How does a cyclotron work?

A cyclotron is constructed of two hollow, D-shaped electrodes that accelerate particles; they are opposite each other and there is a small gap between them. A magnetic field is used to bend the particle tracks so that the same electrodes are used repeatedly to accelerate the particles. The particles start in the centre at the ion source and move outwards in a spiral path as their speeds increase.The AC voltage, (with each electrode of the supply connected to a corresponding Dee), creates an electrical field between the Dees, as the Dees are oppositely charged. The magnetic field is perpendicular to the plane of the Dees.Operation:The acceleration (of speed) occurs only when the particles are between the Dees, due to the electrical field; the field is zero inside the Dees.The time spent inside each dee is constant, as the speed and radius increase together as the particle spirals outwards because r is proportional to v.The AC flips polarity, causing the electrical field to change direction; this allows the particle to accelerate in the direction it is moving when it reaches the gap.The particle travels in a spiral because the magnetic field produces a force on the particle that is perpendicular to the particles velocity, hence it is a centripetal force and so the particle engages in a circular motion.