A cyclotron is a circular
evacuated chamber cut into two D shaped halves with a high voltage across the gap. The
particles are injected at the centre and a magnetic field (strength B) is applied across the whole
of the apparatus perpendicular to the Ds so that the particles are deflected into a circular path.
They start at the centre and are given a kick every time they cross the gap between
the Ds. The energy gain is qV for ions of charge q. As they gain energy from the electric field
their velocity increases, the radius of their path increases and they travel in
a spiral until they emerge at the edge of the apparatus and hit a target.
where m is the mass of the particle and R is the radius of the Ds.