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# Cyclotron

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 Sub Topics Accelerator physics relates primarily to the interaction of charged particles with electromagnetic fields. Accelerators have been used to bombard various experimental objects with streams of accelerated particles ever since the first one was built. An accelerator enables the details of nuclear structure to be studied with the beam of accelerated particles. These investigations encompass both nuclear and sub-nuclear structures. Cyclotron is one of the circular particle accelerator. The idea of cyclotron is first invented by E.O.Lawerence using the possibility of using a magnetic field to recirculate the beam through two of wideroe's drift tubes. The more details are described in each section.

## Definition

A cyclotron is a charged particle accelerator that uses a magnetic field to confine particles to a spiral flight path in a vacuum chamber. An applied electrical field accelerates these particles to high energies, typically on the order of mega electron volts. Using the accelerating field in this fashion allows a cyclotron to produce high energy particles far more efficiently than other accelerators, such as linear accelerators. A cyclotron is a relatively compact accelerator in which the energy is only limited by the diameter and field strength of the magnet.

## Frequency

From the above figure, the two dee's can be seen between the poles of the magnet. An r.f generator excites them with an alternating field of constant frequency. The potential difference between the dee's accelerates the ions as they pass the gap between the two halves of the structure. The field oscillates at the particle's circulation frequency and hence the sign of the potential difference at each gap is always in the accelerating direction.

The force of the magnetic field on the charged particles is described by the following relation:

F = qvB = $\frac{mv^{2}}{r}$

where B is the magnetic field in Tesla, r is the particles radius in meters, m is the particle's mass in kg, q is the particle's charge in Coulombs. This equation can be rearranged to give the particle's velocity as a function of the other variables:

v = $\frac{qBr}{m}$

This velocity can be used to derive the angular frequency of the particle's flight path.

f = $\frac{v}{2\pi r}$ = $\frac{qBr}{m}$ $\frac{1}{2\pi r}$

f = $\frac{qB}{2\pi m}$

The signal applied to the cyclotron's electrodes must oscillate at this frequency.

From the force equation, we can write

F = qvB = $\frac{mv^{2}}{r}$

Cancel the term v on both sides of the above equation.

So, qB = $\frac{mv}{r}$

r = $\frac{mv}{qB}$

where m is the mass of the particle, v is the velocity, q is the charge of the accelerated particle and B is the applied magnetic field.

## Particle

Particle accelerators are used to accelerate charged particles like electron, proton, ions etc. The paths of the accelerated particles may be circular, straight or spiral. Cyclotron produces the spiral path and synchrotron produce the circular path. In both systems, strong magnetic field is to require to control the path of the accelerated particle. The accelerated particle must be charged elementary particle or ions.

Radiation produced by the charged particle which is moving in a circular path under the influence of a strong magnetic field is known as the cyclotron radiation. This radiation is not produced by the moving particle in a strong magnetic field, it is also produced by interstellar medium, plasma etc also. It may be produced in a high altitude nuclear explosion.

## Particle Accelerator

Accelerators are devices that control an electric field in such a way as to efficiently accelerate the charged particle. A linear accelerator (LINAC) controls the electric field to accelerate a beam in a linear path and therefore the LINAC length is proportional to the strength of the electric field and the gain in energy. Conventional linear accelerators do not produce sufficient electric field strength to build a compact system for heavy charged particles although non conventional techniques are being investigated.
In order to accelerate charged particles in a compact machine, it is efficient to reuse the electric field. Therefore, circular machines such as cyclotron or synchrotron are used that repeatedly steer the particle beam across the same electric field. In general, due to the energy required for clinical use, these accelerators are still large. They therefore remain separate entities and feed beam lines, which transport the beam to treatment rooms.

The cyclotron:
A simple cyclotron can be visualized as a vertically as a vertically divided pillbox. An electric field is applied across the gap between the two halves, called dees for their resemblance to the letter and a magnetic dipole field covers both dees. The beam is injected into the center of the cyclotron and accelerated each time when it crosses the electric field.

The Synchrotron:
The synchrotron is a narrow vacuum tube ring contained with magnets. The beam is injected from outside the synchrotron by, a LINAC with an energy of 3 to 7 MeV. The beam circulates within the ring repeatedly through the accelerating structure located at one location in the ring. In order to keep the beam within the closed ring, the magnetic field of the magnets must increase in strength in synchrony with the beam energy increase; hence the name synchrotron.