TEMF, TU Darmstadt, Darmstadt, Germany
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 radio-frequency cavities which are utilized for acceleration as well as for beam diagnostics. In these applications, precise beam dynamics simulations urgently require high-precision 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 high-performance eigenvalue calculations, important features like "low-noise" field evaluations or port-mode boundary approximations to enable traveling-wave transport are addressed.
KU Leuven, Kortrijk, Belgium
TEMF, TU Darmstadt, Darmstadt, Germany
Developing beam dynamics simulation tools using the moment method has advantages in terms of precision and efficiency when interests lie in average or rms dimensions of the beam, projected emittances or total energy. The moment method implemented in the V-Code solves the Vlasov equation by time integration, from an initial particle distribution represented by a discrete set of characteristic moments, accounting for all acting internal and external forces along the particle's path. The moment method delivers highly accurate beam dynamics results within a very small CPU time. This article proposes, illustrates and validates a new beam line element for a radiofrequency quadrupole (RFQ) for insertion in the V-Code. The focus will be on the RFQ cell structure, the electric field distribution and the insertion of the field distribution in the moment code.
TEMF, TU Darmstadt, Darmstadt, Germany
For acceleration of charged particles at the heavy-ion synchrotron at the GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt two ferrite-loaded 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 ferrite-loaded 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 Jacobi-Davidson 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 ferrite-filled cavity resonators are presented.
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.