Question

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

Answer 1

The frequency v_a of the applied voltage (radio frequency) is adjusted so that the polarity of the dees is reversed at the same time that it takes the ions to complete one-half of the revolution. The requirement v_a = v_c is called the resonance condition.

When the frequency of the radio frequency (rf) field was doubled, then the resonance condition are violated and the time period of the radio frequency (rf) field was halved. Therefore, the duration in which a particle completes half revolution inside the dees, radio frequency completes the cycle.

So, particles will accelerate and decelerate alternatively. So, the radius of path in the dees will remain the same.