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
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.