Simulating the dynamical friction force on ions due to a briefly co-propagating electron beam

We present two algorithms for accurate beam-frame simulations of the dynamical friction force on a non-relativistic ion moving for a short time in a low-density electron distribution, in the presence of arbitrary external fields. A special-purpose 4th-order predictor–corrector (“Hermite”) algorithm, taken from the astrophysical dynamics community, has been generalized to work with charged particles in the presence of a constant magnetic field. An alternative algorithm uses operator splitting techniques to solve binary Coulomb collisions (BCC) in the presence of arbitrary external fields. We discuss the close mathematical relationship between the Hermite and BCC algorithms, and their order of convergence. We discuss the parallel efficiency of the BCC algorithm and use it in the parallel simulation framework VORPAL to study problems in a parameter regime relevant to the electron cooling section for the proposed luminosity upgrade of the Relativistic Heavy Ion Collider. In particular, we simulate the field-free case to show how finite time effects strongly modify the traditional Coulomb logarithm, resulting in a significant reduction of the dynamical friction force as calculated by standard theoretical formulas. We show that diffusive dynamics can be correctly simulated, but that it must be artificially suppressed in order to accurately obtain the friction force. We discuss the proposed use of a helical undulator magnet to focus the electron beam and inhibit electron–ion recombination, showing that this device reduces the friction force.