### Professor Bridgman's Introduction to the Physics of Nuclear Weapons Effects

The feeling you get when you open and read Dr Charles J. Bridgman's *Introduction to the Physics of Nuclear Weapons Effects* is the same amazement that you get when you read Glasstone and Dolan's *The Effects of Nuclear Weapons,* Brode's *Review of Nuclear Weapons Effects,* or Dolan's *Capabilities of Nuclear Weapons*.

I read Glasstone and Dolan's book in 1988 when aged 16 on the recommendation of the local Emergency Planning Officer, Brode's paper at the university library in 1990, and Dolan's manual in 1993 after being told by the library staff at AWE Aldermaston that it had been declassified (I had requested the earlier TM 23-200 *Capabilities of Atomic Weapons* which had been cited in various Home Office Scientific Advisory Branch civil defence reports). So it is quite a while since I saw something as comprehensive as Dr Bridgman's book on this subject!

The most surprising thing about most of the published nuclear weapons effects literature (nearly all originating from Glasstone's book) is the theoretical nature of the information provided. I had expected something a lot briefer but based more directly on nuclear test data, and was a little disappointed that the amount of nuclear test data in the book was relatively limited, and that most of the graphs were just curves without any data points shown: the reader has to trust the publication and the editors. In addition, the different kinds of nuclear explosion (underwater, surface burst, air burst, high altitude) were not dealt with separately: instead, you had bits and pieces about each kind of burst scattered in each chapter which is concerned with one type of effect (blast, thermal, nuclear radiation, EMP, etc.). This misleadingly gives the impression to the general reader that all kinds of nuclear explosions produce similar effects, with merely some quantitative differences in the relative magnitudes of those different effects. Nothing could be further from reality: just compare an underwater burst to a high altitude burst!

I think that to improve public understanding of nuclear weapons effects for civil defence purposes, a handbook is needed which has the effects phenomenology (not the damage criteria) organized by burst type (chapter 1: space bursts, chapter 2: air bursts, chapter 3: surface bursts, chapter 4: underground bursts, chapter 5: underwater bursts) so there can be no confusion. I don't think that this will involve much repetition because the blast and thermal effects of air bursts are quite different to those of surface bursts (different blast wave waveforms and different thermal radiation pulses), so there is no overlap. In addition, while the physics needs to be explained concisely as done by Dr Bridgman's book, there is a need for all theoretical prediction graphs given to be justified by the incorporation of nuclear test data points, so the user can judge the reliability of the source of the predictions.

First, it's a book that's more important than Glasstone and Dolan 1977, and about as important for civil defence as Dolan's *Capabilities of Nuclear Weapons* or Brode's *Review of Nuclear weapons Effects*. The reason is that it is quantitative. professor Bridgman doesn't analyze all the nuclear test data, but he does provide most of the theoretical physics equations. To the extent that Bridgman's book is based upon solid physical laws and solid facts - provided that the equations are applied with the right assumptions and that the mechanism they are applied to is the most important mechanism for the effect being considered - it is valuable and reliable.

Professor Bridgman graduated from the U.S. Naval Academy in 1952, did an MSc in nuclear engineering at North Carolina State University in 1958, and then did a PhD in nuclear engineering there in 1963. He is Professor Emeritus of Nuclear Engineering at the Department of Engineering Physics, U.S. Air Force Institute of Technology (AFIT), Wright-Patterson Air Force Base, Ohio. His research specialism is the effects of nuclear weapons, and he has published papers on fallout, radiation effects on electronics and sunlight attenuation in nuclear winter.

His book 'Introduction to the Physics of Nuclear Weapons Effects', 1st edition, is a 535 pages long hardbound textbook published by the U.S. Defense Threat Reduction Agency in July 2001 as a single volume which I bought on the internet at www.Amazon.com from a seller in America. In December 2008, Volume 2 of a revised edition of the book, containing chapters 2, 3 and 4 (these chapters deal in mathematical detail with the physics design of nuclear weapons, such as fission efficiency calculations as a bomb core expands and loses neutrons, compression of nuclear cores by chemical explosive implosion systems, tritium boosting of fission reactions, and the detailed physics of Teller-Ulam fusion systems) was published (252 pages). A revision of the weapons effects chapters (1 and 5-15) is currently in preparation and will be issued separately as Volume 1 when completed.

The first edition is not secret but is marked 'Distribution Limited' on the dust wrapper, front hard cover and on the title page: 'Distribution of this book is authorized to U.S. Government agencies and their Contractors; Administrative or Operational Use, July 2001. Other requests for this book shall be referred to Director, Defense Threat Reduction Agency, 8725 John J. Kingman Road, Ft. Belvoir, VA 22060-6201.'

As a result, I will not be reviewing the mathematical physics of chapters 2, 3 and 4 of the book, pages 72-195 of the first edition, which deal with nuclear explosive details themselves. Those chapters, while unclassified, contain extensive detailed calculations of the (a) neutron multiplication factors in plutonium and uranium spheres of various sizes and densities (implosion compressions), (b) the effect of neutron reflectors (e.g., beryllium) on the fissile core behaviour, (c) the calculation of 'alpha' (the neutron multiplication rate of a fission reaction, measured by the time between successive fission 'generations'), (d) the implosive shock pressure needed to compress metallic uranium and plutonium in various kinds of implosion weapons, (e) the effect of kinetic dissassembly and fuel burn up on fission efficiency in a nuclear explosion, and (f) the calculation of fusion yields by the compression of fuel capsules using ablative X-ray radiation recoil from a fission bomb, and by the 'boosting' system whereby a small amount of fusion material in the centre of a fissile bomb core releases high energy neutrons which greatly increase the efficiency of the fission reactions. All of these topics are exactly the kind of thing I do not want to discuss in mathematical detail on this blog. The mathematical physics information in the book on these subject areas may not be enough to qualify someone to design the latest Los Alamos thermonuclear warhead, but it is certainly not the kind of thing anyone would want to make easily available to any terrorist/rogue nation which already had access to fissile material. I'll avoid the details of three chapters altogether here, since the interest is improved understanding of nuclear weapons effects for civil defence.

The front flap of the dust wrapper states that the book evolved from the class notes for courses given to graduate students at AFIT:

'The notes were motivated by the lack of a textbook covering all of the effects of nuclear weapons. The well known *Effects of Nuclear Weapons* by Glasstone and Dolan offers complete coverage but, by design, does not develop the physical and mathematical modelling underlying those effects. If Glasstone and Dolan were regarded as "Effects 101", then this book is "Effects 201".

'One chapter is devoted to each of the following weapon effects: X-rays, thermal, air blast, underground shock, under water shock, nuclear radiation, the electromagnetic pulse, residual radiation (fall-out), dust and smoke, and space effects. ... Empirical [non-theoretical, data generalizing] formulae are avoided as much as possible ...

'This book complements the *Handbook of Nuclear Weapons Effects: Calculational Tools Abstracted from DWSA's Effects Manual One (EM-1)* [Defense Special Weapons Agency, Alexandria, VA, September 1996] edited by John Northrop. That handbook is a collection of methods and data for predicting nuclear weapon free field intensities and specific target responses. The present book develops the theory behind those calculations found in the handbook.'

The back flap of the dust wrapper states:

'Charles J. Bridgman ... was posted to the Armed Forces Special Weapons Project at Sandia Base where he trained as an atomic weapons officer. He was assigned to the Strategic Air Command as a Nuclear Officer responsible for the Mark 5, 6 and 7 weapons and later was a member of the military assembly team to become operational on the Mark 17, the first operational thermonuclear weapon. Dr. Bridgman joined the AFIT faculty in 1959 as an Air Force Captain. In 1963 he became a civilian member of the Department of Engineering Physics. He was appointed professor and chair of the nuclear engineering committee in 1968. Dr bridgman chaired the nuclear engineering programme for 20 years. During that time he led the conversion of the AFIT nuclear engineering program from a nuclear-power-reactor focused curricula to a nuclear-effects focussed curricula. During those years, he was a frequent lecturer and consultant to the Air Force Weapons Laboratory at Kirkland AFB, New Mexico. ... He has chaired over 100 AFIT MS theses and 14 PhD dissertions. Dr. Bridgman served as the School Associate Dean for research from 1989 to 1997. He retired from that position in 1997 and continues, since that date, to maintain office hours at AFIT as a Professor Emeritus. Dr. Bridgman is a Fellow of the American nuclear Society.'

The fifteen chapters are headed:

1: Atomic and Nuclear Physics Fundamentals (pages 1-71)

2: Fission Explosives: Neutronics (pages 72-134)

3: Fission Explosives: Thermodynamics (pages 135-169)

4: Fusion Explosives (pages 170-195)

5: X-Ray Effects (pages 196-236)

6: Thermal Effects (pages 237-270)

7: Blast Effects in Air (pages 271-304)

8: Underground Effects (pages 305-336)

9: Underwater Effects (pages 337-348)

10: Effects of Nuclear Radiation (pages 249-371)

11: The Electromagnetic Pulse (pages 372-397)

12: Residual Radiation (pages 398-452)

13: Dust and Smoke Effects (pages 453-464)

14: Space Effects (pages 465-492)

15: Survivability Analysis (pages 493-509)

The first impression you get is that the book is a more in-depth treatment of the subjects covered by Glasstone and Dolan, excluding the damage photographs.

In the Preface, Dr Bridgman writes: 'Some comments about Chapters 2, 3 and 4 are in order. The design of nuclear explosives in the United States is by law the exclusive province of the Department of Energy, not the Department of Defense. This book is intended for DoD students. The inclusion of Chapters 2, 3 and 4 is not intended to prepare students to become bomb designers. Those chapters would be woefully inadequate for that task. Rather the inclusion of these three chapters is based on the author's firm conviction that to understand the effects of a nuclear explosion, one has to understand the source. For this reason, Chapters 2, 3 and 4 consist of elementary models of the physical processes occurring during the fission and fusion explosion. They do not include design considerations.'

The Acknowledgements pages show that a long list of experts checked, contributed suggestions, and corrected the draft version of the book.*1: Atomic and Nuclear Physics Fundamentals (pages 1-71)*

At first glance, this chapter looks like routine basic physics. However, a close reading shows that it is very carefully written, and physically deep as well as being more relevant to the subject matter of the book than the typical atomic and nuclear physics textbook.

On page 3, Figure 1-1, 'Energy partition in uranium as a function of temperature', shows at temperatures below 100,000 K, 100% of the energy in uranium is in the kinetic energy of the material (ions and electrons). But at higher temperatures, the energy carried between those charges by radiation starts to become more important. At 1,000,000 K temperature (100 eV energy per particle) 1% of the total energy density is present as photon radiation and 99% is in the kinetic energy of moving matter. At 10,000,000 K (1 keV), 8% is in radiation and 92% in matter. At a temperature of about 32,000,000 K (3.2 keV), which is about twice the core temperature of the sun, there is an even split with 50% of the energy in uranium plasma carried by x-ray radiation and 50% by the ions and electrons of the matter present. Finally, at 100,000,000 K (10 keV), only 9% of the energy density in the uranium is present in the kinetic energy of matter (particles), and 91% is present as x-rays.

This matter-radiation energy distribution occurs because of the Stefan-Boltzmann radiation law, whereby the amount of energy in radiation increases very rapidly as temperature increases: the radiant power is proportional to the fourth power of temperature. Dr Bridgman comments on page 3:

'Thus in temperature regions where the radiation constitutes a large fraction of the energy present, added yield appears mostly as additional radiation and results in only a fourth root increase in temperature. ... In summary, the presence of nuclear radiation from the nuclear reactions themselves, and even more important, the presence of electromagnetic radiation arising from the plasma nature of the exploded debris, make the nuclear explosion unlike a chemical explosion and like the interior of a star.'

Obviously, because of the small mass of a nuclear weapon fireball compared to the immense gravitating mass of the sun, gravitation cannot confine the nuclear weapon fireball as it confines the sun, so the former is able to explode, due to lack of gravitational confinement.

On page 5, Dr Bridgman tabulates physical conversion factors for nuclear weapons effects:

1 cal = 4.186 J

1 bar = 100 kPa

1 kbar = 100 MPa

1 atmosphere = 1.013 bars

1 eV = 1.602*10^{-19} J

1 kt = 10^{12} cal

Page 6 is more interesting and gives the formula (equation 1-1) for the energy density of electromagnetic radiation in space as a function of electric and magnetic field strengths (albeit with an error, the term for magnetic energy density should be (1/2)*(*mu_0*)**H*^{2} or (1/2)*(1/*mu_0*)**B*^{2}, but not (1/2)*[(*mu_0*)**H*]^{2} as printed, where *mu_0* is the magnetic permeability of the vacuum, *H* is magnetic field strength and *B* is magnetic flux density, *B* =(*mu_0*)**H*).

Bridgman then discriminates the electromagnetic spectrum into classical (Maxwellian continuous electromagnetic waves) and quantum waves by suggesting that waves of up to 10^{16} Hz are classical Maxwellian waves, and those of higher frequency are quantum radiation. This is interesting because the mainstream view generally in physics holds that the classical Maxwell radiation is completely superseded by quantum theory, and is just an approximation.

It's always interesting to see classical radiation theory being defended for use in radio theory (long wavelengths, low frequencies) as still a valid theory. If classical and quantum theories of radiation are both correct and apply to different frequencies and situations, this contradicts the mainstream ideas. For example, is radio emission - by a large ensemble of accelerating conduction electrons along the surface of a radio transmitter antenna - physically comparable to the quantum emission of radiation associated with the leap of an electron between an excited state and the ground state of an atom? It's possible that the radio emission is the Huygens summation of lots of individual photons emitted by the acceleration of electrons along the antenna due to the applied electric field feed, but it's pretty obvious that when analyze an individual electron being accelerated and thereby induced to emit radiation, you will get continuous (non-discrete) radiation if an acceleration is continuously applied as an oscillating electric field intensity, but you will get discrete photons emitted by electrons if you cause the electrons to accelerate in quantum leaps between energy states.

From quantum field theory, it's clear as Feynman explains in his book *QED* (Princeton University Press, 1985; see particularly Figure 65), the atomic (bound) electron is endlessly exchanging unobserved (virtual) photons with the nucleus and any other electrons. This exchange is what produces the electromagnetic force, and because the virtual photons are emitted at random intervals, the Coulomb force between small (unit) charges is chaotic instead of the smooth classical approximate law derived by Coulomb using large numbers of charges (where the quantum field chaos is averaged out by large numbers, like the way that the random ~500 m/s impacts of individual air molecules against a sail are averaged out to produce a less chaotic smoothed force on large scales).

Therefore, *in an atom (or very near other charges in general) the electrons move chaotically due to the chaotic exchange of virtual photons with the nucleus and other charges like other electrons,* and when an electron jumps between energy levels in an atom, the real photon you see emitted is just the resultant energy remaining *after all the unobserved virtual photon contributions have been subtracted:* so the distinction between classical and quantum waves is physically extremely straightforward!

Bridgman then gives a discussion of quantum radiation theory which is interesting. Max Planck was guided to the quantum theory of radiation from the failure of the classical theories of radiation to account for the distribution of radiant emission energy from an ideal (black body or cavity) radiator of heat as a function of frequency. One theory by Rayleigh and Jeans was accurate for low frequencies but wrongly predicted that the radiant energy emission tends towards infinity with increasing frequency, while another theory by Wien was accurate for high frequencies but underestimated the radiant energy emission at low frequencies. There were several semi-empirical formulae proposed by mathematical jugglers to connect the two laws together so that you have one equation that approximates the empirical data, but only Planck's theory was accurate and had a useful theoretical mechanism behind it which made other predictions.

There was general agreement that heat radiation is emitted in a similar way to radio waves (which had *already* been modelled classically by Maxwell in 1865): the surface of a hot object is covered by electrically charged particles (electrons) which oscillate at various frequencies and thereby emit radiation according to Larmor's formula for the electromagnetic emission of radiation by an accelerating charge (charges are accelerating while they oscillate; acceleration is the change of velocity *dv/dt*).

The big question is what the distribution of energy is between the different oscillators. If all the oscillators in a hot body had the same oscillation frequency, we would have the monochromatic emission of radiation which would be similar to a laser! Actually, that does not happen normally with hot bodies where you get a naturally wide statistical distribution of oscillator frequencies.

However, it's best to think in these terms to understand what is physically occurring behind Planck's equation for the distribution, although this was first understood not by Planck in 1901 but by Einstein in 1916 when Einstein was studying the stimulated emission of radiation (the principle behind the laser). In a hot object, the oscillators are receiving and emitting radiation.

Radiation received by an oscillator from adjacent oscillating charges can either cause that oscillator to emit stimulated (laser like) radiation of the same frequency as the radiation that the oscillator receives, or alternatively it can cause the oscillator to emit radiation spontaneously.

What Einstein realized was that the probability that an oscillator *will undergo the stimulated emission of radiation* is proportional to the *intensity* (not the frequency) of the radiation, whereas the probability that it will emit radiation *spontaneously* is independent of the intensity of the radiation. For the thermal equilibrium of radiation being emitted from a black body cavity, the ratio for an oscillator of the:

(stimulated radiation emission probability) / (spontaneous radiation emission probability) = 1/[e^{hf/(kT)} -1]

This formula is Planck's radiation distribution law, albeit without the multiplier of 8*Pi*h*(f/c)^{3}. Notice that 1/[e^{hf/(kT)} - 1] has two asymptotic limits for frequency f:

(1) for hf >> kT, the exponential term in the denominator becomes large compared to the subtracted number of 1, so we have the approximation: 1/[e^{hf/(kT)} - 1] ~ e^{hf/(kT)}.

(2) for hf << kT, the approximation e^{x} = 1 + x is accurate for small x, which gives: 1/[e^{hf/(kT)} - 1] ~ 1/[1 + (hf/(kT)) -1] = kT/(hf).

The energy E = hf is Planck's quantum energy, where f is frequency. The energy E = kT is the classical relationship between temperature and emitted energy.*Spontaneous emission of radiation* predominates in black body radiation where the ration of hf/(kT) is high, i.e. for high frequencies in the spectrum, while more laser-like *stimulated* emissions are predominant for low frequencies. This is because the intensity of the radiation is highest at the lower frequencies, causing a a greater chance of stimulated emission.

So Planck's blackbody radiation spectrum law is a composite of two different things:

(1) the distribution of intensity of radiation (which is greatest for the lowest frequencies and falls for higher frequencies)

(2) the distribution of energy as a function of frequency, which is not merely dependent upon the intensity as a function of frequency, but also depends on the photon energy as a function of frequency, which is *not* a constant! Since Planck uses E = hf, the energy carried per quantum increases in direct proportion to the frequency, which means that the energy-versus-frequency distribution differs from the intensity-versus-frequency distribution. The intensity (rate of photon emission) falls off with increasing energy, but the energy per unit photon increases according to E = hf, so the energy-versus-frequency distribution is different from the intensity-versus-frequency distribution.

Really, to understand the mechanism behind the quantum theory of radiation, you need to have graphs not just Planck's energy-versus-frequency distribution law, but additional graphs showing the underlying distribution of oscillator frequencies in the blackbody which determine the energy emission when you insert Planck's E = hf law.

I.e., Planck argued that a black body with N oscillators (radiation emitting conduction electrons on the surface of the filament of a light bulb, for instance) will contain Xe^{-E/(kT)} oscillators in the ground state with E = hf = 0 (i.e. X oscillators are *not* emitting any radiation), Xe^{-2E/(kT)} = Xe^{-2hf/(kT)} in the next highest state, Xe^{-3E/(kT)} = Xe^{-3hf/(kT)} in the state after that, and so on:

N = X + Xe^{-2hf/(kT)} + Xe^{-3hf/(kT)} + ...

This gives you the distribution of *intensity* as a function of frequency f.

Planck then argued that the relative energy emitted by each oscillator is given by multiplying each term in the expansion by the relevant energy per unit photon, e.g., E = hf, E = 2hf, E = 3hf:

E(total) = hfX + 2hfXe^{-2hf/(kT)} + 3hfXe^{-3hf/(kT)} + ...

The ratio of [E(total)]/N is the mean energy per quantum in black body radiation, and by summing the two series and dividing the sums we find:

Mean energy per photon in blackbody radiation, [E(total)]/N = hf/[e^{hf/(kT)} - 1].

Planck's radiation law is:

E_{f} = (8*Pi*f^{2}/c^{3})*[mean energy per photon in blackbody radiation]

Therefore it is comforting to see that the complexity of the Planck distribution is due to the average energy per photon being hf/[e^{hf/(kT)} - 1], and apart from this factor, the law is really very simple! If the average intensity per photon was constant (independent of frequency), then the radiation law would be that the energy per unit frequency would be proportional to the square of the frequency. This of course gives rise to the "ultraviolet catastrophe" of the Rayleigh-Jeans law, which suggests that you get infinite energy emitted at extremely highly frequencies (e.g., ultraviolet light). Planck's radiation law shows that the error in the Rayleigh-Jeans law is that there is actually a variation, as a function of frequency, of the mean energy of the emitted electromagnetic waves.

The mean photon energy hf/[e^{hf/(kT)} - 1] has two asymptotic limits for frequency. For hf >> kT, we find that hf/[e^{hf/(kT)} - 1] ~ hfe^{-hf/(kT)}, and for hf << kT, we find that hf/[e^{hf/(kT)} - 1] ~ kT. Therefore, at high frequencies, Planck's law E = hf controls the blackbody radiation with spontaneous emission of radiation. This gives an average energy per photon of hfe^{-hf/(kT)} at high frequencies. But at low frequencies, stimulated emission of radiation predominates and the average energy per photon is then E = kT.

It's a tragic shame that the Planck distribution law is not presented clearly in terms of the mechanisms behind it in popularizations of physics. To make it clearly understood, you need to understand the two mechanisms for radiation involved (*spontaneous emission which predominates at the low intensities accompanying the high frequency component of the blackbody curve, and stimulated laser-like emission which predominates at the high intensities which accompany the low frequency part of the curve*), and you need to understand that intensities are highest at the lower frequencies because there are more oscillators with the lower frequencies than higher ones. The reason why the energy emitted at any given frequency does not follow the intensity law is the variation in average energy per photon as a function of the frequency. By plotting a graph of the number of oscillators as a function of frequency and another graph of the mean energy per oscillator as a function of frequency, it is is possible to understand exactly how the Planckian distribution of energy versus frequency is produced.

Sadly this is not done in any physics textbook or popular physics book I've seen (and I've seen a lot of them), which just give the equation and an energy-versus-frequency graph and don't explain the mechanism for the events physically occurring in nature that give rise to the mathematical structure of the formula and the graph! I think historically what happened was that Planck guessed the law from a very ad hoc theory around 1900, publishing the initial paper in 1901 but then around 1910 Planck improved the original theory a lot to a simple theory of statistics for a resonators with discrete oscillating frequencies, yet the actual mechanism with the spontaneous and stimulated emissions of radiation contributing was only established by Einstein 1916. So textbook authors get confused and over-simplify the facts by ignoring the well-established physical mechanism for the blackbody Plankian radiation distribution. In general, most popular physics textbooks are authored by mathematical fanatics with a false and dogmatic religious-type ill-founded belief that physical mechanisms don't occur in nature, and that by eradicating all physical processes from physics textbooks the illusion can be maintained that nature is mathematical, rather than the reality that the mathematics is a way of describing physical processes. The problem with the more abstract mathematical models in physics is that they are just approximations that statistically work well for large numbers, and you get into trouble if you don't have a clear understanding of the distinction between the physical process occurring and the way that the equation works:

‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’ - R. P. Feynman, *The Character of Physical Law,* November 1964 Cornell Lectures, broadcast and published in 1965 by BBC, pp. 57-8.**Compton effect**

Bridgman gives a nice discussion on pages 17-18 of the Compton effect, which is a particle-type (rather than wave-type) interaction similar to a billiard ball collision. A gamma ray or X-ray hits an electron, scattering and imparting momentum (thus kinetic energy) to it, while a new "scattered" gamma ray (of lower energy than the incident gamma ray) moves off at an angle, like a billiard ball hitting another, imparting some energy to it and scattering off at an angle itself with reduced energy. Compton scattering is therefore described quite simply if the electrons are free like billiard balls. In reality, of course, most electrons are usually bound to atoms, but if the binding energy of the electron to the atom is much smaller than the energy of the incoming gamma ray, then it is a good approximation to ignore the binding energy and treat the electron as if it were free.**Photoelectric effect**

Bridgman explains on p. 19 that when a bound electron is absorbed by a photon (rather than "scattering" from it as in the Compton process), the electron will be ejected emitted if the energy of the photon exceeded the binding energy of the electron to the atom. The energy the electron will have will be the energy of the incident photon minus the binding energy of the electron to the atom. This is the phoetelectric equation of Einstein, 1905. Obviously, Einstein's equation is just approximate because the impact of the photon will not merely affect the electron (as he assumed); some of the impact energy will also be passed on via Coulomb field interactions to the nucleus and thence the rest of the material. However, because momentum is conserved and the electron is nearly two thousand times less massive than the nucleus, the impact motion induced in the nucleus will be nearly two thousand times less than that induced in the electron, so that the vast majority of the kinetic energy will remain with the electron instead of being passes on to the nucleus and the rest of the material. So Einstein's photoelectric effect equation is a very good approximation to the real, more complicated, physical dynamics.**Pair-production**

Bridgman discusses pair-production on pp. 20-21. If a gamma ray of energy exceeding the rest mass equivalent of two electrons passes through an electric field of strength 1.3*10^{18} v/m or more (i.e., at 33 femtometres from the centre of an electron/proton, or closer), the quanta in the electric field are intense enough to potentially interact with the field of the gamma ray and thereby decompose it into two opposite electric charges, each of which acquires a mass from the vacuum "Higgs field" (or whatever field will be discovered to contribute mass - i.e. gravitational charge - to fermions). This threshold field strength for pair-production was derived by Julian Schwinger (Schwinger’s critical threshold for pair production is E_{c} = m^{2}c^{3}/(e*h-bar). Source: equation 359 in http://arxiv.org/abs/quant-ph/0608140 or equation 8.20 in http://arxiv.org/abs/hep-th/0510040, which corresponds to the limiting range out to which the vacuum contains virtual fermionic annihilation-creation spacetime loops, which polarize themselves radially around real charges like a capacitor's dielectric material, and thus shield part of the charge of the electron, causing the "running couplings" in QFT and the attendant need to renormalize electric charge which appears stronger at small distances where there is less shielding.

(It's fascinating that Schwinger's threshold field strength required for pair production - vital for the IR cutoff in QFT - is physically being totally ignored in all the popular books on QFT, QM, and Hawking radiation. E.g., Hawking radiation is supposed to be gamma ray emission resulting from interactions after spontaneous pair production in the vacuum near the event horizon R = 2GM/c^{2} of a black hole, but when you take account of Schwinger's threshold it turns out that you will only get Hawking radiation if the black hole has an electric charge proportional to the square of the mass of the black hole! Big uncharged black holes can't physically radiate any Hawking radiation. However, fundamental charged particles are extremely efficient Hawking radiators and a corrected form of the Hawking radiation mechanism will physically explain the emission and thus exchange of electromagnetic field quanta by fundamental particles.)

A proper theory of pair-production will explain how bosonic energy acquires rest mass when it becomes fermionic energy, and this isn't a part of the Standard Model of particle physics (mass is described by various types of problematic "Higgs fields" in the existing Standard Model, none of which have been detected, and all of which are ad hoc epicycles, which don't contribute anything to the predictive power of the Standard Model; there's no evidence for electroweak symmetry and the Weinberg mixing angle for the neutral electromagnetic and weak field gauge bosons is totally ad hoc and doesn't specifically require a Higgs field, or prove that the two fields are unified in the way expected at high energy).**Bohr model of the atom**

Bridgman deals very nicely with the Bohr atom on pages 22-29. J. J. Thomson "discovered" (or at least measured a fixed charge-to-mass ratio, for cathode rays) the electron in 1897, and then developed a theory of the atom as a mixed pudding of positive and negative charges. He argued that there could not be a separation of charges within the atom, because that would make the atom unstable and liable to collapse. However, it's hard to see how a mixture of positive and negative charges will be more stable. Rutherford settled the matter by having two research students, Geiger and Marsden, fire alpha particles through thin gold foil and measure the angles of scatter. Some of the alpha particles were scattered back towards the source, and from the distribution of scattering angles Rutherford was able to deduce that the simplest working hypothesis that fitted the data was a central positively charged massive nucleus surrounded by the negatively charged electrons.

Bohr then suggested that the electrons orbit the nucleus rather like planets orbiting the sun, but with the Coulomb attraction of negative and positive charge replacing gravitation. Hence, for hydrogen atoms Bohr set the Coulomb force between an electron and a proton equal to the centripetal acceleration force, F = -mv^{2}/r. Rearranging the result allowed the orbital speed of the atomic electron to be deduced, v = (e^{2}/{4*Pi*permittivity*MR})^{1/2} where M is the electron's mass and R is the radius of the orbit. The linear momentum is then p = Mv, the angular momentum is L = pR, and the kinetic energy is E = (1/2)Mv^{2}.

Bridgman points out in on page 24 that:

"Bohr's unique contribution was his postulate that the electron's angular momentum, L, could take only discrete values [integer multiples of L = pR = n*h-bar, where n = 1, 2, 3, etc.]."

This leads to the correct quantization, which for the total (potential plus kinetic) electron energy gives rise to the line spectra formulae for the wavelengths of light emitted by atomic electrons, such as the Lyman, Balmer, and Paschen series formulae.

Bridgman adds in an enlightening footnote on that page:

"At first exposure one is tempted to ask the question 'How on earth did Bohr come to that conclusion? Why not discrete linear momentum, or energy, or etc.?' Certainly the answer is not obvious from our foreshortened discussion. The actual historical logic can be found in Jammer where it can be seen that the correct postulate came only after several unsuccessful ones."

Rutherford rejected Bohr's hypothesis because it failed to explain why the acceleration of the orbiting electron did not cause it to continuously radiate energy as electromagnetic waves, and thus slow and spiral into the nucleus and oblivion within a second. Rutherford wrote to discourage Bohr:

“There appears to me one grave difficulty in your hypothesis which I have no doubt you fully realize [conveniently not mentioned in your paper], namely, how does an electron decide with what frequency it is going to vibrate at when it passes from one stationary state to another? It seems to me that you would have to assume that the electron knows beforehand where it is going to stop.”

- Ernest Rutherford's letter to Niels Bohr, 20 March 1913, in response to Bohr’s model of quantum leaps of electrons which explained the empirical Balmer formula for line spectra. (Quotation from: A. Pais, “Inward Bound: Of Matter and Forces in the Physical World”, 1985, page 212.)

Bohr never came up with an mechanism that explained the failure of classical electromagnetism; instead he worked out a Mach-type "positivist" philosophy of against asking awkward questions of models that make accurate predictions (which Ptolemy's epicycle followers had hundreds of years earlier used to try to suppress Copernicus), the complementary and correspondence principles which Einstein attacked at the Solvay Congress of modern physics in 1927 and thereafter. According to Bohr, nature corresponds to classical physics on large scales here the action is much bigger than Planck's constant, and to quantum mechanics on small scales where the action is on the order of Planck's constant. Wave descriptions of matter complement rather than contradict particle descriptions, and we must religiously believe in his dogma that there is no possibility of reconciling classical and quantum physics; we must believe that nature has discontinuities and must not ask questions or try to find answers, because it is a waste of time. (This is like the false belief in the 19th century - before stellar line spectra were detected - that nobody would ever know the composition of stars, because they are too hot and too far away to investigate.)

Bohr therefore opposed quantum field theory in the modern second quantization form of Feynman's path integrals (central to the Standard Model today) at the 1948 Pocono conference:

" ... Bohr ... said: '... one could not talk about the trajectory of an electron in the atom, because it was something not observable.' ... Bohr thought that I didn't know the uncertainty principle ... it didn't make me angry, it just made me realize that ... [ they ] ... didn't know what I was talking about, and it was hopeless to try to explain it further. I gave up, I simply gave up ..."

- Richard P. Feynman, in Jagdish Mehra, *The Beat of a Different Drum,* Oxford, 1994, pp. 245-248. (For the story of how Dyson and Bethe overcame hostility and forced the scientific community to lower their guard against path integrals, see Dyson's YouTube video linked here.)

Feynman completely debunks the uncertainty principle (first quantization) quantum mechanics philosophy in his 1985 book *QED:*

‘I would like to put the uncertainty principle in its historical place: When the revolutionary ideas of quantum physics were first coming out, people still tried to understand them in terms of old-fashioned ideas ... But at a certain point the old-fashioned ideas would begin to fail, so a warning was developed that said, in effect, “Your old-fashioned ideas are no damn good when ...” If you get rid of all the old-fashioned ideas and instead use the ideas that I’m explaining in these lectures – adding arrows [path amplitudes] for all the ways an event can happen – there is no need for an uncertainty principle!’

- Richard P. Feynman, *QED,* Penguin Books, London, 1990, pp. 55-56 (footnote).

‘When we look at photons on a large scale – much larger than the distance required for one stopwatch turn [i.e., wavelength] – the phenomena that we see are very well approximated by rules such as “light travels in straight lines [without overlapping two nearby slits in a screen]“, because there are enough paths around the path of minimum time to reinforce each other, and enough other paths to cancel each other out. But when the space through which a photon moves becomes too small (such as the tiny holes in the [double slit] screen), these rules fail – we discover that light doesn’t have to go in straight [narrow] lines, there are interferences created by the two holes, and so on. The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, such as inside an atom, the space is so small that [individual random field quanta exchanges become important because there isn't enough space involved for them to average out completely, so] there is no main path, no “orbit”; there are all sorts of ways the electron could go, each with an amplitude. The phenomenon of interference becomes very important, and we have to sum the arrows [in the path integral for individual field quanta interactions, instead of using the average which is the classical Coulomb field] to predict where an electron is likely to be.’

- Richard P. Feynman, *QED,* Penguin Books, London, 1990, Chapter 3, pp. 84-5.

In QED, the explanation for the question, "why doesn't the orbiting electron radiate and spiral into the nucleus?" is simply: equilibrium between emission and reception. The orbital electron is radiating intensely, but because there is a well-established equilibrium between the intense rate of emission and the intense rate of reception, the radiation appears as invisible "field quanta" to us instead of doing work (e.e., it doesn't make any electrons jump energy levels!). Whenever you have an equilibrium of emission and reception, you just have a zero point field. If you think of the motion of air molecules hitting you, it is not possible to extract that particle energy usefully to do work. Air pressure exerts a force, but it's not possible to get useful work out of it. The vacuum field of virtual photons or field quanta is similar; electrons are bombarded on all sides and there is no useful net work done, no net electric current or anything. So the radiation from a lot of orbiting electrons soon creates an equilibrium and once the electrons are receiving as much radiant power in virtual photons as they radiate, they have attained a "ground state", ceasing to spiral into the nucleus because there is no longer any useful work being done on them to push them in towards the nucleus.

Bridgman then explains the various types of radiation emission from the nucleus, alpha particles (which escape from the nucleus as stable configurations by "quantum tunnelling" through the quantized binding field), beta particles (which have a continuous energy spectrum with a mean energy of usually one-third of the total energy released in beta decay, the remainder of the energy being carried by an antineutrino), and gamma rays (which are released from the nucleus in discrete energies which suggests a shell structure for the nucleons in the nucleus, analogous to Bohr's explanation of the line spectra of light from atomic electrons).**Chapters 2, 3, and 4 (Fission Explosives: Neutronics, Fission Explosives: Thermodynamics, and Fusion Explosives)**

As stated, I will skip a detailed discussion of these chapters which go further than declassified reports like Glasstone and Redman's declassified 1972 introduction to nuclear weapons, here and here, LAMS-2532, Vol. 1, LA-1006, and LA-1.

Neglecting the detailed calculations of nuclear weapon design and prediction of efficiency, the general physics of how a chemical explosive like TNT compresses a solid metal uranium or plutonium core, is of interest because it indicates the minimum possible size for a spherical implosion nuclear weapon. Smaller sizes for cannon shells can be achieved by gun-type assembly, or by linear implosion where a piece of fissile material is simply compressed in one dimension rather than in three dimensions; these designs are both less efficient than spherical implosion but are necessary to fit a nuclear weapon into a small-diameter cannon shell.

On page 121, Bridgman gives curves from M. van Thiel's *Compendium of Shock Data *(Livermore Radiation Lab., report UCRL-50108, v. 1, June 1966) which show how much pressure is needed to achieve given increases in the density of metallic uranium and (alpha phase) plutonium. Doubling the density of plutonium metal requires 4.9 Mbar, and 10 Mbar is needed to do the same to uranium. Doubling the density will shrink the radius by a factor of 2^{1/3} = 1.26, so a 6.2 kg solid plutonium core (the Nagasaki bomb had 6.2 kg of plutonium, but it was not solid since it had an initiator in the centre) shrinks from 4.2 cm radius to just 3.3 cm radius, a reduction of 0.9 cm due to compression.

Work energy, *E = Fx = PAx* = (4.9*10^{6}*10^{5})*(4*Pi*(0.042^{2}))*(0.009 metres) = 9.8*10^{7} J. [This calculation is mine, a back-of-the-envelope estimate and is not based on the detailed numerical calculations of implosion in Bridgman's book; it is not accurate for bomb design just to give an indication of what kind of mass is needed so that the bulk and mass of the terrorist threat can be seen.]

This is the amount of implosion energy needed to double the density of a 6.2 kg solid plutonium core. However, Newton's 3rd law tells us that you can't make a force act in one direction; you always get an equal and opposite reaction force. So in implosion, only 50% of the force of the TNT explosion goes inward as a shock wave to compress the core (the rest acts outwards).

Since TNT produces 4.2*10^{12} J per kt, for the 50% efficiency suggested by Newton's 3rd law you need 46 kg of TNT to compress a plutonium core to double density.

However, this calculation omits the fact that the core isn't all compressed simultaneously. As the shock wave from the TNT reaches the core, it compresses first the outside of the core, and gradually compresses more of the core as it progresses inward, taking something like 8 microseconds to reach the middle and rebound. So the implosion process is extremely complicated to model and requires sophisticated computer calculations. Adding a natural uranium or lead tamper around the core might seem like a good idea to delay the expansion of the core and allow a fission chain reaction to spontaneously set off a nuclear explosion, but that is wrong: it adds more mass to the bomb, and requires more TNT to compress, and the extra force of the rebounding implosion wave when it reaches the centre will disassemble the core just as before.

This indicates the minimum size and mass of an efficient implosion weapon, which might be smuggled in by terrorists. It won't fit into a suitcase. It does not even indicate that terrorists can produce a nuclear weapon from so much plutonium and TNT, because you have to inject neutrons to start the chain reaction during the few microseconds it takes for the implosion shock wave to travel through the core, compressing it. Once the shock wave reaches the centre of the core a few microseconds after reaching it (at velocities on the order of 10 km/s after entering the core), it rebounds and soon causes the core to expand and become subcritical again. The requirement for bomb design - even for the simplest device - is complex and involves detailed calculations and design to ensure that the the neutron chain reaction is initiated at the right time after the TNT has been detonated simultaneously at many points around the surface.

It shows that the theft is plutonium by itself is not a particularly great threat: terrorists would need a great deal more technology to make a nuclear weapon from a piece of plutonium than to simply use conventional explosives like TNT for terrorism. The main threat is therefore rogue states which can afford to invest heavily in the technology and research required to make neutron initiators correctly linked to the electrical firing system and simultaneous detonators of the TNT system.

Miniaturization technology like beryllium neutron reflectors and tritium boosting are so expensive that - regardless of what informatin they had on the subject - these improvements would not be available to terrorists, so any terrorist nuclear weapon which posed a massive threat would itself be large in physical size and therefore difficult to deliver, not at all the "suitcase bomb."

It would be easier for terrorists to use conventional chemical explosives than nuclear explosives. Only with a massive investment in laboratory technology and research could the firing and neutron initiation system for a threatening nuclear weapon be produced.

Injecting 1 gram of tritium gas into the hollow core of an 83 kt fission weapon "boosts" its yield by a factor of about 50% to 124 kt, of which 0.135 kt is due to the fusion of tritium and nearly 41 kt is due to additional neutrons induced in the core material by the fusion neutrons. This technology is beyond most nations; even America finds tritium production a costly business. The nuclear reaction cross-sectional area for the fusion of tritium + deuterium into helium and a neutron plus 17.6 MeV of energy is roughly 100 times higher than the cross-section for deuterium + deuterium fusion, so the tritium + deuterium reaction (which produces 1.49*10^{24} neutrons/kt and 80.6 kt/kg of energy when fused) is all-important in thermonuclear weapons. This requires the use of lithium deuteride capsules which are ablated by X-rays in the Teller-Ulam system, which again requires elaborate laboratory technology plus very sophisticated three dimensional calculations using computers for research and development, which we need not discuss.

Bridgman discusses the temperature and partition between X-rays and case shock (kinetic) energy in the exploding bomb using a similar treatment to Brode's 1968 published article in the *Annual Review of Nuclear Science,* vol. 18, but in greater depth. The total energy at explosion time is the sum of X-ray energy aVT^{4} (where a is the radiation constant which is 4/c times the Stefan-Boltzmann constant, V is volume, and T is temperature) and material energy MCT (where M is mass, C is the specific heat capacity of that mass at constant volume which is 3R/2 for a perfect solid or 3R = 0.02494 cal/(g*K) for an ideal gas such as the highly ionized bomb vapours, and T is temperature): E = aVT^{4} + MCT. For heavy inefficient nuclear weapons (such as a terrorist improvised device) very little energy is emitted in X-rays by this formula, so it can't be used to initiate a Teller-Ulam thermonuclear reaction. A bomb temperature of 11.6 million K corresponds to X-ray radiation quanta of 1 keV. DNA-EM-1 considers X-ray energies from 1 keV to 10 keV for modern nuclear weapons, corresponding to peak bomb temperatures of 11.6 to 116 million K. Only for a high yield-to-mass ratio is there a large proportion of the yield emitted in X-rays which can initiate a Teller-Ulam thermonuclear charge reaction.**X-Ray Effects**

In the chapter on X-ray effects, page 197, Bridgman states that a weapon with a several cm thick dense outer casing and a yield of a few kilotons will be relatively "cold" with an X-ray radiating temperature of 1 keV or less. However, if the outer casing is thin and of lower atomic number, it can be fully ionized and can emit X-rays with a mean energy of several keV. Efficient megaton yield weapons can emit 10 keV X-rays. These X-rays can be used to pump an X-ray laser or to indiscriminately ablate, deflect and destroy re-entry vehicles in outer space over a wide volume during a concentrated nuclear attack. X-ray weapons for high altitude use need special design to minimise the fission yield and the prompt gamma ray output (including that due to inelastic neutron scatter in the case), or there can be substantial damaging EMP effects at ground level.

We mentioned in an earlier post that:

"Ablation can be explained very simply and is very well understood because it's the mechanism by which fission primary stages ignite fusion stages inside thermonuclear weapons: 80% of the energy of a nuclear explosion is in X-rays and the X-ray laser would make those X-rays coherent and focus some of them on to the metal case of an incoming enemy missile. The result is the blow-off or 'ablation' of a very thin surface layer of the metal (typically a fraction of a millimetre). Although only a trivial amount of material is blown off, it has a very high velocity and carries a significant momentum. The momentum isn't immense but it creates a really massive force on account of the small time (about 10 nanoseconds) over which it is imparted (this is because force is the rate of change of momentum, i.e. *F = dp/dt*), and since pressure is simply force per unit area, you get an immense pressure due to Newton's 3rd law of motion (action and reaction are equal and opposite, the rocket principle).

"Hans Bethe and W. L. Bade in their paper *Theory of X-Ray Effects of High Altitude Nuclear Bursts and Proposed Vehicle Hardening Method* (AVCO Corp., Mass., report RAD-TR-9(7)-60-2, April 1960) proposed that missiles can be hardened against X-ray induced ablative recoil by using a layer of plastic foam to absorb reduce the force within the missile by spreading out the change of momentum over a longer period of time, but although this will protect some internal components from shock damage, the missile skin can still be deflected, dented and destroyed by ablation recoil."

Bridgman's book quantifies the X-ray ablation effect on pp. 212-5:

"The energy deposited by X-ray absorption occurs in a very short time, essentially the time duration of the x-ray pulse, perhaps several shakes [1 shake = 10 nanoseconds] for the direct x-rays. because of inertia, the target material will not significantly expand, contract or translate in such a short time. Thus, the energy deposited can be regarded as an instantaneous increase in material internal energy."

He considers a graphite (carbon) heat shield exposed to 10 cal/cm^{2} of 4 keV x-rays. The sublimation energy (energy to vaporize a solid directly) of pyrolytic carbon is 191 cal/gram = 800 kJ/kg. The 10 cal/cm^{2} deposits 1.54 MJ/kg of energy on the front surface of the carbon, so it vaporizes and "blows off" the surface. For a fluence of 10 cal/cm^{2}, the 4 keV x-ray vaporization extends to an effective depth of 81 microns in the pyrolytic carbon. (For double that x-ray fluence, i.e. 20 cal/cm^{2}, the depth of surface blow-off will be increased by a factor of 1/ln_{e}2 ~ 1.44.) On p. 213, Bridgman explains:

"... the vaporized material is often referred to as a blow-off ... there is a rocket exhaust-like momentum which is discharged in a very short time. A time rate of change of momentum to the left of the front surface must be balanced by an equal and opposite time rate of change of momentum or pressure to the right into the shield. This equal and opposite pressure becomes a shock wave into the solid material ..."

Bridgman computes the kinetic energy of the blow-off in the example (for 10 cal/cm^{2} of 4 keV x-rays striking pyrolytic carbon) to be 58.9 kJ/m^{2}, corresponding to a blow-off velocity of 813 m/s. Assuming that the x-ray pulse lasts 20 ns, the ablation recoil force will be on the order of *F = dp/dt ~ mv/t* implying an immense pressure of 72 kbar or 72,000 atmospheres.

Bridgman adds that a 4 keV x-rays fluence of 5 cal/cm^{2} deposits just under the sublimation energy of the carbon shield, so it will not be able to cause any blow-off, but it will still deposit energy in the outer 0.5 mm of the shield, and impart momentum, producing a peak surface pressure on the shield of 14.9 kbar or about 15,000 atmospheres.**Thermal Effects**

Bridgman gives theoretically calculated thermal transmission values for surface explosions which are considerably smaller than in Glasstone and Dolan and other sources. He makes it clear in Fig. 6-1 on p. 237 that the thermal yield is maximised for a burst altitude of about 47 km, where it is 64% of total yield for a 100 kt device. For the same device detonated at sea level it is 35% (with the remainder in blast and nuclear radiation) and for the same device detonated above 75 km it is 25% (with the remainder emitted as X-rays and nuclear radiation).

Bridgman on page 247 calculates that the fireball surface radiating temperature at the time that the shock wave departs from it ("breakaway" time according to Glasstone and Dolan) decreases from 300,000 K for a sea level burst to 75,000 K for a burst altitude of 20 km. This occurs at 3.13W_{kt}^{0.44} ms after a W kt burst at sea level (Bridgman quotes this formula from page 233 of Northrop's book).**Blast Effects**

Bridgman derives Glasstone and Dolan's "Rankine-Hugoniot equations" for idea shock fronts on pages 281-4. He gives a graph of Mach stem heights (not included in Glasstone and Dolan, but included in the *Capabilities* series from 1957 onwards) on page 293. On pages 295-297 he quotes research by Charles Needham on the correlation of nuclear test data on blast from high yield devices, which showed that you get a natural reduction in peak pressures from megaton yield devices because the blast wave energy refracts upwards into the lower density air at higher altitudes where the shock radius is on the order of the 4.3 miles or 6.9 km scale height of the atmosphere (the height at which sea-level air density falls by a factor of e = 2.718):

"During the research which went into the 1 kt nuclear blast standard, we looked very carefully at the blast data from the Pacific as well as from Nevada. We found that the majority of measured pressures from the Pacific data, whether at ground level or from airborne gauges, did not cube root scale to the same pressure versus radius curve that the Nevada Test Site data did. We found that the multimegaton data consistently fell below the calculated curves and the NTS data which agreed with the one-dimensional calculations. Further, we found that the data from small yields shot in the Pacific (there were a few) did agree with the NTS data. More sophisticated two-dimensional calculations confirmed that as the shock radius became an appreciable fraction of the scale height in the atmosphere, more energy went up than out."

Bridgman then gives an analysis of blast gust loading on aircraft. (On p. 495, he also points out that thermal radiation can also be important for aircraft metal skins which can melt at 580 C and can only safely take a temperature of 204 C, corresponding to a 20% change in skin elasticity.) He then gives an analysis of blast loading on buildings. He considers a building with an exposed area of 163 square metres, a mass of 455 tons and natural frequency of 5 oscillations per second, and finds that a peak overpressure of 10 psi (69 kPa) and peak dynamic pressure of 2.2 psi (15 kPa) at 4.36 km ground range from a 1 Mt air burst detonated at 2.29 km altitude, with overpressure and dynamic pressure positive durations of 2.6 and 3.6 seconds, respectively, produces a peak deflection of 19 cm in the building about 0.6 second after shock arrival. The peak deflection is computed from Bridgman's formula on p. 304: deflection at time t,

x_{t} = [A/(fM)]{integral symbol}[sin(ft)](P_{t} + C_{D}q_{t})dt metres,

where A is the cross-sectional face-on area of the building facing to the blast (e.g., 163 square metres), f is the natural frequency of oscillation of the building (e.g., 5 Hz), M is the mass of the building, P_{t} is the overpressure at time t, C_{D} is the drag coefficient of the building to wind pressure (C_{D} = 1.2 for a rectangular building), and q_{t} is the dynamic pressure at time t. (There is a related calculation of the peak deflection of a structure on pages 250-284 of the 1957 edition of the *Effects of Nuclear Weapons*.) Bridgman points out that this equation ignores:

(1) the fact that the net force from the overpressure suddenly ends once the shock front has engulfed the building and is pressing on the rear side with a similar pressure to that that on the front side, and

(2) the end of the building oscillations due to energy loss from causing damage or destruction of the walls and other components of the building.

The effect of these limitations can easily be incorporated into the model by (1) calculating the time taken for the shock front to transverse the length of the building, and (2) using nuclear test data to indicate the peak pressure associated with a given degree of damage or destruction (this allows the amount of deflection of walls to be correlated to the probability that the wall fails).

This 19 cm computed maximum deflection allows us to estimate how much energy is permanently and irreversibly absorbed from the blast wave by a building and transformed into slow-moving (relative to the shock front) debris which falls to the ground and is quickly stopped after the blast has passed it by: *E = Fx,* where *F* is force (i.e., product of total pressure and area) and *x* is distance moved in direction of force due to the applied force from the blast wave. If the average pressure for the first 0.5 second is equal to 12 psi (83 kPa) then the average force on the building during this time is 13 million Newtons, and the energy absorbed is:*E = Fx* = 13,000,000*0.19 = 2.6 MJ.

This is interesting because we have already discussed earlier the problem that Penney found a large attenuation in peak overpressures due to the irreversible energy loss via damage done at Hiroshima and Nagasaki. Although you might expect some overpressure to diffract downwards as the energy is depleted near ground level, the effect of the fall in air density with increasing altitude will tend to prevent this. In any case, only blast overpressure diffracts. Dynamic pressure is a directional (radial) wind effect which does not diffract downwards. Hence, blast energy loss from the wind (dynamic) pressure cannot be compensated for by downward diffraction. This is why shallow open trenches provided perfect protection against wind drag forces at nuclear tests in the 1950s, although the overpressure component of the blast did diffract into them: the wind just blows over the top of the trench without blowing down into it!**Initial Nuclear Radiation**

Bridgman discusses the neutron output spectra given by Glasstone and Dolan (1977), which are of course simplified from more detailed data in Dolan's formerly classified manual, EM-1. The pure fission weapon output indicates that 50% of the neutrons available escape and therefore 50% are captured in the weapon debris. For the typical thermonuclear weapon, fewer neutrons escape. Prompt gamma rays are not produced by fusion, but can be produced when neutrons are inelastically scattered by some nuclei, exciting nucleons within those nuclei to a high energy state.**Residual Radiation**

Page 401 stated that the mass of fallout produced by a surface burst varies from 800 tons/kt for 1 kt to 300 tons/kt for 1 Mt total yield. Bridgman presents the details of the fallout particle-size distribution, cloud rise, diffusion and deposition as mathematical models.

The book then goes into the biological effects radiation. Animals are approximately 70% water, so most of the radiation interactions in the body are related to the ionization of water molecules by radiation. Water molecules, H_{2}O, when ionized form H+ ions and OH- ions. At low dose rates the rate at which these are produced is small, so there are unlikely to be two nearby. At higher dose rates, it is more likely that there will be nearby ions, so mixed-up recombination can form molecules like the oxidising agent hydrogen peroxide, 2OH -> H_{2}O_{2}, which is a chemical poison in high concentrations. Cell nuclei contain chromosomes consisting of DNA molecules. Genes are sections of DNA which carry the instructions for producing a particular protein molecule. Protein molecules in the nucleus work as enzymes, repairing damage to DNA and controlling cellular processes like division. Eggs are examples of single cells. Bridgman discusses only the basic physical processes involved in the biological effects of radiation, and does not evaluate all of the mechanisms and experimental evidence for non-linear dose -effects response in long-term effects.

It would be good if the book included a look at some of the ways that radiation damage can be prevented or reduced by harmless natural vitamins and minerals. According to the March 1990 U.S. Defense Nuclear Agency study guide DNA1.941108.010, report HRE-856, *Medical Effects of Nuclear Weapons* (the guide book to a course sponsored by the Armed Forces Radiobiology Research Institute, AFRRI, Bethesda, Maryland), the free radicals and hydrogen peroxide molecules created from ionized water can be converted back into water molecules by vitamins A, C, and E, glutathione, and the mineral selenium. Vitamins A, C, and E, glutathione help to scavenge free radicals as they are formed by ionization and prevent oxidation type damage. The natural enzyme catalase breaks down hydrogen peroxide into harmless water and oxygen. Selenium as a dietary supplement has a similar function in combination with glutathione. Animal experiments on the benefits of vitamin E for protection against large doses of radiation are reported graphically in that guide. In control experiments (no vitamin E supplement present in the body at exposure time), there was 90% lethality within 30 days after 750 R and 100% lethality within 30 days after 850 R. When vitamin E was supplied, there was 100% survival at 30 days after 750 R and 60% survival at 30 days after exposure to 850 R. *Hence, vitamin E can cause a massive enhancement on survival probability after radiation damage, by helping to eliminate radiation caused free radicals before them can cause any damage to DNA.* Ignorant anti civil defence propaganda ignores all the hard won scientific evidence and then claims falsely that there is no protection possible by any means, least of all dietary supplements. It is true that the doses of natural anti-oxidants needed for protection against lethal radiation exposure can cause toxic side-effects in some cases, but if the alternative is the lethal effect of radiation then such side effects may be acceptable. The guide also shows that the LD50 from radiation only at the Chernobyl nuclear disaster in 1986 was 600 rads, compared to just 260 rads for 97 Nagasaki personnel with who received thermal burns in addition to nuclear radiation. The nuclear radiation proved more lethal in combination with thermal burns because the burns wounds became infected at a time when the radiation temporarily suppressed the white blood cell count (which occurs from 1-8 weeks after exposure), preventing the infections from being fought effectively by the immune system. Preventing thermal burns by simply ducking and covering therefore massively increases the nuclear radiation LD50.**Dust and Smoke Effects**

Bridgman's Chapter 13 is on "Dust and Smoke Effects" which of course is not included at all in Glasstone and Dolan (1977). Hype began in 1983 by Carl Sagan *et al.* ("TAPPS") for a new temporary ice age due to a temperature reduction caused by smoke clouds from mass fires blocking sunlight after a nuclear attack. In firestorms like that at Hamburg or Hiroshima (after a nuclear detonation), a wood-frame construction, highly flammable city (which no longer exist in modern countries), the soot was accompanied by moisture and all visible sign of it had come down as a "black rain" within an hour or so of the explosion. We have documented in some detail many of the gross falsehoods about thermal ignition due to nuclear weapons in forests and cities in an earlier post. Early editions of *The Effects of Nuclear Weapons* grossly exaggerated thermal ignition.

Smoke and dust clouds are rapidly produced near at ground level which shield material from ignition by the remainder of the thermal radiation flash; the early part of the flash does not penetrate deeply enough into the material to cause ignition, just ablation type smoke emission which shields the underlying material. This is before shadowing effects in a forest or city are included (at significant distances, the thermal pulse is over by the time the blast arrives and causes the possible displacement of objects which shield thermal radiation). While it is true that a room in a wooden hut deliberately crammed full of inflammable rubbish, with a large window facing ground zero without any obstruction, underwent nearly immediate "flashover" after the *Encore* nuclear test, an identical set up nearby with a tidy room without the inflammables did not undergo burn down: some items were scorched, but they burned out without setting the room on fire. In addition, people in brick or concrete buildings near ground zero in the Hiroshima firestorm were able to put out fires and prevent their buildingd from burning down.

They did not die from radiation, blast, heat, smoke or carbon monoxide poisoning. Nuclear tests on oil and gas storage tanks in the Nevada showed that even at the highest peak overpressures and thermal radiation fluences tested, they did not ignite or explode even where they were blasted off their stands, dented by impacts, or otherwise damaged. The metal containers easily protected the contents from the brief flash of thermal radiation, while the blast wave arriving some time later later failed to cause ignition. Individual leaves cast shadows on wooden poles at Hiroshima, proving that even very thin materials stopped an intense thermal radiation flash. No mention let alone analysis of any of this solid nuclear weapons effects evidence is done by any of the "nuclear winter" doom mongers, who falsely assume that somehow everything will ignite and then undergo sustained burning like a dry newspaper in a direct line of sight of the fireball.

Bridgman on page 460 explains that:

"These fires will be set by the thermal flash of thousands of separate nuclear bursts. However, the bulk of the burning and smoke generation will occur hours after the nuclear fireballs have risen to their ultimate altitudes. This the smoke, like the smoke from any fire, should remain in the troposphere. This should be the case even if violent fire storms were generated [like Hiroshima and Hamburg]. These tropospheric smoke particles would be subject to the same removal mechanisms [as tropospheric fallout], namely rainout. The mean-life of tropospheric particles was given as about 20 days ... recent observations from the Gulf War oil field fires, indicated that the tropopause rose with the top of the smoke cloud preventing stratospheric injection. It was postulated that the stable air resisted descrnding to replace the buoyant air. Furthermore the real smoke particles cooled at night and became negatively bouyant [descending at night]."**Space Effects**

Chapter 14 is "Space Effects". Bridgman begins by pointing out that explosions above 100 km altitude occur in a virtual vacuum, so there is no significant local x-ray fireball at the burst altitude (which requires air around the bomb to absorb x-rays), although x-rays going downward will produce an x-ray heated pancake of air at an altitude of around 80 km, centred below the detonation point. (X-rays and neutrons are more penetrating than x-rays of course, and will be mainly absorbed in a layer at an altitude of around 30 km.)

However, although they don't produce local x-ray fireballs around the detonation location, high altitude bursts above 100 km do produce UV (ultraviolet) fireballs around the detonation location! The mechanism for the UV fireball in bursts above 100 km is simple and depends on the bomb casing and debris shock wave, which typically carries around 16% of the explosion energy according to Bridgman (x-rays carry 70%, and the rest is nuclear radiation, including 3.8% in residual beta radiation):

"The debris front sweeps up the thin air that it does encounter, imparting kinetic energy to those air molecules. The energized air molecules in the debris-air collision front emit ultraviolet radiation in the 3 to 6 eV range. Thus UV radiation travels outward ahead of the debris-air collision front, at light speed. The cool air ahead of the front ... absorbs the UV radiation ... which produces an [ionized] UV fireball. ... Recombination between the ionized or dissociated molecules in the UV fireball is very slow due to the low density of the particles at altitudes of 100 km and higher. As a result, the UV fireball has a lifetime of 3 to 15 minutes. During this lifetime both magnetic buoyancy and buoyancy due to the heating of the ionized aur cause the UV fireball to rise, lofting the ionized region hundreds of kilometres upward. ...

"Outside of the UV fireball, especially below it, some UV radiation will be absorbed by the air, heating that air without achieving ionization. This heated neutral air will also rise as it expands."

The expanding ionized UV fireball acts as a diamagnetic cavity or bubble, excluding the earth's magnetic field and thus causing the earth's magnetic "field lines" to be excluded and compressed outside the bubble. This causes a magneto-hydrodynamic (MHD) shock wave, producing the slow MHD-EMP to be propagated. Even when the actual expansion halts, the buoyant *rise* of the ionized bubble through the magnetic field produces another MHD-EMP effect from the motion of the ionized charge in the bubble (electrons quickly escape, leaving a net positive charge of slower moving ions in the bubble). KINGFISH (410 kt at 95 km altitude on 1 November 1962) is used by Bridgman to illustrate the UV fireball and the downward beta and ion "kinetic energy patch" or streamer, which follows the direction of the earth's magnetic field lines (the charged particles spiral around the earth's magnetic field vector).

Bridgman adds that the local UV fireball diminishes at very great altitudes and may not be formed above 500 km (it was trivial in the STARFISH test at 400 km altitude). In such extremely high altitude bursts, the only local light source is the bomb debris itself. The bomb debris and any accompanying re-entry vehicle mass (after it cools by emitting most of its energy as x-rays) is an expanding shell which is assumed to carry 16% of the total explosion energy as kinetic energy, E = (1/2)Mv^{2}, implying a bomb debris velocity of 1,640 km/s for a 1 Mt weapon with a mass of 500 kg. This is of the same order of magnitude as the measured STARFISH debris velocity. Bridgman points out that this debris kinetic energy can produce large forces when striking nearby space satellites or re-entry vehicles.

On page 471, Bridgman gives a neat explanation of the Argus "magnetic reflection" effect of trapped electron shells. Electrons spiral around the earth's cived magnetic field vectors from conjugate points at 100-200 km altitude in each hemisphere, being "reflected" back at each conjugate point. How does the reflection process work? Bridgman explains that the conservation of energy applies to the kinetic energy of the electron's velocity component *perpendicular *to, and the kinetic energy of the electron's velocity component *parallel* to, the earth's magnetic field vector or imaginary "line".

Therefore, the sum (1/2)Mv_{perpendicular}^{2} + (1/2)Mv_{parallel}^{2} is a constant. Hence, as the electron approaches the conjugate point where the magnetic field lines converge together, its velocity *perpendicular* to the lines *increases* at the expense of its velocity *parallel* to the lines, due to conservation of energy. So the electron ever slows down in its approach toward the conjugate point as the magnetic field lines converge, but momentum carries it on past that point at which it would simply stop altogether (and merely cicle the magnetic field line), so there is then a force on it to reverse its direction parallel to the field line, and it begins to spiral back around the field line towards the other conjugate point. There the process is repeated, unless the electron happens to be captured by an air molecule in the low density air at 100-200 km. The capture of a sufficient flux of electrons at the conjugate points by air causes auroral effects; this is also the mechanism for the natural "northern lights" and "southern nights" (where cosmic radiation trapped by the earth's magnetic field gradually leaks into the atmosphere at magnetic conjugate points in each hemisphere).

In addition to simply bouncing north-south between conjugate points, the trapped electrons drift eastwards (in the same direction as the earth's rotation, but much faster than earth's rotation) and rapidly form a trapped shell of electrons surrounding the planet. Bridgman explains that the eastward drift is similar in mechanism to the reflection effect (in other words, you resolve the electron motion in two perpendicular directions and apply conservation of energy to the sum of these two kinetic energy components), but instead of the mechanism being the convergence of magnetic field lines near the pole, the mechanism is the *vertical decrease in earth's magnetic field strength with increasing altitude above the earth.*

Bridgman then discusses the effect of electron belts on communications and radar. In the natural atmosphere, there is an electrically conductive "ionosphere" caused by solar and cosmic radiation at altitudes above 60 km. The higher "D" and "E" layers typically contain 10 times as many electrons per cubic centimeter in the daytime than at night, due to the absense of solar radiation produced ionization at night when many electrons can recombine with ions. The lowest or "D" layer is around 80 km and contains around 10^{10} electrons/m^{3}; the "E" layer is around 100 km up and contains around 2*10^{11} electrons/m^{3} in the daytime, while the "F" layer is at 250-500 km up and contains 10^{12} electrons/m^{3} in the daytime. Because of these free electrons, the layers are electrically conductive and can thus reflect radio waves like a metal plate (or like visible light reflecting off a mirror), but less effectively because the electron density and thus conductivity is much smaller.

LF radio waves are reflected back to earth by the lowest or "D" layer; MF is reflected back by the "E" layer, but HF radio waves penetrate both of those layers (albeit with some refraction) and are only finally reflected back to earth by the "F" layer. At frequencies above 30 MHz, an increasing fraction of the radio waves are able to penetrate through all the layers and escape into outer space.

The patches of ionization and the electron shells produced by a high altitude nuclear explosion are in effect additional or enhanced ionospheres. If the electron densities are pumped very high, even VHF and UHF signals (which are not normally affected by the natural ionosphere) can be stopped or seriously attenuated by the electron shells, which can degrade communications like satellite links which pass through the ionosphere (although you can easily increase the up-link power from an earth based transmitter to a satellite to overcome attenuation, the transmission power from the satellite is limited by its small power supply, so if there is a large attenuation in signal strength, it may not be possible to receive a down-link signal from the satellite which exceeds the noise level sufficiently). See also EM-1 chapters here and here.

(This blog post will be updated as time permits; I intend to briefly review the civil defence related effects physics in each chapter. It would be a good idea if the effects material were published as a revised and updated replacement of the traditional unclassified Glasstone book.)

Capabilities of Nuclear Weapons_Part I -

Capabilities of Nuclear Weapons_Part II -

DCPA Attack Environment Manual -