Understanding Cyclotron Oscillations Frequency

[chad mcpeek]

I am having trouble making sense of the frequency of oscillations for a cyclotron. What I don't understand is, if a the voltage difference of the two dees is switched twice ( each time the particles are about to enter them), then why is the frequency of oscillation the same as the frequency at which the particle moves through the cyclotron. To me it seems that the frequency of oscillation should be twice the frequency of the particles but obviously that is not the case.

 

[M Quack]

When the particles (say electrons) cross from the left Dee to the right, then the left Dee has to be negative and the right positive.
1/2 turn later the particles cross from the right to the left. To be accelerated, the right has to be negative and the left positive, i.e. the exact opposite.

 

[chad mcpeek]

I get that but if the dees change signs twice after one revolution of a particle then how is the frequency of oscillation of the dees the same as the frequency of the particles moving through one revolution because it seems like it would be be twice that value since the voltage switches twice in one particle revolution.

 

[M Quack]

So how often do the x- and y-components of the electron's velocity vector change sign during one full period?

 

[chad mcpeek]

Maybe I am misunderstanding what the frequency of osscilation of the cyclotron is but what I thought that was referring to was the frequency at which the voltages of the dees are reversed. What I don't get is how the frequency of a particle circulating in a cyclotron is the same as the frequency of osscilation of that cyclotron (times the dees voltages are reversed per unit time) because the voltages are switched twice in the time it takes a particle to make one revolution.