The transient behavior of superconducting multi-cell accelerating cavities

Abstract

We employ an equivalent-circuit model of a multi-cell cavity to explore its time-dependent behavior in order to understand differences between the multi-cell model and the commonly-used model of a single-cell resonator. Furthermore, we address tolerances that arise from manufacturing imperfections.

Figures (15)

• Figure 1: Multi-cell cavity based on parallel-circuit RLC resonators, coupled via capacitors $\hat{C}$, and driven by a generator with input impedance $Z_0$.
• Figure 2: Bare multi-cell cavity in which coupling to the generator and the resistors are omitted. Note, however, the capacitors $C_a$ and $C_b$ that represent coupling to the beam pipe.
• Figure 3: Modes and eigenvalues of a five-cell cavity with $\kappa=0.01$.
• Figure 4: Eigenvalues as function of an error $\Delta\kappa_2$ (left) and the relative frequency shift $\Delta\omega_{\pi}/\omega_{\pi}$ of the $\pi$-mode (right).
• Figure 5: Left: real (top) and imaginary (bottom) phase in cells 1, 3, and 5 for the initial 0.4 µ s after the generator is switched on. Right: the corresponding signals for the first 5 µ s.