its stability and resilience to ageing, an important consideration when attention shifted from steep increases in the United States (and Soviet Union) nuclear arsenal to the need of better managing the existing stockpile of bombs and warheads. From the table, one can also see that the W-88 warhead, carried in a multiple configuration by the Trident II submarine-launched missile, reaches only a quite modest yield-to-weight efficiency, despite being the most modern warhead fielded by the United States. This is due presumably to its design choices, which, as it was also the case for the W-87 warhead developed for the land-based MX Peacekeeper missile, optimised the use of fissile material at the expense of actual total yield. A number of factors drive these lower yields on technical grounds. Lighter warheads, using less fissile material, have smaller primaries^xxvii which are less efficient at driving the implosion of the secondary. But also lower efficiency are nothing but the consequences of simple geometrical considerations: the less the "nuclear stuff" in a working warhead, the more relevant the contribution of the casing and fuse components are to its yield-to-weight efficiency ratio.

The quite interesting D - He-3 reaction is

D + He-3 --› He-4 (3.67 MeV) + proton (14.67 MeV).

18.34 MeV of energy are produced in this reaction, with an efficiency slightly higher than is the case in the D-T reaction: about 5 GeV of rest mass, when fusing deuterium (one proton, one neutron in the nucleus) with helium-3 (two protons, one neutron in the nucleus), give rise to 18.34 MeV of energy, a fraction of 3.67 E-3 of the reacting mass is converted into energy, about 4% more efficiently than is the case in D-T fusion. But, in the case of D - He-3 fusion, all of the energy produced in the reaction comes out as electrically charged products. This does not so much matter to weapons designers, for whom the high energy neutrons from the D-T reaction are best used to fast-fission the tamper of the second stage, but this is music to the ears of peaceful fusion reactor dreamers. Indeed, both the reacting deuterium and helium-3 are non-radioactive, nor are the fusion product, helium-4 and a proton; there are (almost, see below) no neutrons, so little or no activation of the fusion reactor vessel; and, last but absolutely not least, the alpha particles (the He-4 nuclei) keep the plasma hot and burning, while the high energy protons could drive a high-conversion efficient direct cycle, dispensing with blankets and thermal turbines to convert high temperature steam into electricity.

It is however somewhat incorrect to term the D - He-3 reaction as fully aneutronic, a totally clean reaction which will prevent any activation of the reactor structure. Indeed, along with D - He-3 reactions proper, some D-D reactions will occur nevertheless, even though D - He-3 reactions will dominate over D-D reactions, since the cross section for D - He-3 fusion is about ten times that of the two D-D reactions combined, as these cross sections peak at comparable temperatures. These D-D reactions will produce both neutrons (with an energy of 2.45 MeV) and - worse - tritium. Of course, this tritium will react with the deuterium, via the "normal" D-T reaction, producing the very energetic 14.1 MeV neutrons one sought to dispose of in the first place. If, on the one hand, the quantity of tritium being generated in this two-step process will be limited, the peak reactivity of the D-T reaction (its cross section), on the other hand, is about ten times that of the D - He-3 reaction. Furthermore, since the D-T cross section peaks at lower temperatures than the D - He-3 cross section, densities profiles will need to be carefully optimised, lest to have a relatively higher D-T reaction rate in the outer regions of the plasma, closer to the vessel inner walls and where temperatures are lower. In the end, it turns out that a "simple" D - He-3 reactor will not be truly aneutronic, but it will produce a neutron radiation field intensity about 10% that of a D-T reactor of the same fusion power. One should, however, not infer unduly from these arguments than advanced fuels, like D - He-3, hold no promise for future energy-producing fusion reactors. Reducing the flux of 14.1 MeV by 90% would be an extraordinary feat and, we recall, this result has been derived for equal fusion power outputs; if one takes into account that a D - He-3 reactor will not need a thermal to electrical converter system, the advantage in lower neutron activation at equal electrical output would be proportionally even higher. But bright ideas never die and, a number of years ago, schemes were proposed to use polarised deuterium nuclei in the D - He-3 mixture, to suppress the D-D reaction responsible for the tritium production. The idea of polarised nuclei did not receive much continuing attention, despite its stimulating character, as it remains technically quite a formidable one: how to maintain aligned spins in a nuclear burning mixture with temperatures in the range of 100 to 400 keV?

Purely aneutronic character aside, if the D - He-3 reaction is however so attractive, why then nuclear fusion is normally foreseen, at least for first generation fusion power stations, as being based on the D-T reaction? For one thing, the D-T is the easiest to achieve, since its cross section peaks at about 100 keV, whereas the D - He-3 reaction cross section peaks at about 400 keV. But, of course, the chief reason is that there is hardly any He-3 available on Earth, aside from traces in the atmosphere arising from cosmic rays and from volcanism^xxviii. Tritium, on the contrary, can be produced rather more easily in a number of ways: for peaceful purposes, as by-product of Candu power reactors, and in future fusion reactors by breeding it out of lithium in the reactor blanket^xxix. It has been surmised by some authors that He-3, on the other hand, might perhaps one day be mined on the surface of the Moon to fuel a more advanced nuclear fusion-based world economy; this would be certainly an intriguing, albeit perhaps not yet entirely practical, possibility.