Wakefield accelerators in the blowout regime with mobile ions

In the Plasma Wakefield Accelerator a high current drive-beam excites a large wake that can accelerate trailing particles. The wake is created when the space charge of the drive beam displaces plasma electrons. The plasma ions provide the restoring force on the displaced electrons. For symmetric bunches, the peak accelerating gradient is proportional to the current over a pulse length. For example, for a Gaussian bunch with 6nC of charge and bunch length σz≅0.6 mm, a gradient of 1GeV/m can be obtained. For the case of dense (beam density greater than plasma density), narrow (beam spot size σr smaller than c/ωp) beams the plasma response is non-linear and is dominated by the radial blow out of all the plasma electrons. However, such dense beams are strongly focused by the plasma lens effect. As a result they become so dense that ion motion should become important even on the electron plasma frequency time-scale. We will present analytic and 2-D particle-in-cell (PIC) models of wake excitation including mobile ions. The effect of the ion motion on the accelerating and focusing wake and the dynamics of the drive beam are discussed