CYCLOTRON PREPARED BY Dr. P. K. Sharma
Cyclotron A device which is used for accelerating positively charged particles like proton, deuteron, etc. It was invented by E.O. Lawrence & M.S. Livingston in 1934, California University. It is also known as magnetic resonance accelerator. Principle Cyclotron is based on the principle that a positively charged particle can acquire sufficiently high energy (i.e can be accelerated) with a comparatively small alternating potential difference by making them to pass through cross fields (electric field is perpendicular to magnetic field). Also, time period does not depend on velocity of the particle & radius of the circular path.
Construction Cyclotron It primarily consists of two D-shaped hollow evacuated semicircular metal chambers called dees placed horizontally with a small gap separating them. These are connected to a high frequency oscillator, which can produce a potential difference of the order of at a frequency of . The dees are enclosed in a metal steel box, which is evacuated and well insulated. The whole apparatus is placed in a strong magnetic field produced by two poles of strong electromagnetic NS. Cyclotron
TOP VIEW OF CYCLOTRON
Cyclotron: H F Oscillator W N S B B D1 D2 + D2 D1 W D1, D2 – Dees N, S – Magnetic Pole Pieces W – Window B - Magnetic Field Working: Imagining D1 is positive and D2 is negative, the + vely charged particle kept at the centre and in the gap between the dees get accelerated towards D2. 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 D2, D2 becomes + ve and D1 becomes – ve. Therefore the particle is again accelerated into D1 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.
Theory: The magnetic force experienced by the charge provides centripetal force required to describe circular path. mv2 / 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 If t is the time taken by the charge to describe the semi-circular path inside the dee, then 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. t = π m B q t = π r v or If T is the time period of the high frequency oscillator, then for resonance, T = 2πm B q T = 2 t or
Cyclotron frequency The frequency of cyclotron is given by Where, represents the time period of oscillating electric field. This is often called the magnetic resonance frequency. Cyclotron angular frequency is given by
Maximum energy of positive ion Let the maximum velocity and maximum radius of the circular path be represented by respectively. Maximum
ENERGY OF CHARGED PARTICLE The charged particle gains energy two times during one complete revolution, therefore E = 2NVq where, ‘N’ is the number of revolution, ‘V’ is the potential difference across the dees and ‘q’ is the charge on the particle.
Limitations of cyclotron when the speed approaches the speed of light, the mass of the particle becomes very large compared to its rest mass. With the increase in velocity (v), time required to complete the semicircular path (t) also increases. The charged particle begins to lag behind the electric field and it is finally lost by collision against the walls of the dees.
It cannot be used to accelerate electrons It cannot be used to accelerate electrons. This is due to low mass electrons gain speed very quickly. Thus, the relativistic variation in mass makes them out of step with the oscillating electric field. Betatron. When the cyclotron principle is used to accelerated electrons, it has been historically called a betatron.
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