# How does a cyclotron release electromagnetic waves?

I am currently working on a project on fusion reactors and am researching the basics of them. During my research, I encountered "antenna" which produce ion and electron cyclotron frequencies to heat the reactor. Then I encountered cyclotron resonance which brought me to a cyclotron particle accelerator. I then researched how it worked. What I found was that two semi-circular resonant cavities are placed next to each other with a gap in between them. Protons then get accelerated creating a spiral until they are shot out of the cyclotron at the edge. What I understand is that the protons generate electromagnetic waves as they oscillate between the two "dees". What I do not understand is how the electromagnetic waves leave the cyclotron. As far as I know, resonant cavities are supposed to trap electromagnetic waves to generate standing waves. Then how are the electron and ion cyclotron frequency waves released?

• I sense some confusion on what ion and electron cyclotron frequencies in a plasma actually mean. In a plasma in a magnetic field, the charged particle cyclotron frequency is the inverse of the time for the given particle to make one orbit in the magnetic field. It does not have anything to do with a cyclotron particle accelerator except that the concept of the frequency of the orbits is the same. – Jon Custer May 18 at 14:39
• So what you are saying is that the plasma in the reactor generates the electron and ion cyclotron frequencies rather than an external source supplying it to the reactor? – Nicojwn May 18 at 15:09
• No, you still need to pump in rf at the right frequency or frequencies to heat the ions or electrons. But that is just an rf supply, not an actual cyclotron accelerator. – Jon Custer May 18 at 15:20
• look up cyclotron radiation on wikipedia. – niels nielsen May 18 at 18:51

First of all, cyclotrons are only used for protons and ions, but not for electrons. The typical radiation in particle accelerators where particles circulate or spiral (like in a cyclotron) is synchrotron radiation. The intensity $$I$$ of the synchrotron radiation behaves like $$I\sim \gamma^4$$.The relativistic $$\gamma$$ is to be computed as

$$\gamma = \frac{E}{m_0 c^2}$$

Maximal energy $$E$$ of cyclotrons is around 500MeV. However, the intensity of generated synchrotron radiation according to the $$\sim \gamma^4$$ law is too weak in order to be issue in cyclotrons. The mass $$m_0$$ of protons and ions is too large and the energy of these is too low in order to get a large $$\gamma$$ (in difference to electrons, but electrons are not accelerated in cyclotrons).

Therefore the question how the radiation gets out of the cyclotron is of little interest.

Cyclotrons are either self-shielded (where the dees and the vacuum chamber walls are thick enough to block all electromagnetic radiation) or separately shielded (where the cyclotron sits inside a shielded space). This prevents the RF energy which drives the dees from being radiated away into space.

The "radiation" that makes cyclotrons hazardous is in the form of gamma rays, which can escape through the shielding. The gamma rays are produced when particles in the cyclotron beam move off-track and strike the dee walls, triggering a variety of nuclear reactions inside the dee material. Some of those reactions produce gamma rays.

I have set the formula number 41: "Bremsstrahlung radiation loses" here: Useful formula and excel tables for Plasma Physics V08