Fission compared to Solar Energy

How much fission fuel do we have, and how does that stack up against space solar power?

We can breed thorium into U233 for fuel, and U238 into P239 for fuel. The total amount of fuel is 2e-6 of the earth's crust for uranium and 8e-6 for thorium. The earth's crust down to the upper mantle (let's get ambitious here) contains 1e-5 * 1.4e23kg or 1.4e21 grams of potential fuel. Some might be very hard to get to, we would be processing all the Earth's crust and mantle and removing every smidgen of fissile material. But this is the maximum available. Fission yields about 200MeV per nucleon, or 2e8 * 6e23 * 1.6e-19 / 234 = 8e10 joules per gram, for a total of 1.1e32 joules. If the world uses 100 Terawatts of power, that is 3.2e21 joules per year. If we could extract all that fissile material and make energy with 100 percent efficiency, that is 35 billion years worth of power.

More realistically, we might be able to extract 10% of the energy from 1% of the fissile material in the crust, taking a very long time to mine and process all that rock. The available 1.1e29 joules provides a "mere" 35 million years of power, assuming extraction technologies we cannot even imagine.

If we compare that to power from space, assuming 50% conversion of sunlight into usable power in space, then a sun-facing disk with the radius of the moon's orbit (384,000km ) can produce 0.5 * pi * 1366 * 3.84e8^2 watts or 3.2e20 watts, or 1e28 joules per year. In 11 years, that disk intercepts as much energy as we can extract from realistically available fissile material.

The Sun puts out 4pi*1366*1.5e11^2 = 3.8e26 watts. Again, assuming we can turn 50% of that power into useful energy in the long term (perhaps with a Dyson shell of collectors out beyond Uranus, so the waste heat does not warm the Earth significantly) then the sun produces 1.1e29 joules in about 10 minutes, and 1.1e32 joules in about a week.

If the average thickness of the beyond-Neptune (5e12 meters) Dyson shell is 50 nanometers (mostly dipole antennas, perhaps), the volume is about 1.6e19 cubic meters of material, about 30% of the volume of the Earth's crust, or about 10% of the volume of Mars, or 2% of the volume of Venus. In the very long term, that might be doable. However, let's restrict ourselves to the same 1% of the Earth's crust for the volume of our collectors, and assume that in the very long term we capture only 3% of the Sun's power. That means that it will take 30 weeks to produce as much energy as all the available fissile material on Earth. However, the collectors (recycled and remanufactured) can be expected to keep producing that power for 10 billion years, not 30 weeks. Quite a multiplier!

Fusion

Deuterium makes up about 0.03% of the weight of hydrogen in sea water (which is 2/18ths of the weight of the water), or about 3.4e-5 of the 1000kg/m3 of water. 34 grams per cubic meter. The total volume of the ocean is 1.3e18 m3 , so there are about 5e19 grams of deuterium in the ocean. D + D -> T + n + 4MeV, and D + T -> He4 + n + 17.6MeV , so the overall reaction is D -> 1/3 He4 + 2/3 n + 7.2MeV . So a gram of deuterium produces 7.2e6 * 1.6e-19 * 6.02e23 / 2 = 3.5e11 Joules (at 100% efficiency, difficult because most of the energy ends up in hard-to-capture neutrons). The total energy in sea water deuterium is 1.7e31 joules. Perhaps 10% of that is extractable, for 1.7e30 joules of deliverable energy from all the deuterium in the ocean. That is about 16 times the recoverable fission energy. However, fission produces about 100MeV per waste neutron, while fusion produces only 10MeV per waste neutron, so the fusion process is more polluting, as well as quite a bit more difficult.

Again, the sun produces 3.8e26 watts, and at 50% efficiency that will produce 1.7e31 joules in about a day, or in a month if we capture only 3% of the output.

Conclusion

Political and safety issues aside, all the nuclear energy available from all the material on Earth can produce only a tiny fraction of the energy that a small fraction of the sun's output can produce. While Earth's nuclear energy will be helpful to bootstrap the process of extracting space solar energy, it is a tiny fraction of what is available in space. Using space energy in space, and dissipating the waste heat, is the only truly long-term sustainable option.