Resonance condition of a cyclotron.

[esha]

the charged particle undergoes acceleration because of the presence of electric field between the two Dee. as a result the electric field needs to change it's direction according to the motion of the charged particle. since the time period of the charged particle does not depend upon the velocity we can easily find out the frequency at which the electric field needs to change. so wouldn't this frequency of the oscillator be half the frequency of the charged particle. Cause the charged particle meets the electric field every half of its revolution. if that's the case the frequency of the applied voltage won't be equal to the frequency of the cyclotron. then how come resonance condition would occur?

 

[sophiecentaur]

so wouldn't this frequency of the oscillator be half the frequency of the charged particle

What's the basis for that statement? The electrons have to chase the PD changes between the Ds and that requires the same driving frequency for them to remain in step all the time and to gain energy each rev.