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Ions confined using a Paul trap require a stable, high voltage and low noiseradio frequency (RF) potential. We present a guide for the design andconstruction of a helical coil resonator for a desired frequency that maximisesthe quality factor for a set of experimental constraints. We provide anin-depth analysis of the system formed from a shielded helical coil and an iontrap by treating the system as a lumped element model. This allows us topredict the resonant frequency and quality factor in terms of the physicalparameters of the resonator and the properties of the ion trap. We also comparetheoretical predictions with experimental data for different resonators, andpredict the voltage applied to the ion trap as a function of the Q-factor,input power and the properties of the resonant circuit.

On the application of radio frequency voltages to ion traps via helical resonators