A study of beam position diagnostics using beam-excited dipole modes in third harmonic superconducting accelerating cavities at a free-electron laser

Abstract

We investigate the feasibility of beam position diagnostics using Higher Order Mode (HOM) signals excited by an electron beam in the third harmonic 3.9 GHz superconducting accelerating cavities at FLASH. After careful theoretical and experimental assessment of the HOM spectrum, three modal choices have been narrowed down to fulfill different diagnostics requirements. These are localized dipole beam-pipe modes, trapped cavity modes from the fifth dipole band and propagating modes from the first two dipole bands. These modes are treated with various data analysis techniques: modal identification, direct linear regression (DLR) and singular value decomposition (SVD). Promising options for beam diagnostics are found from all three modal choices. This constitutes the first prediction, subsequently confirmed by experiments, of trapped HOMs in third harmonic cavities, and also the first direct comparison of DLR and SVD in the analysis of HOM-based beam diagnostics.

Statistical methods for transverse beam position diagnostics with higher order modes in third harmonic 3.9GHz superconducting accelerating cavities at FLASH

“…Also these inter-coupled modes preclude a local determination of beam position within each cavity in contradistinction to the TESLA 1.3 GHz cavities. There are however a limited number of modes in the fifth dipole band which are not coupled [9]. These have smaller R/Q values compared to those in the inter-coupled region and hence have a reduced resolution for beam position diagnostics [10].…”

“…Thus the transverse beam positions inside the cavity can be determined from the readouts of the two BPMs by linear interpolation. The detailed setup of the FLASH machine for this study can be found in [10]. The goal is to extract transverse beam position from the HOM waveforms.…”

“…1. The digitized data has been filtered such that only the trapped cavity modes in the fifth dipole band from 9040 MHz to 9078 MHz [9] are preserved and then normalized to the beam charge. These modes are of particular interest since they can provide localized beam position information.…”

“…Such beam diagnostics have been previously studied and electronics have been built for the TESLA 1.3 GHz cavities at FLASH, using a dipole mode at approximately 1.7 GHz with large R/Q value [6]. In the 3.9 GHz cavities, however, no obvious candidate mode exists [7]. The spectrum is dense particularly due to most HOMs being above the cutoff frequency of the inter-connecting beam pipes [8].…”

“…In order to evaluate the various frequency regions which could be used for diagnostics, test electronics have been built by FNAL [10,11]. This down-converts the HOM signal measured from one of the two HOM couplers of each cavity containing dipole modes between 4 and 9.1 GHz to 70 MHz with a 20 MHz bandwidth.…”