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# Cyclotron

A cyclotron is a machine to accelerate beams of charged particles by using a high frequency alternating voltage across a magnetic field to spiral the beam out and eventually deflect it once the beam's radius equals its containers. At this point the particles' speed is generally very high. The cyclotron was invented by Ernest Lawrence in 1929, who used it in experiments which required particles of speeds of up to 1 MeV. Cyclotrons are used today in the treatment of cancer, as the particles produced ionise tumours and help to stop or slow cancerous growth.

The cyclotron was designed because of shortfalls in the linear accelerator[?]. These work by accelerating particles through tubes using a series of plates which switch from positive to negative repeatedly. A serious disadvantage is that in order to accelerate particles faster, impractically long tubes were becoming necessary. Cyclotrons work by accelerating particles in a circular path, allowing much more distance to be covered with similarly sized accelerators.

A magnetic field is set up over two large D shaped semi-circular containers. A current flowing perpendicular to a magnetic field experiences a force that is perpendicular to its direction of motion, causing the current to follow a circular path. In the cylotron a voltage causes the particles to move and the magnetic field forces them to travel in a semi-circle around one D. At this point the voltage switches and the particles complete the full circle, covering the other D. The centripetal force is provided by the magnetic field B, and the force on a particle travelling in a magnetic field (which causes it to curve) is equal to Bqv. So,

$\frac{mv^2}{r} = Bqv$

(Where m is the mass of the particle, q is its charge, v is its velocity and r is the radius of its path.)

Therefore,

$\frac{v}{r} = \frac{Bq}{m}$

v/r is equal to angular speed, w, so

$w = \frac{Bq}{m}$

And,

$f = \frac{w}{2 \times \pi}$

Therefore,

$f = \frac{Bq}{2 \times \pi \times m}$

This shows that the frequency does not depend on the radius of the particle's orbit. As the beam spirals out its frequency does not decrease and it must continue to accelerate, as it is travelling more distance in the same time.

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