Before 1929, the best method for accelerating a particles was to allow them to fall through a potential difference, acquiring an energy boost equal to the voltage across the gap multiplied by their charge. This system is still used in cathode ray tubes in televisions. However, it has the energy limiting factor that sparking occurs above a certain voltage.
The cyclotron was invented by a man called Lawrence and represents an enormous leap in the particle energy that could be generated. Magnets are used to bend charged particles around in circles through high voltage electrodes, known as dees. This way, an accelerating voltage could be used not once but many times.
An alternating voltage is applied at the two dees. The particle is introduced at the gap and accelerated into the first dee just as in a cathode ray tube. The magnetic field acts to bend the particle in an arc. While the particle is completing a half revolution inside the dee, the voltage reverses so that the particle can again be accelerated when it next reaches the gap. This repetitive acceleration continues until the particle has enough energy to get to the edge of the dees and escape through the gap.
Intuitively, the problem with the system would be how to correctly time the flipping of the voltage on the dees. Conveniently, however, an orbiting particle in a magnetic field takes the same time for one revolution, regardless of radius or energy. This is proved in appendix one.
However, the cyclotron does have its drawbacks. Firstly, Einstein’s theory of relativity tells us that a particle traveling at a very high speed becomes heavier. This upsets the condition described above and so particle energy is limited. Secondly, it is practically very difficult to keep the beam centered vertically inside the dees for many revolutions. Focusing using the magnetic field causes it to be weaker at the edges of the radius than at the centre, again upsetting the condition and limiting energy by limiting the number of revolutions.