In 1955, John D. Lawson was the first person to systematically derive criteria for a useful thermonuclear reactor. His idea, the famous Lawson Criterion, was so effective that it is still used to determine the progress towards fusion.

Merging nuclei

The goal of fusion research is clear: merging nuclei in order to release a desired amount of energy. However, the realisation of a reactor for electricity production based on the Lawson criteria, must satisfy severe physical and technological constraints. As an engineer, Lawson was able to reduce the complexity of this problem, defining the concrete milestones needed to realise a power plant that uses hydrogen plasma as fuel.

John D. Lawson, Picture: RAL

John D. Lawson, Picture: RAL

Reaching ignition

Lawson started from fundamental physical principles. In order to maintain a constant temperature of the plasma, thus avoiding the shutdown of the fusion reaction, the fusion-generated power should at least compensate the energy losses to the environment. When no energy must be introduced from the outside by way of reactor heating systems, a condition called “ignition” is reached: the reaction is self-sustained just as a wood fire, which does not require a constant supply of external sparks, but just keeps burning and remains hot as long as there are reactants.

A famous triple

From the plasma energy balance, the famous triple product of density (n), temperature (T) and confinement time E) can be derived mathematically. This figure of merit summarises the multiphysics problem of nuclear fusion in a simple inequality, defining the condition for ignition as nTτ E > ƒ(T) where the term on the right hand side is a function of the temperature.

The more, the merrier

The particles’ density must be high enough to facilitate the fusion reaction. In the plasma, an ionised hot gas, hydrogen nuclei, move along their trajectories until they collide with each other. Increasing the number of particles in a given volume makes collisions more probable and fusion reactions more frequent, getting closer to ignition.

Not too hot, please!

Temperature, which is just another way to describe the velocity of the particles, plays a dual role. Collisions between charged nuclei should only happen at sufficiently high speed. This enables the long-range electrostatic repulsion to be overcome and brings them close enough to let the short-range strong nuclear force, responsible for fusion, prevail. However, as the temperature increases, the speed of particles is so high that the duration of interaction between colliding nuclei is too brief for fusion to happen. These facts point to an optimum temperature for ignition.

Think big

The confinement time is a measure of the time in which hot plasma approaches the environment temperature. Imagine a hot metal sphere in a pool of cool water: the larger its radius, the longer the time required to reach the temperature of the water. In the same way, in magnetic fusion, the size of the plasma chamber determines the confinement quality to keep particles hot and this has motivated the design of larger and larger machines.

Creating the sun in a bottle

The next step of the quest to create “a Sun in a bottle” is the implementation of ITER with a confinement time of around one second, a tenfold increase over existing fusion experiments. The optimum temperature for the triple product is above 150 million degrees K, astonishingly ten times hotter than the Sun’s core. Luckily, the density needed to satisfy the triple product is much lower than air density on Earth, making at least this one goal easier to achieve on the way to realising fusion energy.

profile-pic-federico-pesamosca
I am a Nuclear Engineer and I am doing a PhD in the magnetic control of tokamak plasmas at the Swiss Plasma Center in Lausanne (CH). Along with technical and theoretical challenges, I consider science journalism fundamental for fusion due to its ability to share ideas and inspire more people to join this research: I am enthusiastic about making my contribution to this issue.

Federico Pesamosca (25) from Italy is currently based at Eindhoven, NL.  (Picture: private)