Scaling of the longitudinal electric field and transformer ratio in a nonlinear plasma wakefield accelerator

Abstract

The scaling of the two important figures of merit, the transformer ratio $T$ and the longitudinal electric field ${E}_{z}$, with the peak drive-bunch current ${I}_{p}$, in a nonlinear plasma wakefield accelerator is presented for the first time. The longitudinal field scales as ${I}_{P}^{0.623\ifmmode\pm\else\textpm\fi{}0.007}$, in good agreement with nonlinear wakefield theory ($\ensuremath{\sim}{I}_{P}^{0.5}$), while the unloaded transformer ratio is shown to be greater than unity and scales weakly with the bunch current. The effect of bunch head erosion on both parameters is also discussed.