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