  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.
