Investigation of transverse instability in efficient plasma-based accelerators

Simultaneously maximizing power-transfer efficiency and preserving beam quality in plasma-based accelerators is constrained by the transverse beam breakup instability. We present an analytical transverse wake model derived from the plasma wake potential that self-consistently captures deformed cavity boundaries under intense beam loading. This model maps efficiency limits against stability thresholds across a parametric scan to isolate an operating window. Three-dimensional particle-in-cell simulations validate the theoretical model, showing that the analytical centroid evolution matches numerical tracking during the acceleration of a tailored trapezoidal electron bunch over a 1 m propagation distance. The bunch achieves an energy gain of up to 16.5 GeV with nearly preserved transverse emittance, and a wake-to-trailing bunch power-transfer efficiency of nearly 80%, with a final relative energy spread of less than 1.5%. These results show that the efficiency-instability barrier can be circumvented through precise determination of transverse wake force and tailored beam loading, providing a design path toward compact, high-luminosity particle colliders.