A cyclotron oscillator frequency is `10MHz`. What should be the operating magnetic field for accelerating protons? If the radius of its dees is `60cm`, what is the kinetic energy of the proton beam produced by the acceleration in `MeV`?
`(e=1*6xx10^(-19)C, m_p=1*67xx10^(-27)kg, 1MeV=1*6xx10^(-13)J)`

Explanation

The oscillator frequency should be same as proton’s cyclotron frequency. Using Eqs. (4.5) and [4.6(a)] we have
`B = 2pimv//q = 6.3 xx 1.67 xx 10^(-27) xx 10^(7)//(1.6 xx 10^(-19)) = 0.66T`
Final velocity of protons is
`v = r xx 2pi v = 0.6 mxx 6.3 xx 10^(7) = 3.78 xx 10^(7) m//s`.
`E = ½ mv^(2) = 1.67 xx 10^(-27) xx 14.3 xx 10^(14)//(2 xx 1.6 xx 10^(-13)) = 7 MeV`.