Paper  Title  Page 

SAPAG04  HOMMitigation for Future SPS 33Cell 200 MHz Accelerating Structures  35 


The CERN SPS 200 MHz travelling wave (TW) accelerating structures pose an intensity limitation for the planned High Luminosity (HL) LHC upgrade. Higherorder modes (HOMs) around 630 MHz have been identified as one of the main sources of longitudinal multibunch instabilities. Improved mitigation of these HOMs with respect to today’s HOMdamping scheme is therefore an essential part of the LHC injectors upgrade (LIU) project. The basic principles of HOMcouplers in cavities and today’s damping scheme are reviewed, before illustrating the numerous requirements an improved damping scheme for the future 33cell structures must fulfil. These are, amongst others, the mitigation of HOMs situated in the lower part of the structure where there are no access ports for extraction, a sufficient overall damping performance and an acceptable influence on the fundamental accelerating passband (FPB). Different approaches tackling these challenges are investigated and their performance, advantages and pitfalls are evaluated by ACE3P and CST electromagnetic (EM) field solver suites.  
Slides SAPAG04 [2.184 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018SAPAG04  
About •  paper received ※ 19 October 2018 paper accepted ※ 24 October 2018 issue date ※ 26 January 2019  
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SUPAG02 
Fast Multipole Methods for Multiparticle Simulations  


Funding: Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DEAC0506OR23177. The U.S. Government retains a license to publish or reproduce this manuscript for U.S. Government purposes. The fast multipole method (FMM) reduces the computation cost of the pairwise nonoscillating interaction between N particles from O(N^{2}) to O(N). In the FMM, the contribution from a source particle is represented as a multipole expansion, while the contributions from multiple faraway sources can be combined into a local expansion around an objective particle. Without the dependence on a grid covering the whole domain under study, the FMM treats any charge distribution and geometry in a natural way. It avoids artificial smoothing due to the grid size and redundant computation on the free space grids. We will introduce the concept of the FMM using the Coulomb interaction as an example and then explain how the FMM can be extended to arbitrary nonoscillating interactions. Examples and discussions on how the FMM can be used in scientific simulations, especially in accelerator physics will also be provided. 

Slides SUPAG02 [1.705 MB]  
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MOPLG02 
Recent Developments in Wake Field and Beam Dynamics Computation  


Funding: Work partially funded by DESY, Hamburg. Wake potentials and beam coupling impedances can be calculated analytically only for simple structures and for special limiting cases. For the calculation of wake fields in ’realworld’ 3D accelerator structures, one has to rely on numerical electromagnetic field computation. Among the most successful numerical techniques for wake field calculations in the time domain are dispersionfree methods in the moving window. These techniques are particularly useful for shortrange wake field calculations. Recently, this class of methods has been extended to include Surface Impedance Boundary Conditions (SIBC) based on the Auxiliary Differential Equation (ADE) technique. These boundary conditions allow the computation of resistive wall wake fields for 3D structures with arbitrary frequency dependent conductivity. An important application of this method is the calculation resistive wall wake fields in novel accelerator chambers with NEG and amorphous carbon coatings. Other developments to be discussed include the calculation of CSRwakes in bunch compressors and undulator structures for xray sources. This task is computationally very difficult because of the curved bunch trajectory that leads to extremely high frequency and longrange wake fields. Time domain as well as frequency domain methods based on high order DG and FE discretization techniques for the electromagnetic fields computation in such structures will be presented. 

Slides MOPLG02 [2.762 MB]  
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MOPAG03 
Exploring the Validity of the Paraxial Approximation for Coherent Synchrotron Radiation Wake Fields  


Coherent synchrotron radiation (CSR) is an essential consideration in modern accelerators, yet is often computationally difficult to accurately model. A common approach used in simulating CSR effects uses the paraxial, or slowlyvarying envelope approximation with a simple constant crosssection approximation of the geometry. While these approximations are often valid for the simulation of many accelerator components, we aim to more closely analyze the errors introduced by such approximations by comparing them with wake field solutions obtained by fullwave electromagnetic field simulations. The simulations are performed with CSRDG (Coherent Synchrotron Radiation with Discontinuous Galerkin), our GPUenabled MATLAB code. Extended from earlier work [Coherent Synchrotron Radiation and Wake Fields With Discontinuous Galerkin Time Domain Methods, Proceedings of IPAC 2017, Copenhagen, Denmark], CSRDG evolves Maxwell’s equations the time domain after a curvilinear coordinate transformation and a Fourier series decomposition in a transverse direction.  
Slides MOPAG03 [2.149 MB]  
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TUPAF05 
Advances in Accelerator Modeling with Parallel MultiPhysics Code Suite ACE3P  


ACE3P is a comprehensive set of parallel finiteelement codes for multiphysics modeling of accelerator structures including integrated electromagnetic, thermal and mechanical effects. Recent advances of ACE3P have been focused on the development of multiphysics modeling capabilities, implementation of advanced numerical algorithms, and improvement of code performance on stateoftheart highperformance computing (HPC) platforms for largescale accelerator applications. A nonlinear eigensolver using the CORK algorithm [1] has been implemented in the eigensolver module Omega3P to enable accurate determination of damping factors of resonant modes above the beampipe cutoff frequency. It has enabled the firstever direct calculation of trapped modes in the TESLA TTF cryomodules, providing reliable damping factors that were validated against measurements. A newly developed mechanical eigensolver in the multiphysics module TEM3P has allowed the determination of mechanical modes in Fermilab PIPII high beta 650 MHz cryomodule, demonstrating mode coupling between the 6 cavities in the cryomodule. To exploit multicore computer architectures on supercomputers, a hybrid MPI+OpenMP parallel programing has been developed in the particle tracking module Track3P to speed up dark current simulation in multiple cavities for the LCLSII linac. Highlights of these developments and their impacts on accelerator modeling using HPC will be presented.
[1] R. Van Beeuman, Invited talk, this conference. 

Slides TUPAF05 [1.355 MB]  
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TUPAG01  Computation of Eigenmodes in the BESSY VSR Cavity Chain by Means of Concatenation Strategies  253 


Funding: The research leading to these results was supported by the German Bundesministerium für Bildungund Forschung, Land Berlin and grants of Helmholtz Association Invited Talk: The computation of eigenmodes in chains of superconducting cavities with asymmetric couplers is a demanding problem. This problem typically requires the use of highperformance computers in combination with dedicated software packages. Alternatively, the eigenmodes of chains of superconducting cavities can be determined by the socalled StateSpace Concatenation (SSC) approach that has been developed at the University of Rostock. SSC is based on the decomposition of the full chain into individual segments. Subsequently, the RF properties of every segment are described by reducedorder models. These reducedorder models are concatenated to a reducedorder model of the entire chain by means of algebraic side constraints arising from continuity conditions of the fields across the decomposition planes. The constructed reducedorder model describes the RF properties of the complete structure so that the field distributions, the coupling impedances and the external quality factors of the eigenmodes of the full cavity chain are available. In contrast to direct methods, SSC allows for the computation of the eigenmodes of cavity chains using desktop computers. The current contribution revises the scheme using the BESSY VSR cavity chain as an example. In addition, a comparison between a direct computation of a specific localized mode is described. 

Slides TUPAG01 [3.483 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018TUPAG01  
About •  paper received ※ 21 October 2018 paper accepted ※ 28 January 2019 issue date ※ 26 January 2019  
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TUPAG03 
HighPrecision Lossy Eigenfield Analysis Based on the Finite Element Method  


A proper eigenanalysis of resonating particle accelerator components is particularly advantageous to characterize structures with high quality factors. While in former times eigenmode calculations have been concentrating on the lossless cases only, meanwhile also lossy structures with finiteconductive materials or with absorbing boundary conditions like PML or ports even with low quality factors are routinely available. In the lossless case where no damping is present, all eigenvalues are located along the real axis. If damping has to be modeled instead, the corresponding eigenvalues are distributed within the first quadrant of the complex plane that renders their determination much more expensive. One of the critical issues is that no resonance should be missed so that all desired eigenvalues in a given region of the complex plane can be precisely determined. We implemented two different eigenvalue solvers based on a distributedmemory architecture. While the first one is a classical JacobiDavidson eigenvalue solver which has been adopted to be used also within a complexarithmetic environment, the second one is based on the contourintegral method which enables to determine all eigenvalues within a given closed contour in the complex plane. Both solvers are attached to a FEM processor with secondorder edge elements on curved tetrahedra and can be used together in order to improve the computational efficiency. In the presentation a selection of successful realworld applications of the implemented parallel eigenvalue solvers will be given.  
Slides TUPAG03 [15.980 MB]  
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TUPAG04  Statistical Analysis of the Eigenmode Spectrum in the SRF Cavities with Mechanical Imperfections  265 


Funding: Work is supported by Fermi Research Alliance, LLC under Contract No. DEAC0207CH11359 with the United States Department of Energy The superconducting radio frequency (SRF) technology is progressing rapidly over last decades toward high accelerating gradients and low surface resistance making feasible the particle accelerators operation with high beam currents and long duty factors. However, the coherent RF losses due to high order modes (HOMs) excitation becomes a limiting factor for these regimes. In spite of the operating mode, which is tuned separately, the parameters of HOMs vary from one cavity to another due to finite mechanical tolerances during cavities fabrication. It is vital to know in advance the spread of HOM parameters in order to predict unexpected cryogenic losses, overheating of beam line components and to keep stable beam dynamics. In this paper we present the method of generating the unique cavity geometry with imperfections while preserving operating mode frequency and field flatness. Based on the eigenmode spectrum calculation of series of randomly generated cavities we can accumulate the data for the evaluation the HOM statistics. Finally, we describe the procedure for the estimation of the probability of the resonant HOM losses in the SRF resonators. The study of these effects leads to specifications of SC cavity and cryomodule and can significantly impact on the efficiency and reliability of the machine operation 

Slides TUPAG04 [1.810 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018TUPAG04  
About •  paper received ※ 15 October 2018 paper accepted ※ 28 January 2019 issue date ※ 26 January 2019  
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TUPAG07  Efficient Computation of Lossy Higher Order Modes in Complex SRF Cavities Using Reduced Order Models and Nonlinear Eigenvalue Problem Algorithms  270 


Superconducting radio frequency (SRF) cavities meet the demanding performance requirements of modern accelerators and highbrilliance light sources. For the operation and design of such resonators, a very precise knowledge of their electromagnetic resonances is required. The nontrivial cavity shape demands a numerical solution of Maxwell’s equations to compute the resonant eigenfrequencies, eigenmodes, and their losses. For large and complex structures this is hardly possible on conventional hardware due to the high number of degrees of freedom required to obtain an accurate solution. In previous work it has been shown that the considered problems can be solved on workstation computers without extensive simplification of the structure itself by a combination of StateSpace Concatenation (SSC) and Newton iteration to solve the arising nonlinear eigenvalue problem (NLEVP). First, SSC is applied to the complex, closed and thus lossless RF structure. SSC employs a combination of model order reduction and domain decomposition, greatly reducing the computational effort by effectively limiting the considered frequency domain. Next, a perturbation approach based on SSC is used to describe the resonances of the same geometry subject to external losses. This results in a NLEVP which can be solved efficiently by Newton’s method. In this paper, we expand the NLEVP solution algorithm by a contour integral technique, which increases the completeness of the solution set.  
Slides TUPAG07 [11.204 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018TUPAG07  
About •  paper received ※ 18 October 2018 paper accepted ※ 24 October 2018 issue date ※ 26 January 2019  
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TUPAG22  Main and Fringe Field Computations for the Electrostatic Quadrupoles of the Muon g2 Experiment Storage Ring  313 


Funding: This work was supported by the U.S. Department of Energy under Contract DEFG0208ER41546 and by Fermi Research Alliance for U.S. Department of Energy under Contract DEAC0207CH11359. We consider semiinfinite electrostatic deflectors with plates of different thickness, including plates with rounded edges, and we calculate their electrostatic potential and field using conformal mappings. To validate the calculations, we compare the fringe fields of these electrostatic deflectors with fringe fields of finite electrostatic capacitors, and we extend the study to fringe fields of adjacent electrostatic deflectors with consideration of electrostatic induction, where field falloffs of semiinfinite electrostatic deflectors are slower than exponential and thus behave differently from most magnetic fringe fields. Building on the success with electrostatic deflectors, we develop a highly accurate and fully Maxwellian conformal mappings method for calculation of main fields of electrostatic particle optical elements. A remarkable advantage of this method is the possibility of rapid recalculations with geometric asymmetries and mispowered plates. We use this conformal mappings method to calculate the multipole terms of the high voltage quadrupole used in the storage ring of the Muon g2 Experiment (FNALE0989). Completing the methodological framework, we present a method for extracting multipole strength falloffs of a particle optical element from a set of Fourier mode falloffs. We calculate the quadrupole strength falloff and its effective field boundary (EFB) for the Muon g2 quadrupole, which has explained the experimentally measured tunes, while simple estimates based on a linear model exhibited discrepancies up to 2%. 

Slides TUPAG22 [3.780 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018TUPAG22  
About •  paper received ※ 15 October 2018 paper accepted ※ 28 January 2019 issue date ※ 26 January 2019  
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WEPLG05  Review of Spectral Maxwell Solvers for Electromagnetic ParticleinCell: Algorithms and Advantages  345 


Electromagnetic ParticleInCell codes have been used to simulate both radiofrequency accelerators and plasmabased accelerators. In this context, the ParticleInCell algorithm often uses the finitedifference method in order to solve the Maxwell equations. However, while this method is simple to implement and scales well to multiple processors, it is liable to a number of numerical artifacts that can be particularly serious for simulations of accelerators. An alternative to the finitedifference method is the use of spectral solvers, which are typically less prone to numerical artifacts. In this talk, I will review recent progress in the use of spectral solvers for simulations of plasmabased accelerators. This includes techniques to scale those solvers to large number of processors, extensions to cylindrical geometry, and adaptations to specific problems such as boostedframe simulations.  
Slides WEPLG05 [2.861 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018WEPLG05  
About •  paper received ※ 06 November 2018 paper accepted ※ 28 January 2019 issue date ※ 26 January 2019  
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