Higher order mode damping in a five-cell superconducting rf cavity with a photonic band gap coupler cell

We present a study of higher order mode (HOM) damping in the first multicell superconducting radio-frequency (SRF) cavity with a photonic band gap (PBG) coupler cell. Achieving higher average beam currents is particularly desirable for future light sources and particle colliders based on SRF energy-recovery linacs (ERLs). Beam current in ERLs is limited by the beam breakup instability, caused by parasitic HOMs interacting with the beam in accelerating cavities. A PBG cell incorporated in an accelerating cavity can reduce the negative effect of HOMs by providing a frequency selective damping mechanism, thus allowing significantly higher beam currents. The five-cell cavity with a PBG cell was designed and optimized for HOM damping. Monopole and dipole HOMs were simulated. The SRF cavity was fabricated and tuned. External quality factors for some HOMs were measured in a cold test. The measurements agreed well with the simulations.

Figure 1

Frequency of eigenmode solutions in an infinite photonic crystal as a function of the wave vector in the plane of the crystal. The crystal has a triangular lattice of metal rods with a ratio of the rod radius, $a$, to the spacing between the rods, $b$, equal to 0.15. Frequencies for the monopole and the dipole modes are shown with dashed straight lines in a resonator formed by a single removed rod.

Figure 2

Drawing of the 2.1 GHz five-cell cavity with the PBG cell replacing one of the elliptical cells.

Figure 3

PBG cell as seen from the $Z$ axis pointing along the beam trajectory. The vacuum region is shown in blue.

Figure 4

The design accelerating the gradient profile, compared to the profile measured in the welded cavity using the bead-pulling method. The field in the center cell is intentionally lowered to ensure an equal peak surface magnetic field in every cell.

Figure 5

Transverse impedance calculated by CST Particle Studio for the electron beam displaced in the $X$ direction (a) and the $Y$ direction (b) by 6.35 mm. The ten most dangerous modes correspond to the biggest peaks in impedance.

Figure 6

Shunt impedances (a) and external $Q$ factors (b) for monopoles and dipoles in the five-cell PBG cavity (simulation). Only modes with $R/Q\ge 1\mathrm{\Omega }$ are shown.

Figure 7

BBU figure of merit $(R/Q)Q_{\mathrm{ext}}f$ for the dipole modes for two different cavities: the nine-cell TESLA and the five-cell PBG. Dipole shunt impedance is in units of ohms. The dashed lines mark the highest values of the figure of merit for HOMs with frequencies below the corresponding beam pipe cutoffs. Data for the TESLA cavity are from Refs. [14, 37].

Figure 8

Halves of the elliptical cells after being welded together at the irises (a). Photo of the PBG cell with welded rods (b). Final photo of the fabricated five-cell cavity (c).

Figure 9

Normalized phase shift in the $S_{21}$ signal obtained during the bead pull at the frequency corresponding to the $X_2$ mode. For comparison, the phase shift simulated in HFSS is shown.