What affects the value of cyclotron frequency for protons?

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arunashish
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Can anyone tell me the value of cyclotron frequency with full mathematical proof and explanation?
 
on Phys.org
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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