Stagnation Pressure of Imploding Hollow Shells
Movie: Self-similar solution of a spherically imploding shell in a radius-time diagram. The inner shell surface and the trajectory of the reflected shock are represented by thick lines. Fluid elements move on dotted trajectories with almost constant velocities. The movie shows the evolution of the density profiles with time. The fluid element at r=r0 and t=t 0 is considered as an outer boundary.
Our motivation for employing this model is that the shell compression at the time of stagnation (t=0) in realistic capsule implosions -- as they would typically occur in inertial confinement fusion capsules -- can be modeled surprisingly accurate by the self-similar description. This leads to a scaling law for the ignition energy of ICF capsules which corresponds quite well to numerical simulations of capsule implosions.
For the whole story, see Phys.Rev.Lett. 86(15), 3336 (2001)