Title: Computing resonant modes of accelerator cavities by solving nonlinear eigenvalue problems via rational approximation

Abstract

Here, we present an efficient and reliable algorithm for solving a class of nonlinear eigenvalue problems arising from the modeling of particle accelerator cavities. The eigenvalue nonlinearity in these problems results from the use of waveguides to couple external power sources or to allow certain excited electromagnetic modes to exit the cavity. We use a rational approximation to reduce the nonlinear eigenvalue problem first to a rational eigenvalue problem. We then apply a special linearization procedure to turn the rational eigenvalue problem into a larger linear eigenvalue problem with the same eigenvalues, which can be solved by existing iterative methods. By using a compact scheme to represent both the linearized operator and the eigenvectors to be computed, we obtain a numerical method that only involves solving linear systems of equations of the same dimension as the original nonlinear eigenvalue problem. We refer to this method as a compact rational Krylov (CORK) method. We implemented the CORK method in the Omega3P module of the Advanced Computational Electromagnetic 3D Parallel (ACE3P) simulation suite and validated it by comparing the computed cavity resonant frequencies and damping Q factors of a small model problem to those obtained from a fitting procedure that uses frequencymore » responses computed by another ACE3P module called S3P. We also used the CORK method to compute trapped modes damped in an ideal eight 9-cell SRF cavity cryomodule. This was the first time it was possible to compute these modes directly. The damping Q factors of the computed modes match well with those measured in experiments and the difference in resonant frequencies is within the range introduced by cavity imperfection. Therefore, the CORK method is an extremely valuable tool for computational cavity design.« less

Authors:

Van Beeumen, Roel  ^[1];

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Marques, Osni ^[1]; Ng, Esmond G. ^[1]; Yang, Chao ^[1]; Bai, Zhaojun ^[2]; Ge, Lixin ^[3]; Kononenko, Oleksiy ^[3]; Li, Zenghai ^[3]; Ng, Cho -Kuen ^[3]; Xiao, Liling ^[3]

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+ Show Author Affiliations

1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2. Univ. of California, Davis, CA (United States)
3. SLAC National Accelerator Lab., Menlo Park, CA (United States)

Publication Date:

Fri Aug 10 00:00:00 EDT 2018

Research Org.:

SLAC National Accelerator Lab., Menlo Park, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), High Energy Physics (HEP); Research Foundation - Flanders (FWO) (Belgium)

OSTI Identifier:

1490813

Alternate Identifier(s):

OSTI ID: 1477414; OSTI ID: 1702373

Grant/Contract Number:  

AC02-05CH11231; AC02-76SF00515; 12J2217N

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Computational Physics

Additional Journal Information:

Journal Volume: 374; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; 43 PARTICLE ACCELERATORS; Accelerator modeling; Nonlinear eigenvalue problem; CORK method; accelerator modeling; nonlinear eigenvalue problem