A Fast Point to Point Interaction Model for Charged Particle Bunches by Means of Nonequispaced Fast Fourier Transform (nfft)

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 [5]. 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) [3, 4], 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. INTRODUCTION The design of particle accelerators requires a sophisticated understanding of the dynamic behaviour of the particle bunch. Therefore several algorithms have been developed to determine the trajectories of the particles in the six-dimensional phase space. Assuming the energy spread of the charged particles to be small, the space-charge forces may be computed in the bunch’s rest frame by superposing the electrostatic field of each particle. The electric field at the position of the j-th particle rj ∈ R in the rest frame is given by