Analytical solutions are derived for both transient and steady state gradient distributions in the traveling wave (TW) accelerating structures with arbitrary variation of parameters over the structure length. The results of the unloaded and beam loaded cases are presented. Finally, the exact analytical shape of the rf pulse waveform was found in order to apply the transient beam loading compensation scheme during the structure filling time. The obtained theoretical formulas were cross-checked by direct numerical simulations on the CLIC main linac accelerating structure and demonstrated a good agreement. The proposed methods provide a fast and reliable tool for the initial stage of the TW structure analysis.
Superconducting linacs are capable of producing intense, stable, high-quality electron beams that have found widespread applications in science and industry. The 9-cell 1.3-GHz superconducting standing-wave accelerating RF cavity originally developed for e + /e − linear-collider applications [B. Aunes, et al. Phys. Rev. ST Accel. Beams 3, 092001 (2000)] has been broadly employed in various superconducting-linac designs. In this paper we discuss the transfer matrix of such a cavity and present its measurement performed at the Fermilab Accelerator Science and Technology (FAST) facility. The experimental results are found to be in agreement with analytical calculations and numerical simulations.
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.
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