A particle accelerator is a machine that produces beams of tiny sub-atomic particles travelling at very high speeds.

Particle accelerators come in various shapes and sizes depending on the particle energy and their practical purpose, from van-sized accelerators used for cargo scanning, to kilometre-long linear accelerators like the Stanford Linear Accelerator, and the 27 kilometres-long ring of the Large Hadron Collider. Their size and overall design depends on the type of particles that are accelerated (typically electrons or protons) and the energy they reach.

Structure of matter​

Matter is made up of atoms, and atoms are made up of three types of particles: protons, neutrons and electrons.

• Protons weigh approximately 1.67x10-27 kilos, that is, 0.000,000,000,000,000,000,000,000,001,67 kilos, and have a positive electric charge of 1.6x10-19 coulombs.

• Neutrons have similar mass to protons but have no electric charge.

• Electrons are almost 2000 times lighter than protons and neutrons, and have the same electric charge as the protons but with opposite sign. That means that protons and electrons attract each other.

Protons and neutrons form the nucleus of the atom, which is positively charged. Electrons, which are negatively charged, move around the nucleus forming like a “cloud”.

Particle accelerators take the electrons

or protons from the atoms and accelerate

them to very high speeds.

As electrons and protons have electric charge, they can be attracted or repelled by other electric charges. It is this electric force that accelerates particles.

Charges accumulated in a capacitor create an electric field that can accelerate other charges. The amount of acceleration depends on the intensity of the electric field. Electric field intensities are measured in volts per meter. If we connect a 1 volt battery to two metallic plates separated by 1 meter, then we will have an electric field of 1 volt per meter between the plates.

If we put a charged particle close to one of the plates and let it accelerate in the 1 volt per meter field, it will reach the other plate with an energy of 1 Joule per coulomb (*). The charge of the electron is 1.6x10-19 coulombs, so an electron traveling one meter in an electric field of 1 volt per meter will gain an energy of 1.6x10-19 Joules.

This amount of energy is in fact used by atomic and nuclear physicists as the basic unit of energy, and it is conveniently called electron-volt (eV).

1 eV = 1.6x10-19 Joules

This amount of energy is tiny compared with everyday standards, because the mass of the electron is tiny! To put it into perspective, a flying mosquito (which is much much heavier than an electron) has an energy of approximately 1,000,000,000,000 electron-volts.

An electron with one electron-volt of energy travels at a speed of 593 kilometres per second. When electrons have energies higher than 500,000 eV (which is quite small for modern accelerator standards) their speed start to get close to the speed of light. Then the relationship between the energy and speed of the electrons becomes a little complicated as it needs to consider the equations of Einstein’s theory of relativity. The speed of the particles becomes less meaningful, and that is why physicist prefer to talk in terms of energy.

(*) We have to remove all the air in between the plates, otherwise the particle would collide with the air molecules and never reach the other plate!

1 electron-volt (eV) is the energy acquired by an electron when it is accelerated by an electric potential of 1 Volt

1 keV = 1,000 eV

1 MeV = 1,000,000 eV

1 GeV = 1,000,000,000 eV

1 TeV = 1,000,000,000,000 eV

1 TeV is approximately the energy of a flying mosquito.

The technique described above was used in the early days of accelerators to accelerate particles to a few millions of electron-volts (MeV). These are called electrostatic accelerators. Modern particle accelerators reach energies of many billions of electron-volts, and even trillions.

So, if I connect a trillion-volt battery to the two metallic plates in our electrostatic accelerator, then I will be able to accelerate particles to one trillion electron-volts in just one meter, right?

Not so easy!

It is not possible to put a very large voltage in between two metallic plates before a huge spark destroys the whole setup, unless the two plates are very very far from each other, which is not practical.

There is a maximum value to the voltage that can be applied to the two plates, called breakdown voltage, which depends on the kind of substance that is in between them. In air, the breakdown voltage is approximately 3 megavolts per meter (the exact value depends on factors like the air pressure and humidity). If the pressure is reduced, the breakdown voltage increases significantly.

A particle accelerator must be empty of air, so that the particles do not hit anything as they travel along the accelerator. However, the voltage inside the electrostatic accelerator is limited by breakdown at the power supply, that is the “battery” that supplies voltage to the plates. In practice, this limit is around 10 megavolts. Therefore the maximum achievable energy in an electrostatic accelerator is of the order of a few MeV.

Consider the following setup:

We have set of metallic plates connected to batteries with alternate polarities so that inside each pair of plates there is an electric field with opposite direction to the neighbouring ones.

If we put an electron in between the first pair of plates, it will be accelerated forward as in the previous example. The plot on the right shows the particle energy increasing over time.

As the particle reaches the second plate – a hole on the plate allows the particle to move from one region to the next – the voltage flips and the particle continues to be accelerated:

By switching the charge on the plates in coordination with the particle motion we can cause the particles to always “see” a forward accelerating field and keep gaining energy even though the voltage between the plates is kept at a safe value.

For example, if the plates are separated one meter and the potential between each pair of plates is 1 million volts, at the end of the cavity the particle will have gained 4 MeV. Notice that in order to gain the same energy in an electrostatic accelerator we would have needed 4 million volts! In principle, we could add more stages and the particle would continue to accelerate, with the voltage never exceeding 1 million volts.

What we have inside the system of plates is an oscillating electric field, as opposed to a static one. In particle accelerators the electric field oscillates with frequencies of megahertz to gigahertzs, that is the frequency range of radio waves. For that reason, these structures are called radiofrequency cavities, or rf cavities for short.

Modern radiofrequency cavities have a size of the order of a mater, and can sustain accelerating gradients of a few tens of megavolts per meter. This limit is dictated by the same phenomenon of breakdown described above. Therefore, in order to reach the GeV energies, or higher, that are required in many scientific applications, it is necessary to use many of these cavities one after the other (linear accelerators), or large rings where the particles pass through the same cavities over and over again (circular accelerators). In either case, the more energy we want to obtain from an accelerator, the longer it has to be.

Some particle accelerators have to be hundreds of meters or even several kilometres long in order to achieve the required energy. The table below shows some examples.

A new type of accelerator that uses plasma instead of radiofrequency cavities can sustain acceleration rates that are 1,000 times higher, making it possible to reach high particle energies with much smaller machines.

Particle accelerators are machines that produce beams of high-energy sub-atomic particles, such as electrons and protons. These particle beams can be used in different ways, for example:

• Particle colliders, like the Large Hadron Collider in Geneva (Switzerland). Two beams of particles propagating in opposite directions are made to crash into each other at very high speeds to discover new particles, the properties of known ones, and the fundamental forces of nature.

• Synchrotron light sources, like Diamond near Oxford (UK) or Elettra in Trieste (Italy). Beams of high-energy electrons traveling in circles are used to produce very intense light by a process called synchrotron radiation. The synchrotron light in turn is used to investigate the properties of materials or the structure of biological matter like viruses and proteins.

• Free-electron lasers (FEL). Electron beams can also be made to produce laser-like light when they pass by an especially arranged set of magnets. FELs are more powerful than synchrotrons, and the light they produce can reach much further in our understanding of the structure of matter.

• Radiotherapy machines in hospitals. Beams of electrons produced in a linear accelerator are made to hit a metallic target, producing x-rays in the process. The x-rays are then used to kill cancerous cells. Beams of protons can also be used directly to treat tumours (proton therapy) which presents some advantages over the treatment with x-rays.

There are many other applications of particle accelerators that are used routinely in a diverse range of industry for manufacturing, quality control, food processing, cargo scanning, etc.

A plasma is a fluid of charged particles. Plasma is one of the four states of matter.

You may have been told that matter comes in three states: solid, liquid, and gas. Well, it turns out there is a fourth one: plasma. Even though plasma is not very common on Earth, it is the most abundant state of matter in the Universe. Lightning and electric sparks are plasmas. The sun, and all stars, are giant balls of plasma.

In a solid substance, like ice, the molecules that make up the substance are arranged in a structured manner, binding together to form lattices. If we had heat, the solid melts into a liquid. That means that the molecules don’t form structures anymore but are still loosely bonded through long-range forces. If we add more heat, the liquid ends up evaporating into a gas. In a gas, the molecules move freely, too quickly and too far from each other to stick together. If we keep adding heat the molecules eventually dissociate into their constitutive atoms and, at even higher temperatures, the electrons start to detach from their atoms, becoming a plasma, where negative and positive electric charges are separate from each other.

You can create a plasma by heating up a material to very high temperatures (tens of thousands of degrees Celsius), but you can also create a plasma through an electric discharge. This is the most common way to create plasmas in the laboratory. With an electric discharge in a low density gas you can create a plasma without needing vast amounts of heat. That is the case with fluorescent tubes that are used to illuminate your room and the plasma balls that you may have seen in science fairs.

A plasma ball with filaments extending between the inner and outer spheres.

Another way to generate plasma is by shooting a laser through a gas. The laser light removes the electrons (ionises) the molecules in the gas, creating a plasma state.