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
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
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
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