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Presentation

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Name: SYED SHAHEEN SHAH

CLASS: BS 7th SEMESTER

TOPIC: CYCLOTRON

Institute of Physics and Electronics

Date: 03/10/2013

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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,

𝑲.𝑬 =𝟏

𝟐𝒎𝒗𝟐.

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 𝐸 a charged particle is accelerated.

In Magnetic field 𝐵 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

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• The cyclotron consists of two flat semicircular

metallic boxes 𝑫𝟏 & 𝑫𝟐 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 𝑫𝟏 and then towards 𝑫𝟐. Thus 𝑫𝟏 and 𝑫𝟐

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 𝑫𝟐 . 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 𝑫𝟐 , 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 𝑫𝟏 along circular arc of greater radius as shown in the figure.

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𝑫𝟏 𝑫𝟐

• Here, the time passage to complete the semi –circle in the 𝑫𝟏 remains the same as in 𝑫𝟐.

• If the time of travel in 𝑫𝟏 is equal to half of the time period of the oscillator voltage, the positive ions coming from 𝑫𝟏 will find the reversed field and hence, they are accelerated again in the gap between the Dees.

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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

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• In magnetic field magnetic force

acts as a centripetal force.

𝒒𝒗𝑩 =𝒎𝒗𝟐

𝒓𝒓 =

𝒎𝒗

𝒒𝑩(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,

𝒗 =𝒒𝒓𝑩

𝒎𝒓𝝎 =

𝒒𝒓𝑩

𝒎𝒂𝒔 𝒗 = 𝒓𝝎

𝝎 =𝒒𝑩

𝒎(2)

𝒂𝒔 𝝎 = 𝟐𝝅𝒇 So the frequency is

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𝒇 =𝒒𝑩

𝟐𝝅𝒎(3)

Now time period T, 𝑎𝑠 𝒇 =𝟏

𝑻

𝑻 =𝟐𝝅𝒎

𝒒𝑩(4)

Frequency and Time period is

independent of radius.

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 𝒗𝒎 of the ion may be written as:

𝒗𝒎 =𝒒𝑹𝑩

𝒎(5)

And so the maximum kinetic energy of the ion will be given by

𝑬𝒎 =𝟏

𝟐𝒎𝒗𝒎

𝟐 =𝑹𝟐𝒒𝟐𝑩𝟐

𝟐𝒎

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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.

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𝒇 =𝒒𝑩

𝟐𝝅𝒎=

𝒒𝑩 𝟏−𝒗𝟐

𝒄𝟐

𝒎𝟎

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 𝒇 =𝒒𝑩

𝟐𝝅𝒎is very high,

due to which velocity increase so rapidly that it

becomes out of step very soon.

It is used for experiment

in nuclear physics, where

high energy collisions are

required.

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