Contraction Geometry In Inertial Confinement Fusion Hydrodynamic Instability Theory And Numerical Studies

In inertial confinement fusion, a variety of fluid instabilities can destroy the symmetry and integrity of the capsule, and even fail the ignition. The understanding of the growth of perturbations is of extreme important for achieving the ignition and high gain. Fluid instabilities become more complex in convergent geometry than planar geometry and many essential problems keep undone. In this article, some results of the theoretical derivation and computational campaign performed to study the fluid instabilities in convergent geometry are presented.The Rayleigh-Taylor(RT) instability in cylindrical and spherical geometries was analized in this thesis, based upon velocity potential theory. At linear stage, the theoretical growth rate for the RT instability in cylindrical and spherical geometries was enhanced (or reduced) due to the decrease (or increase) in the perturbation wavelength during an implosion (or explosion). Even in the absence of an acceleration the perturbation could grow in the convergent geometries. The amplitude growth rate was proportional to the cube of the convergent ratio in spherical geometry and to the square of the convergent ratio in cylindrical geometry. In addition, it was the sign of the initial amplitude growth rate, not the manner of the interface motion that determined whether the amplitude could increase. At weakly nonlinear stage, mode-coupling equations were derived in cylindrical and spherical geometries. It showed that the nonlinear terms were inversely proportional to the position of the interface in cylindrical and spherical geometries. The nonlinearity was enhanced during an implosion and reduced during an explosion inversely. The analytical solution in cylindrical geometry showed convergent effect caused the instability differently growing on both sides of the interface in convergent geometry. The inward part of the unstable interface was made narrow by the inertial forces and the outward of it was made wide inversely. Finally, convergent geometry had an important effect on the perturbance coupling between the interfaces of the finite fluid. The attenuation factor of perturbance coupling from the outer interface in was greater than the one from the inner out.Computational simulations are the main method to study fluid instability during an implosion in inertial confinement fusion. In this article, physical equations and relative three-dimensional finite-difference formulae in cylindrical and spherical geometries were derived and two- and three-dimensional code in cylindrical and spherical geometries for direct-drive by laser was made, based on the LARED-S code in planar geometry. It consisted of the processes such as the inverse bremsstrahlung absorption, electic heat conduction and fluid dynamics. Firstly, two-dimensional RT instability in cylindrical geometry was simulated by the LARED-S code and the results agreed well with the linear theory of RT instability in cylindrical geometry. Secondly, nonlinear threshold of two-dimensional RT instability was analyzed in planar and cylindrical and spherical geometries. Density amplitude was defined relating to instable interface and formulae of nonlinear threshold values for RT instability in three geometries were given, then the LARED-S code was used to simulate two-dimensional RT instability in three geometries and simulation results agreed well with the formulae. Thirdly, multimode-coupling phenomena in cylindrical geometry was analyzed by the simulation. The growth of every mode and its harmonic was qualitatively compared well with the solutions of mode-coupling equation. Fourthly, the RT instability in cylindrical and spherical geometries was calculated during an implosion. The strength of convergent shock was enhanced in cylindrical and spherical geometries than in planar geometry. The bubble became more wide and big and the spike became more narrow and long. It showed in spherical implosion that the spike close to the symmetrical axis grew faster than the ring one away from the symmetrical axis. The difference was...