What is a cyclotron? Discuss the principle of a cyclotron.

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(N/A) cyclotron is a device used to accelerate charged particles like protons,deuterons,$\alpha$-particles,etc.,to very high energies. It was invented by $E.O. Lawrence$ and $M.S. Livingston$ in $1934$.
The cyclotron uses both electric and magnetic fields in combination to increase the energy of charged particles. As the fields are perpendicular to each other,they are called crossed fields.
The cyclotron operates on the principle that the frequency of revolution of a charged particle in a magnetic field is independent of its energy.
Principle: $A$ charged particle can be accelerated to very high energies by making it pass through a moderate electric field multiple times. This is achieved with the help of a perpendicular magnetic field,which forces the charged particle into a circular motion. The frequency of this circular motion (cyclotron frequency) is independent of the speed of the particle and the radius of the circular orbit.

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$A$ cyclotron's oscillator frequency is $10 \text{ MHz}$ and the operating magnetic field is $0.66 \text{ T}$. If the radius of its dees is $60 \text{ cm}$, then the kinetic energy of the proton beam produced by the accelerator is: (in $\text{ MeV}$)

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Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency $(rf)$ field were doubled.

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