Electron self-injection in a plasma wakefield accelerator in the strongly nonlinear regime due to inhomogeneous plasma density

We study self-injection into a plasma wakefield accelerator (PWFA) in the blowout (or bubble) regime with an inhomogeneous background plasma density. Using an analytic model and particle-in-cell simulations, we explore an injection mechanism into a PWFA, where a growing bubble causes reduction of the electron Hamiltonian in the co-moving frame, which leads to electron trapping [1]. In contrast to earlier work with steep density gradients, growth of the blowout region is caused by a slow decrease in plasma density along the propagation direction. To demonstrate this trapping mechanism, we generalize an analytic model for the wakefields inside the bubble [2], to derive expressions for the fields outside. With this extended model, we study the trapping of initially quiescent plasma electrons into the growing ultra-relativistic bubble, and show that a return current in the bubble sheath layer plays an important role in determining the trapped electron trajectories. We estimate the plasma density gradients and driver beam parameters required for self-injection, and compare our results with particle-in-cell simulations. This work is supported by the US DOE grants DE-FG02-04ER41321 and DE-FG02-07ER54945. \\[0pt] [1] S. Kalmykov {\it et al}, {\it Phys. Rev. Lett.} {\bf 103}, 135004 (2009).\\[0pt] [2] W. Lu {\it et al}, {\it Phys. Plasmas} {\bf 13}, 056709 (2006).