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

Precise and fast 3D space-charge calculations for bunches of charged particles are still of growing importance in recent accelerator designs. A widespread approach is the particle-mesh method computing the potential of a bunch in the rest frame by means of Poisson's equation. Whereas an adaptive discretization of a bunch is often required for efficient space charge calculations in practice, such a technique is not implemented in many computer codes. For instance, the FFT Poisson solver that is often applied allows only an equidistant mesh. An adaptive discretization following the particle density is implemented in the GPT tracking code (General Particle Tracer, Pulsar Physics). The disadvantage of this approach is that jumps in the distribution of particles are not taken into account. In this paper we present a new approach to an adaptive discretization which is based on the multigrid technique. The goal is that the error estimator needed for the adaptive distribution of mesh lines can be calculated directly from the multigrid procedure. The algorithm will be investigated for several particle distributions and compared to that adaptive discretization method implemented in GPT.

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

Demanding applications such as heavy ion fusion, high energy colliders and free electron lasers require the study of beam phenomena like space-charge induced instabilities, emittance growth and halo formation. Numerical simulations for instance with GPT (General Particle Tracer, Pulsar Physics) calculate the mutual Coulomb interactions of the tracked particles *. The direct summation of the forces is rather costly and scales with O(N²). In this paper we investigate a new approach for the efficient calculation of particle-particle interactions: the fast summation by Nonequispaced Fast Fourier Transform (NFFT) **, whereas the NFFT is a generalization of the well known Fast Fourier Transformation (FFT). We describe the algorithm and discuss the performance and accuracy of this method for several particle distributions.

• 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.