George I. Bell

Status of the R&D towards electron cooling of RHIC

The physics interest in a luminosity upgrade of RHIC requires the development of a cooling-frontier facility. Detailed calculations were made of electron cooling of the stored RHIC beams. This has been followed by beam dynamics simulations to establish the feasibility of creating the necessary electron beam. The electron beam accelerator will be a superconducting Energy Recovery Linac (ERL). An intensive experimental R&D program engages the various elements of the accelerator, as described by 24 contributions to the 2007 PAC.

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.

Numerical algorithms for modeling electron cooling in the presence of external fields

The design of the high-energy cooler for the Relativistic Heavy Ion Collider (RHIC) recently adopted a nonmagnetized approach. To prevent recombination between the fully stripped gold ions and co-propagating electrons, a helical undulator magnet has been proposed. In addition, to counteract space-charge defocusing, weak solenoids are proposed every 10 m. To understand the effect of these magnets on the cooling rate, numerical models of cooling in the presence of external fields are needed. We present an approach from first principles using the VORPAL parallel simulation code. We solve the n-body problem by exact calculation of pair-wise collisions. Simulations of the proposed RHIC cooler are discussed, including fringe field and finite interaction time effects.

Electron cooling in the presence of undulator fields

The design of the higher-energy cooler for Relativistic Heavy Ion Collider (RHIC) recently adopted a non-magnetized approach which requires a low temperature electron beam [1]. However, to avoid significant loss of heavy ions due to recombination with electrons in the cooling section, the temperature of the electron beam should be high. These two contradictory requirements are satisfied in the design of the RHIC cooler with the help of the undulator fields. The model of the friction force in the presence of an undulator field was benchmarked vs direct numerical simulations with an excellent agreement. Here, we discuss cooling dynamics simulations with a helical undulator, including recombination suppression and resulting luminosities.

Simulations of Dynamical Friction Including Spatially‐Varying Magnetic Fields

A proposed luminosity upgrade to the Relativistic Heavy Ion Collider (RHIC) includes a novel electron cooling section, which would use ∼55 MeV electrons to cool fully‐ionized 100 GeV/nucleon gold ions. We consider the dynamical friction force exerted on individual ions due to a relevant electron distribution. The electrons may be focussed by a strong solenoid field, with sensitive dependence on errors, or by a wiggler field. In the rest frame of the relativistic co‐propagating electron and ion beams, where the friction force can be simulated for nonrelativistic motion and electrostatic fields, the Lorentz transform of these spatially‐varying magnetic fields includes strong, rapidly‐varying electric fields. Previous friction force simulations for unmagnetized electrons or error‐free solenoids used a 4th‐order Hermite algorithm, which is not well‐suited for the inclusion of strong, rapidly‐varying external fields. We present here a new algorithm for friction force simulations, using an exact two‐body collis...

Select Advances in Computational Accelerator Physics

Computational accelerator physics has changed and broadened over the last decade or so. Part of the change is due to the advent of multiple ways of parallel computing. Another part comes from algorithmic developments. The multiple ways of parallel computing include distributed memory parallelism and on-chip parallelism, with the latter coming from architectures (CPU and GPU) having multiple processing elements (cores or streaming multiprocessors) and wide vector (SIMD) instruction units. The basics of these new architectures and their application to computational accelerator physics are briefly reviewed. Algorithmic advances in the select areas of spin tracking, cavity calculations, plasma acceleration, and electron cooling are also reviewed. In some cases the algorithms provide increased fidelity improving the overall accuracy, while in other cases, such as controlled dispersion, the algorithms provide increased fidelity by better modeling the essential physical interaction. Finally, the use of computational frameworks, which provide the basic computational infrastructure, while allowing the capability developer to concentrate on the math and physics, is reviewed in the context of the Vorpal application, which has found use across accelerator physics and many other fields.