Heavy ion beam interaction with spherical shell and super-range planar targets

A simple model for the heavy ion beam driven implosion of uniform spherical shell targets is constructed. The model equation is obtained by averaging the fluid equation of conservation of energy over the thickness of the shell. The energy balance contains the thermal and kinetic energies of the region absorbing the beam energy. The driving power is considered as a constant. The model gives the dependence of the implosion properties on the ion energy and the results are in agreement with published simulation data. The dynamics of a plane slab heated by an intense ion beam with range smaller than the slab thickness is described by a modified version of the model. It yields the temporal behavior of the hydrodynamics efficiency and its dependence on the ratio between the payload and the absorber masses such as is observed in simulation results.