Beam Matching into and Out of a Plasma Wakefield Accelerator

Electron beam emittance preservation in a beam-driven, nonlinear plasma wakefield accelerator relies upon matching the beam to the plasma. This occurs when the linear focusing forces of the ion column acting on the electron beam are perfectly balanced against the emittance-driven divergence of the beam. The matching condition is satisfied when the square of the beam size equals the product of the geometric emittance and the inverse betatron wave number of the beam inside the plasma. In practice, however, the matched beam size is too small to achieve with conventional beam delivery systems operating in vacuum. Here, a passive, tapered plasma density ramp at the entrance (exit) of the plasma source is described that can focus the electron beam to (from) the necessary matched size at a rate exceeding the adiabatic plasma focusing limit without diluting the beam's emittance. A numerically derived empirical model predicts both the plasma ramp shape and parameter tolerances required for beam matching as a function of the incoming beam parameters. These results can be easily scaled for the purpose of designing sequential plasma stages in a high-energy linear collider.