Particle Accelerators

Charged particles such as electrons or protons are accelerated by an electric field to speeds almost equal to the speed of light. They are made to collide with one another and in such collisions some of the kinetic energy is turned into matter and new particles are created. Particle accelerators are used to increase the speed.

## LINAC

In a Linear Accelerator (LINAC) charged particles are accelerated in a straight line, into electrode which are connected to an alternating potential difference. This cases an alternating electric field which attracts and repels charges particles between electrodes. As soon as the charged particles leave an electrode, the alternating potential difference supple reverses and repels the charged particle and subsequent electrodes attracts the particle, for example an electron would be attracted to a positive electrode and repelled from a negative electrode. Therefore, between the electrodes the charged particles are accelerated, there is no electric field within the electrode. As the velocity of the charged particle increases, the length of the tube increase to keep the time in each electrode constant as the potential difference is alternating at a constant rate

The equation for LINAC is **E=nqv**, where n is point charge per nit volume, q is the charge of the particle and v is the velocity.

## Cyclotron

A cyclotron uses both magnetic and electric fields unlike LINAC which only uses electric, in the centre there is a superconducting magnet which holds the charged particle. The charged particles are then accelerated between the gaps of the Dees via an electric field using the same principles as a LINAC where the charged particle is attracted to the next and repelled for the previous. Again, the time in each Dee must be constant so as the velocity increase, radius increases, due to **v=Bqr/m** where B, q and m are constant, the charged particles travel further in each Dee and the frequency of the alternating voltage remains constant. For the charged particle to travel in a circular motion within the Dees a perpendicular magnetic field is applied via electromagnets above and below the Dees. Whilst the charged particles are in the Dees the velocity is constant as the magnetic field only affects directions, as it is moving in a circular motion it has a centripetal element, so centripetal equations can be applied: The equation for a cyclotron in **F=Bqv** and as it is traveling in a circular motion the equation **F=mv2/r** can be used. To derive the equation for a radius in a cyclotron, equate the equations **Bqv=mv~~2~~/r**, cancel v **Bq=mv/r** and make v the subject **v=Bqr/m.**

Eventually the radius is large enough that the charged particle travels through a beam tube to initiate a nuclear reaction. A limit of cyclotrons is that when going at relativistic speeds, the mass increases which causes the time in each Dee to alter and that affects the constant alternating voltage, so this isn't used at energies higher than 20MeV.

## Synchrotron

Synchrotron are similar to cyclotron and LINAC, it is a ring with accelerating cavities at different points and

magnets situated above and below the ring in varying places with varying field strength to keep them moving in a circular motion, the varying field strength also allows it to be alerted when speed and mass changes at higher energies. The accelerated cavities around the ring increases speed like with a LINAC, an electric potential is used within the accelerating cavities. Before the charged particles enter the synchrotron, they are accelerated in a pre-accelerator like a LINAC to increase the speed beforehand. As a large magnet is not needed in the centre like with cyclotrons, the radius of the circular path can be much larger.

However, as the charged particles move in a circular path they lose kinetic energy which is in the form of a type of electromagnetic radiation called Synchrotron Radiation. Therefore, as they lose energy they slow down and to prevent it slowing down too much, the synchrotron provides extra energy, which means the synchrotron can act as a source of electromagnetic radiation. The same equation used with cyclotrons can be applied with synchrotrons.