• J. Xu, B. Mustapha, J.A. Nolen, P.N. Ostroumov
  ANL, Argonne

We are developing highly scalable solvers for space charge dominated beams based on both Particle-In-Cell (PIC) and direct Vlasov models. For the PIC model, particles are distributed evenly on different processors and space charge effect has been counted by solving Poisson's equation on a finite mesh. Several Poisson solvers have been developed using Fourier, Spectral Element (SEM) and Wavelet methods. Domain decomposition (DD) has been used to parallelize these solvers and all these solvers have been implemented into the PTRACK code. PTRACK is now widely used for large scale beam dynamics simulations in linear accelerators. For the Vlasov model, Semi-Lagrangian method and time splitting scheme have been employed to solve Vlasov equation directly in 1P1V and 2P2V phase spaces. 1D and 2D Poisson solvers have been developed with SEM. Similarly, DD has been used for parallelization of Poisson and Vlasov solvers. New efforts on developing Vlasov and Poisson solvers on unstructured mesh will also be reported.

• F. Lin, A.U. Luccio, N. Malitsky, W. Morse, Y. Semertzidis
  BNL, Upton, Long Island, New York
• C.J. Onderwater
  KVI, Groningen
• Y.F. Orlov, R.M. Talman
  CLASSE, Ithaca, New York

In the proposed electric dipole moment (EDM) experiment, with an estimated spin coherence time of 10⁰⁰ s, the spin precession due to an EDM of 10^-29 e.cm will produce a change in the vertical spin component of approximately 10 μrad during the storage time. Such high sensitivity needs an extremely high accurate and reliable simulation environment of the beam and spin behavior during the storage time. Therefore, several spin-related accelerator programs have been considered and investigated. The paper surveys the computational algorithms of these approaches and provides their comprehensive analysis from multiple perspectives: accuracy, performance, extensibility, and scope of potential applications.

• 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.