  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.
