Resolving a problem with Longmire's high altitude burst early time EMP prediction formula
"In fact, I basically designed the first boosted bomb device. ... I got interested in what's called nuclear effects, the effects of nuclear explosions. In fact, I really got interested in that in 1962 when we had the high altitude test series, Operation Dominic. And I started working in that, and it turned out that the AEC, or Los Alamos Laboratory, was not really very interested in the effects of nuclear explosions by that time. In the early days, they had done a lot of good work on blast and shock and fallout and that kind of stuff. But by that time, most of the people there regarded their main job as putting bombs in the stockpile, and there wasn't too much appreciation that it was important to understand about the physics of nuclear effects, for example, EMP. ... way back in the 1970s, early seventies, there was a fellow at the RAND Corporation, this is after the RDA physics group [Harold Brode et al] left. His name was Cullen Crane [see illustration below], who, I don't know if you've ever heard of him—well, anyway, this fellow was saying that EMP is a hoax. These guys are either crazy or they're doing it to, you know, perpetuate their salaries. And so the Jason group got tasked by DNA to look into this. Now, in this case, in my opinion, the Jason group didn't do a very good job, because instead of reading the reports and trying to settle the argument, they started out from scratch and first did their own version of EMP, and at least, I didn't think that was necessary at the time. ... They do not, you know, when they begin to look into something, they don't go back and make sure that they've read all the earlier references and stuff like that. But you don't expect physicists to be your formally good historians."
- Dr Conrad Longmire, interview given to American Institute of Physics's Finn Aaserud, 30 April 1987.
The attack quoted above by Longmire on RAND Corporation Cullen M. Crain's alternative method of calculating EMP, by summing individual electron EMP emissions rather than solving Maxwell's equations, seems a bit over the top. Yet that is the standard, very paranoid, response which often greets alternative theories in physics. Crain's unclassified version of the 1973 paper, his 1982 Calculation of Radiated Signals from High-Altitude Nuclear Detonations by Use of a Three-Dimensional Distribution of Compton Electrons (DTIC ADA114738 or RAND N1845) gives results that agree with other more standard techniques in the applicable cases. There is a tendency to be extremely defensive about the first theory to arrive on the scene, to the point of trying to use it to close down efforts to work on alternatives! If you have an alternative idea, you first try the polite method, but you get brushed off rudely, like a fly. Then you give them a taste of their own medicine, and they have the temerity to call you rude! This is a pretty standard problem. Whatever approach you take, some contrived, specious excuse is used to silence it.
High altitude EMP data is compiled in an earlier post, linked here. The January 2014 issue of DTRIAC Dispatch discussed late-time EMP, which is extremely low frequency (ELF) and therefore penetrates some metres into dry ground, where it couples to very long cables. What's generally more dangerous is the early time or E1 phase of the EMP which delivers frequencies up to 100 MHz, in the UHF spectrum, with intensities of up to 50 kV/m for a fraction of a microsecond. The problem is that although EMP effects from a 1.4 megaton burst at 400 km (Starfish) in 1962 are well known, the correct scaling laws for the terrorist threat from say North Korea detonating 7 kt (the yield of its last nuclear test) at say 100 km altitude, are not openly discussed. EMP Theoretical Notes are now online, and they document the early-time EMP research by people like Conrad Longmire of Los Alamos, who is credited with being the first to understand the Starfish EMP from 1962, where the earth's magnetic field deflected Compton electrons, producing an EMP. (Glasstone discusses EMP in the April 1962 edition of The Effects of Nuclear Weapons, but not that mechanism.) Longmire's EMP mechanism was first published openly by RAND Corporation's Karzas and Latter, report RM-4306 (DTIC document AD607788), crediting him.
The only published paper giving plots of early EMP peak field strength versus yield (of prompt gamma rays escaping from the weapon) and burst height is the Master's Thesis of Louis W. Seiler, Jr. His plots show a generally very weak and complex dependence of yield and burst height on the EMP. The problem with numerically integrating differential equations with a computer is the lack of understanding that results. This problem also plagues weapons design and other nuclear effects computer codes. Hence, there is a need to try to come up with analytical solutions. Naively, you might take the equation for electromagnetic wave energy density in terms of field strength (energy per unit volume is half the product of the permittivity of free space, and the square of the electric field strength), and give the EMP a volume equal to the that of the prompt gamma ray pulse (a 10 ns pulse for instance is a shell 3 metres thick, since the gamma rays and EMP are going at light velocity which moves 3 m in 10 ns). This gives a simple formula where EMP field strengths are proportional to the square root of the yield, divided by the distance from the bomb. This naive theory is completely misleading, largely because the Compton current is largely cancelled out by an opposing conduction current, at least for small distances (between bomb and atmosphere), and large yields. (In addition, you need to take account of how far the Compton electrons travel before absorption in the air at the altitude in question, in comparison to the their gyro radius in the geomagnetic field.) However, Karzas and Latter found an analytical solution to this conduction current limitation of the EMP in their equation 52 (the symbol sigma is the air conductivity, signifying the conduction current term in equations 51 and 52):
I've highlighted the two key parts in red. The first is ellipse covers the Compton current contribution, basically the Compton current density j integrated over a radial line through the deposition region, with the EMP also inversely proportional to distance. The second term, multiplying the first, is a exponential attenuation factor for the effect of the conduction current. In fact, this general analytical solution to the EMP first appears in equation 12 of another RAND Corporation paper on EMP issued more than a year earlier, W. Sollfrey’s RAND Corporation report RM-3744-PR, An Analytically Solvable Model for the Electromagnetic Fields Produced by Nuclear Explosions, July 1963, EMP Theoretical Note TN53. This analytical solution was generally ignored or solved numerically, and was not simplified into a simple model for EMP field strength calculations. Our argument is that it can be simplified with good approximations (such as taking the air conductivity to be constant through out the gamma ray deposition region "pancake" under the burst), to give a simple model to explain Seiler's curves. Moving ahead to 1987, Longmire and others reinvent the wheel (in separate parts!) in equations 9 and 10 of EMP Theoretical note 354:
Longmire's 1987 EMP theoretical note in a way helps by breaking the product into two parts that can be multiplied together. Each part, Compton contribution and conduction current, lead to questions and answers that are very important. First, EMP like radio is the time-derivative of the net current, not its integral (the opposite of taking a derivative!), so how can you get a correct result from equation 9?
The answer to this is profound for Maxwell's theory of electromagnetism, for it means that Longmire's EMP, radiated due to the sideways deflection of Compton electrons travelling at nine-tenths of velocity of light, is showing us how radiation really occurs, in all cases. There's a duality between Gauss's law of static charge (the radial electric field) and electromagnetic radiation due to charge acceleration. In other, plainer, words: when the Compton electrons are deflected sideways, part of their radial field (modelled conventionally by Gauss's law!) is converted into synchrotron radiation. Conventionally, Maxwell's equations say that the radiation from an oscillating charge is not the Gauss field (see for example, equation 28.3 of the Feynman Lectures on Physics, volume 1, where separate terms are given for fields due to charge acceleration and static charge).
Take mass and energy. They were once considered completely different. Then it was discovered that under certain conditions, significant conversions between them could occur (e.g. in fission and fusion). By analogy, the validity of Longmire's result means that the Gauss field and electromagnetic radiation are the same thing in certain conditions. What we're pointing out here is that if you have an electron moving at 0.9c and deflect it sideways by a magnetic field, the Longmire equations prove that some of its c-velocity Gauss field is being sheared off, and is continuing along its original path without deflection. That's the mechanism of electromagnetic radiation by accelerating charge.
The lost field energy from the electron then appears as a deceleration of the electron (loss of kinetic energy). This is proved by the very fact that Longmire's proof-tested equation must be a duality to Maxwellian synchrotron radiation. In quantum field theory, the Gauss field isn't static at all but is composed of light velocity exchange radiation, virtual photons (electromagnetic gauge bosons). So this really makes the case for understanding the Maxwell equations in terms of moving virtual photons; it's obvious that these virtual photons become real photons (observable radio waves or EMP, for instance) when the charge is accelerated, breaking the normal equilibrium of exchange of virtual photons between charges, which constitutes the field extending throughout space.
Secondly, this analytical solution provides easy predictions of EMP, explaining Seiler's graphs. Here are the first couple of pages from my draft paper on this topic, which are needed here because the symbols are hard to typeset neatly in a blog's font:
(To be continued.)