Phase space matching between two plasma-accelerator (PA) stages and between a PA and a traditional accelerator component is a critical issue for emittance preservation of beams accelerated by PAs. The drastic differences of the transverse focusing strengths as the beam propagates between different stages and components may lead to a catastrophic emittance growth in the presence of both finite energy spread and lack of proper matching. We propose using the linear focusing forces from nonlinear wakes in longitudinally tailored plasma density profiles to provide exact phase space matching to properly transport the electron beam through two such stages with negligible emittance growth. Theoretical analysis and particle-in-cell simulations show how these structures may work in four different scenarios. Good agreement between theory and simulation is obtained.
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