Group Members :

Sahib Ullah (BEE-F14-207)

Faisal Khan (BEE-F14-291)

Zain Aslam (BEE-F14-270)

Introduction to cyclotron.

Principles.

Construction.

Diagram

Working of cyclotron.

Calculations.

Applications.

Limitations.

Advantages.

A cyclotron is a device used to accelerate charged particles to high energies without use of high

voltage

It is a circular particle accelerator capable of generating particle energies between a 1 MeV to

more than 100 MeV

Accelerate charged particles like protons, deuterons, etc. ions using electric and magnetic

field

The cyclotron was one of the earliest types of particle accelerators, and is still used as the

first stage of some large multi-stage particle accelerators.

One of the most interesting applications of motion of charge particles in electric and

magnetic fields is Cyclotron.

Cyclotrons produce very high energy Charge Particles,

𝑲.𝑬 =𝟏

𝟐𝒎𝒗𝟐

E.O Lawrence and M.S Livingston invented this machine in 1934.

This is a charged particle accelerating device. The motion of the charged particle

under perpendicular magnetic field is only applied in the apparatus named cyclotron.

Cyclotron works on the principle that a charged particle moving normal /

perpendicular to a magnetic field experiences magnetic Lorentz force due to which the

particle moves in a circular path.

Lorentz’s Force is the basic principle of Cyclotron.

Conceptually this device is very simple but it has huge uses in the field of engineering,

physics and medicine.

This device basically has three main constructional parts:

Large sized electromagnet to create uniform magnetic field in between its two

face-to-face placed magnetic opposite poles.

Two low height hollow half cylinders made of high

conductive metals. These components of cyclotron are called Dees.

A high-frequency alternating high voltage source.

I. Magnetic system.

II. Ion source system.

III. Dees.

IV. RF system.

V. Extraction system.

VI. Vacuum system.

VII. Target assembly.

When a positive ion of charge q and mass m is emitted from the source, it is

accelerated towards the Dee having a negative potential at that instant of time.

Due to the normal magnetic field, the ion experiences magnetic Lorentz force and

moves in a circular path.

By the time the ion arrives at the gap between the Dees, the polarity of the Dees

gets reversed.

Hence the particle is once again accelerated and moves into the other Dee with a

greater velocity along a circle of greater radius.

Thus the particle moves in a spiral path of increasing radius and when it comes near

the edge, it is taken out with the help of a deflector plate (D.P).

The particle with high energy is now allowed to hit the target T.

o When the particle moves along a circle of radius r with a velocity v, the magnetic

Lorentz force provides the necessary centripetal force.

Bqv = v m 2/ r

Production of charge particle

Acceleration of charge particle

Extraction of beam

Bombardment of target

In magnetic field magnetic force acts as a centripetal force.

𝒒𝒗𝑩 =𝒎𝒗𝟐

𝒓

𝒓 =𝒎𝒗

𝒒𝑩

Radius at each turn increase due to increase in velocity, therefor its behaves like

Spiral. Now angular frequency, from equation above we get,

𝒂𝒔 𝝎 = 𝟐𝝅𝒇 So the frequency is

𝒇 =𝒒𝑩

𝟐𝝅𝒎

Now time period T, 𝑎𝑠 𝒇 =𝟏

𝑻

𝑻 =𝟐𝝅𝒎

𝒒𝑩

Frequency and Time period is

independent of radius.

𝒗 =𝒒𝒓𝑩

𝒎𝒓𝝎 =

𝒒𝒓𝑩

𝒎𝒂𝒔 𝒗 = 𝒓𝝎

𝝎 =𝒒𝑩

𝒎

On the basis of

Ions

Shielding

Energy

Direction

Best source of high-energy beams used for experiment in nuclear physics, where high

energy collisions are required.

Cyclotrons can be used in particle therapy to treat cancer.

Cyclotron beams can be used to bombard other atoms to produce short-lived positron-

emitting isotopes suitable for PET imaging .

Maintaining a uniform magnetic field over a large area of the Dees is difficult.

At high velocities, relativistic variation of mass of the particle upsets the

resonance condition.

At high frequencies, relativistic variation of mass of the electron is appreciable

and hence electrons cannot be accelerated by cyclotron.

It cannot accelerate neutron, because neutron do not have any charge.

The energy of charged particles emerging from cyclotron, is limited due to variation of mass with

velocity, i.e.

𝒎 =𝒎𝟎

𝟏 −𝒗𝟐

𝒄𝟐

Where 𝒎𝟎 is the rest mass, m is the mass in motion when velocity is v and c is the velocity of light.

Utilizes a single, electrical driver.

o This saves energy and $.

High power due to continuous stream of particles.

Compact design.