Rostock University, Faculty of Computer Science and Electrical Engineering, Rostock, Germany
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.
SLAC, Menlo Park, California, USA
We present and discuss the properties of coherent electromagnetic fields of a very short, ultra-relativistic bunch, which travels in a rectangular vacuum under the influence of a bending force of a magnet. The analysis is based on the results of a direct numerical solution of Maxwell’s equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields. We also discuss coherent edge radiation. We present a clear picture of the field using the electric field lines constructed from the numerical solutions. This approach should be useful in the study of existing and future concepts of particle accelerators and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned.
Saint-Petersburg State University, Saint-Petersburg, Russia
We analyze radiation of a small bunch crossing a boundary between two dielectrics in a cylindrical waveguide. The total energy of radiation was studied earlier for such problem but dynamics of an energy loss as well as a field structure was not investigated. Meanwhile these questions are of essential interest for the wakefield acceleration technique and for new methods of generation of microwave radiation. Our research is based on original approach used previously for the case of the vacuum-plasma boundary*. The principal difference of presented work consists in generation of Cherenkov radiation in dielectric and so-called Cherenkov-transition radiation in vacuum. Algorithms of computations for the field and the energy loss are founded upon certain transformations of integration path. Comparison of analytical results with numerical ones shows a good coincidence. We consider two instances in detail: the bunch is flying from vacuum into dielectric and from dielectric into vacuum. In both cases we compare the energy losses by transition radiation and by Cherenkov one. Our investigation shows, for example, that energy loss can be negative at certain segments of the bunch trajectory.
* T.Yu. Alekhina and A.V. Tyukhtin, Phys. Rev. E. 83, 066401 (2011)
St. Petersburg State University, St. Petersburg, Russia
Rostock University, Faculty of Computer Science and Electrical Engineering, Rostock, Germany
For the design and optimization of Higher-Order-Mode 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 high-order DERivatives (ADER) approach, applied on the Discontinuous Galerkin finite-element method (DG-FEM) is demonstrated for solving 3-D 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 DG-FEM for spatial discretization of the Maxwell equations. Accuracy and performance is analyzed by a suitable benchmark.
* Nodal Unstructured Discontinuous Galerkin in C++
TEMF, TU Darmstadt, Darmstadt, Germany
Efficient and accurate computation of eigenvalues and eigenvectors is of fundamental importance in the accelerator physics community. Moreover, the eigensystem analysis is generally used for the identifications of many physical phenomena connected to vibrations. Therefore, various types of algorithms such that Arnoldi, Lanczos, Krylov-Schur, Jacobi-Davidson etc. were implemented to solve the eigenvalue problem efficiently. In this direction, we investigate the performance of selected commercial and freely available software tools for the solution of a generalized eigenvalue problem. We choose two setups by considering spherical and billiard resonators in order to test the robustness, accuracy, and computational speed and memory consumption issues of the recent versions of CST, Matlab, Pysparse, SLEPc and CEM3D. Simulations were performed on a standard personal computer as well as on a cluster computer to enable the handling of large sparse matrices in the order of hundreds of thousands up to several millions degrees of freedom. We obtain interesting comparison results with the examined solvers which is useful for choosing the appropriate solvers for a given practical application.