In order to reach its maximum luminosity, the electron-ion collider (EIC) is being designed to use microbunched electron cooling (MBEC) to cool the hadron beam. This involves having the hadron beam imprint on a beam of electrons, enhancing the perturbations in the electron beam using the microbunching instability, and feeding back on the original hadron beam to correct deviations in hadron energy, and, through the use of dispersion, the transverse emittances. This process has been modelled

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... tically in the linear regime*. However, in order to maximize the cooling rate, we wish to know how much saturation in the electron beam is acceptable before the effects of nonlinearity cause significant deviations from the analytic results. To understand this, we have developed a code to do fast one-dimensional plasma simulations of hadrons and electrons as they move through the MBEC section of the EIC. In addition to permitting us to understand the effects of saturation, other effects are included which do not fit easily in the analytic formalism.