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.
TUD, Darmstadt, Germany
TEMF, TU Darmstadt, Darmstadt, Germany
GSI, Darmstadt, Germany
In a synchrotron, particles are accelerated by repeatedly passing through RF cavities. In the SIS18 synchrotron at GSI, ferrite cavities are used. Each cavity is equipped with local control systems to adjust the amplitude and phase of the accelerating field. In this paper, we consider ferrite cavities of the type that is currently used in the SIS18 at GSI and will be used in the future SIS100 which is being built in the frame of the FAIR project. We analyze the dynamics of the cavities in conjunction with their local control loops. An emphasis is put on the cavities' reaction to changes in the desired amplitude or resonant frequency. Using simulations, we show that the cavities' dynamics hardly influence longitudinal dipole oscillations, and conclude that a high-level model for the RF cavities is sufficient.
TU Darmstadt, Darmstadt, Germany
In order to test RF control systems for accelerator cavities without being dependent on available prototypes, a resonator-simulator has been developed. The Simulator is based on a Xilinx-VIRTEX-4 FPGA-module and has been configured using MATLAB-Simulink with a special Xilinx-Blockset. The underlying model for this configuration is a parallel RLC-circuit that has been parameterised with common RF-quantities like the resonance frequency, driving frequency, bandwidth and quality factor. This approach allows to simulate the behaviour of normal conducting cavities with quality factors up to 104 as well as superconducting cavities with quality factors up to 109. Besides, it can as well be operated in a continuous-wave as in a pulsed mode. We report on the mathematical model, its digital representation and on the benchmarking against real cavity behaviour.
GSI, Darmstadt, Germany
CERN, Geneva, Switzerland
Tracking of high intensity effects for few turns of a circular accelerator is at reach of present computational capabilities. The situation is very different when the prediction of beam behaviour is extended to hundred of thousands of turns, where special approaches for the control of computer artifact are necessary sometimes to the expense of a complete physical modeling. The identification of the key physical ingredients helps to the development of computer algorithms capable of treating the long term tracking. In this talk it is presented the actual state of simulations for long term tracking of high intensity bunches of the SIS100 addressing the self consistent treatment of beam loss. A more realistic modeling of the incoherent effect of electron cloud is addressed as well.
CERN, Geneva, Switzerland
PSI, Villigen, Switzerland
ETH, Zurich, Switzerland
The new X-ray 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 3-D 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 skin-effect 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.
CERN, Geneva, Switzerland
EPFL, Lausanne, Switzerland
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.