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Question:
what is resonance condition in cyclotron
Answer:

A Cyclotron Accelerator consists of two Dee shaped magnetic plates placed in between a magnetic field generated in perpendicular direction to the electric field. Bothe these magnetic plates are separated from each other by a very small distance. These plates are connected to an alternating electric source which changes the polarity of the electric field periodically. A charged particle like proton is placed at the centre of the gap between the plates. Suppose the particle is proton, then it will be attracted towards the negative plate D2. As it enters the plate, it is acted upon by the magnetic field and we know that a charge moving with velocity v perpendicular to the magnetic field B will move in circular fashion. As soon as this proton exits the plate and enters the gap, the polarity of the plates changes and positively charged plate D1 becomes negatively charged. Hence proton will now get attracted towards the new negatively charged plate D1 and will accelerate towards it. This increases the energy of the proton. As it enters the plate D1, due to the magnetic field, it will move in circular path, but this time as it got accelerated while entering, the radius of the circular path will be larger. Again, as it exits D1, the polarity gets reversed and now, D2 gets negatively charged. Hence the particle will now attract towards D2 and will accelerate towards it. This increases the energy of the proton further. As it enters D2, it will again start moving in circular motion due to magnetic field. But since it was accelerated before entering the plate D2, the radius of the circle will be larger than previous one. This cycle continues and the particle keeps moving spirally.

To maintain this spiral movement, the polarities of the Dees have to be reversed in a time interval T/2T2, where T is the period of revolution of the particle.

 

T = 1/vc

 

Where, vc is the cyclotron frequency. If we denote the applied voltage by vava, then the requirement is vava=vcvc. This condition is called resonance condition.

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