Drift compression and final focus options for heavy ion fusion

A drift compression and final focus lattice for heavy ion beams should focus the entire beam pulse onto the same focal spot on the target. We show that this requirement implies that the drift compression design needs to satisfy a self-similar symmetry condition. For un-neutralized beams, the Lie symmetry group analysis is applied to the warm-fluid model to systematically derive the self-similar drift compression solutions. For neutralized beams, the 1D Vlasov equation is solved explicitly and families of self-similar drift compression solutions are constructed. To compensate for the deviation from the self-similar symmetry condition due to the transverse emittance, four time-dependent magnets are introduced in the upstream of the drift compression such that the entire beam pulse can be focused onto the same focal spot.