Cyclotrons use circular orbits to accelerate particles

Magnetic Fields & Forces — AQA A-Level Physics

Key Definition

Cyclotron — A particle accelerator that uses a uniform magnetic field and an alternating electric field to accelerate charged particles along a spiral path to high speeds.

Structure

Two hollow semicircular electrodes called 'dees' (D-shaped).
A uniform magnetic field perpendicular to the plane of the dees.
An alternating electric field in the gap between the dees.

How it works

Particles are released from a source at the centre.
Inside a dee: the magnetic force acts perpendicular to velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹., causing circular motion at constant speed.
In the gap: the electric field accelerates the particles, increasing their speed and kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. by QV per crossing.
Faster particles travel in bigger circles ($r = mv/BQ)$, so the radius grows with each half-turn.
Time spent in each dee is constant. Faster particles cover larger semicircles, but the extra distance cancels with the higher speed. This is why the alternating field stays in sync.
The electric field flips direction each half-cycle so particles always accelerate towards the opposite dee.
Particles spiral outward until they reach the exit energyThe capacity to do work. Measured in joules (J)..

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Role of each field

Magnetic field: provides centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion. to bend particles into circular arcs within the dees.
Electric field: accelerates particles in the gap, increasing their kinetic energyThe energy an object possesses due to its motion..
Medical use: producing radioactive tracers for PET scans, generating beams for radiotherapy.

Common Mistake MEDIUM

Students often: Avoid saying the magnetic field accelerates the particles.
Instead: The magnetic field only changes direction, never speed. Speed increases happen in the gap between the dees, where the electric field does work on the charge.