Adiabatic matching of a bright beam into a transport focusing channel, while avoiding beam halo formation, is considered. Gradual changes in nonlinear focusing fields result in the modification of an initially nonlinear beam distribution into a distribution matched with the linear focusing channel. A plasma lens with a specific distribution of particles along the channel provides an ideal way to create an appropriate nonlinear focusing field. Another method employs an alternating-gradient focusing quadrupole structure with a multipole component of sixth order (duodecapole component). In this case, the initial matched beam profile has to be close to square instead of the conventional circular beam cross section. Analytical results are illustrated by simulations using the particle-in-cell method.
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