1. SRF Cavity Imperfection Studies Using Advanced Shape Uncertainty Quantification Tools*
V. Akcelik, L-Q Lee, Z. Li, C-K Ng, L. Xiao and K. Ko,
SLAC Menlo Park, CA 94025, USA
Abstract: The deviation of a SRF cavity from the designed shape may have a significant impact on cavity performance and its wakefields with unexpected effects in beam dynamics. Most of these deviations are unknown in the final cavity installation because of the complicated process of fabrication and tuning. It is desirable to quantify these deviations using measurable RF parameters so that one can better predict the cavity performance and implement realistic tolerance criteria on design and manufacturing to improve quality assurance. As part of the DOE SciDAC ComPASS project, SLAC has developed advanced Shape Determination Tools that can recover the real cavity shape from cavity data by solving an inverse problem. The capabilities of these tools and their successful application to identify the cause of the BBU in the CEBAF 12 GeV Upgrade will be presented.
Motivation
Deformation of TDR cavity
SRF cavities real shape differs from original shape due to loose machine tolerance and tuning process for the accelerating mode.
The deformation of the cavity leads to changes in higher order mode frequencies, field distribution and their damping affects, and may result in beam instabilities.
Direct measurement of cavity shape is not feasible.
Infer cavity shape from measured rf parameters.
Objective function includes monopole and dipole frequencies, and monopole field values along the cavity axis.
Inversion algorithm successfully reduced the frequency error for the deformed cavity to the noise level.
2nd Dipole Band
Stability threshold
(R/Q) x Qe
8 TESLA cavity
measurements
Dipole mode measurements in a TDR module
Frequency misfits for the ideal and deformed shapes
Solve an inverse problem to determine the deformed cavity shape.
Use measured rf parameters such as frequency, external Q and field profile as inputs.
The inversion variables are the shape deviations.
Objective function is to minimize weighted least square misfit of the computed and measured response
The nonlinear least squares problem is solved using Gauss-Newton method.
Nonlinear optimization algorithm typically converges within a handful of iterations.
Inverse Problem for Shape Determination
Beam Breakup in CEBAF 12-GeV Upgrade
BBU observed at well below the designed beam current.
HOMs with exceptionally high Q measured.
HOM
coupler
Qext of vertical modes for ideal and deformed cavities
Field profile of high-Q modes in deformed cavity
Ideal
Deformed
Ideal and deformed cavities
Solutions to the inverse problem identified the main cause of BBU: Cavity is 8 mm shorter – subsequently confirmed by measurements.
Fields of the 3 abnormally high Q modes shifted away form the coupler.
Importance of quality control underscored.
*Work supported by the U.S. DOE ASCR, BES, and HEP Divisions under contract No. DE-AC02-76SF00515