Cyclotron

Cyclotron

1. Priyanka Jakhar Physics Lecturer GGIC Vijay Nagar Ghaziabad U.P. Cyclotron Class 12th Physics

2. 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. Cyclotron 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 . One of the most interesting applications of motion of charge particles in electric and magnetic fields is Cyclotron.

3. Principle :--- Lorentz’s Force is the basic principle of Cyclotron. Working of cyclotron is based on the motion of charged particle in combined electric and magnetic field . In this two facts are used simultaneously When a charged particle passes through the electric field the particle get accelerated as a result it kinetic energy increase by passing the particle repeatedly through the electric field, very high kinetic energy is given to the particle . When a charged particle enters the uniform magnetic field perpendicularly, it starts moving on a circular path in a plane perpendicular to the magnetic field. Radius of the circular path increases with the velocity .Frequency of resolution of particle does not depend on the radius or velocity of particle but remains constant.

4. CONSTRUCTION D 1 , D 2 – Dees :-- Cyclotron consists of two semicircular dees D1 and D2,enclosed in chamber close to each other such that their diameters are parallel to each other. The discs(D) perform mainly 2 functions: to block(shield) electric field inside it (known as electrostatic shielding) . act as a capacitor outside the region between the 2 discs to provide some electric field. N, S – Magnetic Pole Pieces :-- This chamber is placed in between two strong magnets. Os cillator :-- An ac voltage is applied in between D1 and D2. The oscillator’s job is to reverse the direction of electric field at the time interval of each revolution of charge, meaning frequency of oscillator  f  should be same as the frequency of cyclotron  f c . It is because when the charge moves from one D to another, the direction of electric field should always be such that the charge always accelerates(and never decelerates). An ion :-- An ion kept in a vacuum chamber. In the space between two dees a source of positive charged is placed at the centre P, which will emit positively charged particle. vacuum chamber:-- The chamber is evacuated so the charged particle should not lose its energy after colliding with the molecule.

5. N S D 1 D 2 + W B Cyclotron: H F Oscillator D 2 D 1 Working: Imagining D 1 is positive and D 2 is negative, the + vely charged particle kept at the centre and in the gap between the dees get accelerated towards D 2 . Due to perpendicular magnetic field and according to Fleming’s Left Hand Rule the charge gets deflected and describes semi-circular path. When it is about to leave D 2 , D 2 becomes + ve and D 1 becomes – ve . Therefore the particle is again accelerated into D 1 where it continues to describe the semi-circular path. The process continues till the charge traverses through the whole space in the dees and finally it comes out with very high speed through the window. W B

6. At certain instant, let D1 be positive and D2 be negative, Ion(+ ve )will be accelerated towards D1 and describes a semicircular path(inside it).When the particle reaches the gap, D2,becomes negative and D1 become positive. So ion is accelerated towards D2 and undergoes a circular motion with larger radius . This process repeats again and again. Thus ion comes near the edge of the dee with high K.E This ion can be directed towards the target by a deflecting plate.

7. Theory: The magnetic force experienced by the charge provides centripetal force required to describe circular path. mv 2 / r = qvB sin 90 ° (where m – mass of the charged particle, q – charge, v – velocity on the path of radius – r, B is magnetic field and 90° is the angle b/n v and B) v = B q r m Time period :--- If t is the time taken by the charge to describe the semi-circular path inside the dee, then t = π r v or t = π m B q Time taken inside the dee depends only on the magnetic field and m/q ratio and not on the speed of the charge or the radius of the path. If T is the time period of the high frequency oscillator, then for resonance, T = 2 t or T = 2 π m B q Cyclotron Frequency :---- If f is the frequency of the high frequency oscillator (Cyclotron Frequency), then f = f = 2 π m B q Frequency of oscillator is adjusted in such a manner that the time in which particle completes its half cycle, in the same time the polarity of the changes. Therefore the working condition of cyclotron is f is the frequency of alternating PD . This is known as the condition of resonance. C

8. Maximum Energy of the Particle: Kinetic Energy of the charged particle is K.E. = ½ m v 2 = ½ m ( B q r m ) 2 = ½ B 2 q 2 r 2 m Maximum Kinetic Energy of the charged particle is when r = R ( radius of the D’s ). = ½ B 2 q 2 R 2 m K.E. max The expressions for Time period and Cyclotron frequency only when m remains constant. (Other quantities are already constant.) m = m [1 – (v 2 / c 2 )] ½ If frequency is varied in synchronisation with the variation of mass of the charged particle (by maintaining B as constant) to have resonance, then the cyclotron is called synchro – cyclotron . If magnetic field is varied in synchronisation with the variation of mass of the charged particle (by maintaining f as constant) to have resonance, then the cyclotron is called isochronous – cyclotron . NOTE: Cyclotron can not be used for accelerating neutral particles. Electrons can not be accelerated because they gain speed very quickly due to their lighter mass and go out of phase with alternating e.m.f. and get lost within the dees . But m varies with v according to Einstein’s Relativistic Principle as per A charged particles crosses the dees twice in one complete rotation . Gain in kinetic energy of a charged particle in one time crossing the dees qV . Therefore gain in kinetic energy in one rotation is equal to 2qV. If particle completes N rotation before coming out of the dees , the kinetic energy of the particle at the exit will be K = 2 NqV

9. Limitations (1 ) As the particle gains extremely high velocity, the mass of particle will be changed from its constant value. This will affect the normal working of cyclotron as frequency depends of mass of particle. (2) Another limitation of cyclotron is that very small particles like electron can not be a accelerated using cyclotron. This is because as the mass of electron is very small the cyclotron frequency required becomes extremely high which is practically difficult. Cyclotron cannot accelerate electrons because electrons are of very small mass. A cyclotron cannot be used to accelerate neutral particles. It cannot accelerate positively charged particles with large mass due to the relativistic effect. Uses of the Cyclotron • For decades best source of high energy beams for physics experiments . • Conceptually this device is very simple but it has huge uses in the field of engineering, physics and medicine. • In the study of nuclear reaction • To produce radioactive materials which are used in medal Medical Sciences . • By planting ions in solid to improve deer qualities in the the synthesis of new material or substances. Treatment for Cancer – Proton Therapy.