How do you trigger fusion reactions in large numbers? You have to be able to confine a sufficiently dense and hot plasma efficiently enough. Why do we do this? We explain below …
As in the example of a cooking pot, the plasma’s energy balance is determined by the energy sources that feed the plasma and the energy losses that cool it. For the plasma to be stationary (i.e. not change over time), this balance must be balanced, i.e. the sources must compensate for the losses.
- Energy sources : Pfusion and Pexternal
Fusion power : Pfusion :
The total power produced by the D-T Pfusion fusion reaction is divided between the products of the reaction, the alpha particles, i.e. the helium nuclei (He), and the neutrons.
This gives :
Pfusion = Palpha + Pneut
Neutrons carry away around 80% of the energy, while the heavier alpha particles retain around 20%. But this energy does not end up in the same place :
- Palpha: the main source of energy for the plasma comes from alpha particles. These charged particles are confined by the tokamak’s magnetic field and give off their energy to the plasma through collisions.
- Pneut: in contrast, the neutrons (n) produced by the fusion reaction are not sensitive to the magnetic field because they have no charge, so they escape quickly, without having had time to give up their energy to the plasma. They are stopped in the materials of the components surrounding the tokamak’s vacuum chamber.
External power Pexternal :
If the energy from the fusion reactions is not sufficient to compensate for the losses, the plasma must be maintained by supplying energy from outside, using an additional heating system. This is the external power : Pexternal
- Energy losses : Plosses
The confinement of the plasma by the magnetic field is not perfect: particles and heat diffuse outwards from the centre of the discharge. The losses associated with this transport of particles and heat are considerable.
Like a hot body, plasma also cools by radiation in a variety of ways. The electrons emit braking radiation as they are slowed down by the ions (‘Bremsstrahlung’). They also emit synchrotron radiation due to their gyration around the field lines, which can become significant when the plasma is heated to very high temperatures. Finally, the impurities emitted by the wall surrounding the vacuum chamber produce line radiation during the various atomic physics processes that take place in the plasma. This term can become very significant if the discharge is heavily polluted, and can even lead to a sudden loss of plasma confinement: this is known as a disruption.
The sum of all these terms gives the total power lost by the plasma Plosses
- Balance sheet
The time variation in plasma energy W can therefore be written as : dW/dt = Palpha + Pexternal – Plosses
Remember: only alpha particles give up their energy to the plasma, the rest of the fusion power is dissipated in the components surrounding the plasma.
If the source term is greater than the loss term (dW/dt >0), the plasma gains energy, otherwise (dW/dt < 0) it loses energy. If the sources compensate exactly for the losses (dW/dt =0), the plasma is stationary. From this, we can define several useful quantities.
- Energy confinement time tE
This is the characteristic decay time of the plasma’s energy, in other words, the time it takes for the plasma to empty itself of its energy content if the sources feeding it are suddenly cut off. So we have :
W/ tE= Plosses
NB: this time has nothing to do with the duration of the discharge, which is determined by the capacities of the machine’s magnetic system or the instabilities of the plasma. At Tore Supra, for example, the energy confinement time is of the order of 200 milliseconds (or 0.2 seconds), whereas the discharges last several tens of seconds or even minutes.
- The amplification factor Q
This is the ratio between the power generated by the fusion reactions and the external power supplied to the plasma by the heating systems :
Q = Pfusion / Pexternal
This figure describes the energy balance of the plasma: if it is greater than 1, it means that more energy was produced by the fusion reactions than had to be supplied to maintain the plasma.
NB : le facteur Q ne doit pas être confondu avec le rendement global de l’installation.
- The Break-even
This is the stage corresponding to Q = 1, i.e. the point at which the amount of energy produced by the fusion reactions is equal to that required to maintain the plasma. ( Pfusion= Pexternal). This is an interesting step from a scientific point of view, because the plasma is heated to a significant extent by alpha particles and not just by additional heating, which is closer to the situation in the reactor.
- Ignition
This is the stage when the power supplied by the fusion reactions alone is sufficient to compensate for the losses ( Palpha= Plosses ) where the external power can be cut off. This corresponds to an infinite amplification factor Q ( Pexternal = 0). The plasma is then self-sustaining, like the candle which, once ignited by the match (the external power), burns itself out.
Most of the current experimental machines, designed for research and not yet for electricity production, operate at Q<1, meaning that the plasma consumes more energy than it supplies. They use only deuterium as fuel, which means that the necessary physics studies can be carried out without using radioactive tritium, and the results obtained in D-D fusion can then be extrapolated to D-T fusion. Only 2 machines have so far experimented with tritium: the American TFTR machine, now closed, and the European JET machine, which holds the world record for D-T fusion power, with 16 MegaWatts produced, corresponding to an amplification factor of 0.64.