Year of Engineering: Injecting Relativity into Engineering

Albert Einstein published the theory of special relativity in 1905

There are many areas where science and engineering work together, but relativity rarely makes an appearance. Most of our daily challenges can be solved by using simpler classical mechanics, where we (correctly) assume that objects travel at speeds which are a minute fraction of the speed of light, and weigh many times less than planets or stars. However, two engineering applications used every day at Diamond involve conditions which breach those assumptions, and so they must enter the strange world of relativity.

If you mention Einstein’s theory of relativity to a physicist, they will tell you how it provides a more accurate solution to any classical mechanics problem - but often with a lot more work involved! Inside Diamond’s linac and booster accelerators, the presence of relativistic effects instead allows for some clever engineering solutions which simplify the difficult task of controlling the movement of five billion electrons.

The theory of relativity is divided into two main branches: “Special relativity” concerns the movement of objects relative to each other and accounts for effects seen when this movement approaches the speed of light, and “general relativity” covers the effect of gravity and how it warps time and space around very heavy objects. One well-known engineering application of relativity is satellite global positioning systems, which uses general relativity⁺ to predict that the satellite’s precision clocks run 45 microseconds per day faster than those on Earth due to the lower gravity in space. Without this correction, the timing-based positioning would fail within two minutes!

At Diamond, the electrons we accelerate are not heavy like the Earth (they weigh just 9.1 x 10-31 kg!), but they do travel very fast. So fast in fact, that special relativity must be taken into consideration in order to predict their behaviour. Normally, when an electron experiences an electric field, it feels a force which causes it to accelerate and change velocity. However, special relativity tells us that as the speed of the electron approaches the speed of light, more of the extra energy it gains from the acceleration is stored as increased mass and less is used to increase the speed of the particle.

The linac, with the gun at the far end and the accelerating structures coming towards us. The electrons are already more than 0.95 times the speed of light by the time they emerge from the copper rings at the back.

Inside the Diamond linac, electrons are already at 0.95 times the speed of light before they enter the two main copper accelerating cavities, which means that during the rest of their acceleration in the linac and booster they will actually increase very little in speed, but a lot in mass! This effect is very useful for the radio frequency cavities used to provide the acceleration.

Because these cavities use a periodic structure which the electron passes through at specific times, the fact that the speed remains similar throughout the acceleration means that the cells in the structure are all the same length and can therefore be designed and manufactured as the same part. This reduces the cost of manufacture and removes a possible source of error in the design.

The booster uses a different design of cavity with far fewer cells, but the electrons pass through it 189,000 times before leaving for the storage ring. As they increase in energy, the relatively constant speed means that the frequency of the 60 kW radio waves we feed into the cavity can remain constant, and only the magnetic field must increase with energy in order to account for the increased mass due to special relativity and keep them in their fixed orbit. This makes the radio systems much easier and cheaper to implement. Thanks Einstein!

⁺ In fact, GPS calculations also include special relativity - because the satellites are travelling so fast relative to an Earth observer, their clocks also appear 7 microseconds slower!