An atomic clock including an ion trap assembly, a C-field coil positioned for generating a first magnetic field in the interrogation region of the ion trap assembly, a compensation coil positioned for generating a second magnetic field in the interrogation region, wherein the combination of the first and second magnetic fields produces an ion number-dependent second order Zeeman shift (Zeeman shift) in the resonance frequency that is opposite in sign to an ion number-dependent second order Doppler shift (Doppler shift) in the resonance frequency, the C-field coil has a radius selected using data indicating how changes in the radius affect an ion-number-dependent shift in the resonance frequency, such that a difference in magnitude between the Doppler shift and the Zeeman shift is controlled or reduced, and the resonance frequency, including the adjustment by the Zeeman shift, is used to obtain the frequency standard.