When atomic nuclei are fused, in what form is usable heat produced?
Recently I found out I was wrong about a pretty fundamental part of nuclear fission - the radiation produced in the fission reaction is relatively small compared to the kinetic energy of the daughter nuclei flying apart at 1/3rd the speed of light (because they both carry such big positive charges). The nuclei fly into surrounding materials and convert that energy into intense heat, which can cause secondary radiation emission.
So I wanted to dig into the corresponding process for nuclear fusion, and couldn’t figure out what’s going on. Some neutrons are released, but there aren’t any daughter nuclei to fly apart like in fission. So how is all that energy being generated?
Fission doesn’t have remotely near enough energy to send the daughter nuclei flying apart at 1/3 c, and energetic reactions that release multiple particles usually dump most of the energy into the lightest particles (in this case, neutrons and gamma rays), for reasons of momentum.
According to Wikipedia, I am correct that the bulk of energy released by fission comes from kinetic energy of separating nuclear fragments. Gamma and other particles are only a small contribution to the energy output. The output of fission is about 200 MeV, and of that, 170MeV comes from the energy of the daughter nuclei separating at a velocity of about 3% the speed of light (I misstated this as 1/3rd, but it’s still in relativistic territory).
But having set that straight, what is the corresponding balance for fusion? I can’t find anything on that (or at least not in terms that I can readily interpret). I understand it has to be exothermic because the resulting mass is less than the inputs, but I don’t understand the form of the energy output.
In all energy-positive nuclear fusion reactions, two or more products are produced as the result of the “release” of binding energy in the reaction, which is realized as kinetic energy of the products. For instance, in the deuterium-tritium (D-T) reaction, ionized isotopes of 2H and 3H are fused, producing an alpha particle (ionized 4He) with 3.52 MeV and a neutron (n0) with 14.06 MeV. Note that the alpha particle has almost exactly 1/4 the energy of the neutron because of conservation of momentum (the alpha particle, with two protons and two electrons, masses just slightly less than four times the individual neutron because a proton has just slightly less mass than a neutron.) Because none of the resultant products are charged the only way to directly recover that energy is through thermalization, i.e. the particles have to transfer some momentum to other particles in the surrounding medium, thus “heating” them. (The neutron could be used to “breed” fissile or fissionable materials or even initiate fission reactions in a subcritical fission-fusion reactor, but that involves more reactions beyond the initial fusion event.)
D-T reactions are the focus of most attempts at nuclear fusion power production because it has the lowest triple product and Lawson criterion, and highest power density condition, and also has the highest yield of any common fusion reaction, but the neutronicity is an issue because neutrons damage all common structural materials and will activate many substances, making them radioactive. Aneutronic reactions (those that produce essentially no neutrons) would be more ideal because most of the products are charged particles from which kinetic energy can be converted directly into electricity via electrostatic grids or some other means of charge interaction. This is why there is so much enthusiasm about obtaining and using Helium-3 in D-3He reactions, and to a lesser extent proton-11Boron (p+-11 B) reactions because there is a very low probability of neutron production. (Proton-proton (p-p) chain fusion that powers the Sun and most stars on the H-R main sequence phase is also aneutronic but has extremely lower power density and requires confinement conditions that can only be achieved by enormous mass, and so are not a practical consideration for terrestrial power generation.) However, the power requirements and criteria for these reactions are much higher than D-T fusion and power density is a couple of orders of magnitude lower, so if you want a reasonably compact source of controlled, energy-positive nuclear fusion D-T is essentially your bag.
As for the essential question of the o.p. regarding how the energy is being generated, when fusion occurs the fuels ‘lose’ potential energy in the form of being bound together; even though it requires enormous pressure and temperature to oppose the electrostatically repulsive Coulomb forces of the protons in order to bring them together close enough for the strong attraction to bind them together, once they are bound together they release even more energy because of the deficit. This is analogous to the gravitational potential energy “released” when a meteor from space falls to Earth. The resulting reaction produces energy in the form of momentum of the products as described above. The specific details depend upon the reaction and the mechanisms applied to achieve conditions for nuclear fusion.
This is probably beyond the scope of your question but there is there is a good, relatively inexpensive reference for an introductory explanation for nuclear fusion power generation: Principles of Fusion Energy. You can find explanations for p-p, helium burning, and CNO fusion in any introductory text on stellar astrophysics but be prepared for a lot of math.
I think this is the specific nugget I was looking for. So… the products end up with a lot of kinetic energy. I’m not clear what happens to a particle that suddenly gains a lot of kinetic energy, but not in any particular direction? It’s vibrating a lot, or does it just accelerate in some random direction?
It does have a particular direction. What that direction is is random, but it goes zipping off in some direction or other (with the other product(s) in the opposite direction, to conserve momentum).
The statistical energy threshold for fast neutrons in reactor physics (assuming 235U fission) is about 3 MeV. That is a velocity of about 0.08 c relative to the reaction reference frame. I think about the maximum kinetic energy of neutrons released in normal fission is about 10 MeV, which would have a corresponding speed of about 0.15 c. Neutrons above 20 MeV are classified as relativistic neutrons but the only natural sources of these are neutrons accelerated by gravitational phenomena, e.g. a rotating black hole or neutron star, or just being emitted from a source moving at relativistic velocity relative to the observer’s reference frame.
The particle does have a specific velocity. Exactly how much momentum gets transferred to a particle depends on the relative masses of the products and the directions they go off in because overall momentum has to be conserved, but because the neutrons are much lighter than other nuclear fission reaction products so they get the highest speeds. All particles are “vibrating” (i.e. are harmonic isolators) in a quantum mechanics sense, but they aren’t literally shaking up and down in the sense of mechanical vibration; when we refer to the kinetic energy of the particle you can essentially treat it as you would with a macroscopic object like a cue ball. The direction that the neutrons are released in isn’t exactly random (at least, in the case of an induced fission by a thermal neutron) but it is close enough that you may as well consider it to be so as you can generally ignore the momentum that the inciting neutron brings into the reaction.
Remember you need to generate steam, and it’s not like you can pipe water into the plasma. In DT fusion, the bulk of the energy conveniently leaves via neutrons that can be captured with a lithium blanket. Implementation of which is still a work in progress.
This also regenerates tritium. In theory.