## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## Cyclotron

A cyclotron is a type of particle accelerator in which charged particles accelerate outwards from the center along a spiral path. The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying (radio frequency) electric field.

## Principle of operation

Cyclotrons accelerate charged particle beams using a high frequency alternating voltage which is applied between two "D"-shaped electrodes (also called "dees"). An additional static magnetic field $B$ is applied in perpendicular direction to the electrode plane, enabling particles to re-encounter the accelerating voltage many times at the same phase.[1] To achieve this, the voltage frequency must match the particle's cyclotron resonance frequency

$f = frac{q B}{2pi m}$,

with the relativistic mass m and its charge q. This frequency is given by equality of centripetal force and magnetic Lorentz force. The particles, injected near the centre of the magnetic field, increase their kinetic energy only when recirculating through the gap between the electrodes; thus they travel outwards along a spiral path.

Their radius will increase until the particles hit a target at the perimeter of the vacuum chamber, or leave the cyclotron using a beam tube, enabling their use e.g. for particle therapy. Various materials may be used for a target, and the collisions will create secondary particles which may be guided outside of the cyclotron and into instruments for analysis.

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