UMD, College Park, Maryland
Transfer maps for magnetic elements in storage and damping rings can depend sensitively on nonlinear fringe-field and high-order-multipole effects. The inclusion of these effects requires a detailed and realistic model of the interior and fringe magnetic fields, including their high spatial derivatives. A collection of surface fitting methods has been developed for extracting this information accurately from 3-dimensional magnetic field data on a grid, as provided by various 3-dimensional finite element field codes. The virtue of surface methods is that they exactly satisfy the Maxwell equations and are relatively insensitive to numerical noise in the data. These techniques can be used to compute, in Lie-algebraic form, realistic transfer maps for the proposed ILC Damping Ring wigglers. An exactly-soluble but numerically challenging model field is used to provide a rigorous collection of performance benchmarks.
SLAC, Menlo Park, California
UNM, Albuquerque, New Mexico
The goal is to construct a symplectic evolution map for a large section of an accelerator, say a full turn of a large ring or a long wiggler. We start with an accurate tracking algorithm for single particles, which is allowed to be slightly non-symplectic. By tracking many particles for a distance S one acquires sufficient data to construct the mixed-variable generator of a symplectic map for evolution over S. Two ways to find the generator are considered: (i) Find its gradient from tracking data, then the generator itself as a line integral *. (ii) Compute Hamilton's principal function on many orbits. The generator is given finally as an interpolatory C2 function, say through B-splines or Shepard's meshless interpolation. A test of method (i) is given in a hard example: a full turn map for an electron ring with strong sextupoles. The method succeeds where Taylor maps fail, but there are technical difficulties near the dynamic aperture due to oddly shaped interpolation domains. Method (ii) looks more promising in strongly nonlinear cases. We also explore explicit maps from direct fits of tracking data, with symplecticity imposed on local interpolating functions.
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.
ANL, Argonne
The electron accelerator simulation software elegant is being parallelized in a multi-year effort. Recent developments include parallelization of input/output (I/O), frequency map analysis, and position-dependent momentum aperture determination. Parallel frequency map and momentum aperture analysis provide rapid turnaround for two important determinants of storage ring performance. Recent development of parallel Self-Describing Data Sets file (SDDS) I/O based on MPI-IO made it possible for parallel elegant (Pelegant) to take advantage of parallel I/O. Compared with previous versions of Pelegant with serial I/O, the new version not only enhances the I/O throughput with a good scalability, but also provides a feasible way to run simulations with a very large number of particles (e.g., 1 billion particles) by eliminating the memory bottleneck on the master with serial I/O. Another benefit of using parallel I/O is reducing the communication overhead significantly for the tracking of diagnostic optical elements, where the particle information has to be gathered to the master for serial I/O.