The few times that I have seen a cyclotron I have been surprised about how small it is. It is in the order of 30cm diameter. It is one of the earliest particle accelerators. The two metal halves are called Ds. The Ds are metal so that they can be given an electric potential. Hence there is a potential difference across the gap. positive particles are injected into the centre. A strong magnetic field acts perpendicular to the D - ie into the plane of this picture. The magnetic field is perpendicular to the motion of the charged particle so by Fleming's Left Hand Rule a force acts of the particles which acts towards the centre and pulls the particle round in a circle. The potential difference is alternating so that when the particle completes a half circle and returns to the middle, the potential switches which accelerates the particle across the middle and into the other D. Each time the particle crosses the middle, it gets faster and so orbits at a bigger radius. The clever thing is that no matter what the radius, it takes the same time to complete a half circuit so all particles in the apparatus can be accelerated at the same time. The limit on the size is that if it were biggest, relativistic effects would increase the mass and thus cause a particle to go more slowly, not reaching the middle at the same time.
