Paper  Title  Page 

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.  
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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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TUPAG08 
Uncertainty Quantification for the Fundamental Mode Spectrum of the European XFEL Cavities  


Funding: The authors would like to acknowledge the support by the DFG (German Research Foundation) in the framework of the Scientific Network SCHM 3127/1,2 that provided the basis for this collaborative work. The fundamental mode spectrum of superconducting cavities is sensitive to small geometry deformations introduced by the manufacturing process. In this work we consider variations in the equatorial and iris radii of the 1.3 GHz TESLA cavities used at the European XFEL. The cavities with slightly perturbed geometry are simulated using a finite element based eigenvalue solver. Employing uncertainty quantification methods such as sparsegrids, statistical information about the fundamental mode spectrum can be efficiently calculated. Moreover, using global sensitivity analysis, in particular Sobol indices, the impact of the individual geometry parameters on the quantities of interest, i.e. resonance frequencies, fieldflatness and the celltocell coupling coefficient, can be computed. We will explain important aspects of the uncertainty quantification methodology and give numerical results for illustration. 

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WEPLG02 
REPTIL  A Relativistic 3D Space Charge Particle Tracking Code Based on the Fast Multipole Method  


Funding: This work is supported by the DFG in the framework of GRK 2128. Modern free electron lasers and high current energy recovery linacs accelerate electron beams with particle bunch charges reaching up to several nanocoulombs. Especially in the low energy sections, such as the photoinjector of the accelerator, space charge interaction forces are the dominating effect influencing the dynamics of the electron beam. A direct computation of space charge forces is numerically very expensive. Commonly used simulation codes typically apply mesh based particleincell methods (PIC) to solve this problem. Our simulation tool, REPTIL, is a relativistic, threedimensional space charge tracking code, which computes the interaction forces based on a meshless fast multipole method (FMM). The FMM based space charge solver is more flexible regarding the choice of the interaction model and yields maximum accuracy for the near field forces between particles. For this reason, the FMM is very suitable for the simulation of the influence of space charge on the particle emission process in high current photoinjectors. In this contribution, we present a numerical study of the efficiency and the accuracy of the method. Therefore, we perform a case study for the PITZ photoinjector used for the European XFEL at DESY. Furthermore, we compare the performance of REPTIL with commonly used PIC codes like e.g. ASTRA. Finally, we investigate a hybrid approach by using the FMM on a mesh. The latter method makes further increases in the particle number possible, which translates to a higher resolution in the phase space of the electron bunch. 

Slides WEPLG02 [2.443 MB]  
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