Modeling and Analysis of Radio Frequency Structures Using AN Equivalent Circuit Methodology with Application to Charged Particle Accelerator RF Resonators

The delineation of analysis techniques for high power radio frequency resonators, used as a fundamental component of particle accelerators, receives little attention in the literature. This dissertation reviews, describes, and develops techniques for resolving a transmission line mode rf resonator into an approximate equivalent circuit. Specifically, it presents a toolbox of techniques used to model and represent rf structures. One technique develops models of transmission lines with varying characteristic impedance (referred to as non-uniform) using multiple series connected circuits consisting of lumped elements and constant impedance transmission lines based on a conserved energy approach. This technique is tested for exponentially tapered and linearly tapered quarter-wave resonators. Another technique developed, maps transmission lines with arbitrary cross-sections (referred to as nonstandard) to a standard structure that preserves the characteristic impedance and loss properties of the original line. The techniques developed are applied to the analysis of the complex K1200 Superconducting Cyclotron rf resonators at the National Superconducting Cyclotron Laboratory (NSCL). The results predicted from the model are compared to measurements. The K1200 rf resonators are tunable over the frequency range of 9.5 to 27 MHz with tuning stems that vary from 300 cm to 11 cm respectively. The resonators are operated in the continuos wave (cw) mode and sustain peak voltages of up to 180 kV requiring drive power of up to 250 kW. Using the techniques developed, the resonant frequency versus tuning stem position was predicted to within a positioning error that varied from 1 to 3.5 cm over the tuning range of 9.5 to 27 Mhz. The discrepancy between model predictions and the experimental data for the resonator power dissipation is postulated to be due to high surface resistance in regions where the rf surfaces were heavily worked or welded. After adjusting the surface resistance of these regions uniformly, the equivalent shunt circuit resistance was predicted accurately across the tuning range to within the maximum measurement accuracy of +/-5%.