Drift Compression and Final Focus Options for Heavy Ion Fusion

A drift compression and f i n d focus lattice for heavy ion beams should focus the entire bepulse onto the same r o d spot on the tnrget. We show thnt this requircmont implies thnt the drift cornprmion design necds to satisfy a self-similar symmetry condition. Far un-neutmdizcd hems, the Lie symmetry group annlysis i6 applied to the wnrm-fluid model to sy;tematicdly derive thc self-similar drift compression solutions. For neutrnlized be-, the 1D Vlosov equation iti salved explicitly and families of self-similnr rlrift compression solutions are constructed. To compensate for the deviation from the selfsimilar symmetry condition due to the transverse emittance, four timedependent magnets nre introduced in the upstrewn of the drift compression such that the entire b e m pulse can be facwed onto the t h e 5 m e focd spot.