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Working :
F= qVBsin90 ̊
F = qVB............... (2)
qB = mV/ r
r = mV/ qB
This represents the expression for the radius of circular path of cyclotron .
Cyclotron
Introduction:
Cyclotron is one among the important inventions in science. The invention of cyclotron has made it possible for scientists around the world to accelerate charged particles like proton, neutron, electron, deutron etc. This device with an incredible qualities was developed by Ernest O. Lawrence and Living stone in 1929– 1930 at the University of California, Berkeley, and patented in 1932.
cyclotron has been an important invention in the last century which allows us to treat patients which are suffering from tumors. cyclotrons can be used in particle therapy to treat cancer. However, Ion beams from cyclotrons can be used, as in proton therapy, to penetrate the body of the patients and kill Tumors caused by the radiation damage, while minimizing the damage to the healthy tissue along their path.
Principle :
A cyclotron employs a uniform magnetic field and an electric field. The magnetic field is fully responsible for the circular motion of the charged particle while as the electric field is responsible for increasing the speed of the charged particle.
Construction of cyclotron :
Cyclotron consists of two D-shaped hallow evacuated chambers D₁ and D₂ called as Dees. These Dees are placed in horizontal position and are slightly separated from each other. These Dees are connected to the high frequency oscillator Which can produce a potential difference of 10⁴volt. The Dees are placed face to face with a narrow gap between them, creating a cylindrical space within them for the particles to move.
The two Dees are enclosed in an evacuated steel box, and the steel box is placed in a strong magnetic field produced by two pole pieces of strong electro magnet NS. The magnetic field is placed perpendicular to the plane of Dees. The magnetic field causes the particles path to bend in a circle due to the Lorentz Force perpendicular to their direction of motion. P is the place of source of positively charged particles.
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cyclotron
The positive ion which is to be accelerated is produced at place P. At this moment, imagine the charges of Dees as negative and positive. suppose we consider D₁ to be negative and D₂ to be positive. Therefore, the positive ion will be accelerated towards D₁. But as it enters inside of D₁ ,it finds no electric field inside hallow dee D₁. However, the magnetic field is acting perpendicularly on it. Hence, the path described by a positive ion is circular.
After a short time, for example ' t ' ,the positive ion will come out of D₁. Exactly at this time, both the Dees change their signs, that's D₁ becomes positive and D₂ becomes negative, due to the high frequency oscillator. Also, the positive ion is accelerated between the two Dees and it enters dee D₂ with an increased velocity. As the positive ion goes inside the dee D₂ , it finds no electric field inside the hallow dee D₂ ,However, the magnetic field is acting perpendicularly on it. Hence the path described by a positive ion is circular. After some time, for example, 't', the positive ion will come out of dee D₂.
After doing this process, the positive ion comes in the space that's between the two Dees, again D₁ becomes negative and D₂ becomes positive. Also the positive ion starts accelerating again that's it starts entering into the Dees D₁ , with greater velocity. Also, it will describe a circular path of increased radius and so on.
Thus it becomes clear that the path of positive ion is spiral. Ultimately, as the particle comes near the edge, it is taken out of a window W with the help of deflection plates. The particle is then allowed to hit a target T.
Theory:
Calculation of the radius of circular path of cyclotron :
Let us consider a positive ion of mass 'm' and having charge 'q'. The magnetic field acts perpendicular to the plane of dees. Due to this magnetic field, the positive ion will describe a circular path.
Hence, the centripetal force (F) acts on it, which is given by
F = mv²/r.................(1)
Also, force acting on the positive ion due to magnetic field B is given by ;
F = q (V ̄ ͐ ×B ̄ ͐)
F= qVBsin90 ̊
F = qVB............... (2)
from equations 1 and 2 , we get;
qVB = mv²/r
qB = mV/ r
r = mV/ qB
This represents the expression for the radius of circular path of cyclotron .
Uses :
cyclotron is having many uses. Below I have discussed some of them.
1) They are used in researches to study about electromagnetic waves, and to study the properties of nucleus of an atom in nuclear physics.
2) They are used in particle therapy like cancer ,wherein the radiations are used to penetrate the tissues of the body and damage the cancer cells ,senescent cells , etc.
cyclotron
Limitations:
1) The cyclotron can accelerate charged particles up-to a certain limit.
2) It doesn't accelerate uncharged particles.
3) It is suitable only for accelerating positive ions etc. The electrons cannot be accelerated by cyclotron.
Conclusion :
This report has discussed the importance of the invention of cyclotron. This report also provides you information related to its construction and working. It also includes some of the uses and limitations of cyclotron . By the end of the report the information about cyclotron is clear.
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