Paper  Title  Page 

MOADI1  High Precision Cavity Simulations  43 


Funding: Work supported by DESY, Hamburg The design and optimization of particle accelerator components are fundamentally based on beam dynamics simulations. The knowledge of the interaction of moving charged particles with the surrounding materials and fields enables to optimize individual devices and consequently to take the best advantage of the entire machine. Among the essential accelerator components are radiofrequency cavities which are utilized for acceleration as well as for beam diagnostics. In these applications, precise beam dynamics simulations urgently require highprecision data of the electromagnetic fields. Numerical simulations based on Maxwell’s equations have to represent the resulting fields on an acceptable level of quality even with limited amount of degrees of freedom. On the other hand, the particle beam itself gives rise to the excitation of undesired modes which have to be extracted from the cavities. In the current work, some of the challenges faced in high precision cavity simulations are summarized. Based on highperformance eigenvalue calculations, important features like "lownoise" field evaluations or portmode boundary approximations to enable travelingwave transport are addressed. 

Slides MOADI1 [4.234 MB]  
MOADC2  Implementational Aspects of Eigenmode Computation Based on Perturbation Theory  48 


Funding: Work supported by Federal Ministry for Research and Education BMBF under contracts 05H09HR5 and 05K10HRC. Geometry perturbations affect the eigenmodes of a resonant cavity and thereby can improve but also impair the performance characteristics of the cavity. To investigate the effects of both, intentional and inevitable geometry variations parameter studies are to be undertaken. Using common eigenmode solvers involves to perform a full eigenmode computation for each variation step, even if the geometry is only slightly altered. Therefore, such investigations tend to be computationally extensive and inefficient. Yet, the computational effort for parameter studies may be significantly reduced by using perturbative computation methods. Knowing a set of initial eigenmodes of the unperturbed geometry these allow for the expansion of the eigenmodes of the perturbed geometry in terms of the unperturbed modes. In this paper, we study the complexity of a numerical implementation of perturbative methods. An essential aspect is the computation and analysis of the unperturbed modes since the number and order of these modes determine the accuracy of the results. 

Slides MOADC2 [2.431 MB]  
MOADC3  An Application of the Nonconforming CrouzeixRaviart Finite Element Method to Space Charge Calculations  51 


The calculation of space charge effects in linear accellerators is an important prerequisite to understand the interaction between charged particles and the surrounding environment. These calculations should be as efficient as possible. In this work we explore the suitability of the CrouzeixRaviart Finite Element Method for the computation of the selffield of an electron bunch.  
Slides MOADC3 [1.028 MB]  
TUAAI1 
Numerical Modelling of RF Electron Sources for FELAccelerators  


Funding: Work supported by DESY, Hamburg RF sources represent a key component for FEL radiation sources. The most important tool for their analysis is numerical simulation. However, the broad spectrum of phenomena involved, including spacecharge interaction, retardation effects as well as cavity wakefields, make this type of simulations extremely demanding. Beam dynamics simulation codes are faced with the challenge of reproducing all these effects occurring at different temporal and spatial scales while using a possibly small amount of computational resources and simulation times. According to the physical assumptions employed, these codes may be categorized as


Slides TUAAI1 [1.578 MB]  
TUACI1  Numerical Modeling of Collective Effects in Free Electron Laser  81 


In order to have a free electron laser (FEL) of high performance we need to design and optimize it taking into account the dynamics of electrons and their interactions with each other and with their surroundings. An accurate selfconsistent simulation of collective effects in the charged beams remains a challenging problem for numerical analysis. In this paper we consider only the modeling of FEL process in an undulator section. We give a short overview of the numerical methods adopted in different FEL codes. Advantages and drawbacks of these methods will be discussed. Some approaches to improve the accuracy and efficiency of the codes will be presented and the remaining challenges in FEL modeling will be highlighted.  
Slides TUACI1 [2.659 MB]  
TUACC2  WAVE  A Computer Code for the Tracking of Electrons through Magnetic Fields and the Calculation of Spontaneous Synchrotron Radiation  86 


WAVE has been developed since 1990 at BESSY  now HelmholtzZentrum Berlin (HZB)  to calculate spontaneous synchrotron radiation for arbitrary magnetic fields. A variety of field models for dipoles, wavelength shifters, and undulators is available. Field maps and tables can be read and written. Many routines to handle magnetic fields are implemented, including simulations of field error e.g. due to misalignment. Coherent radiation of electrons in a bunch and energy losses due to radiation are taken into account. Phase space distribution of electrons are taken into account by various algorithms. Generating functions and linear transfer matrices for particle tracking purposes can be calculated. Subroutines to calculate the effects of insertion devices on the storage ring are included. The program runs in batch mode, controlled by input files, but a simple GUI is also provided. The results are given as ASCII data or binary formats of the programs PAW, ROOT, and HDF5. Parallel runs of WAVE on a cluster are supported. WAVE has been checked and validated with the synchrotron radiation code of the German National Bureau of Standards (PTB) based on Schwinger's formula.  
Slides TUACC2 [3.685 MB]  
TUACC3  A Fast Integrated Green Function Method for Computing 1D CSR Wakefields Including Upstream Transients  89 


Funding: This work is supported under DOE Contract No. DEAC0205CH11231. An efficient numerical method for computing wakefields due to coherent synchrotron radiation (CSR) has been implemented using a onedimensional integrated Green function approach. The contribution from CSR that is generated upstream and propagates across one or more lattice elements before interacting with the bunch is included. This method does not require computing the derivative of the longitudinal charge density, and accurately includes the shortrange behavior of the CSR interaction. As an application of this method, we examine the importance of upstream transient wakefields within several bending elements of a proposed Next Generation Light Source. 

Slides TUACC3 [2.060 MB]  
TUSDC2  Rapid Integration Over History in Selfconsistent 2D CSR Modeling  112 


Funding: This work has been supported by DOE under DEFG99ER41104 In our selfconsistent algorithm for calculating 2D CSR effects we reduce the field calculation to a 2D integral over the 2D charge and current densities of the bunch and their time history. Our code VM3@A (VlasovMaxwell Montecarlo Method @ Albuquerque) implements this in a time stepping algorithm as discussed in PRSTAB 12, 080704 (2009). A major expense is the integration over history at each time step. By going to Fourier space the 2D integral is reduced to a 1D convolution over history. This may on its own have a computational advantage, however, using the kernel compression technique of Alpert, Greengard and Hagstrom [1, 2], we approximate the convolution kernel by a sum of exponentials. This allows a time step to be taken using information only from the previous time step, thus eliminating the integral over history. Of course 2D Fourier transforms must be calculated at each step, these can be done with an FFT (or NFFT). We discuss the flop count for the two approaches. In addition we implement this as an option in VM3@A and compare efficiencies of our new and old approaches in the context of a bunch compressor system for the LCLS. [1] SIAM J. Numer. Anal. 37(2000) 1138. See also PhD thesis at http://web.njit.edu/~jiang/pub.html [2] S. R. Lau, J. Math. Phys. 46, 102503, (2005). Supported by DEFG0299ER41104 

Slides TUSDC2 [0.485 MB]  
WESAI1 
Advanced Modeling and Measurements of LHC Beam Halo and Collimation  


The Large Hadron Collider at CERN has an advanced beam cleaning system, which relies on about 100 collimators with various material and orientations. This system constrains the beam phase space in such a way that any stray protons or ions in the LHC are intercepted and efficiently absorbed at collimators, thus protecting the superconducting magnets against any direct beam loss. The allowed leakage from the collimators is less than 0.002% of the impacting load. The numerical methods used in the design of the system are presented. It is shown that the measured performance agrees very well with the expectations and design goals.  
Slides WESAI1 [14.192 MB]  
WEP08  Comparison of Different Electromagnetic Solvers for Accelerator Simulations  155 


Funding: Chinese Academy of Science Electromagnetic simulations are fundamental for accelerator modeling. In this paper two highorder numerical methods will be studied. These include continuous Galerkin (CG) method with vector bases, and discontinuous Galerkin (DG) method with nodal bases. Both methods apply domain decomposition method for the parallelization. Due to the difference in the numerical methods, these methods have different performance in speed and accuracy. DG method on unstructured grid has the advantages of easy parallelization, good scalability, and strong capability to handle complex geometries. Benchmarks of these methods will be shown on simple geometries in detail first. Then they will be applied for simulation in accelerator devices, and the results will be compared and discussed. 

WEP11  Stochastic Response Surface Method for Studying Microphoning and Lorenz Detuning of Accelerator Cavities  158 


Funding: This research is funded by grant KUL_3E100118 and grant KUL_3E080005. The dependence of the eigenfrequencies of a superconductive cavity on its geometry are represented by a stochastic response surface model. The model is constructed on the basis of both information on the eigenfrequencies as on their sensitivities with respect to the geometry. The eigenmodes are calculated using the 2D or 3D finite element method or finite integration technique. The stochastic representation does not only model uncertainties on the geometrical parameters but also inaccuracies of the eigenmode solvers, e.g. due to remeshing. Variations or optimisations of the geometry are carried out on the surrogate model. The model allows an efficient evaluation of microphoning and Lorentz detuning of accelerator cavities. 

Poster WEP11 [0.665 MB]  
WEP12  Realistic 3Dimensional Eigenmodal Analysis of Electromagnetic Cavities using Surface Impedance Boundary Conditions  161 


Funding: The work of the first author (H. Guo) was supported in part by grant no. 200021117978 of the Swiss National Science Foundation. The new Xray Free Electron Laser (SwissFEL) at the Paul Scherrer Institute (PSI) employs, among many other radio frequency elements, a transverse deflecting cavity for beam diagnostics. Since the fabrication process is expensive, an accurate 3D eigenmodal analysis is indispensable. The software package Femaxx has been developed for solving large scale eigenvalue problems on distributed memory parallel computers. Usually, it is sufficient to assume that the tangential electric field vanishes on the cavity wall. To better approximate reality, we consider the cavity wall conductivity is large but finite, and thus the tangential electrical field on the wall is nonzero. We use the surface impedance boundary conditions (SIBC) arising from the skineffect model. The resulting nonlinear eigenvalue problem is solved with a nonlinear Jacobi–Davidson method. We demonstrate the performance of the method. First, we investigate the fundamental mode of a pillbox cavity. We study resonance, skin depth and quality factor as a function of the cavity wall conductivity. Second, we analyze the transverse deflecting cavity to assess the capability of the method for technologically relevant problems. 

WESCI1  EM Simulations in Beam Coupling Impedance Studies: Some Examples of Application  190 


In the frame of the SPS upgrade an accurate impedance model is needed in order to predict the instability threshold and if necessary to start a campaign of impedance reduction. Analytical models, 3D simulations and bench measurements are used to estimate the impedance contribution of the different devices along the machine. Special attention is devoted to the estimation of the impedance contribution of the kicker magnets that are suspected to be the most important impedance source in SPS. In particular a numerical study is carried out to analyze the effect of the serigraphy in the SPS extraction kicker. An important part of the devices simulations are the ferrite model. For this reason a numerical based method to measure the electromagnetic properties of the material has been developed to measure the ferrite properties. A simulation technique, in order to account for external cable is developed. The simulation results were benchmarked with analytical models and observations with beam. A numerical study was also performed to investigate the limits of the wire method for beam coupling impedance measurements.  
Slides WESCI1 [1.571 MB]  
THACI1  Lumped Equivalent Models of Complex RF Structures  245 


Funding: partly funded by EU FP7 Research Infrastructure Grant No. 227579 The prediction of RF properties of complex accelerating structures is an important issue in computational accelerator physics. This paper describes the derivation of state space equations for complex structures based on real eigenmodes of sections of the decomposed complex structure. The state space equations enable the calculation of system responses due to port excitations by means of standard ordinary differential equation solvers. Therefore, the state space equations are referred to as lumped equivalent models of such complex RF structures. Besides fast computation of system responses, the equivalent models enable the calculation of secondary quantities such as external quality factors. The present contribution discusses theoretical aspects and illustrates an application example. 

Slides THACI1 [1.538 MB]  
THACC2  Eigenmode Computation for FerriteLoaded Cavity Resonators  250 


Funding: Work supported by GSI For acceleration of charged particles at the heavyion synchrotron at the GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt two ferriteloaded cavity resonators are installed within the ring. Their eigenfrequency can be tuned by properly choosing a bias current and thereby modifying the differential permeability of the ferrite material. The goal of the presented work is to numerically determine the lowest eigensolutions of accelerating ferriteloaded cavities based on the Finite Integration Technique. The newly developed solver includes two subcomponents: Firstly, a magnetostatic solver supporting nonlinear material for the computation of the magnetic field which is excited by the specified bias current. This enables to linearize the constitutive equation for the ferrite material at the current working point, at which also the differential permeability tensor is evaluated. Secondly, a JacobiDavidson type eigensolver for the subsequent solution of the nonlinear eigenvalue problem. Particular emphasis is put on the implementation to enable efficient distributed parallel computing. First numerical results for biased ferritefilled cavity resonators are presented. 

Slides THACC2 [1.105 MB]  
FRAAC2  Arbitrary HighOrder Discontinuous Galerkin Method for Electromagnetic Field Problems  275 


Funding: Work supported by Federal Ministry for Research and Education BMBF under contract 05K10HRC For the design and optimization of HigherOrderMode Coupler, used in RF accelerator structures, numerical computations of electromagnetic fields as well as scattering parameter are essential. These computations can be carried out in time domain. In this work the implementation and investigation of a time integration scheme, using the Arbitrary highorder DERivatives (ADER) approach, applied on the Discontinuous Galerkin finiteelement method (DGFEM) is demonstrated for solving 3D electromagnetic problems in time domain. This scheme combines the advantage of high accuracy with the possibility of an efficient implementation as local time stepping scheme, which reduces the calculation time for special applications considerable. It is implemented in NUDG++*, a framework written in C++ that deals with the DGFEM for spatial discretization of the Maxwell equations. Accuracy and performance is analyzed by a suitable benchmark. * Nodal Unstructured Discontinuous Galerkin in C++ 

Slides FRAAC2 [6.767 MB]  