According to this there are 5.3 million tons of obtainable uranium as of 2011.
With 0.7% being fissionable, that makes it 37,000 tons. A kg of U-235 is equal to 17 kilotons of TNT.
So 33.63 million kg of U-235 works out to about 572 gigatons. The asteroid that killed the dinosaurs was equal to about 100 teratons (about a thousand times more powerful)
But that neglects all the other fissionable materials out there that can be made (plutonium 239), and all the other uranium we can’t currently get.
I don’t think that the plutonium Dagwood sandwich would work. We talk colloquially of a critical mass, but what’s really important is a critical configuration: How the mass is arranged is just as important as how much there is. And a sandwich of layers, separated by a distance small compared to the size of the layers, would probably be critical.
The fissionable material in the 2nd and later stages of a fission-fusion bomb is the U-238 used as a tamper. Lots of U-238 around, thorium will fission as well. Thousands of tons of that stuff available. You have lithium isotopes undergoing fusion as well. One of our early test in the Pacfic had a substantial quantity of lithium-7 that wasn’t expected to contribute. Ooops. Test had three times the expected yield. From Wiki - “The “Castle Bravo” shot of 1 March 1954, was the first test of a deployable (solid fuel) thermonuclear weapon, and also (accidentally) the largest weapon ever tested by the United States (15 megatons). It was also the single largest U.S. radiological accident in connection with nuclear testing. The unanticipated yield, and a change in the weather, resulted in nuclear fallout spreading eastward onto the inhabited Rongelap and Rongerik atolls, which were soon evacuated.”
The plutonium sandwich won’t work. You can’t get enough of it close enough in a multi-plate configuration. The stuff is pretty HOT. Back in the US Army tactical nuke days, we were limited to how many small diameter PU weapons we could store in a magazine - not many - and they had to be in a specific configuration to “lessen” interaction with the other warheads.
Pretty sure the fission limit is roughly 500 kt… ISTR reading about some test in the 1950s that required all sorts of tricky stuff to get what is pretty near the limit for pure fusion implosions.
Boosted fission could certainly go higher, and I imagine that using the Teller-Ulam principle to compress a fissile secondary could get an even higher yield than boosted fission, but there’s still probably some limit.
Fusion on the other hand, is pretty much limited to the number of stages- Tsar Bomba was a 3 stage design; a primary fission trigger compressed and ignited a fusion secondary, which did the same to a larger fusion tertiary stage. There’s no practical reason why someone couldn’t build an absolutely huge 5 or more stage bomb, except the point of diminishing returns that Mach Tuck talks about- at some point, you just make a bigger mushroom cloud, without really making the blast/flash much bigger.
And… fusion bombs like the Tsar Bomba are actually some of the cleanest bombs by yield out there- 97% of its yield was fusion, since it had lead(?) secondary and tertiary casings. Had they used the natural uranium ones, the yield would have been the designed 100 megatons.
Well, hold on: pre-ignition, there’s no limit to how far apart the plates might be. I could stack them one every ten feet…or every 100 feet…or ever 1,000 feet…
That’s the big problem! Not how to hold it in place pre-ignition, but how to ignite it. I’m not convinced the engineering issue can’t be solved. Obviously, nobody wants to solve it, and nobody is ever actually going to do so, but it seems to me that some means could be made of slamming the plates – perhaps held in frames, like picture-frames – down into each other in a synchronized manner.
I have a huge amount of faith in engineers! “The impossible takes a little longer.”
Maybe the plates could be slid into conjunction, like dropping the toast into a toaster. It could happen in various directions: some slid in from the north, some from the south, east, west, etc. The only two things that matters is that they are held far enough apart to begin with, and then are put in close conjunction very fast.
Oh, yeah, and that nobody ever actually does this… That’s kinda important too!
I thought about that, and mentioned it, but I don’t know where the breakpoint would be. Fission happens so very, very fast, it could outpace the break-up of the material, way up to some absurd size of the fissionable mass.
As a very rough estimate, nuclear reactions are as much faster than electronic reactions as electronic reactions are faster than mechanical reactions. Look at how fast your Pentium chips is compared to a computer using dials, gears, rods and cams and things – and then note that fission is just about that much faster again. The flying-apart of the material mass is a mere mechanical reaction…
However a fission reaction is a chain reaction - it isn’t a single step. In order to get any useful energy out of the fissile mass you need the neutrons to multiply exponentially for a reasonable amount of time. Every extra nanosecond of confinement where the flux of neutrons is increasing is getting you more yield. The bounds of getting little more than a big flash and a spray of molten metal versus megatons of yield is very fine. This is why compressing the mass and flooding it with neutrons from an initiator is do important. The initiator jumps past many many chain reaction steps - and steps saved at the start are steps you get to use at the end. Compression increases the rate of reaction very significantly. A very large mass may well engage in the reaction, but it may not be involved in enough steps to make a useful addition to the yield. The photon pressure inside the mass is insane, and accelerating the mass apart more than fast enough to eject most of the material unspent. The insane physics is what I find so fascinating. There are energy densities that are simply impossible to grasp in any ordinary way.
Thats part of the problem. The fissiony thingy happens way faster than the mechanically thingy.
Which means it wants to start reacting as soon as you “put it together”. The bigger it is the harder its going to be to get it together before it starts taking itself apart. And the bigger it is the better it is going to be at doing so.
So, without doing the calculations (my napkin isn’t quite big enough) I can certainly believe that you could reach an actual size limit. And if not an actual size limit a point of diminishing returns that at some point are absurd (like its twice as big but only a few percent stronger).
Also, I suspect the diminishing returns thing may apply to “just add more hydrogen” to the hydrogen bomb as well as a pure fission bomb.
Another consideration. If you are using the explosive compression method at some point the thing is going to be big enough that the compressive shock wave won’t have reached the core before the out parts are already blowing apart due to the fission process.
The physics is going to get complicated pretty quick.
Ok this page Nuclear weapon - Wikipedia says only 1% of the uranium in Little Boy and 20% of the plutonium in Fat Man underwent fission. Does anyone know how efficient modern weapons are?
Have at it. Even if this doesn’t give you your answer, I think you’ll still find the information at the Archive interesting.
From it, my guess is that the ultimate yield is limited either by the number of stages one can chain together (is it possible to fuse a very large 4th stage from the energy released by a fissioning 3rd stage?) and by how much fissionable tamper one can get to react from the emitted fusion neutrons from the 2nd stage.
As a practical matter, for terrestrial destruction, large yields are largely wasted, as Mach Tuck quotes from Rhodes. All you’re doing with a bigger bomb is shoving the atmosphere in line of sight of the bomb into space that much faster. Now, if we needed to split, e.g., Hale-Bopp for some reason, then sure, bring on the gigaton warheads. I suppose if you wanted to make a really big underground cavern at the bottom of a Macondo-type well, a gigaton-yield device might have some purpose.
For question of efficiency, it depends on how we frame the question. Are you asking which bombs have the greatest energy for their size, or are you asking which bomb burns up the greatest percentage of its nuclear material? For the first, the link shows that the final design for Tsar Bomba was about 4 times as efficient as a warhead like the modern W-87. Of course, the W-87 has different design criteria, and much greater utility and safety than the Tsar Bomba. For the second, you’ve got me. You’d have to know how much nuclear material was in the bomb to being with, for one thing.
It’s the asterisked section at the bottom of the page. More or less as I remembered, except you don’t lift a larger piece of atmosphere as weapon yield is increased - you just lift the same piece faster.
It used a Lead tamper instead of Uranium because, had they used Uranium, it would have been twice as powerful (100MT) but it would have also been many times ‘dirtier’. Some estimates say it would have nearly doubled the total amount of radioactive fallout on the planet in one fell swoop. Even at 50MT there was tremendous blowback. The aircraft crew figured they had a 50/50 chance of survival.
One thing: The Tsar Bomba and other three-stage bombs are fission-fusion-fission. The vast majority of the energy created comes from the last stage’s fissioning. Basically conventional explosives compress Plutonium causing it to fissile, the heat & pressure of the fission reaction creates a fusion reaction, which not only creates heat & a pressure wave but also a tremendous X-Ray pressure wave, and those are directed around a Plutonium ‘spark plug’ compressing it into another fission reaction, but on an order of magnitude faster & greater than conventional explosives can, causing a tremendous blast of neutrons into the Uranium tamper accelerating the fission reaction even further.
Theoretically this could be continued indefinitely with more stages. As others have said the real limiting factor, besides blowback, is that soon the fireball is so huge that most of the energy is expelled above the atmosphere out into empty space.
Are you sure? I always got the impression that a “stage” was a assembly of fusible material that was compressed by the stage before, and that what you’re describing is basically opportunistic fission of the fusion tamper by fast neutrons generated by the fusion reactions.
In other words, changing the material of the fusion tamper doesn’t change the number of stages that the weapon has.
Well yes and no. you can increase the yield in a fusion bomb with more fissile material up to a certain point.
when the Russians made the Czar bomb they back out some of the fissile material to lower the yield. As mentioned earlier they were afraid of the fallout of the originally intended bomb.
To answer the op there are 2 answers. A fissile nuclear bomb has a practical limit of about 1 megaton (don’t remember why). A fussion bomb has a practical limit of about 100 megatons because the blast would travel out of the atmosphere and into space. It could be made larger but it would not yield the destructive force. I am parroting what I heard from a show discussing this topic.