Transient analysis of RF cavities under beam loading

Abstract

The conventional electrical model analogy of a RF cavity is a shunt RLC circuit supplied by two current sources representing the RF amplifier and the beam. In the literature, the impedance of the cavity is often calculated in the Fourier domain. This type of cavity modelling has two drawbacks: First, it assumes a perfect matching between the cavity and the amplifier therefore it neglects the reflected voltage. And, second, it does not provide any information about the cavity transient response, for example at start-up or upon beam arrival, while this information can be very important for the design of the regulation loops. In this work we will remove these drawbacks by calculating the cavity impedance in Laplace domain taking the reflected voltage into account. We will then modify our model so that it also includes the influence of the beam on the cavity. For transient RF simulations, though, a typical problem is the long simulation time due to the relatively slow transient response compared to the RF period. To overcome this problem, finally, we will use a mathematical method to map the cavity frequency response from RF to baseband to reduce the simulation time significantly.