Interaction of imploding shock waves with expanding central plasma in spherical pinch experiments: Simulation analysis

In the spherical pinch scheme, the hot D-T plasma produced in the center of the high pressure spherical vessel is confined by means of imploding shock waves launched from the periphery of the vessel for a time sufficiently long to achieve break-even conditions for plasma fusion. Theoretical studies on spherical pinch made so far have been limited up to the conditions of substantial expansion of the central plasma and the well-defined time delay between the creation of central plasma and the launching of the peripheral shock which led to the conclusion that, in realistic situations of SP experiments, negative time delays should be adopted, i.e., the launching of the imploding shock wave should precede the formation of the central plasma. However, the interaction of converging shock wave with the central plasma causing an additional heating and compression of the central plasma favoring plasma fusion conditions was not taken into account. Starting from the hydrodynamic equations of the system, the proposed simulation code deals with the propagation of converging shock waves and its interaction with the expanding central plasma. Considering the above-mentioned interaction in a self-consistent manner, the temporal evolution of temperature of central plasma is studied. Some results of the numerical simulation on the dynamics of shock wave propagation are also compared with the predictions of point strong explosing theory.