Parallel Simulation of Electron Cooling Physics for Relativistic Ion Beams David L. Bruhwiler, Tech-X

Novel electron-hadron collider concepts are a high priority for the long-term plans of the international nuclear physics community. Orders of magnitude higher luminosity will be required for the relativistic ion beams in such particle accelerators. Higher luminosity can only be achieved by some dissipative mechanism that reduces the effective phase space volume occupied by the ion beam. A promising technique for this purpose, known as electron cooling, propagates an overlapping electron beam with the same velocity as the ions, for a small fraction of the collider circumference, allowing the ions to give up some of their thermal kinetic energy via Coulomb collisions. This very brief and subtle interaction provides weak damping of the effective ion phase space volume (i.e. cooling), which accumulates turn by turn to successfully combat a variety of mechanisms that increase this volume, including intra-beam scattering and beam-beam collisions. We will discuss four numerical approaches for simulating electron cooling physics, which essentially involves the accurate beam-frame calculation of dynamical velocity drag on a non-relativistic ion moving for a short time in a low-density electron distribution, in the presence of relevant external fields. 1) A scientific success was achieved using a molecular dynamics (MD) approach, pushing particles with a 4th-order predictor-corrector algorithm that aggressively varies the time step to resolve close Coulomb collisions -- simulations resolved a long-standing discrepancy between alternate analytical descriptions of the dynamical velocity drag for solenoid-based cooling systems. 2) Another scientific success was achieved with a modified MD algorithm, that assumes binary collisions dominate N-body interactions, using 2nd-order operator-splitting techniques to include external fields -- simulations verified a conjecture that the strong, coherent electron oscillations in a helical undulator magnet would only weakly decrease the velocity drag. 3) We present a proof-of-principle demonstration of thermal equilibration for a two species system, using a parallel implementation of the self-consistent Langevin approach. 4) We describe a proposal to address the problem with electrostatic particle-in-cell techniques. Because simulations to date have been restricted to a few hundred processors or less, we discuss the potential merits of each numerical approach for scaling up efficiently to petascale architectures.