Total Resource: Fusion

This is the third in our series on the physical limits to energy resources available on Earth. The previous two entries covered chemical energy including fossil fuels, and nuclear fission. This time we'll review the vast potential for fusion energy, if humans can ever master the technology. 

Energy from nuclear fusion has been touted for decades as a potential major future energy source, but achieving practical fusion power production has proved difficult. The new International experimental reactor, "ITER" will explore the parameters for a practical reactor, but commercial production is still decades away.

Nevertheless, the potential yield from fusion seems vast: it's the energy that powers the stars, and almost any of the light elements can potentially act as a fusion fuel, though experimental reactors so far have focused primarily on the hydrogen isotopes deuterium and tritium (which can be generated from deuterium). The main conversion process in the Sun combines four protons into one helium-4 nucleus (through a series of indirect reactions), with a net energy release of 26.7 MeV, or 6.675 MeV/nucleon. The conversion of 2 deuterium nuclei to He-4 yields 23.8 MeV (D + D + D -> He4 + n + p + 21.6 MeV, n + p -> D + 2.224 MeV) or about 6 MeV/nucleon. Per unit mass this is over 6 times the yield from U-235.

Natural hydrogen contains 156 ppmv of deuterium (about 1 in 6000 hydrogen atoms) which amounts to 312 ppm by mass. Hydrogen constitutes about 1/9 of the mass of Earth's oceans, or 1.5x10^20 kg out of 1.37x10^21 kg total. Earth's crust is estimated to hold about 0.14% hydrogen by mass as well, yielding another 1.9x10^20 kg, for about 3.4x10^20 kg of hydrogen. At 312 ppm, that yields close to 10^17 kg of deuterium potentially accessible in Earth's oceans and crust.

Multiplying by 6 MeV/nucleon or 5.8x10^14 J/kg, we find a total energy potential from 10^17 kg of deuterium of about 6x10^31 J, or 1.5x10^11 years of present-day energy use.

Just as with fission, there is potentially more fusion energy available from the other elements; 60% of the Earth is made up of elements lighter than iron (almost all silicon, oxygen or magnesium) which can in principle combine through fusion reactions to yield net energy. For example, two carbon-12 nuclei can combine to form magnesium-24, yielding about 14 MeV. Two oxygen nuclei can combine to form sulfur-32, yielding 17 MeV of energy. The total potential fusion yield from Earth's light elements should be somewhere between 0.5 and 1 MeV per nucleon, or 5 to 10x10^13 J/kg. At 10^23 kg, that gives us about 10^37 J just from Earth's crust (a bit over 10^16 years worth of present use). With a mass of close to 6x10^24 kg, the potential energy available from fusion for the entire planet could be as large as 3x10^38 J (almost 10^18 years).

The ultimate energy source is not fusion, but mass itself through Einstein's E=mc^2 relation. This immense store of energy could theoretically be made useful in a future world if we happened upon an equivalent store of antimatter, or perhaps more realistically, a gravitational singularity into which we could dump bits of our planet piece by piece. For 6x10^24 kg multiplying by the speed of light squared gives 5.4x10^41 J, or over 10^21 years at year-2000 levels.

But even that is not the ultimate limit to energy accessible to human society, thanks to the immense universe we live in. With a mass 300,000 times Earth's at 2x10^30 kg and a composition primarily of hydrogen, the total energy yield possible from fusion for the Sun is about 10^45 J, or enough to power the year-2000 world for over 10^24 years. The Sun is using up its fuel relatively slowly, with billions of years of material left; we can figure out the present rate of energy release from the light received at Earth's orbit of about 1386 W/m^2 and Earth's orbital radius of 150 million km. At 4 pi r^2 the total area at Earth's orbital distance is 2.8x10^23 m^2, so the total energy flow from the Sun must be 3.8x10^26 W or 38x10^13 TW, about 3x10^13 times present energy use by humans on Earth. With hundreds of billions of stars in our galaxy, total energy generated is over 10^24 times present human use, and there are orders of magnitude still more available if we ever venture beyond.

The total energy possibly available to us from fusion is truly vast. It should be understood that we don't need to master the technology ourselves if we can make better use of the fusion reactors already out there - the Sun in particular. We'll take a look at the potential scale of solar energy resources next.

Created: 2007-07-15 23:50:01 by Arthur Smith
Modified: 2007-07-17 15:47:48 by Arthur Smith