Let’s translate the plasma energy balance in terms of the plasma’s physical parameters: this is Lawson’s criterion. The three keys to the success of a fusion machine derive from this: confinement efficiency, plasma density and temperature.
Let’s go back to our energy balance. At steady state (dW/dt = 0), we have :
Palpha + Pexternal = Plosses = W/ tE
By replacing Pexternal by Pfusion /Q and using the fact that the plasma energy W and the fusion power Pfusion depend on the density n (i.e. the number of particles per unit volume) and the temperature T of the plasma, we obtain a relationship expressing the constraints on the plasma parameters (density, temperature and energy confinement time) if we want to obtain a discharge with a given amplification factor Q. This is known as the Lawson criterion, which gives the value of the product of plasma density multiplied by the energy confinement time tE at a plasma temperature T to achieve an amplification factor Q. Would you like to see a demonstration? Click here.
In practice, for interesting conditions for a reactor, we obtain :
n T tE > 1021 (keV m-3 s) with T of the order of 10 à 20 keV
In other words, to be able to produce energy from fusion reactions, we need to be able to confine them effectively ( tE, not to be confused once again with the duration of the discharge) sufficiently hot plasma (T) and sufficiently dense (n) * .
* NB: in what follows, we focus on fusion by magnetic confinement, which works with relatively low densities while striving to achieve long confinement times. There is another method, inertial confinement (bombardment of a solid target of deuterium and tritium by very intense laser beams or particles), which works with very high densities (material compressed by the laser or particle beams) and very short times.
The difficulty lies in obtaining all three parameters simultaneously. For example, when the density n is increased by injecting gas into the machine or the temperature T by coupling additional power to the plasma, the confinement (tE) of a tokamak tends to deteriorate.
In a tokamak, the achievable plasma densities, i.e. the number of particles per unit volume, are of the order of some 1020 per cubic metre (m–3): this is in fact very low, much lower than the density of the air that surrounds us, for example, and corresponds to conditions close to those of a vacuum. We can’t go much further than this, because instabilities will arise if we exceed a density threshold, with the pressure exerted by the plasma becoming greater than that of the magnetic field. Efforts are therefore focused on the confinement time tE, which we are trying to extend beyond one second by developing complex physics scenarios (the performance achieved at the moment is barely more than 0.8 seconds).
Progress in fusion research is illustrated by the increase in the triple product n TtE, shown in the figure opposite, which has increased by three orders of magnitude from the first experiments in the late 1960s to today’s largest machines (such as JET in Europe, TFTR in the United States and JT60U in Japan), which are approaching the break-even zone. All that remains to be gained is a factor of 10 to enter the realm of the reactor.
The next-generation machine, ITER, designed to demonstrate the scientific and technical feasibility of controlled thermonuclear fusion, is designed to achieve an amplification factor of 10, and may even reach ignition in certain physics scenarios. This major international project, launched at the end of the 1980s and initially involving four partners (Europe, Japan, the United States and Russia), has entered the final design phase. Now involving three partners (Europe, Japan and Russia), it is awaiting the construction decision, in particular the choice of a site for one of the partners. Studies are underway to assess Cadarache’s potential as a candidate European site.
It should be noted that the future reactor does not need to be ignited (infinite Q factor) in order to operate, but simply to reach a sufficient Q factor so that the overall efficiency of the reactor can be increased ηreacteur of the plant is attractive, taking into account the conversion of thermal energy into electricity by conventional means (turbine etc) and the fact that part of the energy produced is reused to power the additional heating systems used to maintain the plasma.
Typical figures for a reactor are an amplification factor of the order of a few tens, corresponding to an overall ηreactor efficiency of 35 % and a fraction of plasma heating by Fα alphas of 90% (i.e. 10% of the remaining heating is provided by additional heating systems).