Can anyone tell me the value of cyclotron frequency with full mathematical proof and explanation?
Honestly, the Wikipedia article does a satisfactory job of doing so.
Two things the above formula for proton cyclotron resonance misses:
1) At higher proton energies, the mass in the denominator of the equation becomes relativistic, causing the resonance frequency to drop.
2) For vertical orbit stability, the vertical B field Bz(r) must decrease as a function of r (radius) of orbit.
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