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In a tokamak reactor (toroidal, magnetic confinement chamber), the most common reaction is fusion of Deuterium and Tritium, leading to a production of an alpha particle and neutron with ~3.5 Mev and ~14.1 MeV respectively. As I understand it, ideally the Deuterium and Tritium ions are magnetically confined to rotate around the toroid via magnetic field lines. Every so often they will have enough energy (1-100 keV) for this fusion reaction to occur.

When the Deuterium and Tritium fuse it seems to me that the alpha particle and neutron will fly off in opposite but random directions relative to the center of mass frame. The problem I have with this is that the alpha particle is supposed to heat up the Deuterium-Tritium fuel, leading to a self-sustaining fusion reaction. If the alpha particles are just as likely to speed the D-T fuel up as they are to slow them down, how can the alpha particles be expected to heat up the plasma?

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You state :

When the Deuterium and Tritium fuse it seems to me that the alpha particle and neutron will fly off in opposite but random directions relative to the center of mass frame.

Right, but the whole construct of the Tokamak magnetic field design is aimed at keeping charged particles in the plasma . Alpha particles will be confined in the plasma and statistically add to the kinetic energy/heat of the whole. The neutron kinetic energy as a neutral particle will be absorbed in the wall of the container and add to its heat and the eventual heat energy used to make steam.

Here is an early paper reviewing the modeling of alpha particles in the Tokamak. It seems that theory describes the experimental measurements.

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When the Deuterium and Tritium fuse it seems to me that the alpha particle and neutron will fly off in opposite but random directions relative to the center of mass frame.

Indeed, but remember that these are effectively random, and not necessarily opposite, directions in the lab frame.

The problem I have with this is that the alpha particle is supposed to heat up the Deuterium-Tritium fuel, leading to a self-sustaining fusion reaction.

The randomness in the lab frame causes, on average, a heating of the plasma particles. Rather than thinking about the way momentum is transferred (i.e. particles are deflected in one direction or another), it might be more useful to think about the way energy is transferred and that it goes from the alpha particles to the DT plasma soup.

If the alpha particles are just as likely to speed the D-T fuel up as they are to slow them down, how can the alpha particles be expected to heat up the plasma?

Speeding up the D-T fuel would mean shifting its distribution to the right (+v axis).

That is, if you had a Maxwell-Boltzmann distribution of particles with a mean velocity of $v=1$, it is given by $f(v) \propto \exp(-(v-1)^2)$. If you were to speed that up, it would look like $f \propto \exp(-(v-2)^2)$

Heating something means broadening its distribution in phase space.

In that case, $f$ looks more like $f \exp (-0.25(v-1)^2)$. Notice how this function has the same average velocity but falls off half as fast as $|v|$ is large.

Alpha particle heating results in the latter, rather than the former. So the alpha particle heating results in more, faster, D-T fuel particles that occupy the sweet spot for D-T reactions. That's how you get to the self-sustaining reaction

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