(The Impossibility of) Lighting Atmospheric Fire

Dongwoo Chung
February 16, 2015

Submitted as coursework for PH241, Stanford University, Winter 2015


Fig. 1: Arthur Compton and Werner Heisenberg, 1929 at Chicago. (Source: Wikimedia Commons)

The construction of large-scale high-energy physics experiments in the 21st century, such as the Relativistic Heavy Ion Collider at Brookhaven or the Large Hadron Collider at CERN, have raised various exotic scenarios for artificial extinction. In both cases, scientists have stepped forward to publicly rebut such possibilities as far-fetched, if not impossible. [1,2]

It is no surprise that a mid-20th century precedent in such fears exists in nuclear physics. Due to the secretive, military nature of the scientific work, however, it is also no surprise that scientists did not publicly rebut the apocalyptic risks of nuclear weapons in any detail until decades after the non-apocalyptic success of the Manhattan Project, allowing public fears to persist and renew in these later years.

Fears Raised During the Manhattan Project

The Manhattan Project scientists clearly took lighting atmospheric fire to be a serious possibility, although how they dealt with this possibility seems to be a matter of some historic contention. A 1959 interview with Pearl S. Buck with Arthur Compton, a leader of the Manhattan Project (pictured in Fig. 1 well before World War II, with fellow physicist Werner Heisenberg), tells a highly melodramatic account of these considerations. Buck starts the account with a phone call from Oppenheimer to Compton asking to meet immediately to discuss "something very disturbing—dangerously disturbing ...": [3]

Briefly, it was that the scientists under his [Oppenheimer's] leadership had discovered the possibility of nuclear fusion (as distinguished from simple fission). In other words, the principle of the hydrogen bomb.

It was the supreme danger, tremendous and unknown, much worse than atomic explosion.

"Hydrogen nuclei," Arthur Compton explained to me, "are unstable, and they can combine into helium nuclei with a large release of energy, as they do on the sun. To set off such a reaction would require a very high temperature, but might not the enormously high temperature of the atomic bomb be just what was needed to explode hydrogen?

"And if hydrogen, what about the hydrogen in sea water? Might not the explosion of the atomic bomb set off an explosion of the ocean itself? Nor was this all that Oppenheimer feared. The nitrogen in the air is also unstable, though in less degree. Might not it, too, be set off by an atomic explosion in the atmosphere?"

"The earth would be vaporized," I said.

"Exactly," Compton said, and with what gravity! "It would be the ultimate catastrophe. Better to accept the slavery of the Nazis than to run the chance of drawing the final curtain on mankind!" [3]

Curiously enough, the Nazis themselves encountered similar worries, which perhaps prevented the government from fully supporting its own physicists in nuclear weapons research. (For a more full account of German nuclear research in World War II, see Wendorff. [4]) In his memoirs, Albert Speer recounts Heisenberg's evasiveness as to the question of whether fission was guaranteed to be controlled:

Actually, Professor Heisenberg had not given any final answer to my question whether a successful nuclear fission could be kept under control with absolute certainty or might continue as a chain reaction. Hitler was plainly not delighted with the possibility that the earth under his rule might be transformed into a glowing star. Occasionally, however, he joked that the scientists in their unworldly urge to lay bare all the secrets under heaven might some day set the globe on fire. [5]

In drastic contrast to such images, Bob Serber, writer of Los Alamos Laboratory Report LA-1 (dubbed the Los Alamos Primer), provided a far less dramatic account at odds with Compton's own account, and downplayed the prominence of such fears within the Manhattan Project:

Edward [Teller] brought up the notorious question of igniting the atmosphere. Bethe went off in his usual way, put in the numbers, and showed that it couldn't happen. It was a question that had to be answered, but it never was anything, it was a question only for a few hours. Oppy made the big mistake of mentioning it on the telephone in a conversation with Arthur Compton. Compton didn't have enough sense to shut up about it. It somehow got into a document that went to Washington. So every once in a while after that, someone happened to notice it, and then back down the ladder came the question, and the thing never was laid to rest. [6]

Whereas Serber seems to dismiss the discussion as short and Compton's concerns as overblown, Buck's interview with Compton tells a prolonged process supervised in part by Compton that eventually ruled out the scenario, but only after far more than a few hours' consideration:

During the next three months scientists in secret conference discussed the dangers of fusion but without agreement. Again Compton took the lead in the final decision. If, after calculation, he said, it were proved that the chances were more than approximately three in one million that the earth would be vaporized by the atomic explosion, he would not proceed with the project. Calculations proved the figures slightly less - and the project continued. [3]

Both accounts certainly have an appealing dramatic flair in their respective ways, but when they paint such different pictures of the discussions involved, we must consider their exact details lost to posterity.

On a historical note, Serber's account actually follows on from recounting Edward Teller's attachment to his idea of a thermonuclear weapon, "the so-called classical Super". [6] Hans Bethe, according to Serber's account, "playing his usual role, knocked it to pieces" repeatedly. [6] Eventually, however, with revisions to the core idea, fusion devices were indeed successfully developed, and their testing and proliferation renewed concerns of planet-wide fire from some corners.

Fears Renewed by the Advent of Thermonuclear Bombs

A prime example of a concerned citizen was H. C. Dudley, a professor of radiation physics at the University of Illinois Medical Center in Chicago. In 1975, Dudley wrote an article in the Bulletin of the Atomic Scientists asking for further consideration of the possibility of "the ultimate catastrophe" arising due to nuclear explosions. [7] Dudley argued that even though fusion and fission devices had been successfully tested without incident, new information and ideas in nuclear physics required scientists to investigate this possibility anew:

These studies show that fission and fusion can be triggered by lasers; that the rate of radioactive decay can easily be altered; that half-lives once thought to be constant are easily varied; and that the energy yields of fusion devices are not accurately predictable. [7]

Given such uncertainty in the face of "the present nuclear overkill capability both of the United States and Soviet Union," Dudley called for someone to "please use modern computer techniques to repeat the calculations of Oppenheimer, Compton and Fermi" to determine risks of fission and fusion explosions causing "a vast nuclear accident" or "a sustained chain reaction in the presence of seawater," possibly aided by extreme pressures at depths beneath the hydrogen-rich seas. [7]

In response, Hans Bethe—apparently central in the wartime discussions that took place, if we take Serber at face value—wrote an unambiguously dismissive rebuttal published in the Bulletin seven months later. The rebuttal was subtitled "No chance whatever that an atomic weapon might ignite the atmosphere or the ocean" and began:

In the November 1975 issue of the Bulletin, H. C. Dudley claimed that it is possible that an atomic weapon might ignite a thermonuclear reaction in the atmosphere (or the ocean) and thus destroy the Earth. This claim is nonsense. [8]

In large part, Bethe's rebuttal simply refers to and provides an overview of the Los Alamos Laboratory report LA-602 by E. J. Konopinski, C. Marvin, and—oddly enough—Edward Teller (pictured in Fig. 2), the original proponent of the thermonuclear weapon. According to Bethe, although the report was circulated in 1946 and declassified in 1973, "[t]his work was done before the first nuclear test at Alamogordo in July 1945," and its exclusion of atmospheric ignition unaffected by the subsequent development of fusion weapons. [8] This report, titled "Ignition of the Atmosphere with Nuclear Bombs", gives a detailed accounting of possible energy gain and loss mechanisms that would contribute to—or rule out—a global fusion catastrophe.

LA-602: Fears Quelled in the 1940s

Fig. 2: Edward Teller, as pictured on his wartime Los Alamos Laboratory badge. (Source: Wikimedia Commons)

The report first establishes a few key facts: that detonation of a nuclear bomb "produces a high temperature which will stimulate the reaction of atomic nuclei of the air with each other" and that this will propagate to the entire atmosphere "[i]f an ignition point exists and is surpassed". [9] This, perhaps trivially, would require "that the energy production in each newly entered region exceed the losses from that region." [9]

For energy gains, the report chiefly considers runaway nitrogen-nitrogen reactions, with additional consideration given to reactions involving protons, as nitrogen nuclei were perhaps the least stable element present in the atmosphere in significant quantities. In particular, the reaction that Konopinski et al. saw as "adopting the most dangerous assumptions" was [9]

N14 + N14 → Mg24 + α + 17.7 MeV

The energy that results from this reaction is enough to surmount the Coulomb barriers of the product particles, which is given as approximately 7 MeV, which, as Bethe explains, means that "the product nuclei can emerge from the reaction without any difficulty." [8,9]

Due to lack of empirical knowledge of nitrogen-nitrogen cross sections, the report makes certain simplified assumptions about the reaction cross section, allowing for an expression for the energy production rate per nitrogen nucleus, dependent on the temperature. Konopinski et al. also consider the nitrogen-proton reaction given by

N14 + p → C11 + α + 3.0 MeV

and here too, the produced energy surmounts the Coulomb barriers of the product particles (given as approximately 2.3 MeV). However, due to the much lower reaction cross-section and energy yield compared to the N-N reaction, the report argues that the energy contribution of this reaction would not be significant. [9]

Konopinski et al. state that the chief energy loss mechanism that would counter the energy production from N-N reactions would be Bremsstrahlung ("braking radiation") of the electrons, which rapidly radiate their share of the energy away in the nuclear reaction. [9] Energy lost this way cannot feed the fusion reaction in air. The report thus establishes the "safety factor" as the ratio between the Bremsstrahlung energy loss rate and the N-N reaction energy production rate. [9] The greater the safety factor, the more the energy loss dominates over the energy gain, and the less likely it is for the temperature to be kept sufficiently high to sustain atmospheric fire.

Here, the calculations give cause for concern: while the safety factor calculated in this way fails to fall below 1, it does fall sharply with nuclear temperature from 1 MeV, where the safety factor is about 1000, to about 10 MeV, where the safety factor is just above 2. [9] Bethe notes that even a 1 MeV temperature is equivalent to 11 billion Kelvin, whereas fission and fusion weapons only produce temperatures "usually of the order of a hundred million degrees," with even one billion degrees being an inconceivable temperature. [8] Thus, if Bethe's temperatures are correct, the safety factor for any current nuclear weapon should far exceed even 1000.

Still, for the authors of the report, having a minimum safety factor of order unity at any temperature appears to have been too close for comfort, as they go on to consider additional energy loss mechanisms. One of these is from energy transfer within the air, which adds the constraint of having to heat a certain minimum volume of air to a sufficient temperature for the reaction to propagate. The conjectured minimum volume is a sphere of 57 meters radius, the heating of which would require burning up at least 1.5 × 106 kilograms of material for a fission weapon, and an 8-meter radius sphere of liquid deuterium for a classical Super bomb. [9] These are ludicrous amounts of material for a nuclear weapon.

The danger is somewhat underestimated here, as the authors note, because they have assumed that all nitrogen nuclei undergo alpha particle emission. There is a reaction that, at lower temperatures (order of below 10 MeV), may actually have a higher reaction cross-section and thus occur with higher frequency: [9]

N14 + N14 → O12 + C16 + 10.6 MeV

This reaction may occur without the two nitrogen nuclei actually coming into contact—if the nuclei are sufficiently close, one nitrogen nucleus may split off a deuterium nucleus that then attaches to the other nitrogen nucleus, forming the products indicated above. [8,9] Using this reaction, the report only requires the heating of a 7-meter radius sphere of air, and the required amounts of active material drop significantly. However, since less energy is actually produced by this reaction than the alpha emission reaction (only 3/5 of the alpha emission energy), the safety factor increases by a factor of 5/3. [9]

The report considers one final energy loss mechanism: the inverse Compton effect. As the volume of air under consideration increases, emitted photons become more likely to collide with the electrons in the atoms of air molecules. This forces the outgoing radiation to reach equilibrium with the electron gas, and in the process, the electrons lose energy to this radiation. [6,8,9] The energy loss due to this effect provides a non-negligible increase over just the Bremsstrahlung loss. If we consider photons losing energy to a gas of electrons at temperature Te contained in a sphere of radius R, the ratio of the inverse Compton energy loss to the Bremsstrahlung energy loss is

(10/3) (Te/mc2) R/λ

where m refers to the electron mass, c is the speed of light, and λ is the Compton mean free path in air, i.e. how far a photon would travel on average without colliding with an electron, which is given as 42 meters. [9] Note that in the report, Te, although dubbed the electron temperature, is consistently given as an energy. Te in fact is shorthand for the electron temperature in temperature units (Kelvin, for instance) multiplied by the Boltzmann constant kB, which is in units of energy over temperature.

Recall that previously, the report claimed that sustained atmospheric fusion required sufficient heating of a sphere of air with R equal to either 57 meters or 7 meters, depending on which fusion reaction dominates. Furthermore, the authors of the report deem the safety factor, defined as the ratio of Bremsstrahlung losses to fusion gains, to be dangerously close to unsafe at a minimum Te of 400 keV, corresponding to Te/mc2 = 0.8. At this temperature, for a sphere of air with a radius of 57 meters or 7 meters, the inverse Compton effect augments energy loss by 360% or 40% over just the Bremsstrahlung loss. [9] Note also that this enhancement ratio only increases with the electron temperature, whereas the safety factor becomes roughly constant with temperature beyond Te/mc2 = 0.8. In this way, the inverse Compton effect does provide a computational failsafe for Konopinski et al. to fall back on for additional reassurance.

In case this enhanced energy loss did not already quell fears of catastrophe, the authors also note that this inverse Compton effect would "quench nuclear disintegration of the atmosphere as soon as this reaction has extended over a radius of a few hundred meters" when considering the propagation of the resulting detonation wave. [9] This powerful energy loss mechanism, according to Serber, was the same mechanism that Bethe thought of "that knocked Edward's calculations [for the classical Super] into a cocked hat, and they never actually recovered." [6]

The authors do add a cautionary note:

Even if the reaction is stopped within a sphere of a few hundred meters radius, the resultant earth-shock and the radioactive contamination of the atmosphere might become catastrophic on a world-wide scale. [9]

In addition to this note, the authors assert their wariness regarding the admitted "absence of satisfactory experimental foundations" on the matter. [9] Nonetheless, the authors declare:

One may conclude that the arguments of this paper make it unreasonable to expect that the N + N reaction could propagate. An unlimited propagation is even less likely. [9]

Bethe Quells Fears Again in the 1970s

Fig. 3: Hans Bethe, swarmed by journalists. (Source: Wikimedia Commons)

In his rebuttal in the Bulletin of the Atomic Scientists, Bethe (pictured in Fig. 3) does not explicitly address Dudley's call for use of contemporary computer-aided methods, instead relying chiefly on the calculations of the 1946 report. However, in affirming the enormous safety factor against sustained propagation of the N + N reactions, Bethe does note that information gained about thermonuclear reactions since 1945 reinforces the impossibility of ignition, and that this information accounts for Teller's abandonment of the classical Super design for the Teller–Ulam design. [8] Bethe then moves to briefly dismiss Dudley's proposal of a sustained runaway reaction in the ocean, presenting four possible nuclear reactions for water:

O16 + H1 → F17 + γ
D2 + D2 → H3 + H1
D2 + D2 → He3 + n
D2 + H1 → He3 + γ

Bethe discounts the first reaction as being too slow, citing empirical and astrophysical evidence. Furthermore, while the second and third reactions have "a priori a good probability," the low abundance of deuterium drastically lowers the actual frequency of collisions that would lead to these reactions—as well as to the fourth reaction, which is already improbable on its own. [8] Bethe further dismisses Dudley's claim that the ocean is a sufficiently high-pressure environment to sustain fusion reactions, noting that fusion in the Sun occurs under pressures of trillions of tons per square inch, compared to the mere tons per square inch of pressure one may expect in the sea. [8]

Bethe concludes by describing Dudley's claims as "nightmares which have no relation to reality," noting that while he shares Dudley's opposition to nuclear war, "it is totally unnecessary to add to the many good reasons against nuclear war one which simply is not true." [8]

© Dongwoo Chung. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] A. Kent, "A Critical Look at Risk Assessments for Global Catastrophes," Risk Anal. 24, 157 (2004).

[2] B. Koch, M. Bleicher, and H. Stoecker, "Exclusion of Black Hole Disaster Scenarios at the LHC," Phys. Lett. B 672, 71 (2009).

[3] P. S. Buck, "The Bomb - the End of the World?" The American Weekly, 8 Mar 1959.

[4] A. Wendorff, "German Nuclear Program Before and During World War II,", PH241, Stanford University, Winter 2014.

[5] A. Speer, Inside the Third Reich (Simon and Schuster, 1970), p. 227.

[6] R. Serber, The Los Alamos Primer: The First Lectures on How to Build an Atomic Bomb (U. of California Press, 1992).

[7] H. C. Dudley, "The Ultimate Catastrophe," Bull. Atomic Scientists 31, No. 9, 21 (1975).

[8] H. A. Bethe, "Ultimate Catastrophe?," Bull. Atomic Scientists 32, No. 6, 36 (1976).

[9] E. J. Konopinski, C. Marvin, and E. Teller, "Ignition of the Atmosphere with Nuclear Bombs," Los Alamos National Laboratory, LA-602, April 1946.