Particle Accelerators

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Particle accelerators are an incredibly useful piece of technology and a diverse set of artifacts produced for many purposes. While particle accelerators are often invoked as weapons of war in science fiction, and have captured the public attention as giant research systems the size of cities, they have an incredible widespread range of applications. There are also many, many ways to build a particle accelerator, depending on what effects you need to achieve and what circumstances you work under.

This article aims to be a general primer on particle accelerators, their physics and a selection of technologies and construction styles. In detail, all particle accelerators are high-tech engineering customized to their circumstances in many, many aspects.

Further pages covering application fields are in the work.

Accelerator physics

The simple explanation is that we use electric fields to accelerate charged particles. But from this basic principle of leveraging the electromagnetic forces springs an entire set of accelerator technologies with different performances, trade-offs and characteristics. The most basic particle accelerators are just a big high-voltage source and can still be found in old CRT TV’s and dentist x-ray machines around the world. Things rapidly get more complex from there, but first we need to lay out some terms so we can all have a common conversation.

The first thing to keep in mind with particle accelerators is that we are talking about charged beams here, even if we neutralize them later. So no neutrons, photons, or other innately neutral particles. Your choices range from the simple electron up to anti-uranium and more, but they all must be charged. The particle of choice determines just about everything else about the accelerator and any potential uses. Really heavy particles (like large ions) don’t accelerate easily and take a lot of energy to get relativistic enough for time dilation tricks to take into place. Really light particles (like electrons) accelerate super easily, but can have other radiation problems to worry about.

The second most important thing to know about a given accelerator is the particle energy. This is a measurement of the kinetic energy of any individual electron, ion, whatever in the beam and is measured in a unit called the electron-volt or eV for short. The lower bound for any worthwhile particle accelerator is in the MeV (or million eV) range and we typically want a lot more! Inside of the accelerator we tend to talk about the electric field doing the accelerating (measured in Volts/meter). For singly charged particles (like electrons) this gets really to figure out the energy because of how the eV is defined. We just take the electric field (also called the accelerating gradient) and multiply by the length of the machine! Boom, now you have particle energy! For more complex particles you have to do some scaling based on mass and charge state.

Also a quick trick to help you with deciding if something is relativistic or not is to divide the particle energy by one plus the mass energy of the accelerated particle (0.511 MeV for electrons/positrons and about 1 GeV for a proton). The resulting number is called the Lorentz gamma value and is used all over in accelerator engineering. Once you get above a value of 1, you have relativistic particles. Once that number is in the hundreds you get an ultra-relativistic beam. Figure 1 helps show the relationship between Lorentz gamma and speed of the particle.

The third most important feature of a particle accelerator is the emittance which is just a fancy term for divergence of the beam and can be thought of similar to the wavelength of lasers. No beam is made perfect and they will naturally want to expand outwards. The smaller the emittance, the longer the beam will stay in a tight spot. Emittance can be altered with a wide variety of beam engineering techniques that take entire books to discuss, but one other cheating thing you can do is drive the beam energy higher. This naturally lowers the emittance by a factor of Lorentz gamma due to the cheating effect of special relativity! Thank god for Einstein!

Acceleration forces

Every accelerator tries to build an electric gradient appropriate for the charge of the particles it is accelerating. The greater the electric gradient, the bigger the amount of work that can be done, the more energy is imparted on a particle as it travels through the gradient, and thus the higher the acceleration. The simplest way to build up a gradient is simply two charged electrodes with a strong potential between them. Many other accelerator methods use electromagnetic fields, in the form of waves confined in electrically conductive structures. In this case we exploit that electromagnetic fields have both an electric and a magnetic component. The magnetic component cannot be used to accelerate particles (only bend their trajectory - which can be exploited for effects like deflection or focusing) but as the electromagnetic waves oscillate, so does an electric field. This naturally creates a charge difference across half of the phase of an electromagnetic wave - this electrical gradient can accelerate particles. Both of these technologies encounter problems with the physical materials asked to contain the electric or electromagnetic energy. Eventually the fields get so intense that solid materials get broken down and an arc is formed. As such, various advanced concepts use clouds of charged particles and plasmas, which are not subject to the material limitations of solid matter.

The strong and weak nuclear force as well as gravity (which are all of the forces we know of at the time of writing) are not suitable for accelerating particles. This is related to the power and range of these forces. The strong and weak nuclear force have extremely short ranges - even if we had a means to artificially shape them like with electromagnets, their range would be too short. Gravity has the range but is incredibly weak. To generate a measly 1 G of acceleration, 9.81 m/s², requires the mass-energy of the entire earth, some 5.97e24 kg of mass, to do the job! The acceleration involved in particle accelerators is much, much, much larger (on the order of 10^13 times larger or more).

Interestingly, one source of very high-energy particles are giant gravity wells. Black holes generate conditions around them that can eject particles with enormous energies. The jets of particles that shoot from the north and south poles of many such stellar entities are particle accelerators.

If you want to use a force other than electromagnetism to accelerate particles, it’ll have to be a fictional one. The forcefields of various sci-fi properties could be considered, since they can often apply forces to particles. If you propagate a wave of such forcefields down a tube, you could have something quite a lot like many particle accelerator systems!

The particle bunch

Essentially all high energy particle beams are not constant streams of particles, but a time sequence of discrete groups of particles, commonly referred to as “bunches”. These bunches can be described both in their distribution in lateral space to the traveling direction (x and y axis) and longitude (z axis) along the traveling direction, anchored on an origin point (0,0,0) that moves in time.

Bunches can have various profiles. Generally they are somewhat distributed in the lateral direction just because the charged particles have slightly different starting positions and lateral velocities (also called transverse emittance). In longitudinal space, differing acceleration experienced by individual particles as well as dynamics within the bunch scatter them out, with “noses” and “tails” that contain fewer particles. The end results is that most beam profiles follow a gaussian distribution, though there are exceptions.

This bunching behavior allows us to analyze other properties of particle beams very similar to lasers. There is a “pulse frequency” given in Hertz. Each bunch contains a certain energy, which can be large enough that we give it in Joules and not electronvolts. There is an average output energy over a given timespan, given in Watts. We have a beam peak power, given by how quickly a bunch arrives at a target and deposits its energy, which we give in Watts. Related to this we also have a related peak intensity depending on how much area/volume the beam is deposited into, with units of either W/m² or W/m³. If we have charged particles being accelerated, we get a beam voltage, the same way as in a wire. Beams can also have a temperature, the same way as any other group of particles with random motion from their energy, given in Kelvin or eV.

The systems that generate particle beams of course have efficiencies, with the wall plug efficiency (power inserted into the entire system versus power deposited in the particle beam) being the most interesting for first-order engineering. They also have an operating temperature.

Particles for acceleration

With the constraint that our particles must have an electric charge in order to be accelerated with anything but fantastic technology, we can discuss quite a large family of particles, from the conventional to the exotic. They differ in the applications they can be interesting for. Some can be similar, but no two particles behave entirely alike.

Electrons

The ubiquitous electron is the most common particle to be accelerated and the first one ever pushed up near the speed of light by humans. Due to its excellent charge to mass ratio (the best possible due to the extremely low mass and charge of 1e) electrons are very easy to get up to relativistic speeds. Electron accelerators for radiography and sterilization are often portable by a single person and not much larger than a laptop in size (although they can be much bigger for power output reasons). The ease in which electrons reach relativistic speeds means that electron RF accelerators can be designed with no speed changes assumed (since the electrons are already moving at effectively light speed) and thus tend to be highly efficient and have the highest acceleration gradients achievable. For similar reasons electrons are also able to be accelerated in plasma based accelerators, allowing for even higher acceleration gradients and smaller machines for a given energy. The major downside of electrons is that due to their large charge to mass ratio they will radiate energy like crazy when bent by a magnetic field. Thus ring shaped accelerators are of limited use for electrons since you have to make the ring extremely large to not just lose all of your energy as beams of x-rays coming out of the machine! This very trick is used to make high quality x-ray sources for industrial and research applications.

When electrons hit matter they tend to release their energy as photons in a process called bremsstrahlung, or braking radiation. These extremely high energy photons (roughly ~⅓ the peak energy of the electron on average) then proceed to make electron/positron pairs that then make photons that then make pairs that then make photons… This whole thing is a massive cascade of radiation that ionizes, heats and can even damage on a nuclear level! At high enough energies you will generate every particle known and might even make some new ones!

Proton

Protons are the next most common particle to be accelerated and are currently used by the absolute largest particle accelerator ever made (the Large Hadron Collider or LHC) as the primary particle of choice. Since they have ~2000X lower charge to mass ratio than electrons, protons are about ~2000X harder to get up to speed. Unlike electrons they are not promptly at light speed so we have to send protons through a series of various accelerators depending on the energy of choice. For example the protons in the LHC the protons go through 5 different particle accelerators plus the extremely low energy stage that first makes the beam of ions! This difficulty in reaching highly relativistic speeds has two other bad side effects. Firstly, if we want to transmit our protons through empty space we will probably need to neutralize them with a beam of electrons.

Note: When shooting extremely high current (kA), relatively low energy (not highly relativistic or in some cases relativistic at all) beams in the atmosphere the higher mass and positive charge of protons gives them many beam propagation advantages over electrons if the beams can be made. In this case no neutralization is required as the atmosphere itself becomes a plasma and neutralizes the beam.

Luckily this is not very hard and will add almost nothing to your comparatively large proton accelerator, but may increase your beam spread a little bit via some neutralization physics. This does mean your beam is technically plasma, which is cool! Second, we effectively cannot use those neat plasma based accelerators for protons since we would need nearly TeV class proton beams to inject into the plasma accelerator and by the time you reach those energies you have basically already done all of the work. Maybe in the future there will be ways around this, but as of right now we are limited! There is one major benefit to this poor charge to mass ratio though, and that is the lack of synchrotron radiation! Ring shaped accelerators are ideal for protons, and basically all ions.

When protons hit matter they can interact with all of the four fundamental forces, although only two of them (Strong Nuclear and Electromagnetism) tend to play big roles. Protons barrel on in causing huge ionization cascades and can also release bremsstrahlung photons at high enough energies. They are also ideal at knocking neutrons, protons, deuterons and more out of the target nuclei which just adds to the fun! Protons also come with a neat trick known as the Bragg peak, where they deposit a large portion of their energy right at the end of their trajectory through a target material. This is a very useful trick for medicine and means you can “tune” the beam to almost ignore large portions of material and primarily heat, ionize, and destroy the area of interest. You can imagine how useful this is for cancer therapy or more nefarious things!

Light ions

Light ions are a rather fuzzy term but here we will use the definition of any ion heavier than a proton but lighter cobalt. The fuzzy reasoning here is that you get on the other end of the nuclear binding curve (i.e. can’t get net energy from fusion) at iron, so cobalt will then no longer be “light” and has to be made in a different process. Feel free to pick your own cut off! Historically beams up to neon have been experimented with for nuclear fission, nuclear fusion and medical therapy applications. Light ions have even worse charge to mass ratios than protons (Z/A times worse) and typically you will find light ions have about ½ the charge to mass ratio of a proton on average, although the isotope 3He is a notable exception. This means they are even slower to accelerate, although often the exact same machines as protons can be used with minor tweaks. Light ions have similar requirements for neutralization as protons, although their heavier mass can help fight beam bloom for a similar beam speed (not energy since the increased mass means the particles are higher energy for a given speed). The decreased charge to mass ratio also means that synchrotron radiation is even lower so beams can be driven to higher speeds before radiating. Light ions have similar target interaction physics as protons, although the ion itself will break up at very low speeds and add to the radiation environment.

Heavy ions

Heavy ions are being defined here as cobalt up to whatever unstable element you can jam into your accelerator! Typically heavy ion beams are made of elements like lead (used in some runs on the LHC), gold (used in the Relativistic Heavy Ion Collider) and even californium (used in some runs on the Argonne Tandem Linac Accelerator System). These beams tend to be for pure nuclear physics research, but there has been a long standing interest in heavy ion beams for inertial confinement fusion research and as potential methods of propelling spacecraft. These extremely heavy ions will be even harder to accelerate to ultra high speeds than light ions and much slower for a given energy, but they do provide a lot of momentum to make up for that! They have the same neutralization requirements and same potential upsides for beam bloom as light ions, but will most likely be orders of magnitude slower reaching our targets than the lighter beams. Heavy ions can also be used in the same machines as protons with small modifications and generate almost no synchrotron radiation as a result of their much smaller charge to mass ratio. They also have similar interaction physics to protons and light ions, but will stop in much thinner layers of materials. While electron, proton and light ion beams tend to both mechanically destroy and irradiate targets through-out, heavy ion beams will act much more like lasers and burn in from the outside of the target on in. There will still be a spray of ionizing radiation, but far less of one than an equivalent energy electron, proton, or light ion beam. The much higher momentum per particle, lower radiation concerns and ease of deflection makes heavy ion beams very interesting for beamed propulsion purposes.

Macrons

Macrons are typically defined as macroscopic particles, such as extremely large molecules or even grains of sand, that are charged up and accelerated via similar technologies as traditional particle accelerators. There are many difficulties with getting macrons up to appreciable speeds due to the extremely low charge to mass ratio, engineering difficulties with getting consistent and good charging, phase matching with accelerating cavities and lack of effective focusing optics. There are so called “dust accelerators” in existence that utilize the first stage of ion accelerators to generate their “beams” and proposals have been made to create better versions using updated technology. Macrons will interact just like a very small and very fast bullet unless they are designed to carry a nuclear payload to boost this output. Antimatter is an assured option for getting energy gain from a macron impacting a target, although there are potentially options for fusion, fission and fission/fusion given the correct sizes (mm scale or bigger), clever target design and the right impact speeds (most likely >>100 km/sec). The various energy gains versus speeds can be seen in Figure X.

It can be seen that antimatter proves to be worth it up near the speed of light, but both fission and fusion stop providing much gain well below the relativistic regime. This also helps explain why heavy ion uranium beams are not going to provide some incredible advantage over any other ion.

Antimatter

Antimatter is the evil cousin of normal matter and whenever the two meet a release of energy equivalent to their combined mass energy follows. Now this does sound like an amazing option for beams but there are two downsides. First, antimatter is energetically expensive to make! Positrons (antimatter electrons) are the “cheapest” at 1.02 MeV of input energy at a theoretical best, but they only give you that much energy back when hitting a target. Since a typical positron beam can be expected to be equivalent to an electron beam, there is little gain in adding 1.02 MeV per particle to a multiple GeV (or even TeV) beam. You can see this explicitly in Figure X below.

Note: Positrons can potentially fill an interesting niche either as a co-propagating neutralizing beam for electrons or perhaps as a higher performance atmospheric beam than electrons due to the positive charge. In this case the annihilation properties are no what is of interest, rather the positive charge and relative ease of acceleration compared to ions. Since positrons share all properties with electrons except for charge, they can be accelerated just as easily and even co-accelerated with electrons in the same machine.

For anti-protons the math becomes more favorable, but creating these particles is much more difficult and energy consuming. At best anti-protons require ~2 GeV of input energy to create, but in practice >400 GeV per anti-proton has been needed. Luckily significant energy gain is had up to several GeV of beam energy, so if anti-protons can be made at a central facility of some kind and easily stored (neither being easy things) then there may be some advantage to such a beam. Heavier ions are significantly harder to make since fusion with antimatter must be performed to generate those ions. Barring a naturally occurring source being found, antimatter heavier than a proton is most likely not worth using.

Muons

Muons are an interesting cousin of electrons and positrons. They are unstable and heavy cousins of electrons, massing about 200X more than electrons and living about 2 microseconds in the lab frame before decaying into an electron (or positron) and a neutrino. If we accelerate them up to relativistic speeds (about 10X easier than protons and the muons are typically born relativistically thanks to how we make them) then the muons can be made to “live” far longer. Muons have long been of interest to accelerator physicists due to their position as an almost ideal intermediary between electrons and protons. The requirement to make them on site has always been an impediment though and muons are currently only used for certain niche experiments. During the planning stages for a potential muon collider it was also noted that a muon collider would also have a serious issue with neutrino radiation! This is due to how neutrinos are more likely to interact with matter at high energies and a muon collider would be generating a LOT of really high energy neutrinos in a ring around the machine. This has been proposed as a sort of super weapon even!

Muons should interact with matter in a similar fashion to electron beams and the beams will probably be treated in a similar manner. They can propagate through the atmosphere quite well in theory and should outperform electron and proton beams for a given beam energy, although at quite a cost… Muons are typically generated with proton beams impacting targets and will create an equal number of positive and negative muons at high energies that must be carefully captured. This would allow for the easy creation of a neutral muon beam though, which may make for a great giant doom beam! Do note that negative muons also can help catalyze nuclear fusion so a very high power beam hitting a fusion fuel tank could produce some rather… Interesting results!

Other exotic options

There are a wide variety of odd particles that could also be chosen for use in beams given a specific need for them, although generation and utilization of these particles will be quite difficult! Extremely short lived particles like pions, kaons and taus can be generated and accelerated up to extreme speeds to help propagate them far enough to matter, although that will need some very extreme speeds. At the upper end of extreme there are even proposals for accelerating tiny charged blackholes!

Accelerator technologies

There are a wide variety of accelerator technologies and here we try to summarize them as best as possible. Different accelerator types may be sequenced one after another. Some particle accelerator technologies depend on the particles fulfilling certain requirements of speed (thus energy) and hence different systems may be employed in sequence. Accelerator systems are described in terms of their efficiency of turning input power into particle energy, their acceleration gradient measured in electric field which translates to volts per meter, and the mass per length meter. An interesting secondary parameter is their operating temperature. Some accelerators can operate well at high temperatures. Others require cold or cryogenic conditions to work well.