Longitudinal phase space dynamics of witness bunch during the Trojan Horse injection for plasma-based particle accelerators

Abstract

In the Trojan Horse injection process for plasma-based particle accelerators, we have investigated how the longitudinal phase space of the witness bunch would be governed by the parameters of the ionization laser and background plasma in the limit of quasistatic wakefield approximation. The tunneling ionization rate distribution by the laser pulse is introduced to describe the ionization time interval and initial distribution of the witness electrons. The quasilinear (or equivalently quasistatic) regime of the charged particle beam-driven wakefield is considered to make the phase of the wake potential constant in time in the driver beam frame. In the simulations, it is shown that the ionization laser phase on the quasistatic wake potential determines the longitudinal space-charge field of the witness bunch. We also find that the relative energy spread of the witness bunch can be estimated by the sum of three effects: The ionization time interval, wakefield slope, and space-charge fields of the witness bunch. Analytical expressions for the characteristic distance from the ionization to trapping positions, rms length, and relative energy spread of the witness bunch are obtained approximately and compared with the particle-in-cell simulations.