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Presentation

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Name: SYED SHAHEEN SHAHCLASS: BS 7th SEMESTERTOPIC: CYCLOTRON

Institute of Physics and Electronics

Date: 03/10/2013

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Cyclotron

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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.

It is a machine use to accelerate charge particles.

Cyclotrons produce very high energy Charge Particles, .

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

Introduction

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The Cyclotron works on the principles that:In Electric Field a charged particle is

accelerated.In Magnetic field a charged particle can be

turned around. It makes use of the magnetic force on a

moving charge to bend moving charges into a semicircular path between accelerations by an applied electric field. The applied electric field accelerates charged particle between the "Dees" of the magnetic field region.

Principle

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DESCRIPTION & DESIGN

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DESCRIPTION & DESIGN

• The cyclotron consists of two flat semicircular metallic boxes called the Dees on account of their shape like the letter D.

• The two Dees are separated by a narrow parallel gap.

• A high Frequency of oscillator, which provides an alternating current is connected between the two Dees.

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• Oscillator establishes an alternating electric field in the gap between the Dees, i.e. the electric field is once directed towards and then towards . Thus and become alternating positive and negative at the same rate as the frequency of the oscillator.

• A source is place at the center of the Dees which supplied positive ions to accelerate.

• These Dees are mounted inside a vacuum chamber; the chamber is mounted horizontally between the pole pieces (N&S) of a huge electromagnet capable of producing a vertical field.

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WORKING

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WORKING

The positive ions emitted from the source will be accelerated in the gap towards the Dee which is negative at that time.

Let it be . Since, there is no electric field inside the Dees, the positive ion move with constant velocity along circles of constant radius under the influence of magnetic field which is perpendicular the Dees.

If by the time the ions emerge from , the polarity of the applied potential is reversed, the positive ions will again face the negative Dee and thus will be again accelerated by the Electric field in the gap.

Since, there velocity is increased, they will now move through along circular arc of greater radius as shown in the figure.

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𝑫𝟏 𝑫𝟐

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• Here, the time passage to complete the semi – circle in the remains the same as in .

• If the time of travel in is equal to half of the time period of the oscillator voltage, the positive ions coming from will find the reversed field and hence, they are accelerated again in the gap between the Dees.

𝑫𝟏

𝑫𝟐

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• In this way the positive ions move faster and faster moving in ever – expanding circles until they reach the outer edge of the Dees, where they are deflected by deflector flat and strike the target.

• Here it should be remembered that the time required for the positive ions to make one complete turn within Dees is the same for all speeds and is equal to the time period of the oscillator.

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Calculations

• In magnetic field magnetic force acts as a centripetal force.

(1)• Radius at each turn increase due to increase in velocity, therefor its behaves like Spiral

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Now angular frequency, from equation (1) we get,

(2)

So the frequency is

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(3)Now time period T,

(4)Frequency and Time period is independent of radius.

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ENERGY OF A CHARGE PARTICLE ACCELERATED BY A CYCLOTRON The ions will have maximum

energy when it travels at the boundary of the Dee. If the outside radius of the Dee is R, then according to equation (1), the maximum velocity of the ion may be written as:

(5) And so the maximum kinetic

energy of the ion will be given by

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LIMITATIONS 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.,

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

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Thus, the frequency of rotation of charged particle decreases with increase of velocity.

Consequently, the charge particle takes a longer time to complete semicircular path. Now the particle continuously goes on lagging behind the alternating potential differences till a stage is reached when it is no longer be accelerated further.

It cannot accelerate electron. The mass of electron is so small that the frequency is very high, due to which velocity increase so rapidly that it becomes out of step very soon.

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USES

It is used for experiment in nuclear physics, where high energy collisions are required.

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