Resonant excitation of high order modes in the 3.9 GHz cavity of the Linac Coherent Light Source

Construction of the Linac Coherent Light Source II (LCLS-II) is underway for the world’s first hard x-ray free-electron laser. A central part of the LCLS-II project is a 4 GeV superconducting radio frequency electron linac that will operate in the continuous wave (cw) mode. The linac is segmented into four sections named as $L0$, $L1$, $L2$, and $L3$. Two 3.9 GHz cryomodules, each housing of eight third-harmonic cavities similar to the cavities developed for the European X-ray Free Electron Laser (XFEL), will be used in section $L1$ of the linac for linearizing the longitudinal beam profile. In this paper, we present a study of trapped high order modes (HOMs) excited by a cw electron beam in the third-harmonic cavities of the LCLS-II linac. A detailed comparison of the original XFEL design and the LCLS-II design with a modified end group is performed in order to estimate the effect of a reduced beam pipe aperture on the efficiency of HOM damping. Furthermore, we apply a statistical analysis of the eigenmode spectrum for the estimation of the probability of resonant HOM losses and influence of HOMs on beam dynamics.

Figure 1

(a) Scheme of the LCLS-II third-harmonic section. BLA is the HOM beam line absorber, and CM1 and CM2 are the first and second cryomodules, respectively. (b) Layout of 3.9 GHz cavities in the cryomodule.

Figure 2

Trapped modes in the infinite chain of third-harmonic cavities with a random HOM spectrum: (a) type I high-$Q$ HOM is localized within the cavity volume, (b) type II medium-$Q$ HOM occupies the cavity and adjacent beam pipes, and (c) type III low-$Q$ HOM distributed along the cavity chain. All plots show the complex magnitude of the electric field, where a blue color corresponds to zero amplitude.

Figure 3

ANSYS HFSS model for the eigenmode analysis of the chain of three 3.9 GHz cavities.

Figure 4

Complex magnitude of the electric field in the second monopole band (7.048–7.612 GHz) of the 3.9 GHz LCLS-II cavity (fields are normalized to 1 J stored energy).

Figure 5

HOM shunt impedances (left) and external quality factors (right) in the ideal 3.9 GHz LCLS-II cavity.

Figure 6

Resonant HOM excitation, average power (left) and transverse voltage (right), of the ideal 3.9 GHz LCLS-II cavity.

Figure 7

Nominal geometry of the 3.9 GHz LCLS-II cavity (alpha is a reference parameter given in degrees; the other parameters are all in millimeters).

Figure 8

Operating $\pi$ mode in the chain of three 3.9 GHz cavities with mechanical errors.

Figure 9

Frequency standard deviations for the first monopole band of the 3.9 GHz cavity.

Figure 10

Resonant HOM losses (left) and transverse kick (right) in 3.9 GHz XFEL and LCLS-II cavities with mechanical errors.

Figure 11

Resonant excitation of the first monopole band in the 3.9 GHz LCLS-II cavity with 0.3 mA average beam current.

Figure 12

Spread of HOM parameters for high-risk trapped modes in the 3.9 GHz LCLS-II cavity.

Figure 13

Radiation of the middle cavity trapped HOMs through the left and right beam pipes.

Figure 14

Cumulative probability of HOM power radiation through coupler ports in the single 3.9 GHz cavity (left) and in the third-harmonic section (right) of the LCLS-II linac.

Figure 15

Cumulative probability of HOM transverse kick in the single 3.9 GHz cavity (blue line) and in the third-harmonic section (red line) of the LCLS-II linac.