The influence of target requirements on the production, acceleration, transport, and focusing of ion beams

We have calculated the energy gain of ion-driven fusion targets as a function of input energy, ion range, and focal spot radius. For heavy-ion drivers a given target gain, together with final-lens properties, determines a 6-D phase space volume which must exceed that occupied by the ion beam. Because of Liouville´s theorem and the inevitability of some phase space dilutions, the beams´s 6-D volume will increase between the ion source and the target. This imposes important requirements on accelerators and on transport and focusing systems.