Increasing the luminosity of relativistic hadron beams is critical for theadvancement of nuclear physics. Coherent electron cooling (CEC) promises tocool such beams significantly faster than alternative methods. We presentsimulations of 40 GeV/nucleon Au+79 ions through the first (modulator) sectionof a coherent electron cooler. In the modulator, the electron beam copropagateswith the ion beam, which perturbs the electron beam density and velocity viaanisotropic Debye shielding. In contrast to previous simulations, where theelectron density was constant in time and space, here the electron beam has afinite transverse extent, and undergoes focusing by quadrupoles as it passesthrough the modulator. The peak density in the modulator increases by a factorof 3, as specified by the beam Twiss parameters. The inherently 3D particle andfield dynamics is modeled with the parallel VSim framework using a $\delta$fPIC algorithm. Physical parameters are taken from the CEC proof-of-principleexperiment under development at Brookhaven National Lab.
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