Webb, S.D. Bruhwiler, D.L. Burov, A.V. Cook, N.M. Lebedev, V.A. Nagaitsev, S. JACoW Publishing Geneva, Switzerland 978-3-95450-200-4 10.18429/JACoW-ICAP2018-WEPLG03 English 341-344 WEPLG03 plasma wakefield impedance dipole simulation Contribution to a conference proceedings 2019 2019-01 https://doi.org/10.18429/JACoW-ICAP2018-WEPLG03 http://jacow.org/icap2018/papers/weplg03.pdf Plasma wakefield accelerators achieve accelerating gradients on the order of the wave-breaking limit, m c² k_{p}/e, so that higher accelerating gradients correspond to shorter plasma wavelengths. Small-scale accelerating structures, such as plasma and dielectric wakefields, are susceptible to the beam break-up instability (BBU), which can be understood from the Panofsky-Wenzel theorem: if the fundamental accelerating mode scales as b⁻¹ for a structure radius b, then the dipole mode must scale as b⁻³, meaning that high accelerating gradients necessarily come with strong dipole wake fields. Because of this relationship, any plasma-accelerator-based future collider will require detailed study of the trade-offs between extracting the maximum energy from the driver and mitigating the beam break-up instability. Recent theoretical work* predicts the tradeoff between the witness bunch stability and the amount of energy that can be extracted from the drive bunch, a so-called efficiency-instability relation . We will discuss the beam break-up instability and the efficiency-instability relation and the theoretical assumptions made in reaching this conclusion. We will also present preliminary particle-in-cell simulations of a beam-driven plasma wakefield accelerator used to test the domain of validity for the assumptions made in this model.