The effects of temperature and RF power level on the tuning of the water-cooled SSC Low-Energy Booster cavity

The SSC Low-Energy Booster (LEB) cavity must rapidly tune from 47.52 to 59.78 MHz. The cavity tuner will use transversely biased ferrite to control the cavity resonance. The thermal expansion of a cavity materials affects its resonance. There are two other known temperature mechanisms that affect resonance in the water-cooled LEB cavity. The saturation magnetization of the ferrite is a function of temperature, and since the ferrite permeability is dependent an the saturation magnetization, the ferrite permeability is also temperature dependent. The ferrite cooling water is present in the tuner RF field, hence the water permittivity, which is very temperature dependent, also affects cavity resonance. While taking data on the SSC Test Cavity to quantify the effect of temperature on the resonance, we observed that the RF power level also perturbed the resonance. It was readily apparent from the data that the power level affected the resonance much more strongly at low values of control bias than at high values. In fact, when we calculate an apparent modified control-bias H field that produces the observed resonance shift, we noticed an almost perfect, though non-linear, correlation between the ratio of H_rf to H _bias and the apparent modified bias field, H_app. This paper will present a set of equations to predict the resonance shifts produced by changes in temperature and RF power level. It will also present the techniques, both theoretical and empirical, by which these equations are derived. Finally, some of the methods for dealing with these resonance shifts will be discussed