• N. Okuda
  University of Tokyo, Tokyo
• K. Yokoya
  KEK, Ibaraki

Recently, calculation of wake field and impedance has become more important. In many cases they are usually calculated numerically by using a mesh. It will be shown here that the mesh calculation based on the paraxial approximation can be much faster than ordinary methods when the bunch is very short. There are two advantages. One is to be able to choose the longitudinal mesh size independent of the bunch length. The other is that the problem can be solved as an initial-value problem in spite of frequency domain calculation.

• V. Kornilov, O. Boine-Frankenheim
  GSI, Darmstadt

The head-tail instability represents a potential intensity limitation for bunched beams in the synchrotrons of the FAIR project. Parametrical studies with numerical simulations over very long time scales are necessary in order to understand the effect of direct space charge, nonlinear synchrotron oscillations and image charges, which are all important in FAIR synchrotrons. Existing analytic approaches either neglect space charge or describe simplified models, which require a numerical or experimental validation. For our simulation studies we use two different computer codes, HEADTAIL and PATRIC. In this work we verify models for wake-field kicks and space-charge effect using the analytic solution for head-tail mode frequencies and growth rates from the barrier airbag model.

• A. Adelmann, Y. Ineichen, C. Kraus
  PSI, Villigen
• Y.J. Bi, J.J. Yang
  CIAE, Beijing
• S.J. Russell
  LANL, Los Alamos, New Mexico

OPAL (Object Oriented Parallel Accelerator Library) is a tool for charged-particle optic calculations in accelerator structures and beam lines including 3D space charge, short range wake-fields and 1D coherent synchrotron radiation. Built from first principles as a parallel application, OPAL admits simulations of any scale, from the laptop to the largest High Performance Computing (HPC) clusters available today. Simulations, in particular HPC simulations, form the third pillar of science, complementing theory and experiment. In this paper we present a fast FFT based direct solver and an iterative solver, namely a solver based on an algebraic multigrid preconditioned conjugate gradient method able to handle efficiently exact boundary conditions on complex geometry's. We present with timings up to several thousands of cores. The application of OPAL to the PSI-XFEL project as well as to the ongoing high power cyclotron upgrade will demonstrate OPAL's versatile capabilities. Plans for future developments towards a 3D finite element time domain Maxwell solver for large structures and simulation capabilities for 3D synchrotron radiation will be discussed.

• A. Markoviḱ, G. Pöplau, U. van Rienen
  Rostock University, Faculty of Computer Science and Electrical Engineering, Rostock

A single bunch instability caused by an electron cloud has been studied using analytical and semi-analytical methods with the wake field. The wake field in these cases was computed in the classical sense as excited electromagnetic field that transversally distorts those parts of the bunch trailing certain transversal offset in the leading part of the same bunch. The transversal wake force in this case is only depending on the longitudinal distance between the leading part of the bunch producing the wake force and the trailing parts of the bunch feeling the wake force. However during the passage of the bunch through the electron cloud the density of the electron cloud near the beam axis changes rapidly which does not allow the single variable approximation for the wake field. In this paper pursuing the idea of K. Ohmi we compute numerically the wake forces as two variable function of the position of the leading part of the bunch and the position of the bunch parts trailing the leading offset in the bunch.