In **cyclic accelerators**, particles move in a circle until they acquire sufficient high energy. Examples of such accelerators are cyclotron, betatron, synchro-cyclotron, synchrotron, proton synchrotron.

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**Construction and Working of a Cyclotron**

**What is cyclotron** ?

It is a device designed by Lawrence and Livingston in 1931 to accelerate heavy particle charged particles (like proton, deuteron, and Alpha particles, etc.) by passing them again and again in a radio frequency electric field along a closed path.

**Principle of Cyclotron**

It is based on the principle that charged particles can acquire high energy when they are repeatedly passed through an alternating electric field.

**Construction of Cyclotron**

It consists of an evacuated chamber divided into two sections D1 and D2 called “dees” because of their shapes. These days are arranged in such a way that there is a small gap between them.

The dees are connected to the terminal of a high-frequency oscillator of the order of ** 10^{7}** Hz and potential of the order of 10000 V. The Chamber containing the dees is placed between pole pieces of a huge Electromagnet which produces a strong magnetic field perpendicular to the plane of dees.

The positive Ions are produced in the gap between the two dees by ionizing the gas. Hydrogen gives protons and deuterium produces deuterons and Helium produces Alpha particles.

**Working of Cyclotron**

The positive ion produced at the center of the gap is attracted towards a “dee” which is at the negative potential at that instant. The ion enters the dee where there is no electric field and due to the presence of the perpendicular magnetic field, the ion moves along a semicircular path inside the dee and then finally comes back to the gap between the two dees.

The frequency of the oscillator is so chosen that the time required to describe this semicircle corresponds to one-half cycle.

Thus the ion will reach the gap just at the proper time to be further accelerated by the reversed electric field across the gap into the opposite Dees. Since the particle is now moving with greater velocity so it will describe a semicircle of Greater radius in the second dee.

It is absolutely essential that the resonance condition is maintained throughout, otherwise the ions will not reach the gap in proper phases to be accelerated.

Thus the resonating conditions, the ions go on traveling in ever-widening semicircles until they reach the dee periphery. Now the ions or particles are extracted out onto the target by means of the deflecting electrode.

Cyclotrons are usually described in term of diameter of the pole pieces of the magnet. The first machine built by Lawrence and living stone had a magnet with pole piece 11 inches in diameter and produced 1.2 MeV Protons.

A 60 inches cyclotron can produce Protons of about 10 MeV, deuterons of about 20 MeV, and Alpha particles of about 40 MeV. The maximum energy attained by means of University of Michigan USA cyclotron is 35 MeV protons, 50 MeV for deuterons, and 80 MeV for Alpha particles.

**Cyclotron Theory**

Let m be the mass of the ion to be accelerated, B be the magnetic field and q be the charge on the ion which moves with a velocity v in a semi circle of radius r.

The magnetic force acting on the charge inside a dee = qvB

This force provides the necessary centripetal force ( mv2/r ) to the ion to describe semi-circle inside a dee.

If t be the time taken to complete the semi-circle path, then

But

It is clear from eq. (2) that time taken by the ion to complete the semi-circle is independent of the speed and radius of the circular path in which it moves, provided B, q and m remain constant.

Angular frequency of the cyclotron is

**Energy of the ion**

If the average value of the radio frequency potential applied to dee is V and N be the number of ions accelerated, then the final energy attained by the beam of ion is given by

For a singly charged ion, q = e

Which is the maximum energy acquired by ion or particle.

**Advantage of Cyclotron**

The main advantage of the cyclotron is that it requires comparatively low voltage source for producing high particles.

**Limitations of Cyclotron**

**Cyclotron cannot accelerate electrons**. The energy gained by the particle in a cyclotron is limited due to the relativistic of mass of the particle with velocity.

The variation of the mass of an electron with velocity is given by

Where m0 = rest mass of the electron,

v = velocity of the electron,

c = velocity of light ( = 3 * **10**^{8}** ms^{-1}**)

Thus, the time taken by the electron to describe semi circle is given by

Thus, t increases as v increases so the electron takes long time to describe the semicircular path and hence arrives too late in the gap. It means the electron goes out of phase with the applied electric field and hence cannot be further accelerated. That is why, the electrons (light particle ) can not be accelerated by the cyclotron.

- Cyclotron cannot accelerated neutral particle like neutron.