TEMF, Darmstadt
The X-FEL project and the ILC require a high quality beam with ultra short electron bunches. In order to predict the beam quality in terms of both, single bunch energy spread and emittance, an accurate estimation of the short range wake fields in the TESLA crymodules, collimators and other geometrically complex accelerator components is necessary. We have presented earlier wake field computations for short bunches in rotationally symmetric components with the code ECHO. Most of the wake field effects in the accelerator, however, are due to geometrical discontinuities appearing in fully three dimensional structures. For the purpose of simulating such structures, we have developed the Parallel Beam Cavity Interaction (PBCI) code. The new code is based on the full field solution of Maxwell equations in the time domain, for ultra-relativistic current sources. Using a specialized directional-splitting technique, PBCI produces particularly accurate results in wake field computations, due to the dispersion free integration of the discrete equations in the direction of bunch motion. One of the major challenges to deal with, when simulating fully three dimensional accelerator components is the huge computational effort needed for resolving both, the geometrical details and the bunch extensions by the computational grid. For this reason, PBCI implements massive parallelization on a distributed memory environment, based on a flexible domain decomposition method. In addition, PBCI uses the moving window technique, which is particularly well suited for wake potential computations in very long structures. As a particular example of such a structure, the simulation results of a complete module of TESLA cavities with eight cells each for a um-bunch will be given.
TEMF, Darmstadt
Extremely short bunches are used in future linear colliders, such as the International Linear Collider (ILC). Accurate and computationally efficient numerical methods are needed to resolve the bunch and to accurately model the geometry. In very long accelerator structures, computational efficiency necessitates the use of a moving window in order to save memory. On the other hand, parallelization is desirable to decrease the simulation times. Explicit schemes are usually more convenient to parallelize than implicit schemes since the implementation of a separate potentially time-consuming linear solver can thus be avoided. Explicit numerical methods without numerical dispersion in the direction of beam propagation are presented for fully 3D wake field simulations and for the special case of axially symmetric structures. The introduced schemes are validated by comparing with analytical results and by providing numerical examples for practical accelerator structures. Conformal techniques to enhance the convergence rate are presented and the advantages of the conformal schemes are verified by numerical examples.
TEMF, Darmstadt
Transient 3D simulations are carried out for two types of superconductive dipole magnets. Eddy-current effects in the yoke are treated by homogenising the laminated iron composite whereas interstrand eddy-current effects are resolved by either a cable magnetization model or a cable eddy-current model. The simulations reveal the Joule losses in the magnets.
TEMF, Darmstadt
The driving terms of instabilities in particle accelerators depend on the beam surroundings which are conveniently described by coupling impedances. In the case of critical components, for which analytical calculations are not available, direct measurements of the coupling impedances on a prototype are usually needed. However, this obvious drawback on the design of particle accelerators can be overcome by electromagnetic field simulations within the framework of the Finite Integration Technique. Here we show results from numerical evaluations of the transverse coupling impedance of a ferrite kicker. In order to excite the electromagnetic fields in the device we implement numerically the conventional twin-wire method. A good agreement with experimental measurements is observed, showing a promising way to determine coupling impedances of components of particle accelerators before construction.
TEMF, Darmstadt
In many applications the self-consistent simulation of charged particle beams is necessary. Especially, in low-energetic sections such as injectors the interaction between particles and fields considering all effects has to be taken into account. Well-known programs like the MAFIA TS modules typically use the Particle-In-Cell (PIC) method for beam dynamics simulations. Since they use a fixed computational grid which has to resolve the bunch adequately, they suffer from enormous memory consumption. Therefore and especially in the 3D case, only rather short sections can be simulated. This may be avoided using adaptive mesh refinement techniques (AMR). Since their application in Finite-Difference methods in time-domain is critical concerning instabilities, usually problem-matched but static meshes are used. In this paper a code working on the basis of a fully dynamic Cartesian grid is presented allowing for simulations capturing both, a high spatial resolution in the vicinity of the bunch and the possibility of simulating structures up to a length of several meters. The code is tested and validated using the RF electron gun of the Photoinjector Test Facility at DESY Zeuthen (PITZ) as an example. The evolution of various beam parameters along the gun is compared with the results obtained by different beam dynamics programs.
TEMF, Darmstadt
For devices in which the bunch dimensions are much smaller than the dimensions of the structure the numerical field solution is typically hampered by spurious oscillations. The reason for this oscillations is the large numerical dispersion error of conventional schemes along the beam axis. Recently, several numerical schemes have been proposed which apply operator splitting to optimize and under certain circumstances eliminate the dispersion error in the direction of the bunch motion. However, in comparison to the standard Yee scheme the methods based on operator splitting do not conserve the standard discrete Gauss law. This contribution is dedicated to the construction of conserved discrete Gauss laws and conservative current interpolation for some of the split operator methods. Finally, the application of the methods in a PIC simulations is shown.
TEMF, Darmstadt
Wake fields are a limiting factor due to their collective effects. In colliders and high energy accelerators used in FEL projects short bunches excite high frequency fields which make the computation of near range wake fields inaccurate. Additionally the length of modern accelerating structures limit the powers of certain codes such as TBCI or MAFIA. Both limiting factors, i.e. short bunches and length of accelerating structures - a multiscale problem, can be dealt with in the following way. Using certain zero dispersion directions of a usual Cartesian grid leads to a decrease of the overall dispersion which usually arises by having discrete field values. Combined with a conformal modelling technique the full time step limited by the Courant criterion is used and a moving window is applied. Thus simulations of short bunches in long structures are possible - dispersion and memory problems have been avoided. In this work ROCOCO (Rotated mesh and conformal code) is presented. The zero dispersion algorithm uses a new discretization scheme based on a rotated mesh combined with the established USC scheme and the moving window technique mentioned above. The advantage of an explicit algorithm is joined with the zero dispersion along the beam's propagation direction. A dispersion analysis for the 2D version of the code is shown as well as some results for common structures of accelerator physics - such as collimators and the TESLA 9 cell structure.
TEMF, Darmstadt
The eigenmode expansion method was used in the early 1980’s in calculating wake potential for 2D rotational symmetric structures. In this paper it is extended to general 3D cases. The wake potential is computed as the sum of two parts, direct and indirect ones. The direct wake potential is obtained by an integral of field components from a full wave solution, which stops just at the end of the structure. The indirect wake potential is then calculated analytically through the eigenmode expansion method. This is to avoid the full wave modeling of a very long outgoing beam pipe, which is computational expensive. In our work, the Finite Integration Technique (FIT) with moving mesh window is used to model the structure. The fields are recorded at the truncation boundary as a function of time. These fields are then expanded according to discrete eigenmodes of the outgoing pipe, and the eigenmode coefficients are found out at each time step. Then, the coefficients are transferred into frequency domain and the integral of wake fields along a path to infinity is computed analytically. In the case that the moving mesh window is narrow, appropriate exploration of time domain coefficients is necessary. Numerical tests show that the proposed method provides an accurate result with as less as three modes for a collimator structure.
TEMF, Darmstadt
The moment method model has been proven to be a valuable tool for numerical simulations of a charged particle beam transport both in accelerator design studies and in optimization of the operating parameters for an already existing beam line. On the basis of the Vlasov equation which describes a collision-less kinetic approach, the time evolution of such integral quantities like the mean or rms dimensions, the mean or rms kinetic momenta, and the total energy or energy spread for a bunched beam can be described by a set of first order non-autonomous ordinary differential equations. Application of a proper time integrator to such a system of ordinary differential equations enables then to determine the time evolution of all involved ensemble parameter under consistent initial conditions. From the vast amount of available time integration methods different versions have to be implemented and evaluated to select a proper algorithm. The computational efficiency in terms of effort and accuracy serves as a selection criterion. Among possible candidates of suited time integrators for the given set of moment equations are the explicit Runge-Kutta methods, the implicit theta methods, and the linear implicit Rosenbrock methods. Various algorithms have been implemented and tested under real-world conditions. In the paper the evaluation process is documented.
TEMF, Darmstadt
Fast kicker modules represent a potential source of beam instabilities in the planned Facility for Antiproton and Ion Research (FAIR) at the Gesellschaft für Schwerionenforschung (GSI), Darmstadt. Containing approximately six tons of lossy ferrite material, the more than forty kicker modules to be installed in the SIS-100 and SIS-300 synchrotrons are expected to have a considerable parasitic influence on the high-current beam dynamics. In order to be able to take these effects into account in the kicker design, a dedicated electromagnetic field software for the calculation of coupling impedances has been developed. Here we present our numerical results on the longitudinal and transverse kicker coupling impedances for the planned components and point out ways of optimization. Besides the inductive coupling of the beam to the external network -relevant below 100 MHz- particular attention is paid to the impact of ferrite losses up to the beam-pipe cutoff frequency.
TEMF, Darmstadt
Particle-In-Cell (PIC) simulations are commonly used in the field of computational accelerator physics for modelling the interaction of electromagnetic fields and charged particle beams in complex accelerator geometries. However, the practicability of the method for real world simulations, is often limited by the huge size of accelerator devices and by the large number of computational particles needed for obtaining accurate simulation results. Thus, the parallelization of the computations becomes necessary to permit the solution of such problems in a reasonable time. Different algorithms allowing for an efficient parallel simulation by preserving an equal distribution of the computational workload on the processes while minimizing the interprocess communication are presented. This includes some already known approaches based on a domain decomposition technique as well as novel schemes. The performance of the algorithms is studied in different computational environments with simulation examples including a full 3D simulation of the PITZ-Injector [*].
*A. Oppelt et al Status and First Results from the Upgraded PITZ Facility, Proc. FEL 2005