Scaling laws for hydrodynamically similar implosions with heat conduction

Abstract

Scaling laws for hydrodynamically similar implosions are derived by applying Lie group analysis to the set of partial differential equations for the hydrodynamic system. Physically this implies that any fluid system belonging to a common similarity group evolves quite in the same manner including hydrodynamic instabilities. The scalings strongly depend on the description of the energy transport, i.e., whether the fluid system is heat conductive or adiabatic. Under a fully specified group transformation the hydrodynamic similarity can still be preserved even when the system is cooperated with such other energy sources as classical laser absorption, hot electrons, local alpha heating, and bremsstrahlung loss. The results are expected to give the basis of target design and diagnostics for scaled high gain experiments in the future.