Question about oxygen-16 fusion

[lucretiabrutus]

I was in a discussion with someone earlier about inducing nuclear fusion (16O+16O) in the mantle of the Earth to blow up the planet (if this is the wrong subforum, please move — I've put it here since I think it's a legitimate science question). Given the nature of these forums, it doesn't go without saying that we are not discussing the Death Star, and that neither of us are trying to find 'cheats' to blow up Alderaan more easily. I want to present this as neutrally as possible, so I won't say what side I'm on, but I will say I don't have sufficient knowledge in the relevant fields to assess this properly.

The contention is this: heating up a section of the crust to 1.5E9 K (average particle energy of 130 keV) would be sufficient to cause 16O+16O fusion (since oxygen-16 is half the mantle by mass), which would lead to a chain reaction that would destroy the planet (since the Earth's gravitational binding energy is 1.4E51 eV, and the oxygen in the mantle comprises c. 30% of the planet's mass (60% of the planet's mass is mantle, and 50% of the mantle's mass is oxygen), meaning that you can get 3E49 fusion events, which release c. E7 eV each). As for confinement, the contention is that a shockwave would be sufficient compression and last long enough for the fusion to take place.

My question is whether or not this is possible / plausible. 130 keV is well below the Coulomb barrier for 16O (the only paper I could find on sub-barrier fusion of 16O was this thesis, which dealt with energies nearly two orders of magnitude higher to determine fusion cross sections), and while stars use these energies, they also have a great deal of mass/time/pressure to work with. Would it be possible to cause a runaway fusion effect within a planet's mantle? Why/why not?

I know there are many well-educated people on this forum (especially given the nature of the main site), so I thought it would be the ideal place to ask the question. Thank you in advance for any help or resources you can offer.

[Lord Revan]

hmm doesn't oxygen fusion need more energy then it produces?

[lucretiabrutus]

No, oxygen fusion releases energy. 32S has a mass defect of -26 MeV relative to 12C, compared to 16O which have -4.7 MeV each (so -9.4 MeV total). That said, 32S would decay immediately if formed (too much excitation energy), evaporating an alpha particle and emitting 9.6 MeV, or evaporating a proton and emitting 7.7 MeV as the most likely channels (found here).

[Zixinus]

I would like to raise a point: temperature isn't what's important when making fusion, it's overcoming strong nuclear force.

With stars, this is done by massive gravity (I would guess that friction and perhaps strong concentration of radioisotopes also plays a role, but I can't cite that off-hand). Simply raising the temperature won't do, plasma expands (it is essentially hot gas) and thus radiates away this energy. In stars, gravity prevents this expansion and forces nuclei to be close together enough that their individual movement energy (which is what temperature is, the average kinetic energy of a given amount of mass) overcomes the nuclear force.
I understand that artificial attempts at creating net-positive energy relies on using electromagnetic fields (tokamak) or inertial electrostatic forces (Polywell) to do the same.

So, how does heating up the crust forces these oxygen nuclei to be also close enough for fusion to occur? More importantly, how does heating up the crust makes the fusion self-perpetuating? Because nuclear weapons have managed to raise temperatures pretty high, high enough for fusion to occur inside the bombs, but the energy of these reaction disperses rather than somehow ignite a planet-wide fusion fire.

[lucretiabrutus]

I thought the difficulty in attaining fusion was overcoming the electromagnetic force (i.e. the Coulom barrier), and once you're close enough the strong force helps you in the process? As far as the plasma's expansion goes, the idea is that the shockwave generated by the material exploding once fusion begins would be sufficient to compress matter ahead of it, perpetuating the cycle. I don't know enough about shockwaves to know whether this is at least possible.

As far as nuclear bombs go, though, none of them have been tested inside the mantle (which is extremely dense compared to the crust), and probably haven't been anywhere near large enough for the purposes of ignition in this idea.

[Zixinus]

I thought the difficulty in attaining fusion was overcoming the electromagnetic force (i.e. the Coulom barrier), and once you're close enough the strong force helps you in the process?

Yes, you're right, it is electromagnatic force that has to be overcome until strong nuclear force kicks in. Brainfart, I remember that I was writing something wrong, but didn't realize what at the time.

[Terralthra]

The earth's mantle is half oxygen by mass, sure, but it's not elemental. It's in molecules with silicon and magnesium, along with iron, aluminium, etc. Fusing oxygen by itself is much simpler than fusing oxygen when it's surrounded by much harder-to-fuse elements. Something that could heat everything up to the point of fusion is likely to tear the crust and mantle apart long before it gets to causing a fusion chain reaction.

[Starglider]

Fusing oxygen by itself is much simpler than fusing oxygen when it's surrounded by much harder-to-fuse elements.

The reduction in reaction cross-section is less than an order of magnitude vs pure oxygen so that's not the main problem assuming you're talking about a thermal reaction not a pure chain reaction. I doubt confinement would be an issue as the timescales for a chain reaction would mean inertial confinement would suffice. The problems for a chain reaction situation are (a) you have to generate sufficient fusion power to overcome the cubic increase in the volume being heated and (b) the proposed initial energy is far too low. Considering all the loses involved I don't think a heavy element fusion reaction can be self-sustaining in the mantle although it could certainly add some additional yield to a super-high-energy strike.

[Ariphaos]

hmm doesn't oxygen fusion need more energy then it produces?

No, but the majority of the energy is released as neutrinos.

[lucretiabrutus]

No, but the majority of the energy is released as neutrinos.

Really? This is quite surprising to me, as I didn't think there'd be any weak decay at all in the fusion, especially since the major modes of removing energy are evaporation. Can you please explain this to me, or provide a source? It sounds interesting.

[Simon_Jester]

The contention is this: heating up a section of the crust to 1.5E9 K (average particle energy of 130 keV) would be sufficient to cause 16O+16O fusion (since oxygen-16 is half the mantle by mass)...

Heating a significant section of the crust to 1.5E9 K would almost by definition require enough energy to vaporize and blow away thousands of times that much crust material; you'd do better to just keep firing whatever you used to do this.

Also, for readily imaginable mechanisms of heating, inertial confinement won't sustain a chain reaction. Assuming you pass the breakeven point and emit more energy than is required to sustain the reaction, you're still heating the surrounding crust to (and far far beyond) the point of vaporization. Those rocks will boil away long before they get hot enough to fuse.

This is sort of like the problem of designing nuclear fission bombs. It's easy to slap two hunks of plutonium together and get a temporary critical mass- but the energy release from that tends to blow the mass apart again. It takes carefully timed detonations of explosive charges to make the mass hold together long enough to release a large, efficient yield from a large mass of fissile material.

[Ariphaos]

Really? This is quite surprising to me, as I didn't think there'd be any weak decay at all in the fusion, especially since the major modes of removing energy are evaporation. Can you please explain this to me, or provide a source? It sounds interesting.

Not much directly from the process of fusion itself, but rather the temperatures and densities required. I had an earlier discussion about finding this out, linking to a bunch of material:
http://bbs.stardestroyer.net/viewtopic.php?f=5&t=157196

[lucretiabrutus]

Thanks for that! I'll give it a read.