Design of a helical resonator with improved figure of merit

A helical resonator serves as a key element for the detection of the trapped charged particles in a Penning trap. In order to compare the performance of the helical resonators, the concept of figure of merit (FOM) was introduced by Ulmer et al. [Nucl. Instrum. Methods Phys. Res., Sect. A 705, 55-60 (2013)]. In this work, we optimized the geometrical parameters of a resonator by numerical simulations keeping its outer dimensions and the diameter of the copper wire fixed and obtained the best possible value of FOM under these constraints. The corresponding 95 MHz helical resonator has been designed and fabricated, and its measured value of FOM is in good agreement with the simulated values. An empirical relationship between the total length of the wire to make the helical coil and the resonance frequency has been obtained. The simulations show that the FOM increases considerably with the increase in the conductivity of the building material, and this would be useful in detecting the feeble trap signal in cryogenic environment.