Nuclear fusion is often seen as the “Holy Grail” of power generation and rocketry. It powers stars and our most powerful weapons, and is ~4X more energy dense than even mighty fission. Fusion is much harder to make occur than fission though, and the choice of fusion fuel has massive implications on both the utility of fusion for a given application and the difficulty of ignition. We will walk through some of the commonly considered fusion reactions and their pros and cons for power generation and propulsion, as well as their difficulty in ignition. Fusion ignition is when a self-sustaining fusion chain reaction occurs. It is a rather fuzzy term that is dependent on the exact fusion reactor scheme in question, but is a widely considered a prerequisite for the successful utilization of nuclear fusion for propulsion or power generation. There are some fringe reactor schemes that may be able to generate usable power or thrust without technically reaching ignition, but we will ignore those for this discussion.

A couple important things to remember about fusion. Unlike nuclear fission, nuclear fusion requires incredible temperatures (on the order of millions of degrees Kelvin minimum) to occur. When matter gets this hot it becomes plasma, the 4th state of matter where the electrons become free of their host atom. You also need to keep this extremely hot fuel close together for some period of time so that a chain reaction can take place. This makes for one complicated method of extracting energy because no material known to man can hold hot plasma without melting, and without quenching the fusion reaction. Thus we need to either pulse the reactors very quickly and use no containment (called inertial fusion), utilize magnetic fields to try and hold the plasma (called magnetic fusion) or some combination of the two concepts (called magneto-inertial). Nature gets to cheat using gravity to contain plasma in stars, but that is not an option we currently have.

Proton-Proton Fusion

Proton-proton fusion is arguably the most important reaction in the universe. It is the primary power source in our sun and billions of other stars and uses normal hydrogen (called protium) as fuel. The proton-proton chain actually involves 6 protons before it is over and relies on very rare nuclear reactions to run to completion. This is part of why you won’t see terrestrial fusion reactors trying to use proton-proton fusion for power. The first step has two protons coming together and undergoing fusion to become 2He. Usually this 2He nucleus promptly breaks apart and goes back to being two protons, but every now and then it undergoes a rapid positive beta decay (emission of a positron and neutrino) to become a heavier isotope of hydrogen known as deuterium.

Proton-Proton Fusion Chain Reaction (Sarang, Public domain, via Wikimedia Commons)

Now that deuterium will then undergo fusion with another proton and become 3He. This exact chain has to happen twice so we end up with two 3He nuclei that can then undergo fusion and become 6Be. The 6Be nucleus then ejects two protons and we are left with stable 4He and a net gain of 26.73 MeV (0.59 MeV of which is in neutrinos), a 4He ion and 2 positrons while only consuming 4 protons. There are a couple of branches for how this reaction can play out but the same general story applies each time.

At first glance this makes the proton-proton chain look like the most ideal nuclear fuel possible. There are no neutrons emitted, no gammas (aside from 0.511 keV photons from the positrons annihilating later), and the fuel is the most common thing in the universe! It also has a staggering energy density of ~640 TJ/kg compared to the ~82 TJ/kg of fission or even the ~337 TJ/kg of DT fusion. As with all things that seem to be too good to be true though, there is a catch. Proton-proton fusion is the least reactive fusion fuel out there and has a truly anemic reaction rate due to that highly improbable deuteron generation event that is needed to kick the whole thing off. Even in the core of our sun, the reaction rate is so low that a human body generates roughly the same amount of heat per unit volume as the core of the sun. This makes for a horrible rocket fuel or terrestrial power plant, especially when you consider how hard it is to make fusion happen in the first place! There seems to be little hope of directly using the proton-proton fusion chain. Some early ideas about fusion propulsion posited that the proton-proton chain could be used, but further understanding of the reaction seems to have quashed that.

CNO Fusion

The CNO (Carbon-Nitrogen-Oxygen) cycle is a fusion reaction that is theorized to be more dominant in stars larger than ours, but we do know it plays some minor role in our own star. CNO is very unique in that it is a catalytic cycle, which means the carbons, nitrogens and oxygens are catalysts that aren not consumed but just help make the reaction happen more easily. In this case protons are fused with 12C to start the chain off, making 13N. The 13N beta decays into 13C and then undergoes another fusion reaction with a proton making 14N. The 14N undergoes yet another fusion reaction with a proton, making 15O which quickly beta decays into 15N. The 15N then undergoes another proton fusion reaction and becomes 16N, which quickly alpha decays into 12C to start the cycle anew. Thus 4 protons are consumed to make a single 4He ion, two positrons, and some neutrinos and gamma rays. There are some other CNO chains that have a different set of reactions, but the broad idea is always the same.

CNO Fusion Chain (Borb, Public domain, via Wikimedia Commons)

CNO fusion is intriguing because it still utilizes the most common fuel in the universe (protons) and has similar energy release as the proton-proton chain (24.7-26.7 MeV depending on the specifics of the cycle). In addition, the probability of a CNO reaction chain (called the cross section) is 15 to 21 orders of magnitude higher than the proton-proton chain depending on the temperature of the fuel! It is still orders of magnitude lower than the worst fuels considered for use in current fusion reactors though, so we won’t see CNO burning reactors anytime soon. Still, there may be some possibility of using this reaction far into the future and for very large reactors.

Deuterium-Tritium Fusion

Deuterium-Tritium reaction diagram By Wykis - This file was derived from: D-t-fusion.png:, Public Domain, https://commons.wikimedia.org/w/index.php?curid=2069575

Deuterium-tritium (called DT) fusion is the reaction most commonly considered for near term use in fusion reactors. It utilizes two heavy isotopes of hydrogen, one of which (tritium) is radioactive and has a half-life of ~12 years. DT has the highest probability of reaction (called cross section) at the lowest temperatures though, so if any fusion reactor will work in the near term it will most likely have to use DT. The cross section peaks at 5 barns, which is in the same range as fast fission reactions and this peak occurs at a “cold” temperature of ~7e8 Kelvin (or in plasma physics 64 keV). The next closest comparable fusion reaction has a cross section of 1/5th that at almost 10X the temperature! DT is also one of only two fusion reactions that has been successfully ignited, although only in nuclear weapons.

Unlike the previous two reactions, DT undergoes a very simple fusion reaction with no complex chains. Upon fusion an alpha particle and neutron are emitted, with the very rare case sometimes emitting a gamma ray. The 3.5 MeV alpha particle hopefully goes and heats up more fusion fuel allowing for further reactions, while the 14.1 MeV neutron (compare this to the 1-2 MeV neutrons from fission) goes flying free to bombard the reactor. Neutron degradation of components is a major concern for future fusion reactors and rockets, but this energetic neutron also provides a method of getting more tritium. If the reactor has a blanket of lithium (or lithium lead to make even more neutrons for better breeding) the neutron can be absorbed into lithium and induce a fission reaction that generates an alpha particle and a tritium ion plus some extra energy in the case of 6Li. If an 7Li nucleus is struck it absorbs some of the neutron’s energy instead but does make another neutron to continue breeding tritium. Careful understanding of the breeding ratios is crucial for future DT fusion reactors and for nuclear weapons. The Castle Bravo nuclear weapons test quite famously had significantly more yield due to a misunderstanding of tritium breeding in the core of the weapon.

DT fusion rocket designs often have significant advantages in energy density even when accounting for the complexities of 14.1 MeV neutrons. The much lower ignition conditions allow for smaller reactors that need less shielding and machinery on the whole. DT fuel also allows for the potential of spin polarization which can lower the neutron load on the ship and lower the ignition conditions even further.

Deuterium-Deuterium

Deuterium-Deuterium (DD) fusion is commonly considered an “advanced” fusion fuel that will be strived for after DT is mastered. DD fusion carries a couple advantages over DT fusion but comes at the cost of being ~30X harder to ignite depending on the scheme, although there are DD/DT spark plug concepts that may allow for lower ignition conditions at minimal extra cost. Unlike DT, DD fusion has two possible reaction paths with each having a ~50% probability of happening. It can emit a 1.01 MeV triton (T) and 3.02 MeV proton or a 0.82 MeV helion (3He) and a 2.45 MeV neutron. The triton is essentially always consumed due to the much higher DT fusion cross section. This ends up making DD fusion roughly 60% neutrons in energy vs 80% for pure DT fusion.

The biggest advantage to using DD fuel is the abundance of deuterium. Deuterium makes up 0.0115% of all hydrogen on Earth and occurs in even higher percentages throughout the solar system. The sheer amount of fuel available makes it a truly inexhaustible resource that can be found anywhere. This is very appealing for far future space applications that rely on insuti resource utilization. DD fusion is also unique in that it is the only other fusion reaction to have been ignited. The Ivy Mike hydrogen bomb utilized liquid deuterium as its fusion fuel of choice.

Deuterium-Helium3

Possibly the most famous spaceship fusion fuel is deuterium-helium3 (D3He). It utilizes deuterium and an isotope of helium (3He) that is rare on Earth but relatively common in the gas giant planets. Some claims have been made about mining 3He from the lunar surface, but this would prove to be exceedingly difficult at the low concentrations present. In the rest of the solar system 3He makes up roughly 0.001% of helium on average and could potentially be a source in the future. 3He is also the decay product of tritium and is made during DD fusion so in principle it can be bred.

The largest appeal of D3He fusion is that the primary reaction does not produce neutrons. A D3He fusion reaction makes a 3.6 MeV alpha particle and a 14.7 MeV proton, thus all reactants are directly usable for propulsion or direct electricity production. This is not the only reaction that occurs though, as the conditions for D3He ignition are not far from those of DD ignition. Thus there are DD side reactions (and then DT tertiary reactions) that turn this “aneutronic” fusion reaction into a neutronic one. Estimates vary based on exact fuel ratios but ~5% of the fusion energy coming out as neutrons is a safe estimate. DHe3 is estimated to be only 16X more difficult to ignite than DT, making it a compelling advanced fusion fuel for fusion propulsion but fuel supply concerns may limit its use.

Proton-Boron11

Proton-boron11 (p11B) fusion is probably the most contentious reaction in the fusion community for a couple of reasons. This reaction is often claimed to be the “Holy Grail” of fusion energy due to the supposed aneutronicity and use of common fuels. Of course the reality of the situation is a bit more complicated.

The fusion reaction starts by forming a highly excited 12C nucleus. This 12C nucleus then undergoes what could easily be called fission into three alpha particles and releases 8.7 MeV of kinetic energy and a 719 keV gamma ray. Interestingly enough though, p11B is slightly less energy dense than fission at 69.7 TJ/kg. This reaction requires exceedingly high temperatures to reach and has two cross section peaks at ~150 keV and ~600 KeV, which is significantly above the required temperatures for DT. The highest cross section (at roughly 600 keV temperature) is roughly 1 barn, which is higher than any fuel other than DT! Seeing these numbers the appeal of the fuel is quite apparent.

The difficulty in reaching ignition is what makes p11B so controversial though. For a traditional thermonuclear reaction, where the electrons and ions are in thermal equilibrium (i.e. the same temperature), the fuel cools off via x-ray emission from the electrons as   assuming the x-rays are not reabsorbed into the plasma. This is very bad for p11B which will have a Zeff 5/2 higher than DT and a T ~2.5X higher than DT AT BEST. Several studies have shown that p11B can not undergo a traditional fusion burn unless a scheme can be constructed that somehow absorbs the extremely energetic x-rays (typically ⅓ of plasma temperature in energy) very efficiently. There are non-thermal schemes to attempt to burn p11B fuel that may provide some hope, but these are considered rather fringe within the fusion community. There have been some tantalizing hints at ways to do this, but nothing concrete enough to bet on yet.

An additional controversy is the claim of aneutronicity, which sometimes translates into people claiming that zero shielding is needed. The reaction produces energetic gamma rays and x-rays directly and neutrons via secondary reactions, so shielding will still be needed. The neutronicity is estimated to be 0.1% which is much lower than all other fusion fuels, but not negligible at high power levels. If p11B fusion can be made to work at a reasonable scale and efficiency it could provide a compelling method of propulsion and energy generation, but the problems to be solved are non trivial.

References and Further Reading

  1. Atzeni, S., & Meyer-ter-Vehn, J. (2009). The physics of inertial fusion: Beam plasma interaction, hydrodynamics, hot dense matter. Oxford, U.K.: Oxford University Press.
  2. Castle Bravo. (n.d.). Retrieved February 12, 2021, from http://large.stanford.edu/courses/2017/ph241/liang2/
  3. Cno cycle. (2021, January 20). Retrieved February 12, 2021, from https://en.wikipedia.org/wiki/CNO_cycle
  4. Experimental evidence of neutrinos produced in the CNO Fusion cycle in the sun. (2020, November 25). Retrieved February 12, 2021, from https://www.nature.com/articles/s41586-020-2934-0
  5. Gilster, P. (2020, October 24). The interstellar ramjet at 60. Retrieved February 12, 2021, from https://www.centauri-dreams.org/2020/04/03/the-interstellar-ramjet-at-60/
  6. Hora, H., Eliezer, S., Nissim, N., & Lalousis, P. (2017). Non-thermal laser driven plasma-blocks for proton boron avalanche fusion as direct drive option. Matter and Radiation at Extremes, 2(4), 177-189. doi:10.1016/j.mre.2017.05.001
  7. Ivy Mike, 1 November 1952 – first full-scale THERMONUCLEAR test. (n.d.). Retrieved February 12, 2021, from https://www.ctbto.org/specials/testing-times/1-november-1952-ivy-mike
  8. Proton–proton chain reaction. (2021, January 26). Retrieved February 12, 2021, from https://en.wikipedia.org/wiki/Proton%E2%80%93proton_chain_reaction
  9. Hare, J. (2019, June 05). New calculations show proton-boron fusion is still difficult. Retrieved February 25, 2021, from http://fusionandthings.eu/2019/06/05/new-calculations-show-proton-boron-fusion-is-still-difficult/

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