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The preservation of beam quality in a plasma wakefield accelerator driven by ultrahigh intensity and ultralow emittance beams, characteristic of future particle colliders, is a challenge. The electric field of these beams leads to plasma ions motion, resulting in a nonlinear focusing force and emittance growth of the beam. We propose to use an adiabatic matching section consisting of a short plasma section with a decreasing ion mass to allow for the beam to remain matched to the focusing force.doi:10.1103/physrevlett.104.155001 pmid:20481996 fatcat:odngpvj7yva6jn674q5fgw7jme