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| Fig. 1: Comparison of energy content in gasoline and water. The energy content of water is computed assuming all deuterium therein is used in the specified fusion reaction. Note the y-axis uses a logarithmic scale. (Image source: R. Przybocki.) |
Nuclear fusion stands at the forefront of revolutionary advancements in energy technology, offering the promise of a clean and virtually limitless power source. Unlike its fission counterpart, fusion involves the merging of atomic nuclei to release energy, emulating the process that powers the sun and other stars.
At the core of this transformative technology lies the need for efficient fuel sources, and deuterium, a stable isotope of hydrogen, is a key fuel component. [1] While a standard hydrogen atom (protium) consists of a single proton in its nucleus (1H), deuterium (D) contains both a proton and a neutron. This additional neutron gives deuterium a greater atomic mass compared to protium.
Deuterium is most commonly encountered in water (H2O), where a small fraction of molecules contain a deuterium atom replacing regular hydrogen. In ocean water, the ratio of deuterium to hydrogen is approximately 1 in 6420. [2] While deuterium is only present in trace amounts, its prevalence is substantial due to the vast quantity of water on Earth, making it readily available and accessible.
Several nuclear reactions have been proposed for energy generation that use deuterium as a major fuel component. The leading candidate of these is deuterium-tritium (D-T) fusion, in which deuterium reacts with tritium (an unstable isotope of hydrogen with two neutrons) in the following reaction: [3]
As denoted in the parentheses on the right-hand side, the D-T fusion reaction is an exothermic process, with a yield of 17.59 MeV in the helium and neutron products.
Tritium is radioactive and naturally occurring in only trace amounts, so for fusion to be a workable technology tritium must be produced through nuclear reactions. [4] Fusion reactor designs have often employed a tritium breeding blanket, using reactions between neutrons and isotopes of lithium to produce a tritium product. [5]
Other fusion reactions have been explored that do not require tritium fuel, the most prominent of which is deuterium- deuterium (D-D) fusion. [6] In D-D fusion, two deuterium nuclei fuse with products dictated by one of two reactions: [3]
| D + D | → | T (1.01 MeV) + 1H (3.02 MeV) |
| D + D | → | 3He (0.82 MeV) + n (2.45 MeV) |
These reactions occur with roughly equal probability and release a net of 4.03 and 3.27 MeV, respectively. Although the D-D fusion reaction is intriguing since it does not rely on tritium fuel, technical hurdles have led researchers to consider D-T fusion as a more feasible energy source. The cross section for D-D fusion, denoting the probability of the reaction, is roughly two orders of magnitude lower than that for D-T fusion, and the maximum cross section is only reached at higher temperatures in the hundreds of keV. [7] In contrast, D-T fusion reaches a maximum cross section at approximately 70 keV, which is more feasible for reactor design. [8]
In this section, we will analyze the energy content of water if all its deuterium can be extracted and used in one of the aforementioned fusion reactions. The molar mass of water is 18.01 g/mol, meaning 1 kg of water contains 55.5 moles of water. Using the ratio 1 part deuterium to 6420 parts hydrogen, 1 kg of water will contain about 0.0173 moles of deuterium, or 1.04 × 1022 deuterium nuclei. The total mass of the deuterium in 1 kg of water is thus about 0.035 g, as shown in the following calculation:
| 1 mol H2O 0.018 kg H2O |
× | 2 mol H 1 mol H2O |
× | 1 mol D 6420 mol H |
× | 0.002 kg 1 mol D |
= | 3.46 × 10-5 kg D / kg H2O |
In the D-T fusion branch, 0.0173 moles of deuterium, when fused with an equal number of tritium nuclei, yields 1.83 × 1023 MeV of energy, or 2.94 × 1010 J. For the D-D fusion reaction, assuming an average yield of 3.65 MeV between the two branches, 0.0173 moles of deuterium yields 1.90 × 1022 MeV, or 3.04 × 109 J. The energy content for D-D fusion is an order of magnitude lower than that for D-T fusion, reflecting both the smaller energy yield in the fusion reaction and the requirement of twice the amount of deuterium as a reactant. The calculation for D-D fusion yield is shown below.
| 3.46 × 10-5 kg D / kg H2O | × | 6.022 × 1023 D atoms 0.002 kg D |
× | 3.65 × 106 eV yield 2 D atoms |
| × 1.602 × 10-19 J eV-1 = 3.04 × 109 J / kg H2O | ||||
Despite only a fraction of the atoms in water being usable deuterium, the energy densities of 2.94 × 1010 J/kg and 3.04 × 109 J/kg for fusion are still orders of magnitude higher than fuels such as gasoline, which contains 4.75 × 107 J/kg. [9] This comparison is illustrated in Fig. 1.
Fusion energy holds promise in part due to the prevalence of deuterium in Earth's water supply, making deuterium an almost limitless and widely available fuel source for fusion reactions. Here we have demonstrated that, under ideal conditions, the energy density of water can be nearly 1000 times greater than that of gasoline if all deuterium contained in the water is used for D-T fusion. Of course, this analysis leaves out the complexities of extracting deuterium from water as well as those involved in harnessing the energy from a fusion reactor. In addition, for D-T fusion to be viable, a stable supply of tritium needs to be developed in a cost-effective manner. These technological problems must be addressed before fusion reactors can feasibly use the deuterium in water as an energy source for the world.
© Ryan Przybocki. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
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