So depleted uranium is mostly U-238 which can't sustain a chain reaction. If you were to compress depleted uranium to a thousand times it's normal density could it then sustain a reaction?
Apparently not. The structure of the U-238 nucleus does not permit a chain reaction to sustain itself. However, hitting a mass of U-238 with a fast neutron flux can cause many individual U-238 nuclei to split, which is what happens in some nuclear devices. http://en.wikipedia.org/wiki/Uranium-238 See the first paragraph of this article.
The cross section of U-238 for a complete fission at energies above 2Mev is roughly 1Barn. Wouldn't compressing it to 1000 times it's normal density effectively make it an almost 100% chance that the atom compleatly fissions while also dropping the probability that the neutron loses all it energy to Inelastic scattering?
The wikipedia page says "238U is not usable directly as nuclear fuel, though it can produce energy via "fast" fission. In this process, a neutron that has a kinetic energy in excess of 1 MeV can cause the nucleus of 238U to split in two. Depending on design, this process can contribute some one to ten percent of all fission reactions in a reactor, but too few of the about 1.7 neutrons produced in each fission have enough speed to continue a chain reaction." Compressing the fuel would not increase the energy of the neutrons produced during the decay. As for losing too much energy via inelastic scatting, I don't see how compressing the fuel would help here either; the scatters would just happen even faster, since there are many more nuclei along any flight path. The cross section for absorbing the neutron would stay exactly the same for any individual nuclei, so about the same number of scatters would occur before absorption in either case. But I think the main issue is that most of the neutrons never have enough energy to cause fission in the first place.
If you had an external neutron source providing neutrons at energies in excess of 1Mev would the increased density increase the probability of a neutron causing a fission in the fuel mass?
In order for a chain reaction to occur, the probability of the nucleus fissioning and releasing 2.5 neutrons after absorbing one neutron must be at least 1/2.5=40%. In other words, for every neutron absorbed, you need at least one new neutron produced. This is possible with fissile isotopes U-233, U-235, Pu-239, and Pu-241. However for U-238, the probability of fission occurring after absorbing a neutron is much less than 40% (more like 2%). The key point here is that the density of the uranium is irrelevant, as the probability of fission depends on the properties of the nucleus itself and not the interactions of the material in bulk. Another key point is that the number of neutrons in the system does not affect the probability of fission occurring, only the total number of fissions. If you use an external neutron source, you will get a number of fissions in proportion to the strength of the source. However you will not increase the probability of fission occurring.
Ok so you wouldn't increase the probability of a fission. Would it decrease the probability of a neutron escaping the mass without interacting with a nucleus in some way, wether that be Inelastic scattering, total fission, partial fission ect ect?
So little? I had picked up the notion that the effective neutron multiplication factor in uranium 238, although below unity, is appreciable. The density of your critical mass starts to matter if it is spread over millions of kilometres.
Yes - it does! The only thing which is affected by change of density is the external surface and thus escape probability of neutrons.
Yes for natural uranium, no for pure U-238. No you are backwards. In an effectively infinite system, density is irrelevant because the neutrons will be absorbed eventually. Density is only a factor in small systems where neutrons can escape if they do not interact with the fuel.
Density will become relevant if the extent of the system is in millions of kilometres because then free neutron decay becomes an appreciable factor in criticality. Fast neutrons, with energy in MeV range, have speed in region of 10 000 km/s; neutron lifetime is in region of 600 s; so if your critical mass is in millions of kilometres then free neutron decay will matter.
So if you had a system in which you were using an external neutron source to fission u-238 you could get higher efficiencies for the same number of source nutrons, because the chances of neutron escape were vastly reduced due to the u-238 being compressed to 1000 times it's normal density?
First, you can't compress uranium to 1000 times its natural density. The natural density of uranium is ~95% theoretical density. Second, I don't understand what you mean by "higher efficiency", you have to define what the goal of the apparatus is to know how good it is at it.
Well ok you got me there. I wouldn't normally consider the entire solar system with a few uranium atoms floating around as a reactor in the traditional sense :uhh:
By efficiency I mean a greater number of neutrons from the neutron source would interact with the uranium mass in some form.
A caveat: the critical mass changes with density only if the change in density changes the surface through which the neutrons can escape. The critical surface density is independent on the volume density! For example, the bare sphere critical mass of uranium 235 at ordinary density is 52 kg. Medium enriched uranium to 20 % is said to have critical mass of 400 kg for bare sphere, containing 80 kg uranium 235. If you could somehow compress uranium to double its normal density while keeping same spherical shape as before, its critical mass would decrease 4 times. For example, if you could compress an 100 kg sphere of uranium into double its original density, the 100 kg sphere would take up as much space as an uncompressed 50 kg sphere. Its diametre would be 2 times smaller tan that of uncompressed 400 kg sphere, its surface area 4 times smaller, so the ratio of its mass to surface area would be the same as that of the uncompressed 400 kg sphere and it could go critical under the same conditions (20 % enrichment). Note that it only helps if the uranium is sufficiently enriched. The critical mass of uranium diverges to infinity somewhere around 6 % uranium 235. 1/4 of infinity is still infinity. The chain reaction is stopped by absorption in uranium 238 alone, even if escape of neutrons is completely stopped. But now imagine that you change the density but do NOT diminish the surface area. Say, you put a fusion bomb inside a fissile uranium shell, which is not critical. Then the bomb inside explodes. It also is a neutron source. When a triton fuses with a deuteron, it produces 17,6 MeV energy, 14 MeV of which are given to neutron. If the neutron were to fiss a uranium nucleus, whether uranium 238 or 235, it could release about 200 MeV energy, which is over 10 times the yield of the original fusion event; if the neutron could initiate a convergent fission chain reaction in a subcritical but nearly critical fissile shell, it would produce several times the energy of one fission and if the fissile material were made supercritical by compression then a single neutron or spontaneous fission could produce lots of energy. But critical mass is only diminished by decrease of surface! If you have an uranium shell around a fusion bomb, then even if the uranium shell were compressed to 1000 times into its original density as the thermonuclear explosion shock wave sweeps it up, it is compressed into a thin metal sheet. Its surface area through which neutrons may escape is not diminished, so if it is not critical before, it is not made any more critical by any amount of compression. Now, if you put the fissile subcritical uranium assembly inside a fusion bomb then yes, you could make it critical if it is subcritical before, or else you could make it nearly critical where it is far from critical before. But note that you are making the neutrons less likely to hit it by diminishing its outer surface!
Would the neutrons be less likely to hit if the uranium was imploding into the neutron source and that was causing the change in density?