A specifically tailored plasma lens could shape a high-energy, heavy-ion be
am into the form of a hollow cylinder without loss of beam intensity. It ha
s been experimentally confirmed that both a positive as well as a negative
radial gradient of the current density in the active plasma lens can be the
underlying principle. Calculations were performed that yield the ideal cur
rent density distribution for both cases. A numerical simulation of an expe
riment with an intense ion beam highlights that the shaping of the beam inc
reases the achievable compression in a lead sample.