# The use of electrons in synchrotrons

I'm researching synchrotrons for a class project, but I can't seem to find a decent answer to one of my questions. It appears that most synchrotrons use electrons as opposed to some other charged particle, while the Large Hadron Collider uses protons instead (I know the LHC has a different setup but I believe the underlying principle is the same). So my question is why are electrons preferred in synchrotrons?

I figured that an electron would be a better choice because its mass is small. Therefore, less energy would be expended to accelerate the electrons to relativistic speeds.

Any other suggestions would be greatly appreciated.

• – Kyle Kanos Nov 20 '15 at 12:40

I'm researching synchrotrons for a class project, but I can't seem to find a decent answer to one of my questions. It appears that most synchrotrons use electrons as opposed to some other charged particle, while the Large Hadron Collider uses protons instead..

The first thing that you should know is that there are two completely different uses for synchrotrons. There are (1) "collider" synchrotrons used for the study of elementary particles, and there are (2) synchrotron light sources, which are synchrotrons designed purely to give off intense x-ray beams which can be used for x-ray diffraction and other experiments. These are two entirely different animals.

"Collider" synchrotrons came first. These types of synchrotrons accelerate particles such as electrons or protons in opposite directions around a circular "racetrack" and observe what new particles are created when the beams collide. At Cornell University where I was a grad student, we had a synchrotron which sent electrons in one direction and positrons in the opposite direction and then studied the new particles created from their collisions. I was told that an advantage of using electrons-positron collisions rather than something like proton-antiproton collisions was that the electrons-positron collisions were "cleaner" and easier to analyze. Proton-antiproton collisions are apparently more difficult to analyze because each proton (or antiproton) is actually made up of three quarks, so there are actually six elementary particles involved in every proton-antiproton collision. On the other hand, I think that an advantage to using proton-antiproton collisions for elementary particle studies is that it's easier to get very high energy collisions between between proton-antiproton pairs than electron-positron pairs because protons have a higher rest mass than electrons and not as much energy is lost to synchrotron radiation when accelerating protons as opposed to electrons.

For the other type of synchrotrons, synchrotron light sources, generating a lot of synchrotron radiation is actually desired for x-ray and other experiments, so electrons have an advantage over protons because they give off a lot more radiation than protons when accelerated to a given energy. There is no need or desire to study particle collisions with this type of synchrotron, so only an electron beam circulating around the synchrotron ring in one direction is generated. There is no electron or positron beam circulating in the opposite direction.

A final note: The Cornell "collider" synchrotron that operated while I was a student there was apparently retired in 2008. However, the machine lives on in its new role as a dedicated synchrotron light source that provides intense x-rays for experiments performed by visiting scientists.

The quantity that determines what a particle beam may be used for is called gamma ($\gamma$). It is defined as $$\gamma = \frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}}.$$ As $v$ gets closer to $c$, $\gamma$ gets larger without bound and equals infinity when $v = c$.

Since particles in a synchrotron are moving at very close to the speed of light ($0.99999999c$ in the case of the LHC*), physicists use another, equivalent formula to calculate $\gamma$. $$\gamma = \frac{K}{m}+1$$ where $K$ is the kinetic energy of the particle in electron-volts (eV) and $m$ is the mass of the particle in eV/c$^2$ (feel free to ask what this unit means). An electron has a mass of about 511,000 eV/c$^2$ or 0.511 MeV/c$^2$, while a proton has a mass of about 1,000,000,000 eV/c$^2$ or 1 GeV/c$^2$ (2,000 times larger than an electron). The LHC runs at 7 TeV (7,000,000,000,000,000 eV) per beam, so the gamma value for these protons is $$\gamma = \frac{7\,TeV}{1\,GeV} + 1 \approx 7,000.$$ For electrons, we get $$\gamma = \frac{7\,TeV}{0.5\,MeV} + 1 \approx 14,000,000.$$ This difference either helps or hurts a beam depending on what you want to do.

Synchrotron radiation is released by a particle when its path is curved. The rate at which energy is released is proportional to the fourth power of gamma ($\gamma^4$). In the case of the LHC, physicists want the particles to collide with the most amount of energy possible. The radiation released while the beam is turned in a circle is wasted. So, since protons have a much larger mass than electrons, they have a much lower gamma, which means they lose much less energy in each turn around the ring. An electron going around the ring is limited to about 200 GeV (this was the energy of the electron-positron beams in the Large Electron-Positron (LEP) collider at CERN, which used the same tunnel as the current LHC). The tradeoff is that protons are complicated particles with inner structure, so the collisions between them are complicated. Future colliders, like the International Linear Collider being build in Japan, will be linear in order to minimize the energy lost when turning the beam. The tradeoff with linear colliders is that you only get one chance to accelerate the particles, whereas, in a ring, you get to accelerate a particle many times through many circulations.

Now, if you want to produce radiation, you want gamma to be as large as possible, so electrons are a natural choice. Facilities called light sources around the world send electron beams through magnets (dipoles or undulators) in order to produce high-power X-rays for other scientists to use. For example:

* If an LHC proton and a photon of light were to have a race to the moon, the photon would only win by about twelve feet. An electron with the same energy would lose by a micron.

• Very nice summary. I posted a question on meta a while back about asking about the level of background of the OP, but when you get a set from my basic answer on upwards, expanded in detail like yours, there is no need. – user81619 Nov 20 '15 at 9:31

When you use electrons, you can produce a source of extremely high intensity light called synchrotron light. This light is produced mainly in the X ray part of the spectrum and can be up to 10 billion times brighter than solar light. Using this light allows a study of matter at a better resolution than using protons.

Electrons can probe matter to smaller scales and with less "by-products" reactions than more complicated protons.

Also, as far as I know, it's cheaper to build and run an electron synchrotron because the magnetic and electrical power needed is not as great as when using protons, as in the LHC.

The principal advantage of using electrons is that the electron is a fundamental particle so electron-electron (or electron-positron) collisions are are well defined process that is relatively eay to describe mathematically, and very accurate measurements can be made.

By contrast the proton is a composite particle. We normally describe the proton as being made up from three quarks but the internal structure is a lot more complicated than this implies. When you collide two protons (or a proton and antiproton) you are colliding two objects with lots of internal structure. The resulting collision is much messier and harder to describe than an electron-electron collision. Accurate measurements can still be made, but it needs much more data and takes far longer.

The principal disadvantage of using electrons is that when you move an electron in a circle it radiates energy in a process called bremsstrahlung or synchotron radiation and you need to pump in more energy to make up for the energy lost as radiation. At LHC energies this would make the collider prohibitively expensive to run. If you're interested there is more on this in Why doesn't the LHC accelerate electrons?.

Although future high energy electron colliders are planned they will be linear colliders, which don't produce bremsstrahlung radiation because they don't move the electrons in a circle. The downside is that it's much harder to get high energies in a linear collider.

Very good answers above! I would just add one simple point to be more specific to your question. The LHC uses anything it can smash together just to see whats inside. The other Synchrotrons use electrons because its easy to shake radiation out of them and Synchrotron radiation is what they want to produce. The same way bumping electrons will produce photons for radio signals or exciting electrons in a filament will produce photons for light.